written by
Allyn Fisher
Martha Ruttle
illustrated by
Tyson Smith
B5SUPTX
This supplement was developed to ensure 100% conformance to Texas state
standards. However, the contents may be used as optional or complimentary
materials in any classroom.
Bridges in Mathematics Grade 5 Texas Supplement
The Bridges in Mathematics Grade 5 package consists of—
Getting Started
Number Corner Teachers Guide Volume One
Bridges Teachers Guide Volume One
Number Corner Teachers Guide Volume Two
Bridges Teachers Guide Volume Two
Number Corner Blacklines
Bridges Teachers Guide Volume Three
Number Corner Overheads
Bridges Teachers Guide Volume Four
Bridges Blacklines
Bridges Overheads
Bridges Student Book Blacklines
Home Connections Blacklines
Work Place Student Book Blacklines
Student Math Journal Blacklines
Word Resource Cards
Manipulatives
Number Corner Student Book Blacklines
Number Corner Calendar Markers
Number Corner Manipulatives
The Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel. 1 800 575–8130.
© 2007 by The Math Learning Center
All rights reserved.
Prepared for publication on Macintosh Desktop Publishing system.
Printed in the United States of America.
QP712 and QP768 B5SUPTX
P0208
The Math Learning Center grants permission to classroom teachers to reproduce blackline
masters in appropriate quantities for their classroom use.
Bridges in Mathematics is a standards-based K–5 curriculum that provides a unique blend
of concept development and skills practice in the context of problem solving. It incorporates the Number Corner, a collection of daily skill-building activities for students.
The Math Learning Center is a nonprofit organization serving the education community.
Our mission is to inspire and enable individuals to discover and develop their mathematical
confidence and ability. We offer innovative and standards-based professional development,
curriculum, materials, and resources to support learning and teaching. To find out more,
visit us at www.mathlearningcenter.org.
ISBN 9781602621961
Bridges in Mathematics Grade 5
Texas Supplement
Introduction
Introduction
1
Grade 5 Activities
Grade 5 Activities & Independent Worksheets Grouped by Skill
3
Number, Operation & Quantitative Reasoning
Common Factors
Activity 1: Prime Factorization & Common Factors
Activity 2: Prime Factorization Number Riddles
Factor Riddles, page 1 of 2
Factor Riddles, page 2 of 2
7
11
14
15
Measurement
Area & Perimeter
Activity 3: Measuring Area
Measuring Area
Activity 4: Measuring Perimeter
Measuring Perimeter
Activity 5: The Ladybugs’ Garden
The Ladybugs’ Garden
Centimeter Grid Paper
Activity 6: Hexarights
Introducing Hexarights
Measuring Hexarights
Hexarights, Perimeter = 24 cm
Volume
Activity 7: Introducing Volume
Cubes and Rectagular Solids
Paper Box Pattern
Activity 8: More Paper Boxes
More Paper Boxes
17
20
21
24
25
28
29
31
34
35
36
37
40
41
43
46
Geometry & Spatial Reasoning
3-Dimensional Figures
Activity 9: 3-D Figure Posters
Net A
Net B
Net C
Net D
Net E
Net F
47
50
51
52
53
54
55
Activity 10: Faces, Edges & Vertices
Faces, Edges & Vertices Gameboard
Transformations
Activity 11: Sketching & Identifying Transformations
Transforming Figures
Name that Transformation
Paper Figures
57
60
61
64
65
66
Probability & Statistics
Using Experimental Results to Make Predictions
Activity 12: Introducing Virtual Spinners
Spinner Experiment, page 1 of 2
Spinner Experiment, page 2 of 2
Activity 13: The 6-4-2 Spinner
The 6-4-2 Spinner, page 1 of 3
The 6-4-2 Spinner, page 2 of 3
The 6-4-2 Spinner, page 3 of 3
67
70
71
73
76
77
78
Patterns, Relationships & Algebraic Thinking
Diagrams & Equations
Activity 14: The Carnival
The Carnival
More Carnival Problems, page 1 of 3
More Carnival Problems, page 2 of 3
More Carnival Problems, page 3 of 3
79
81
82
83
84
Grade 5 Activity Blackline Answer Keys
Answer Keys
85
Grade 5 Independent Worksheets
Grade 5 Independent Worksheets Grouped by Skill
87
Number, Operation & Quantitative Reasoning
Estimation to Solve Addition & Subtraction Problems
Independent Worksheet 1: Using Compatible Numbers to Estimate Answers
Independent Worksheet 2: Are These Answers Reasonable?
Independent Worksheet 3: Travel Miles
Common Factors
Independent Worksheet 4: Factor Trees & Common Factors
Independent Worksheet 5: More Factor Riddles
89
93
97
101
103
Measurement
Area & Perimeter
Independent Worksheet 6: Area & Perimeter Review
Independent Worksheet 7: Measuring Rectangles
105
109
Volume
Independent Worksheet 8: Volume Review
Independent Worksheet 9: The Camping Trip
113
117
Geometry & Spatial Reasoning
3-Dimensional Figures
Independent Worksheet 10: Nets & 3-D Figures
Transformations
Independent Worksheet 11: Transforming Figures, part 1
Independent Worksheet 12: Transforming Figures, part 2
119
123
125
Number, Operation & Quantitative Reasoning
Estimation to Solve Multiplication & Division Problems
Independent Worksheet 13: Using Compatible Numbers to Multiply & Divide
129
Independent Worksheet 14: More Multiplication & Division with Compatible Numbers 131
Independent Worksheet 15: Reasonable Estimates in Multiplication & Division
133
Probability & Statistics
Using Experimental Results to Make Predictions
Independent Worksheet 16: Make & Test Your Own Spinner
135
Number, Operations & Quantitative Reasoning
Place Value to 999 Billion
Independent Worksheet 17: Tons of Rice
Independent Worksheet 18: Inches to the Moon & Other Very Large Numbers
Independent Worksheet 19: More Very Large Numbers
139
143
145
Algebraic Thinking
Diagrams & Equations
Independent Worksheet 20: Padre’s Pizza
Independent Worksheet 21: Choosing Equations & Diagrams
149
153
Grade 5 Independent Worksheet Answer Keys
Answer Keys
157
Appendix
Bridges Grade 5 TEKS Correlations
163
Texas Supplement
Introduction
This supplement was created to ensure that Bridges in Mathematics, Grade Five is fully aligned with the
Texas Essential Knowledge and Skills (TEKS). It includes 14 activities, designed to be used in place of selected sessions in Bridges Grade Five, starting near the end of Unit Three. Specific replacement recommendations are offered in each activity and are listed on the Skills and Activities charts on pages 3–5. There
are also 21 independent worksheets to be completed by students during designated seatwork periods or
assigned as homework. Some of these provide extra support for skills and concepts introduced in regular
Bridges sessions, while others are intended for use after you’ve conducted specific supplement activities.
Most of the activities will fill an entire 1-hour math session, while a few may require part of an additional session. Most make use of manipulatives from your Bridges kit and/or common classroom supplies. Activity 12, Introducing Virtual Spinners, and two related independent worksheets require at least
one computer with Internet access. The blacklines needed to make any overheads, game materials, and/
or student sheets are included directly after each activity. You’ll find the independent worksheets, along
with Answer Keys, in a section of their own on pages 87–162.
Note TEKS not listed on pages 3–5 are already addressed in Bridges and/or Number Corner sessions. For a
full correlation of Bridges Grade Five to the TEKS, see pages 163–170. You will find additional material to support the TEKS on the Math Learning Center web site at www.mathlearningcenter.org/bridges/support.
Bridges in Mathematics, Grade 5 • 1
Texas Supplement
2 • Bridges in Mathematics, Grade 5
Texas Supplement
Grade 5 Activities & Independent Worksheets Grouped by Skill
NUMBER, OPERATION & QUANTITATIVE REASONING
(ESTIMATION TO SOLVE ADDITION & SUBTRACTION PROBLEMS)
Activity
Name
Recommended Timing
Independent Worksheet 1
Using Compatible Numbers
to Estimate Answers
Anytime during the school
year
Independent Worksheet 2
Are These Answers
Anytime during the school
year
Reasonable?
Independent Worksheet 3
Travel Miles
Anytime during the school
year
TEKS Addressed
TEKS 5.4A (5) Use strategies, including
compatible numbers, to estimate solutions to
addition problems.
TEKS 5.4A (6) Use strategies, including
compatible numbers, to estimate solutions to
subtraction problems
NUMBER, OPERATION & QUANTITATIVE REASONING (COMMON FACTORS)
Activity 1
Prime Factorization &
Common Factors
Anytime after Unit One,
Session 10 (May be used to
replace Unit One, Session 12.)
Activity 2
Prime Factorization Number
Riddles
Anytime after Supplement
Activity 1 (May be used to
replace Unit Two, Session 7.)
Independent Worksheet 4
Factor Trees & Common
Factors
Anytime after Supplement
Activity 2
Independent Worksheet 5
More Factor Riddles
Anytime after Supplement
Activity 2
TEKS 5.3D Identify common factors of a set of
whole numbers
MEASUREMENT (AREA & PERIMETER)
Activity 3
Measuring Area
Anytime after Unit Three,
Session 4 (May be used to
replace Unit Three, Session 6.)
Activity 4
Measuring Perimeter
Anytime after Supplement
Activity 3 (May be used to
replace Unit Three, Session 7.)
Activity 5
The Ladybugs’ Garden
Anytime after Supplement
Activities 3 & 4 (May be
used to replace Unit Three,
Session 8.)
Activity 6
Hexarights
Anytime after Supplement
Activities 3 & 4 (May be
used to replace Unit Three,
Session 9.)
Independent Worksheet 6
Area & Perimeter Review
Anytime after Supplement
Activities 3–5
Independent Worksheet 7
Measuring Rectangles
Anytime after Supplement
Activities 3–5
TEKS 5.10B (1) Connect models for perimeter
with their respective formulas
TEKS 5.10B (2) Connect models for area with
their respective formulas
TEKS 5.10C (2) Select appropriate units to
measure perimeter
TEKS 5.10C (3) Select appropriate units to
measure area
TEKS 5.10C (6) Use appropriate units to measure perimeter
TEKS 5.10C (7) Use appropriate units to measure area
TEKS 5.10C (10) Select formulas to measure
perimeter
TEKS 5.10C (11) Select formulas to measure area
TEKS 5.10C (14) Use formulas to measure
perimeter
TEKS 5.10C (15) Use formulas to measure area
Bridges in Mathematics, Grade 5 • 3
Texas Supplement
Grade 5 Activities & Independent Worksheets Grouped by Skill (cont.)
MEASUREMENT (VOLUME)
Activity
Name
Recommended Timing
Activity 7
Introducing Volume
Anytime after Supplement
Activities 3 & 4 (May be
used to replace Unit Three,
Session 10.)
Activity 8
More Paper Boxes
Anytime after Supplement
Activity 7 (May be used to
replace Unit Three, Session 15.)
Independent Worksheet 8
Volume Review
Anytime after Supplement
Activities 7 & 8
Independent Worksheet 9
The Camping Trip
Anytime after Supplement
Activities 7 & 8
TEKS Addressed
TEKS 5.10B (3) Connect models for volume
with their respective formulas
TEKS 5.10C (4) Select appropriate units to
measure volume
TEKS 5.10C (12) Select formulas to measure
volume
TEKS 5.10C (16) Use formulas to measure
volume
GEOMETRY & SPATIAL REASONING (3-DIMENSIONAL FIGURES)
Activity 9
3-D Figure Posters
Anytime toward the end of
Unit Three or later (May be
used to replace Unit Three,
Sessions 17 & 18.)
Activity 10
Faces, Edges, and Vertices
Anytime after Supplement
Activity 9 (May be used to
replace Unit Three, Session 19.)
Independent Worksheet 10
Nets & 3-D Figures
Anytime after Supplement
Activities 9 & 10
TEKS 5.7A (4) Identify essential attributes including parallel parts of 3D geometric figures
TEKS 5.7A (5) Identify essential attributes
including perpendicular parts of 3D geometric figures
TEKS 5.7A (6) Identify essential attributes
including congruent parts of 3D geometric
figures
GEOMETRY & SPATIAL REASONING (TRANSFORMATIONS)
Activity 11
Sketching & Identifying
Transformations
Anytime after Unit Three,
Session 11 (May be used to
replace Unit Three, Sessions
20 & 21.)
Independent Worksheet 11
Transforming Figures, Part 1
Anytime after Supplement
Activity 11
Independent Worksheet 12
Transforming Figures, Part 2
Anytime after Supplement
Activity 11
TEKS 5.8A (1) Sketch the results of translations
on a Quadrant 1 coordinate grid
TEKS 5.8A (2) Sketch the results of rotations
on a Quadrant 1 coordinate grid
TEKS 5.8A (3) Sketch the results of reflections
on a Quadrant 1 coordinate grid
TEKS 5.8B Identify the transformation that
generates one figure from the other when
given two congruent figures on a Quadrant 1
coordinate grid
NUMBER, OPERATION & QUANTITATIVE REASONING
(ESTIMATION TO SOLVE MULTIPLICATION & DIVISION PROBLEMS)
Independent Worksheet 13
Using Compatible Numbers
to Multiply & Divide
Anytime after Unit Four,
Session 9
Independent Worksheet 14
More Multiplication &
Division with Compatible
Numbers
Anytime after Unit Four,
Session 9
Independent Worksheet 15
Reasonable Estimates in
Multiplication & Division
Anytime after Unit Four,
Session 9
4 • Bridges in Mathematics, Grade 5
TEKS 5.4A (7) Use strategies, including
compatible numbers, to estimate solutions to
multiplication problems
TEKS 5.4A (8) Use strategies, including
compatible numbers, to estimate solutions to
division problems
Texas Supplement
Grade 5 Activities & Independent Worksheets Grouped by Skill (cont.)
PROBABILITY & STATISTICS (USING EXPERIMENTAL RESULTS TO MAKE PREDICTIONS)
Activity
Name
Recommended Timing
Activity 12
Introducing Virtual Spinners
Anytime after the February
Number Corner (May be
used to replace Unit Five,
Sessions 12 & 13.)
Activity 13
The 6-4-2 Spinner
Anytime after Supplement
Activity 12 (May be used to
replace Unit Five, Session 14.)
Independent Worksheet 16
Make & Test Your Own
Spinner
Anytime after Supplement
Activities 12 & 13
TEKS Addressed
TEKS 5.12B Use experimental results to make
predictions
TEKS 5.15A (5) Explain observations using
technology
TEKS 5.15A (10) Record observations using
technology
NUMBER, OPERATION & QUANTITATIVE REASONING (PLACE VALUE TO 999 BILLION)
Independent Worksheet 17
Tons of Rice
Anytime after Unit Seven,
Session 8
Independent Worksheet 18
Inches to the Moon & Other
Very Large Numbers
Anytime after Unit Seven,
Session 8
Independent Worksheet 19
More Very Large Numbers
Anytime after Unit Seven,
Session 8
TEKS 5.1A (1) Use place value to read whole
numbers through 999,999,999,999
TEKS 5.1A (2) Use place value to write whole
numbers through 999,999,999,999
TEKS 5.1A (3) Use place value to compare
whole numbers through 999,999,999,999
TEKS 5.1A (4) Use place value to order whole
numbers through 999,999,999,999
PATTERNS, RELATIONSHIPS & ALGEBRAIC THINKING (DIAGRAMS & EQUATIONS)
Activity 14
The Carnival
Anytime after Unit Seven,
Session 14 (May be used to
replace Unit Seven, Session 15.)
Independent Worksheet 20
Padre’s Pizza
Anytime after Supplement
Activity 14
Independent Worksheet 21
Choosing Equations &
Diagrams
Anytime after Supplement
Activity 14
TEKS 5.6A (2) Select from diagrams to represent meaningful problem situations
TEKS 5.6A (3) Select from equations such as
y = 5 + 3 to represent meaningful problem
situations
Bridges in Mathematics, Grade 5 • 5
Texas Supplement
6 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 1
ACTIVITY
Number, Operation & Quantitative Reasoning Prime Factorization & Common Factors
Overview
You’ll need
Students identify the prime and composite numbers
between 1 and 10. Next, they represent 36 as the product
of primes between 1 and 10 and learn how to show the
information on a factor tree. Finally, they create factor
trees for 24 and 30 and use the prime factorization of
both numbers to find their common factors.
H Word Resource Cards (composite number, factor,
prime number, product)
H class set of tile
H small sticky notes (10 for every group of 4 students)
H Student Math Journals
Skills & Concepts
H identifying prime and composite numbers using concrete objects and pictorial models
H exploring prime factorization and factor trees
H identifying common factors of a set of whole numbers
Recommended Timing
Anytime after Unit One, Session 10 (May be used to
replace Unit One, Session 12.)
Instructions for Prime Factorization & Common Factors
1. Have students form groups of 4. Give each group at least 100 tile and 10 small sticky notes. Then list
the numbers from 1 to 10 on the board. Which are prime and which are composite? How do students
know for sure? Use the Word Resource Cards to review the fact that prime numbers only have 2 factors,
while composite numbers have more than 2 factors. Then have each group work together to build all
the possible rectangles for each number you’ve listed. Ask them to label each set with a sticky note on
which they’ve written the number and a P or a C to indicate whether the number is prime or composite.
1P
7P
2P
3P
8C
5P
4C
9C
6C
10 C
2. As they finish, have them compare their work with groups nearby. Then work with input from the
class to erase all but the prime numbers from the board. At this point, you may need to review the fact
that since the number 1 has just one factor (itself), it is considered neither prime nor composite.
Bridges in Mathematics, Grade 5 • 7
Texas Supplement
Activity 1 Prime Factorization & Common Factors (cont.)
3. Now write 36 on the board. Is it prime or composite? If it’s composite, what are its factor pairs? Ask
students to pair-share their ideas, using their tile to help if necessary. Then invite volunteers to share
their thinking with the class. As they do, make a labeled quick sketch of each of the factor pairs named,
and write an equation to match on the board.
36
1
18
2
4
3
6
9
12
Prime numbers between 1 and 10
2 , 3, 5, 7
6
36 = 1 x 36
36 = 2 x 18
36 = 3 x 12
36 = 4 x 9
36 = 6 x 6
36: prime or composite?
4. Next, ask students to consider the list of prime numbers between 1 and 10. Can they think of a way
to write 36 as the product of only these prime numbers? Give them the following example: 36 is the
product of 6 × 6. In turn, 6 is the product of 2 prime numbers, 2 and 3. So it’s possible to write 36 as the
product of 2 × 3 × 2 × 3. Then ask students to find other ways to write 36 as the product of only 2, 3, 5,
and/or 7. Have them work alone or in pairs and record their work in their journal. If they are stuck, encourage them to use one of the equations on the board as a starting point.
5. Then invite them to share their solutions as a whole group. As they will discover, the only way to express 36 as the product of prime numbers is to multiply 2 × 2 × 3 × 3, although you may need to bring
this to their attention during the discussion.
Xavier We started with 36 = 2 × 18. We split the 18 into 2 × 9, and then we split the 9 into 3 × 3,
so we got 2 × 2 × 3 × 3.
Teacher Did anyone get a different answer?
Maria We did. We started with 3 × 12, and split the 12 into 3 × 4. Then we realized we could split
the 4 into 2 × 2, so we got 3 × 3 × 2 × 2.
Teacher Do you notice anything similar about these solutions, including my example?
Delia Not matter how you do it, you get two 2’s and two 3’s, just in different order.
6. Explain that 2 × 2 × 3 × 3 is called the prime factorization of 36. One way to find the prime factorization of a number is by making a factor tree. This involves starting with any pair of factors for a number
and then factoring those factors until you can’t do so anymore. Work with class input to create several
different factor trees for 36 at the board.
8 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 1 Prime Factorization & Common Factors (cont.)
36
6
6
2
36
3
18
2
12
3
9
2
3
2
36
6
2
36 = 2 × 2 × 3 × 3
3
2
3
36 = 2 × 2 × 3 × 3
3
36 = 2 × 2 × 3 × 3
7. Have students list the steps for making a factor tree in their journals, along with an example for 36.
• write the number at the top of the tree.
• choose any pair of factors for the first set of branches.
• keep factoring until you have to stop because all the factors are prime.
Note Advise students that you can start with any pair of factors but, it may be easiest to start with the pair
that includes 2 if the starting number is even, and 3, 5, or 7 if it’s odd.
8. Ask students to make a factor tree for 24 in their journal, starting with a pair of branches that uses
2 as one of the factors. After they’ve had a minute to work, ask them to help you record the tree at the
board. Then explain that prime factorization can be used to find all the factor pairs except the 1 and the
number itself, as shown below.
24
2
12
6
2
2
24 = 2 × 2 × 2 × 3
3
2×2×2×3
24 = 2 × 12
2×2×2×3
24 = 4 × 6
2×2×2×3
24 = 8 × 3
and there is also 24 = 1 × 24
9. Have students make a factor tree for 30 in their journals and use the prime factors to find all the factor pairs. Then record the tree and the factors pairs at the board with their help. Do 24 and 30 share any
Bridges in Mathematics, Grade 5 • 9
Texas Supplement
Activity 1 Prime Factorization & Common Factors (cont.)
of the same factors? Yes: 1, 2, 3, and 6. Explain that these are called common factors. Use a Venn diagram
to summarize the information on the board as students do so in their journals.
30
Factors of 24
2
15
3
30 = 2 × 3 × 5
10 • Bridges in Mathematics, Grade 5
5
2×3×5
30 = 2 × 15
2×3×5
30 = 6 × 5
2×3×5
30 = 3 × 10
and there is also 30 = 1 × 30
12
4
8
24
1
2
3
6
Factors of 30
15
5
10
30
Common Factors
Texas Supplement
Activity 2
ACTIVITY
Number, Operation & Quantitative Reasoning Prime Factorization Number Riddles
Overview
You’ll need
Students review prime factorization and use prime factors
to determine all the common factors of 40 and 60. Then
they work on a set of number riddles that involve prime
factorization.
H Factor Riddles (pages 14 and 15, class set)
H Student Math Journals
Skills & Concepts
H identifying prime and composite numbers
H exploring prime factorization and factor trees
H identifying common factors of a set of whole numbers
Recommended Timing
Anytime after Supplement Activity 1 (May be used to
replace Unit Two, Session 7.)
Instructions for Prime Factorization Number Riddles
1. Ask students to help you list the prime numbers between 1 and 10 on the board. If necessary, remind
them that 1 is neither prime nor composite because it only has 1 factor. Then write the number 40 at the
board. Is it prime or composite? Call on volunteers to share and explain their answers.
Carter It’s composite because it’s even.
Teacher Are all even numbers composite?
Yaritza No, because 2 is an even number, and it’s prime, remember? I think 40 is a composite
number because it has more factors than just 1 and itself, like 4 and 10.
2. Review the fact that a composite number can be written as the product of prime numbers. This is
called prime factorization. One way to find the prime factorization of a number is to make a factor tree.
Work with class input to make a factor tree for 40 at the board. Start with a pair of branches that uses 2
as one of the factors. Ask students to record the tree in their journals and use the prime factorization of
40 to find all the factor pairs. After they’ve had a minute to work, ask them to help you list the pairs at
the board.
Bridges in Mathematics, Grade 5 • 11
Texas Supplement
Activity 2 Prime Factorization Number Riddles (cont.)
40
2
20
10
2
2
5
2×2×2×5
40 = 2 × 20
2×2×2×5
40 = 4 × 10
2×2×2×5
40 = 8 × 5
and there is also 40 = 1 × 40
40 = 2 × 2 × 2 × 5
3. Write the number 70 on the board, and ask students whether they think 70 and 40 have any common
factors. After they’ve had a minute to discuss their conjectures, have them make a factor tree for 70 in
their journals and use it to help list all the factor pairs. Work with their input to record the results at the
board. Then ask students to create a Venn diagram in their journals to show the common factors of 40
and 70 as you do so at the board.
Factors of 40
2×5×7
70 = 2 × 35
2×5×7
70 = 10 × 7
2×5×7
70 = 14 × 5
and there is also 70 = 1 × 70
20
4
8
40
1
2
5
10
Factors of 70
35
14
7
70
Common Factors
4. Now tell students you have a number riddle for them to solve. Write the first clue on the board and
read it with the class.
I am a common factor of 28 and 40.
Give them a few minutes to create a factor tree and list the factor pairs for 28 (1 × 28, 2 × 14, and 4 × 7) in
their journals. Work with their input to record the common factors of 28 and 40 at the board (1, 2, and 4).
5. Write the next two clues on the board and have students use them to identify the mystery number (4).
I am an even number.
I am not prime.
6. Give students each a copy of Factor Riddles. Review the instructions and clarify as needed. You might
allow them to work either individually or in pairs as they choose. Encourage them to work on the challenge problems on page 15 if they finish the other problems with time to spare.
12 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 2 Prime Factorization Number Riddles (cont.)
Extensions
• Utah State University has developed a library of free virtual manipulatives that includes a factor tree
feature that’s fun and easy to use. To access this feature, go online to the following URL:
http://nlvm.usu.edu/en/nav/vlibrary.html. Click on Number and Operations for Grades 3–5, and
then click on Factor Tree. When you’ve reached the Factor Tree screen, click on the Instructions button in the top right-hand corner for directions about how to use this feature. After you’ve explored
Factor Tree yourself, show students how to set up the screen so they can create factor trees for 2 different numbers and then find the common factors. This feature is self-correcting, so students are
able to get feedback as they work.
INDEPENDENT WORKSHEET
See “Factor Trees & Common Factors” and “More Factor Riddles” on pages 101–1-4 in the Independent
Worksheet section of this Supplement for additional practice with factor trees and common factors.
Bridges in Mathematics, Grade 5 • 13
Texas Supplement Blackline Run a class set back-to-back with page 15.
NAME
DATE
Factor Riddles page 1 of 2
Solve each of the riddles below. For each one:
• Make a factor tree and list the factor pairs for each number.
• Find the factors shared by each number (their common factors).
• Use the other clues to find the answer to the riddle.
• Show your work.
1
I am a common factor of 27 and 45.
I am an odd number.
When you multiply me by 3, you get a number greater than 10.
What number am I?
2
I am a common factor of 36 and 48.
I am also a factor of 30.
I am an even number.
I am divisible by 3.
What number am I?
14 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run a class set back-to-back with page 14.
NAME
DATE
Factor Riddles page 2 of 2
3
I am a common factor of 60 and 100.
I am an even number greater than 4.
I am divisible by 4.
What number am I?
CHALLENGE
4
I am an odd number.
I am a common factor of 135 and 210.
I am greater than 7.
What number am I?
5
On another piece of paper, write your own factor riddle for a classmate that includes at least 3 clues. Be sure not to give the answer away before the third clue.
Exchange papers with a classmate and see if you can solve each other’s riddles.
Hint: Start with the prime numbers and then multiply different combinations of
them to get starting numbers.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 15
Texas Supplement
16 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 3
ACTIVITY
Measurement Measuring Area
Overview
You’ll need
Students review the term area and work together to generate a formula for determining the area of rectangles and
squares. In the process, they have an opportunity to see
and handle a square inch and a square foot. Then they
apply the information as they work in pairs to find the
area of various items around the classroom.
H Measuring Area (page 20, class set)
H one 12" × 12" piece of red construction paper
H 10" × 18" blue construction paper (1 piece for every 4
students)
H rulers (class set)
H yardsticks and measuring tapes
Skills & Concepts
H connecting models for area with their respective formulas
H selecting and using appropriate units to measure area
H masking tape
H calculators (optional, class set)
H Student Math Journals
H selecting and using formulas to determine area
H Word Resource Cards (area, dimension)
Recommended Timing
Anytime after Unit Three, Session 4 (May be used to
replace Unit Three, Session 6.)
Instructions for Measuring Area
1. Post the Word Resource Card for area on the board. Ask students to pair-share what they know about
this term. After a minute or two, invite volunteers to share their ideas with the class. As the discussion
unfolds, review the following concepts:
• area is a measure of how much surface something takes up.
• area is measured in square units such as square inches, square feet, or square miles.
area
2. Hold up a single tile and ask students to report its area in square inches. If necessary, have a volunteer measure the dimensions of the tile and work with the class to establish the fact that it’s exactly 1
square inch. Use a loop of masking tape to fasten the tile to the board. Work with class input to label its
dimensions and area.
3. Distribute sets of tile. Ask students to work in groups of four to build a square with an area of exactly
144 square inches. After they’ve had a few minutes to work, have them share and compare their results.
Bridges in Mathematics, Grade 5 • 17
Texas Supplement
Activity 3 Measuring Area (cont.)
Students We thought it was going to be really big, but it’s not so big after all.
We knew it was going to be a 12" × 12" square because 12 × 12 is 144.
We each made 3 rows of 12 and put them together. It went pretty fast for us.
4. Ask each group to measure the dimensions of the square they’ve just built with the inch side of their
ruler. What can they tell you about the square now? As volunteers share with the class, press them to
explain their thinking.
Alex It’s 12 inches on both sides.
Teacher What is the area of your square, and how do you know?
Students It’s 144 square inches because that’s what you told us to do.
It’s 144 square inches because we used 144 tiles, and each tile is 1 square inch.
You can see a 10 × 10 square inside the 12 × 12. Then just add 12 on the top and bottom, and 10 on
both sides. It makes 144 in all.
It’s 12 rows of 12. If you just multiply 12 × 12, you get 144.
5. Show students the 12" × 12" square of red construction paper you’ve prepared. Ask a volunteer to compare the paper to the tile square at his or her table. After confirming that the two are the same size, fasten the paper square to the board. Work with class input to label its dimensions and area. Explain that because it is 12" or 1 foot on each side, it’s called a square foot, and record this information on the board.
12"
12"
144 square inches
1"
1"
1 square inch
1 sq. in.
1 in2
1 square foot
1 sq. ft.
1 ft2
6. Give each group a 10" × 18" piece of blue construction paper. Ask them to find the area of this rectangle, using their rulers and/or the tile to help. Challenge them to find a more efficient method than
covering the entire rectangle with tile. Have them each record the answer, along with any computations
they made, in their journals.
7. When they’ve had a few minutes to work, ask students to share their answers and explain how they
found the area of the rectangle. Record their strategies at the board.
18 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 3 Measuring Area (cont.)
18"
It’s 10 tiles along the side and 18
along the top. 10 rows of 18 is 180.
10"
If you count by 10’s it’s 180.
10" x 18" = 180 sq. in.
8. Chances are, some students will have compared the paper rectangle to the tile square at their table to
find the side lengths, and then used some kind of counting strategy to find the area. Others may have
done the same but multiplied the dimensions to find the area. Still others may have measured the dimensions with their rulers and multiplied. If the third strategy doesn’t come from the students, tape one
of the 10" × 18" pieces of paper to the board and model it yourself.
9. Post the Word Resource Card for dimension on the board. Explain that to find the area of a square or
a rectangle, we measure its dimensions and multiply the 2 numbers. Press students to explain how and
why this works, and then work with input from the class to write the general formula: area = length ×
width or A = lw.
3
dimension
5
10. Explain that in a minute, students will be working in pairs to measure the area of some things
around the classroom. Ask them to look around. Can they spot anything they’d measure in square
inches? What about the calendar grid pocket chart or the whiteboard? Would they find the area of these
in square inches or square feet?
Students I’d use square inches to find out the area of small stuff like my math journal or probably
my desk.
I’d maybe use square feet instead of square inches to get the area of the calendar chart.
I’d definitely use square feet to measure the area of the rug or the whole room.
11. Give students each a copy of the Measuring Area worksheet. Examine the chart together and explain
the tasks as needed. Make sure they know where to find the yardsticks and measuring tapes as they
need them. Then ask them to work in pairs to complete the sheet.
Note Advise students to work to the nearest inch in measuring the dimensions of the items listed on the worksheet. You might also allow them to use calculators to help with the computation, especially if some of your students aren’t yet completely fluent with 2-digit by 2-digit multiplication.
Bridges in Mathematics, Grade 5 • 19
Texas Supplement Blackline Run a class set.
NAME
DATE
Measuring Area
Find the area of each item
listed below.
example
A piece of
blue construction paper
1
Your math journal
2
Your desk or table
3
A geoboard
Dimensions
(Measure to the nearest inch
and show your units: inches
or feet)
Length = 18”
Width = 10”
Area
(Show your work
and label the answer with
the correct units.)
18” x 10” = 180 sq. in.
4
Calendar Grid pocket
chart
5
The top of a bookshelf
6
The front of a chapter
book
7
A Calendar Grid marker
8
A work table larger
than the one where you
sit
9
The whiteboard
10
The classroom
20 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 4
ACTIVITY
Measurement Measuring Perimeter
Overview
You’ll need
Students review the terms area and perimeter, and find
the perimeter of a rectangular and a square piece of
construction paper. Together, they generate formulas for
determining the perimeter of rectangles and squares.
Then they apply the information as they work in pairs to
find the perimeter of various items around the classroom.
H Measuring Perimeter (page 24, class set)
Skills & Concepts
H rulers (class set)
H connecting models for perimeter with their respective
formulas
H yardsticks and measuring tapes
H selecting and using appropriate units to measure
perimeter
H Word Resource Cards (area, perimeter)
H 9" × 12" green construction paper (half class set)
H one 12" × 12" piece of red construction paper
H base 10 mats available
H geoboards available
H Student Math Journals
H selecting and using formulas to determine perimeter
Recommended Timing
Anytime after Supplement Activity 3 (May be used to
replace Unit Three, Session 7.)
Instructions for Measuring Perimeter
1. Post the Word Resource Cards for area and perimeter on the board. Ask student pairs to compare and
contrast the two terms. How are they alike? How are they different? After a minute or two, invite volunteers to share their ideas with the class. As the discussion unfolds, review the following concepts:
• area and perimeter are both measurements.
• area is a measure of how much surface something takes up.
• area is measured in square units such as square inches, square feet, or square miles.
• perimeter is a measure of the total distance around something.
• perimeter is measured in linear units such as inches, feet, yards, or miles.
area
perimeter
2. Explain that you’ll be working with perimeter today. Have students pair up or assign partners, and
ask them to get out their rulers and math journals. Give each pair a 9" × 12" sheet of construction paper
without mentioning the dimensions. Ask them to use the inch side of their ruler to find the perimeter,
or the total distance around the paper. Have them each record the answer, along with any computations
they made, in their journals.
Bridges in Mathematics, Grade 5 • 21
Texas Supplement
Activity 4 Measuring Perimeter (cont.)
3. When they’ve had a couple of minutes to work, ask students to share their answers and explain how they
found the perimeter of the paper. Use numbers and labeled sketches to record the strategies they share.
12"
9"
9 + 12 + 9 + 12 = 42"
9"
12"
2 × 9 = 18"
2 × 12 = 24"
18 + 24 = 42"
(2 × 9) + (2 × 12) = 42"
4. Chances are, some students will have added all 4 side lengths, while others may have multiplied each
of the lengths by 2 and then added. If the second strategy doesn’t come from the students, model it yourself. Then work with input from the class to write a general formula for finding the perimeter of a rectangle: perimeter = 2 × the width + 2 × the length, or P = 2w + 2l.
5. Hold up the 12" square of construction paper. Ask students to estimate the perimeter of this square
based on the measurements they just made. It’s fine if they want to set one of the 9" × 12" sheets directly on top of the square to help make a more accurate estimate. Record their estimates on the board.
Then have a volunteer measure one of the sides of the square and share the measurement with the
class. Ask students how they can use that information to find the perimeter. Is it possible to do so without measuring the other 3 side lengths?
Students Sure! It’s a square, so all the sides are the same.
Just add 12 four times.
Or you could multiply 12 × 4 to get the answer. It’s 48 inches.
6. Work with input from the class to write a general formula for finding the perimeter of a square:
perimeter = 4 × the length of one side, or P = 4s.
7. Ask students to consider the following question: If there are 12" in a foot, what is the perimeter of the
paper square in feet? Have them give the thumbs-up sign when they have the answer and then invite a
couple of volunteers to share their thinking.
Students Each side is a foot, so it’s 4 feet all the way around.
Also, it’s 48 inches and 48 ÷ 12 = 4, so that’s 4 feet.
Wow! That’s pretty big around. My little sister isn’t much taller than about 4 feet.
8. Explain that in a minute, students will be working in pairs to measure the perimeter of some things
around the classroom. Ask them to look around. Can they spot anything they’d measure in inches?
What about the calendar grid pocket chart or the whiteboard? Would they find the perimeter of these
in inches or feet? Hold up a yardstick and ask them if there’s anything in the room with a perimeter it
would make most sense to measure in yards.
Students I’d use inches to find out the perimeter of small stuff like a book or probably my desk.
I’d definitely use feet instead of inches to get the perimeter of the whiteboard.
I’d use yards to measure the perimeter of the rug or the whole room.
22 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 4 Measuring Perimeter (cont.)
9. Give students each a copy of the Measuring Perimeter worksheet. Examine the chart together and explain the tasks as needed. Ask students if they need to measure the length of every side in order to find
the perimeter of their math journal or their desk. Why not?
Make sure they know where to find the yardsticks and measuring tapes as they need them. Then ask
them to work in pairs to complete the sheet.
Note Advise students to work to the nearest inch in measuring the side lengths of the items listed on the worksheet.
Bridges in Mathematics, Grade 5 • 23
Texas Supplement Blackline Run a class set.
NAME
DATE
Measuring Perimeter
Find the perimeter
of each item listed
below.
example
Side Lengths
(Include units: inches,
feet, or yards)
Circle the formula
you need to find the
perimeter.
P = 2w + 2l
9” and 12”
A piece of green
construction paper
P = 4s
1
P = 2w + 2l
2
P = 4s
P = 2w + 2l
3
P = 4s
P = 2w + 2l
Your math
journal
Your desk or
table
A geoboard
4
P = 4s
P = 2w + 2l
5
P = 4s
P = 2w + 2l
6
A base 10 mat
P = 4s
P = 2w + 2l
The whiteboard
P = 4s
P = 2w + 2l
The classroom
P = 4s
P = 2w + 2l
Calendar Grid
pocket chart
The top of a
bookshelf
7
8
Perimeter
(Show your work and
label the answer with
the correct units.)
(2 x 9) + (2 x 12) = 42”
P = 4s
24 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 5
ACTIVITY
Measurement The Ladybugs’ Garden
Overview
Recommended Timing
The Ladybugs are planning their spring garden. They have
exactly 24 centimeters of fencing, and they want to make
a rectangular garden. Students investigate relationships
between area and perimeter as they develop the best
plan for the Ladybugs’ garden.
Anytime after Supplement Activities 3 and 4 (May be
used to replace Unit Three, Session 8.)
Skills & Concepts
H Centimeter Grid Paper (page 29, class set)
H connecting models for area and perimeter with their
respective formulas
H selecting and using appropriate units to measure area
and perimeter
You’ll need
H The Ladybugs’ Garden (page 28, 1 copy on a transparency)
H overhead pens
H a piece of paper to mask parts of the overhead
H rulers (class set)
H selecting and using formulas to determine area and
perimeter
Instructions for The Ladybugs’ Garden
1. Give students each a sheet of Centimeter Grid Paper and ask them to get out their pencils and rulers. Show the prompt at the top of the Ladybugs’ Garden overhead. Read it with the class and clarify as
needed. Give them a few minutes to draw a rectangle on their grid paper that has a perimeter of exactly
24 centimeters.
2. Then invite a volunteer up to the overhead to share his or her work with the class.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Ladybugs’ Garden
1
The Ladybugs are planning to plant a garden this spring. They want it to be
rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper.
Beckett I started by drawing a line that was 10 centimeters along the top. That just seemed like a
good length. Then I drew 2 centimeters down. That added up to 12, and I realized that it would take
12 more to make the rest of the rectangle. It turned out kind of skinny, but it worked.
3. Have your volunteer label each side of his or her rectangle with its length and sit down again. Then ask
2 Now sketch as many different rectangles as you can find that have a perimeter
the rest of the class to write 2 equations
on each
theoneback
their
grid
paper,
with equa- one for the perimeter and one
of 24 centimeters. Label
with its of
perimeter
and area,
along
tions to show how you got the answers.
to determine the area of the rectangle. Remind them to label their answers with the correct units. Have
3
All of your rectangles have a perimeter of 24 centimeters. Do they all have the
same area? Why or why not?
4
Which rectangle would work best for the Ladybugs’ garden? Explain your answer.
Bridges in Mathematics, Grade 5 • 25
Texas Supplement
Activity 5 The Ladybugs’ Garden (cont.)
them pair-share their work as they finish. Work with input from the class to label the rectangle with its
area and write the two needed equations at the overhead. Take the opportunity to review the formulas
for finding the perimeter and area of a rectangle, and ask students to correct their work if necessary.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Ladybugs’ Garden
1
20 sq cm
2 cm
2 cm
The Ladybugs are planning to plant a garden this spring. They want it to be
rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper.
10 cm
10 cm
P: ( 2 x 2) + (2 x 10) = 24 cm
A: 2 x 10 = 20 sq cm
8cm
4 cm
4 cm
4. Have a student who responded differently to the original prompt draw and label his or her rectangle
at the overhead. (If no one had a different response, volunteer one of your own.)
8cm
2
Now sketch as many different rectangles as you can find that have a perimeter
of 24 centimeters. Label each one with its perimeter and area, along with equations to show how you got the answers.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Ladybugs’ Garden
20 sq cm
2 cm
2 cm
3 All of your rectangles have a perimeter of 24 centimeters. Do they all have the
1 Thearea?
Ladybugs
planning
Why are
or why
not? to plant a garden this spring. They want it to be
same
rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper.
10 cm
4 Which rectangle would work best for the Ladybugs’ garden? Explain your answer.
10 cm
P: ( 2 x 2) + (2 x 10) = 24 cm
A: 2 x 10 = 20 sq cm
8cm
4 cm
4 cm
8cm
2
Now sketch as many different rectangles as you can find that have a perimeter
of 24 centimeters. Label each one with its perimeter and area, along with equations to show how you got the answers.
Delia I started with 8 centimeters along the top and then drew 4 down. I saw that was 12, so I just
3 All of your rectangles have a perimeter of 24 centimeters. Do they all have the
did the same thing for the
the other side. It’s 24 in all.
area? Why orand
why not?
samebottom
4 Which rectangle
would work best
for thea
Ladybugs’
garden? Explain
5. Confirm with the class that both
rectangles
have
perimeter
ofyour
24answer.
centimeters. Even before they calculate the area of the second rectangle, would they say the areas are the same or different?
Students The second one looks bigger.
I’m pretty sure there’s more space in the second one.
That’s weird because they both have the same amount of fence around the outside.
6. Ask students to write 2 equations for the second rectangle on the back of their grid paper, one for the
perimeter and one for the area. Then work with their input to label the second rectangle with its area
and write both equations at the overhead. Is the area of the second rectangle the same as the first or dif-
26 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 5 The Ladybugs’ Garden (cont.)
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Ladybugs’ Garden
ferent? Ask students to pair share
ideas about why the areas are different even though the perimeters
are the same. Then invite volunteers
toareshare
their
thinking
the
class.
1 The Ladybugs
planning to
plant a garden
this spring.with
They want
it to be
rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper.
10 cm
2 cm
2 cm
Students The one that’s long and skinny doesn’t have as much area.
20 sq cm
It’s like when you make the sides shorter,
you get more room in the middle.
10 cm
The first rectangle I drew has even more
space inP: ( 2the
middle.
x 2) + (2 x 10) = 24 cm
A: 2 x 10 = 20 sq cm
4 cm
4 cm
7. Then reveal the rest of the overhead. 8cm
Read it with the class and clarify as needed. Let them know that
they need to find at least 4 different rectangles, and it’s fine if one is a square because squares are also
rectangles. Make sure students understand that a 2 × 10 and a 10 × 2 don’t count as 2 different rectangles. Ask them to respond to questions 3 and 4 on the back of their grid paper.
8cm
2
Now sketch as many different rectangles as you can find that have a perimeter
of 24 centimeters. Label each one with its perimeter and area, along with equations to show how you got the answers.
3 All of your rectangles have a perimeter of 24 centimeters. Do they all have the
same area? Why or why not?
4
Which rectangle would work best for the Ladybugs’ garden? Explain your answer.
8. When most students have finished, reconvene the class to share and compare their results. They’ll find
that there are 6 different rectangles with a perimeter of 24 cm: 1 × 11, 2 × 10, 9 × 3, 8 × 4, 7 × 5, and 6 ×
6. Each has a different area (11 sq cm, 20 sq cm, 27 sq cm, 32 sq cm, 35 sq cm, and 36 sq cm respectively),
the square having the most. Encourage students to continue to explain why the areas vary from one rectangle to the next. (The closer rectangles with the same perimeter get to being square, the larger their area.
Some students may be interested to know that a circle is the shape that has the maximum area for any
given perimeter.) Also encourage students to discuss and debate the best rectangle for the Ladybugs’ garden. Some may feel that the 6 × 6 is best because it offers the most space. Others may believe that the
3 × 9 or 4 × 8 is better because it’s easier to water all the plants, including ones in the middle.
INDEPENDENT WORKSHEET
See “Area & Perimeter Review” and “Measuring Rectangles” on pages 105–108 in the Independent Worksheet section of this Supplement for more practice selecting and using appropriate units and formulas to
determine area and perimeter.
Bridges in Mathematics, Grade 5 • 27
Texas Supplement Blackline Run 1 copy on a transparency.
The Ladybugs’ Garden
1
The Ladybugs are planning to plant a garden this spring. They want it to be
rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper.
2
Now sketch as many different rectangles as you can find that have a perimeter
of 24 centimeters. Label each one with its perimeter and area, along with equations to show how you got the answers.
3
All of your rectangles have a perimeter of 24 centimeters. Do they all have the
same area? Why or why not?
4
Which rectangle would work best for the Ladybugs’ garden? Explain your answer.
28 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run a class set.
NAME
DATE
Centimeter Grid Paper
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 29
Texas Supplement
30 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 6
ACTIVITY
Measurement Hexarights
Overview
You’ll need
Students continue to investigate relationships between
area and perimeter as they measure and construct polygons called “hexarights” (hexagons with pairs of adjacent
sides that meet at right angles).
H Introducing Hexarights (page 34, 1 copy on a transparency)
Skills & Concepts
H Centimeter Grid Paper (page 29, class set, plus a few extra)
H connecting models for area and perimeter with their
respective formulas
H piece of paper to mask parts of the overhead
H selecting and using appropriate units to measure area
and perimeter
H rulers marked with both centimeters and inches (class set)
H Measuring Hexarights (page 35, half-class set, cut in half)
H Hexarights, Perimeter = 24 cm (page 36, class set)
H 2 or 3 transparencies and overhead pens
H selecting and using formulas to determine area and
perimeter
H identifying essential attributes of two-dimensional
geometric figures
Recommended Timing
Anytime after Supplement Activities 3 and 4 (May be
used to replace Unit Three, Session 9.)
Instructions for Hexarights
1. Show the top portion of Introducing Hexarights at the overhead, masking the rest with a piece of paper. Give students a minute to pair-share any observations they can make. Then invite volunteers to
share their thinking with the class. Record some of their ideas in the space to the left of the shape.
2. Then reveal the definition below the shape, still keeping the rest of the overhead covered. Read and
discuss it with the class. As you do so, review the meanings of the terms hexagon, perpendicular, and
right angles.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
Introducing Hexarights
1
•
•
•
•
•
•
Describe this shape.
has 6 sides
has 5 maybe 6 right angles
has parallel lines
some of the lines are perpendicular
kind of like 2 rectangles stuck together
none of the lines are the same length
This shape is a hexagon because it has 6 sides, but let’s call it a hexaright. A
hexaright is a hexagon in which every pair of sides that touch each other is perpendicular. (That is, they meet at right angles.)
2 Here are 2 examples of shapes that are not hexarights. Can you see why?
a
b
Bridges in Mathematics, Grade 5 • 31
Texas Supplement
Activity 6 Hexarights (cont.)
3. Next, reveal the two counter-examples show in the middle of the overhead. Can students explain
why neither of these are hexarights? Have them share at the overhead so their classmates can see what
they’re talking about.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
Introducing Hexarights
1
•
•
•
•
•
•
Describe this shape.
has 6 sides
has 5 maybe 6 right angles
has parallel lines
some of the lines are perpendicular
kind of like 2 rectangles stuck together
none of the lines are the same length
This shape is a hexagon because it has 6 sides, but let’s call it a hexaright. A
hexaright is a hexagon in which every pair of sides that touch each other is perpendicular. (That is, they meet at right angles.)
2 Here are 2 examples of shapes that are not hexarights. Can you see why?
a
3
a
b
Find the area and perimeter of the hexarights below.
b
Students Shape a isn’t a hexaright because there are 2 angles that aren’t right angles.
I thought they were wrong about shape b because it’s all right angles, but then I realized there are 10
sides! A hexaright can only have 6 sides.
4. Now show the 2 hexarights at the bottom of the overhead and briefly discuss strategies for finding the
area and perimeter of each. Then give students each a copy of the Measuring Hexarights half-sheet. Ask
them to experiment with both the inch side and the centimeter side of their rulers. Which unit of measure works best? Students will quickly discover that most of the measurements don’t come out evenly
unless they use centimeters.
5. Solicit agreement from the class that they’ll work in centimeters and square centimeters rather than
inches and square inches, and let them get started. Encourage them to share and compare their strategies and solutions as they work.
6. When most students have finished finding the perimeter and area of at least one of the hexarights,
place a blank transparency on top of the overhead and invite volunteers to share their work with the
class. Move or replace the transparency each time a new volunteer comes up to the overhead to accommodate several different presentations. Here is an example of the sort of work you might expect from
students, although some will divide the hexarights differently.
32 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 6 Hexarights (cont.)
2 cm
2 x 3 = 6 sq cm
3 cm
3 cm
4 cm
6 + 2 + 3 + 3 + 4 = 18 cm
P = 18 cm
A = 18 sq cm
4 cm
q cm
1 cm
m
qc
=7s
1x7
7 cm
=4s
3 x 4 = 12 sq cm 3 cm
8 cm
1x4
2 cm
6 cm
1 cm
1 + 8 + 4 + 1 + 3 + 7 = 24 cm
P = 24 cm
A = 11 sq cm
7. As students share, discuss the methods they’re using to find the area and perimeter of these shapes.
Did they use the perimeter formulas they developed during Activity 4? Why not? (Because these are
irregular polygons. All you can do is simply add all the different side lengths.) Did they use the area
formula they developed during Activity 3? How? (To find the area without covering the shape with centimeter square units or drawing them in, you need to divide each hexaright into 2 rectangles. Then you
can use A = lw to find the area of each and add them.)
8. After 2 or 3 strategies have been shared for each hexaright, explain that there is more than one
hexaright with a perimeter of 24 centimeters. Give students each a copy of More Hexarights. Review
the instructions together and clarify as needed. Place a small stack of grid paper on each table and give
students the remainder of the math period to work. Encourage them to share and compare their strategies for finding other hexarights with perimeters equal to 24 centimeters. What are some of the areas
that result? Are they all equal? (No. See the Activity Answer Key on page 85 for some of the possible
hexarights as well as sample responses to the last question.)
Texas Grade Five Supplement Blackline
NAME
DATE
Hexarights, Perimeter = 24 cm
1 Draw 2 different hexarights with a perimeter of 24 cm, and find the area of
each. Then draw a third hexaright with a perimeter of 24 cm. This time, make
the area as large as possible.
2
You can use the space below and the back of this sheet. Or, you can draw your
hexarights on centimeter grid paper, cut them out, and glue them to this sheet.
Use your ruler to help make the lines straight and accurate.
3 Label your hexarights with their dimensions, perimeter, and area. Use numbers, sketches, and/or words to show how you found the perimeter and area of
each hexaright.
4
On the back of the sheet, write at least 2 sentences to describe what you found
out about the areas of hexarights with a perimeter of 24 cm.
Reconvene the class to share strategies and solutions either at the end of the period or at another time.
Note “Hexaright” is not some long-forgotten concept from your high school geometry days. It is a made-up
term borrowed from Measuring Up: Prototypes for Mathematics Assessment (Mathematical Sciences Education Board National Research Council, 1993. Washington, DC: National Academy Press). You may want to
let students know this so that they won’t expect to see, or use it on standardized texts.
Bridges in Mathematics, Grade 5 • 33
Texas Supplement Blackline Run 1 copy on a transparency.
Introducing Hexarights
1
Describe this shape.
This shape is a hexagon because it has 6 sides, but let’s call it a hexaright. A
hexaright is a hexagon in which every pair of sides that touch each other is perpendicular. (That is, they meet at right angles.)
2 Here are 2 examples of shapes that are not hexarights. Can you see why?
a
3
b
Find the area and perimeter of the hexarights below.
a
34 • Bridges in Mathematics, Grade 5
b
© The Math Learning Center
Texas Supplement Blackline Run a half-class set and cut the sheets in half.
NAME
DATE
Measuring Hexarights
Find the area and perimeter of the hexarights below. Show all your work.
NAME
DATE
Measuring Hexarights
Find the area and perimeter of the hexarights below. Show all your work.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 35
Texas Supplement Blackline Run a class set.
NAME
DATE
Hexarights, Perimeter = 24 cm
1
Draw 2 different hexarights with a perimeter of 24 cm, and find the area of
each. Then draw a third hexaright with a perimeter of 24 cm. This time, make
the area as large as possible.
2
You can use the space below and the back of this sheet. Or, you can draw your
hexarights on centimeter grid paper, cut them out, and glue them to this sheet.
Use your ruler to help make the lines straight and accurate.
3
Label your hexarights with their dimensions, perimeter, and area. Use numbers, sketches, and/or words to show how you found the perimeter and area of
each hexaright.
4
On the back of the sheet, write at least 2 sentences to describe what you found
out about the areas of hexarights with a perimeter of 24 cm.
36 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 7
ACTIVITY
Measurement Introducing Volume
Overview
You’ll need
In this activity, students move toward increasingly efficient
methods of finding the volume of cubes and rectangular
solids.
H Cubes and Rectangular Solids (page 40, 1 copy on a
transparency)
Skills & Concepts
H centimeter cubes (class set)
H connecting models for volume with their respective
formulas
H scissors
H selecting and using appropriate units to measure
volume
H selecting and using appropriate formulas to determine
volume
H identifying essential attributes including parallel, perpendicular, and congruent parts of three-dimensional
geometric figures
Recommended Timing
H Paper Box Pattern (page 41, class set)
H scotch tape
H rulers (class set)
H Student Math Journals
H Word Resource Cards (congruent, edge, face, parallel,
perpendicular, vertex)
Advance Preparation Display the Word Resource Cards
where students can see them before conducting the
activity.
Anytime after Supplement Activities 3 and 4 (May be
used to replace Unit Three, Session 10.)
Instructions for Introducing Volume
1. Give students each a centimeter cube and allow several minutes for them to record as many observations as they can about the cube in their math journals. Call their attention to the Word Resource Cards
before they start writing and challenge them to include at least 3 of the words in their observations.
2. Have them pair-share their observations, and then call for whole-group sharing. Record some of their
observations at the top of the Cubes and Rectangular Solids overhead, keeping the rest of the transparency covered for now. If it doesn’t come up in the discussion, ask students to find examples of parallel,
perpendicular, and congruent edges and faces as they examine their cubes.
3. Ask students to estimate the length of one of the edges of their cube. Then have a volunteer measure
to confirm that each edge is 1 centimeter. Next, ask students to determine the area of one of the cube’s
faces. Finally, explain that because their cube is 1 centimeter long, wide, and high, it is called a cubic
centimeter. Just as centimeters are used to measure length and square centimeters are used to measure
area, cubic centimeters are used to measure volume. Add this information to the overhead, along with the
abbreviations for each measure.
Bridges in Mathematics, Grade 5 • 37
Texas Supplement
Activity 7 Introducing Volume (cont.)
4. Next, reveal the picture of the rectangular solid on the overhead. Have students write at least 3 observations about this figure in their journals. Then invite volunteers to share their observations with the
class as you record at the overhead. After you’ve recorded 8–10 observations, work with input from the
students to label all 3 dimensions of the solid: length, width, and height.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
Cubes and Rectagular Solids
•
Cube
•
•
•
•
length of edge = 1 cm
area of face = 1 sq cm (cm2)
colume of cube = 1 cubic cm (cm3)
Rectangular Solid
•
•
•
•
•
•
height
•
•
length
h
dt
wi
•
•
square on every side
8 vertices
has parallel and perpendicular sides
all faces are congruent
all edges are congruent
has 3 pairs of parallel faces
sides that touch are perpendicular
6 faces
12 edges
faces are rectangles
6 faces, 8 vertices, 12 edges
all right angles
sides that touch are perpendicular
3 pairs of parallel sides
opposite sides are congrunent
Build this rectangular solid with your centimeter cubes. Find the volume without
counting
each cube 1 by 1.
5. Give each table a good supply
of centimeter
cubes. Ask each student to build several different rectan15 + 15 + 15 = 45 cm
gular solids that have a volume of exactly 12 cubic centimeters. Be sure they understand that their con9 x 5 = 45 cm
structions have to be solidly filled in, without gaps or holes between cubes. Ask them to share and comcounted by rows of 5 (5 x 9 =45 cm )
pare their constructions as they’re working.
3
3
3
18 + 18 = 36 36 +9 = 45 cm3
length x width xAsk
height several volunteers to describe their
6. After a few minutes, call a halt to the construction process.
5 x 3description
x 3 = 45 cm
constructions by length, width, and height. Record each
at the board, along with an equation
to confirm that the total is 12 cubic centimeters.
3
Rectangular Solids with Volume = 12 cm3
Length = 2 cm
Width = 2 cm
Height = 3 cm
Length = 6 cm
Width = 2cm
Height = 1cm
Length = 12 cm
Width = 1 cm
Height = 1 cm
2 x 2 x 3 = 12 cm3
6 x 2 x 1 = 12 cm3
12 x 1 x 1 = 12 cm3
7. Now reveal the rectangular solid at the bottom of the overhead. Ask students to replicate it with their
cubes and determine its volume without counting every cube one by one. As they finish, invite volunteers to share their strategies with the class, as you record at the overhead. If it doesn’t come from one of
the students, ask them what would happen if you multiplied length × width × height. Would it result in
the same answer they’ve shared? Why or why not? Press them to explain their thinking and then work
with their input to write the equation and solve the multiplication problem.
38 • Bridges in Mathematics, Grade 5
Rectangular Solid
•
Texas Supplement
•
height
•
•
Activity 7 Introducing Volume (cont.)
length
h
idt
w
•
•
faces are rectangles
6 faces, 8 vertices, 12 edges
all right angles
sides that touch are perpendicular
3 pairs of parallel sides
opposite sides are congrunent
Build this rectangular solid with your centimeter cubes. Find the volume without
counting each cube 1 by 1.
15 + 15 + 15 = 45 cm3
9 x 5 = 45 cm3
counted by rows of 5 (5 x 9 =45 cm3)
18 + 18 = 36 36 +9 = 45 cm3
length x width x height
5 x 3 x 3 = 45 cm3
8. Ask students to clear their cubes to the side for now and get out their scissors. Give each student a
copy of the Paper Box Pattern and supply each table with some scotch tape. Have them cut, fold, and
tape their paper patterns to make a box. Ask early finishers to help others near them.
Texas Grade Five Supplement Blackline Run a class set.
Paper Box Pattern
Cut out this pattern. Fold along the dashed lines and tape to make a box.
9. When everyone has finished, ask students to estimate the volume of the box. How many centimeter
cubes do they think it will take to fill the box completely? Record some of their estimates on the board.
Then challenge them to work in pairs to determine the actual volume of the box without filling it to the
top with cubes, dumping them out, and counting them one by one. As they finish, have them record
their solution in their journal, along with a detailed description of their strategy.
10. Toward the end of the period, reconvene the class. Ask volunteers to share their strategies and solutions with the class. If the idea of measuring the dimensions of the box and multiplying them doesn’t
come from one of the students, ask them to get out their rulers and try it. Does it result in the same solution they got using other methods? Why? (Students should find that the taped box holds 54 centimeter
cubes. It is 6 centimeters long, 3 centimeters wide, and 3 centimeters high. 6 × 3 × 3 = 54 cm3.)
Bridges in Mathematics, Grade 5 • 39
Texas Supplement Blackline Run 1 copy on a transparency.
Cubes and Rectagular Solids
Cube
Rectangular Solid
Build this rectangular solid with your centimeter cubes. Find the volume without
counting each cube 1 by 1.
40 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run a class set.
Paper Box Pattern
Cut out this pattern. Fold along the dashed lines and tape to make a box.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 41
Texas Supplement
42 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 8
ACTIVITY
Measurement More Paper Boxes
Overview
You’ll need
Using paper boxes and centimeter cubes, students work
together to generate efficient methods, including the
standard formulas, for finding the volume of cubes and
rectangular solids.
H More Paper Boxes (page 46, half-class set, plus a few
extra)
Skills & Concepts
H scotch tape
H connecting models for volume with their respective
formulas
H rulers (class set)
H selecting and using appropriate units to measure
volume
H Counting on Frank by Rod Clement (optional)
H centimeter cubes (class set)
H scissors
H Student Math Journals
H selecting and using formulas to determine volume
Recommended Timing
Anytime after Supplement Activity 7 (May be used to
replace Unit Three, Session 15.)
Instructions for More Paper Boxes
1. Ask students to pair up, or assign partners. Students will need their rulers, scissors, and journals for
this activity. Give each pair a copy of More Paper Boxes, along with some scotch tape. Have them cut out
and tape together Box A, leaving Boxes B and C uncut for now. Ask early finishers to help others nearby.
2. When most students have finished constructing Box A, ask them to estimate how many centimeter
cubes it will take to fill the box completely. Have them each record an estimate in their journals. Then
ask volunteers to share and explain their estimates as you record at the board.
Lauren It looks like it’s going to take about 10 to fill the bottom, and it’s about 3 cubes high, so I
think 30 cubes will do it.
Tonio I say 40 because it’s maybe 10 on the bottom and 4 up. That would be 4 × 10, so that’s 40.
Marisa I said 54 cubes because it looks like it’s 3 across and maybe 6 long. That’s 18. I think it’s going to be 3 layers high, so I multiplied 3 × 18 to get 54.
3. Distribute centimeter cubes and ask student pairs to find the actual volume of Box A. Explain that
they can use any method they want except filling the box completely, dumping out the cubes, and
counting them one by one. As they finish, have them record their answer, along with a description of
their strategy in their journal.
Bridges in Mathematics, Grade 5 • 43
Texas Supplement
Activity 8 More Paper Boxes (cont.)
4. After they’ve had a few minutes to work, ask volunteers to share their solutions and strategies with
the class.
Carter It took 21 cubes to cover the bottom of the box. Then we stacked cubes in one corner to find
out how high the box was. It was 4 cubes up, so we said 4 × 21 is 84 cubes.
Abby We just used the cubes to make kind of an outline inside the box. It was 7 on the long side
and 3 on the short side, so we knew the first layer would be 21. Then we went up one corner like
Carter and Xavier, and it was 4. Then we knew it was 84 cubic centimeters because 4 × 21 is 84.
5. If the idea of measuring the dimensions of the box and multiplying them doesn’t come from the students, ask them to get out their rulers and try it. Does this strategy result in the same solution they got
using other methods? Why? Work with class input to record an equation that matches what they just
did: 7 × 3 × 4 = 84 cm3.
6. Ask students to cut out and tape together Box B and record an estimate of the volume in their journals. As they’re working, collect the centimeter cubes. When most have finished, ask volunteers to share
their estimates as you record at the board. Then challenge students to find the actual volume of the box
using their rulers instead of cubes. Have them record the answer, along with any computations they
made, in their journal.
7. After they’ve had some time to work, ask volunteers to share their solutions and strategies with the
class. Then work with input from the class to write a general formula for finding the volume of a rectangular solid (length × width × height = volume), along with an equation for Box B (6 × 4 × 2 = 48 cm3).
Have students record this information in their journals.
8. Now tell them that some fifth graders in another class said they thought they could find the volume of
Box C without cutting and taping it together. Do your students agree with these fifth graders? Why or why
not? Have them pair-share their responses and then ask volunteers to share their thinking with the class.
Students We said you could do it by just using a ruler, but you should cut out the box and put it together first.
We think they’re right. It looks like it’s going to be a cube, so if you just measured one edge, you could
figure it out.
9. Ask students to measure one or more edges of the uncut box to help make as accurate an estimate as
possible. Have them record their estimate, along with an explanation in their journal. (If they’re sure
their estimate matches the actual volume, that’s fine.)
10. After a few volunteers have shared and explained their estimates, ask students to cut out and tape together Box C. Have them measure it to determine the actual volume, and record the answer, along with
any calculations they made, in their journals.
11. Have volunteers share and explain their solutions and strategies. Was it possible to determine the
volume of the figure by measuring only 1 edge? Why or why not? Would it have been possible to find the
answer without cutting and taping the cube? Why or why not? Then have students write an equation for
the volume of Box C (4 × 4 × 4 = 64 cm3) in their journals.
44 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 8 More Paper Boxes (cont.)
Extensions
• Explain that because the length, width, and height of a cube are all equal, mathematicians generally
use a slightly different formula for finding the volume of a cube:
s × s × s = s3, where s is the length of one edge of the cube
Record this at the board, and ask students to compare it to the formula for finding the volume of a
rectangular prism. How are the two alike? How are they different? Ask them to record the general
formula for finding the volume of a cube in their journals.
• Have volunteers use lightweight cardboard and tape to construct a cubic inch and a cubic foot, and
share them with the class. Ask students to list in their journals some of the things they’d measure in
cubic inches and some of the things they’d measure in cubic feet.
• Read Counting on Frank by Rod Clement before or after this session.
INDEPENDENT WORKSHEET
See “Volume Review” and “The Camping Trip” on pages 113–118 in the Independent Worksheet section
of this Supplement for more practice selecting and using appropriate units and formulas to determine
length, area, and volume.
Bridges in Mathematics, Grade 5 • 45
Texas Supplement Blackline Run a half-class set.
More Paper Boxes
A
C
B
46 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 9
ACTIVITY
Geometry & Spatial Reasoning 3-D Figure Posters
Overview
You’ll need
After discussing some of the attributes of a prism, students work in groups of 4 to construct 3-dimensional
figures and create posters about them.
H Nets A–F (pages 50–55, see Advance Preparation)
Skills & Concepts
H cereal box or something similar
H identifying essential attributes including parallel, perpendicular, and congruent parts of three-dimensional
geometric figures
Recommended Timing
Anytime toward the end of Unit Three or later (May be
used to replace Unit Three, Sessions 17 and 18.)
H blank transparencies
H overhead pens
H 18" × 24" chart paper, 1 piece for every 4 students
H 21 /2" × 51 /2" pieces of copy paper, 2–3 per student
plus extra
H poster supplies (scissors, tape, glue sticks, felt markers)
H Student Math Journals
H Word Resource Cards (congruent, edge, face, parallel
lines, perpendicular lines, vertex)
H math dictionaries or access to the Internet (optional)
Advance Preparation Run one copy of each Net blackline on heavy paper or cardstock. If you have more than
24 students, run an extra copy of one of the sheets for every 4 additional students. Place the Word Resource Cards
on display before the activity.
Instructions for 3-D Figure Posters
1. Tell the class that you’re going to do some work with 3-dimensional figures, or solids today. Then hold
up the cereal box and ask students to pair-share mathematical observations about it.
2. Make a rough sketch of the box on a transparency at the overhead. Work with student input to label
the parts of the figure, and take the opportunity to review the meanings of the words face, edge, and vertex. Introduce the term base as well (a base is a “special face”, often thought of as the top or the bottom of
a 3-dimensional figure).
3. Ask volunteers to come to the front of the room and identify parallel, perpendicular, and congruent
edges and faces on the box itself. Though many students may be familiar with parallel and perpendicular lines, the idea that edges and faces can be parallel may be new to some. As they find these parts, explain that the box is called a rectangular prism because it has 2 congruent rectangular bases and 4 faces
that are quadrilaterals. Prisms always have 2 bases, while some other 3-dimensional figures have only 1
Bridges in Mathematics, Grade 5 • 47
Texas Supplement
Activity 9 3-D Figure Posters (cont.)
(a pyramid) or even none (a sphere). Here is an example of how your overhead might look after labeling
the sketch and recording some of the observations shared by the class.
Base (a special face:
the top and bottom)
Edge: where
2 faces meet
Face: flat surface
Base
Vertex: corner point
Rectangular Prism
• 6 faces all rectangular (2 are bases)
• 12 edges
• 8 vertices
• 2 congruent parallel rectangular bases
• 2 pairs of congruent parallel faces
• every pair of faces that meets is perpendicular
• lots of parallel and perpendicular edges
4. Ask students to form groups of 4 or assign groups. Show them the Net sheets, along with a piece of
chart paper. Explain that a net is a 2-dimensional figure that can be cut and folded to form a 3-dimensional figure. In a minute, each group will get a net to cut, fold, and tape. When they’re finished, they’ll
cut and tape their figure and then create a poster about it, recording as many observations as they can,
much as you’ve just done at the overhead.
5. Hold up a few of the copy paper strips. Explain that each student in the group will be responsible for
writing at least 3 observations, each one on a separate strip, to glue onto the poster. They’ll need to work
together to make sure that their observations are true and different from all the others written by the
group. Their poster needs to include the name of the figure as well as their observation strips. Their observations need to address all the terms on the Word Resource Cards you’ve posted, including parallel,
perpendicular, and congruent edges and faces. Ask students not to attach the figures to the posters because you’ll need them for another activity.
6. Review the poster requirements with the class by jotting them on the overhead. You may want to add
others, such as using complete sentences; making their work neat, organized, and attractive; labeling
the poster with their names; and so on.
48 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 9 3-D Figure Posters (cont.)
Net Posters
• Cut, fold, and tape figure.
• Each write at least 3 different observations,
1 per paper strip.
• Observations need to include comments about parallel,
perpendicular, and congruent edges and faces.
• Glue strips to poster.
• Label poster with the name of your figure.
• Do not attach figure to the poster.
7. When students understand what to do, give each group a Net sheet, a piece of chart paper, and a handful of paper strips, and let them go to work. If they don’t know the name of the figure they’ve made, have
them look it up at the back of their math journal. You might also encourage them to use any math dictionaries you have on hand or go online to find figure names and also more information to add to their
posters. Students might also be interested in listing some of the places their figure could be found in the
environment and adding some drawings or even photos of real-life examples.
8. When students are finished, display the posters along with the figures. Pin the figures on or near their
posters in such a way that you can take them down when you do Activity 10, and then put them back up.
Note Here is a list of the figures formed by the Net blacklines:
Net A—Cube
Net B—Rectangular Prism
Net C—Hexagonal Prism
Net D—Triangular Pyramid
Net E—Square Pyramid
Net F—Triangular Prism
Bridges in Mathematics, Grade 5 • 49
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
Net A
�
50 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
Net B
�
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 51
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
Net C
�
52 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
�
Net D
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 53
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
Net E
�
54 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run 1 copy on heavy paper or cardstock.
Net F
�
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 55
Texas Supplement
56 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 10
ACTIVITY
Geometry & Spatial Reasoning Faces, Edges & Vertices
Overview
You’ll need
This activity features a whole-group game in which students identify various attributes of 6 different geometric
figures.
H Faces, Edges & Vertices Gameboard (page 60, 1 copy
on a transparency)
Skills & Concepts
H overhead pens
H identifying essential attributes including parallel, perpendicular, and congruent parts of three-dimensional
geometric figures
H double overhead spinner overlay
Recommended Timing
Note It would be ideal if each group of 4 students could
have a set of 3-dimensional figures to examine as you’re
playing this game with the class. If your entire school is
using Bridges, you may want to borrow sets of wooden
3-D figures called geoblocks from a third or fourth grade
teacher for this purpose. If you’re able to borrow some
sets, pull the 6 matching figures from each set and put the
rest of the blocks away for now.
Anytime after Supplement Activity 9 (May be used to
replace Unit Three, Session 19.)
H paper figures from Supplement Activity 9
H geoblocks (optional, see note)
Instructions for Faces, Edges & Vertices
1. Divide the class into 2 teams and explain that they’re going to play a game with the 3-D figures they
made during Activity 9. Set the 6 figures with their letters facing outward on the whiteboard ledge or a
small table near the overhead and review the name of each figure with the class.
Cube
Rectangular
Prism
Hexagonal
Prism
Triangular
Pyramid
Square
Pyramid
Triangular
Prism
~
=
congruent
=
2. Place the gameboard on display at the overhead and set the double spinner overlay on top of the spinners. Explain that the letters on the first spinner correspond to the letters on the 6 figures. Review the
terms on the second spinner and introduce the symbols for congruent, parallel, and perpendicular:
parallel
perpendicular
Bridges in Mathematics, Grade 5 • 57
Texas Supplement
Activity 10 Faces, Edges & Vertices (cont.)
Texas Grade Five Supplement Blackline
Faces, Edges, and Vertices Gameboard
D
B
Pairs of
Edges
C
Pairs of
Faces
Team 1
Figure Name
~
=
Edges
=
E
~
=
Faces
=
F
A
Pairs of
Edges
Pairs of
Faces
Team 2
Points
Figure Name
Points
3. Ask a volunteer from the first team to spin both spinners and record the name of the figure spun.
Then invite a volunteer from the second team to come up. Have both students examine the figure very
carefully to count the number of congruent faces or edges or determine how many pairs of parallel or
perpendicular faces or edges there are. (What they count depends on the spin.) If there is disagreement,
invite a second pair of students to examine the shape until both teams agree.
Note If a figure has a set of 2 or 3 congruent faces or edges, each face or edge in the set counts. For instance,
the triangular prism below has 2 congruent triangular faces and 3 congruent rectangular faces. That’s 5 in all.
It has 3 congruent edges on each base and 3 congruent edges in between the bases. That’s 9 in all.
David We spun F, which is the triangular prism, and we’re supposed to find pairs of perpendicular edges.
Teacher Camila, you’re on the other team. Please come up and examine this figure carefully with
David to see how many pairs of perpendicular edges the two of you can find. Both teams have to
agree before we can award any points.
58 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 10 Faces, Edges & Vertices (cont.)
Camila Okay, perpendicular edges are the ones that meet at right angles, right? So none of the
edges on the triangle-shaped faces are perpendicular.
David I agree. I think each of the rectangle faces has 4 pairs of perpendicular edges. That would be
12 pairs in all because there are 3 rectangles. I think we get 12 points, unless I’m missing some.
Camila I agree with David. I think Team One gets 12 points on this one.
4. Award the agreed upon number of points to Team One for their first turn. Have Team Two take their
turn. Then play back and forth until both teams have taken 5 turns in all. Ask students to add their
points at the end of the game to determine the winner.
KEY
Congruent
Faces
Congruent
Edges
Pairs of Parallel
Faces
Pairs of Parallel
Edges
Pairs of
Perpendicular
Faces
Pairs of
Perpendicular
Edges
Cube
6
12
3
12
8
24
Rectangular Prism
6
12
3
12
8
24
Hexagonal Prism
8
18
4
18
12
24
Triangular Pyramid
4
6
0
0
0
0
Square Pyramid
4
8
0
2
0
4
Triangular Prism
5
9
1
6
6
12
Figure
INDEPENDENT WORKSHEET
See “Nets & 3-D Figures” on pages 119–121 in the Independent Worksheet section of this Supplement for
more practice identifying essential attributes including parallel, perpendicular, and congruent parts of
three-dimensional geometric figures.
Bridges in Mathematics, Grade 5 • 59
Texas Supplement Blackline Run 1 copy on a transparency.
Faces, Edges & Vertices Gameboard
D
B
Edges
C
Pairs of
Faces
Pairs of
Faces
Team 1
Figure Name
60 • Bridges in Mathematics, Grade 5
~
=
Pairs of
Edges
=
E
Faces
=
F
A
~
=
Pairs of
Edges
Team 2
Points
Figure Name
Points
© The Math Learning Center
Texas Supplement
Activity 11
ACTIVITY
Geometry & Spatial Problem Solving Sketching & Identifying Transformations
Overview
You’ll need
Students sketch examples of translations (slides), rotations
(turns), and reflections (flips) on a Quadrant 1 coordinate
grid. Then they identify more examples of these transformations on Quadrant 1 coordinate grids.
H Transforming Figures (page 64, 1 copy on a transparency, plus a class set on paper)
Skills & Concepts
H Name that Transformation (page 65, 1 copy on a trans-
H Paper Figures (page 66, quarter-class set, cut into
fourths)
parency, plus a class set on paper)
H sketching the results of translations, rotations, and
reflections on a Quadrant 1 coordinate grid
H 2 pieces of paper to mask parts of the transparencies
H identifying the transformation that generates one figure
from the other when given two congruent figures on a
Quadrant 1 coordinate grid
H overhead pens
H scissors
Recommended Timing
Anytime after Unit Three, Session 11 (May be used to
replace Unit Three, Sessions 20 and 21.)
Instructions for Sketching & Identifying Transformations
1. Display the first grid on the Transforming Figures transparency, keeping the other three covered for
now. Ask students to share what they notice about the grid and the figure on it. Most likely, they will
comment on the two numbered axes and the properties of the trapezoid (e.g., one pair of equal sides,
one pair of parallel sides, and so on). Some may also identify the coordinates of any or all of the vertices
of the trapezoid.
Texas Grade Five Supplement Blackline Run a class set and 1 copy on a transparency.
NAME
DATE
Transforming Figures
Sketch the results of each transformation on the grids below.
1
2 Rotate this figure.
Translate this figure.
12
12
11
11
10
10
9
9
8
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7
7
6
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1
0
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1
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6
Rotate this figure.
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
4 Reflect this figure.
2. Now give each student a copy of the Transforming Figures sheet, along with a quarter sheet of Paper
Figures. Ask them to sketch what would happen if they translated (slid) this trapezoid to another loca12
12
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10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
Bridges in Mathematics, Grade 5 • 61
Texas Supplement
Activity 11 Sketching & Identifying Transformations (cont.)
tion on the same grid. Where would it end up? How would it be positioned? Invite them to cut out the
trapezoid from the Paper Figures blackline if they need to physically carry out the translation before
sketching it or if they need to trace the figure.
3. When they finished, ask them to compare their sketches with those of classmates sitting nearby. How
are their sketches similar and how are they different? Students will probably find that they have translated the trapezoid in a variety of ways. After they have had a minute to talk, invite volunteers to sketch
their trapezoids on the overhead and show with their finger or the closed tip of the overhead pen how
the translation would occur. Suggest that if they identify the coordinates of the four vertices on the grid
it may be easier for them to replicate their work at the overhead.
Jorge I made another trapezoid kind of up and over diagonal from the first one, but it’s kind of
hard to show where it ended up.
Teacher Jorge, it might help if you look at your paper and see where the vertices of the trapezoid
lie. For example, I notice on your paper that this vertex is at the point (6, 7). Could you do the same
thing with the other three vertices to position your trapezoid on the overhead? Then show us with an
arrow how you translated or slid the trapezoid to its new position.
Jorge Oh, I see. Okay, the others are at (10, 7), (9, 9), and (7, 9). See, this is how I moved it. I just
made one slide, I mean translation, up diagonally.
Texas Grade Five Supplement Blackline Run a class set and 1 copy on a transparency.
NAME
DATE
Transforming Figures
Sketch the results of each transformation on the grids below.
1
2 Rotate this figure.
Translate this figure.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
0
3
1
1
2
3
4
5
6
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
4 Reflect this figure.
Rotate this figure.
4. As volunteers share their work at the overhead, be sure students understand that they can slide the
trapezoid horizontally, vertically, or diagonally, but they can’t turn or twist it in any way when they
make a translation. One way to confirm this is to check that each vertex has moved the same distance
in the same direction. In the example above, for instance, the vertex at (1,2) has moved to (6,7), while
the vertex at (2,4) has moved to (7,9). In fact, all 4 vertices have moved over 5 and up 5.
12
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10
9
9
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3
2
2
1
1
5. Repeat this process with the other three grids on the transparency. Three examples of each transformation are shown below; in these examples, the original figure is gray, and the transformed figures are
shown in white.
0
62 • Bridges in Mathematics, Grade 5
1
2
3
4
5
6
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
Texas Supplement
Activity 11 Sketching & Identifying Transformations (cont.)
Texas Grade Five Supplement Blackline Run a class set and 1 copy on a transparency.
NAME
DATE
Transforming Figures
Sketch the results of each transformation on the grids below.
1
2 Rotate this figure.
Translate this figure.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
0
3
1
1
2
3
4
5
6
7
8
9
10 11 12
0
2
3
4
5
6
7
8
9
10 11 12
7
8
9
10 11 12
4 Reflect this figure.
Rotate this figure.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
0
1
1
1
2
3
4
5
6
7
8
9
10 11 12
0
1
2
3
4
5
6
6. Next, display the Name that Transformation transparency and give each student his or her own copy
as well. Now that they have sketched three different kinds of transformations, they are going to identify
which transformation has been performed on the gray figure to get to the white figure on each grid. Do
the first one together as a class.
7. Give students all but the last 5 or 10 minutes of the period to complete the page. Take the last 5 or 10
minutes to review and discuss the answers as needed.
Extensions
• Have students label the verticies of each figure on both blacklines with their x- and y-coordinates.
• Make additional copies of the Transforming Figures sheet and ask students to show two or more different solutions for each transformation. Challenge them to translate along diagonals, rotate using
different vertices as points of rotation, and to reflect so that the resulting figure does not share any
sides or vertices with the original.
INDEPENDENT WORKSHEET
See “Transforming Figures, Part 1” and “Transforming Figures, Part 2” on pages 123–127 in the Independent Worksheet section of this Supplement for more practice sketching the results of transformations on
Quadrant 1 coordinate grids and identifying the transformation that generates one figure from another.
Bridges in Mathematics, Grade 5 • 63
Texas Supplement Blackline Run a class set and 1 copy on a transparency.
NAME
DATE
Transforming Figures
Sketch the results of each transformation on the grids below.
1
2 Rotate this figure.
Translate this figure.
12
12
11
11
10
10
9
9
8
8
7
7
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64 • Bridges in Mathematics, Grade 5
2
3
4
5
6
7
8
9
10 11 12
7
8
9
10 11 12
4 Reflect this figure.
Rotate this figure.
12
0
1
7
8
9
10 11 12
0
1
2
3
4
5
6
© The Math Learning Center
Texas Supplement Blackline Run a class set and 1 copy on a transparency.
NAME
DATE
Name that Transformation
For each pair of figures below, select the transformation that takes the gray figure
to the white figure.
1
2
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
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4
4
3
3
2
2
1
1
0
1
2
3
4
translation
3
5
6
7
8
9
rotation

10 11 12
reflection


0
4
12
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10
10
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7
7
6
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5
4
4
3
3
2
2
1
1
1
2
3
4
translation

© The Math Learning Center
5
6
7
rotation

8
9
10 11 12
reflection

2
3
4
translation
12
0
1
0
2
translation

6
7
8
9
rotation

1
5
reflection

3
4
5
6
7
rotation

10 11 12

8
9
10 11 12
reflection

Bridges in Mathematics, Grade 5 • 65
Texas Supplement Blackline Run a quarter-class set and cut the sheet in fourths.
Paper Figures
Cut out these shapes to help complete the transformations or to trace them on the
grids.
Cut out these shapes to help complete the transformations or to trace them on the
grids.
Cut out these shapes to help complete the transformations or to trace them on the
grids.
Cut out these shapes to help complete the transformations or to trace them on the
grids.
66 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 12
ACTIVITY
Probability & Statistics Introducing Virtual Spinners
Overview
You’ll need
During this activity you’ll go online with the class to introduce a virtual spinner that can be set up in a variety of
ways. Today, you and the students will set up a spinner
that’s 2/3 one color and 1 /3 another. Then students will
work in pairs to conduct and record the results of an
experiment with the spinner.
H Spinner Experiment (pages 70 and 71, class set not run
back-to-back)
Skills & Concepts
H using experimental results to make predictions
H describing the probability of various outcomes or
events
H listing all the possible outcomes of a simple probability situation
H reading and interpreting bar graphs
H explaining and recording observations using technology
Recommended Timing
Anytime after February Number Corner (May be used to
replace Unit Five, Sessions 12 and 13.)
H computer(s)
H access to the Internet (see Advance Preparation)
H computer projection equipment (optional)
Advance Preparation Utah State University has developed a library of free virtual manipulatives that includes
a spinner feature that’s fun and easy to use. You’ll need
to familiarize yourself with their web site and the spinner
before you teach the activity. Go to http://nlvm.usu.edu/
en/nav/vlibrary.html. Click on Data Analysis and Probability, and select Spinners. When the Spinners feature comes
up, click on the “Instructions” button in the top right-hand
corner and follow the directions to explore this virtual
manipulative.
Note If you have the capacity to project the computer
screen, you can conduct this activity with your whole
class at the same time. If not, plan to work with small
groups as time allows.
Instructions for Introducing Virtual Spinners
1. Explain to students that you’re going to introduce a web site that will enable them to do spinner experiments on the computer. Have them sit where they can see the screen and demonstrate how to access the Virtual Manipulatives web site. Then show them how to open Spinners.
2. When you reach the Spinners screen, take a few minutes to demonstrate how to spin the spinner and
how to change the number and color of regions on the spinner.
3. Then work with input from the class to set up a spinner that’s 2⁄3 purple and 1⁄3 yellow. Ask students
to pair-share the probability of landing on purple if you spin the spinner just once. Invite volunteers to
share their thinking with the class.
Students You have a better chance of landing on purple because it takes up more than half the spinner.
You have a 2⁄3 chance of getting purple, but only a 1⁄3 chance of getting yellow.
Bridges in Mathematics, Grade 5 • 67
Texas Supplement
Activity 12 Introducing Virtual Spinners
4. If students don’t mention the terms more and less likely than, review the fact that purple is more
likely than yellow to come up on one spin, and yellow is less likely than purple to come up. Two-thirds,
66.66%, and 2 out of 3 are other ways of expressing the theoretical probability of getting purple on a
single spin. One-third, 33.33%, and 1 out of 3 are other ways to express the theoretical probability of getting yellow on a single spin. Spin the spinner once. What happens?
5. Now click on the Record Results button so the bar graph is visible. Ask students to make conjectures
about the results of spinning the spinner 12 times. Because the spinner is two-thirds purple and onethird yellow, some may hypothesize that the spinner will land on purple 8 times and on yellow 4 times.
While these figures reflect 2⁄3 and 1⁄3 of 12, remind students that the results of experiments don’t always
match the theoretical probabilities.
6. Ask students to help you list all the possible outcomes of 12 spins on the board.
Our spinner is 23 purple and 31 yellow.
What are the possible outcomes of 12 spins?
•
•
•
•
•
•
•
0 P, 12 Y
1 P, 11 Y
2 P, 10 Y
3 P, 9 Y
4 P, 8 Y
5 P, 7 Y
6 P, 6 Y
7 P, 5 Y
8 P, 4 Y
9 P, 3 Y
• 10 P, 2 Y
• 11 P, 1 Y
• 12 P, 0 Y
•
•
•
7. Invite 12 different volunteers to click the Spin button. Then discuss the data displayed on the bar
graph screen.
Students It came out 7 purples and 5 yellows. I knew it would come out more purple.
I was sure we’d get 8 and 4, though. Can we do it again?
8. Click the Clear button on the bar graph screen. Then repeat step 7 and record the results of both sets
of 12 spins on the board.
7 P, 5 Y
10 P, 2 Y
9. Ask students to pair up or assign partners. Explain that you’re going to have them continue this experiment on their own. Give each pair a copy of the Spinner Experiment sheets. Review the instructions
with the class and spend a little time discussing students’ conjectures before they get started.
Teacher Which outcomes do you think you’ll get most and which least if you do 20 sets of 12 spins,
and why?
68 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 12 Introducing Virtual Spinners
Students We should get 8 and 4 the most because the spinner is 2⁄3 and 1⁄3.
I don’t think it’s all that easy to get 8 and 4. I think maybe we’ll get 7 and 5 or 9 and 3 the most. You
just hardly ever get exactly what you’re supposed to with spinners.
You can get almost anything, but I don’t think we’re going to get all purples or all yellows very much.
That just seems almost impossible.
10. Ask student pairs to complete questions 1–3 right now and to finish the rest of the assignment when
they have access to one of the computers in your classroom or in the lab.
Extensions
• When all the pairs have completed their sheets, pool and discuss the class data. What outcomes came
up the most frequently? Which came up least? Encourage students to reflect on their results and explain them the best they can.
• Have students use the Bar Chart feature on the NLVM web site to create and print out a graph of
their own, or even the pooled data from the whole class. They might set up the graph to show how
many times they got the 3 or 4 most frequent outcomes. The Bar Chart feature includes a place to
title the graph and label the columns.
Bridges in Mathematics, Grade 5 • 69
Texas Supplement Blackline Run a class set. Do not run back-to-back with page 71.
NAME
DATE
Spinner Experiment page 1 of 2
•
•
•
•
Go to the Virtual Manipulatives web site at
http://nlvm.usu.edu/en/nav/vlibrary.html
Click on Data Analysis & Probability.
Click on Spinners.
When you get to Spinners click the Change Spinner button and set up a spinner that’s 23 one color and 13 another. You can choose your own colors. Set one
of the colors to 2 and the other to 1. Set all other colors to 0.
1
List all the possible outcomes in the left-hand column on the chart below. Use
abbreviations for your colors if you want, but be sure to list the outcomes in order. There should be 13 of them.
Possible Outcome
70 • Bridges in Mathematics, Grade 5
How many times did you get this outcome?
© The Math Learning Center
Texas Supplement Blackline Run a class set. Do not run back-to-back with page 70.
NAME
DATE
Spinner Experiment page 2 of 2
2a
Before you start spinning, put stars beside the three outcomes on the chart
you think you’ll get most often. Record them in the space below also.
b
Explain your answer. Why do you think you’ll get those outcomes the most?
3a
Circle the two outcomes on the chart you think you’ll get least often. Record
them in the space below also.
b
Explain your answer. Why did you circle the 2 outcomes you did?
4
Now start spinning. Stop at the end of 12 spins and record the outcome on the
chart on the previous page. When you’re finished, click the Clear button on the bar
graph screen and start over. Record the outcome of each set of 12 spins on the
chart until you’ve done 20 sets of spins. Be sure to click the Clear button after each set.
5
Which outcome did you get the most? Which outcomes came in second and
third place?
6
List at least 3 other observations about your results below.
7
How well did your results match what you thought was going to happen? Why
do you think this experiment turned out the way it did?
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 71
Texas Supplement
72 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 13
ACTIVITY
Probability & Statistics The 6-4-2 Spinner
Overview
You’ll need
Using the virtual spinner introduced in Activity 12, student
pairs explore the idea that the more times an experiment
is repeated, the more likely it is that the results will be
good estimates of the theoretical probabilities.
H The 6-4-2 Spinner (pages 76–78, class set run back-toback)
Skills & Concepts
H computer projection equipment (optional)
H using experimental results to make predictions
H computer(s)
H access to the Internet (see Advance Preparation)
H color tile available
H describing the probability of various outcomes or
events
H calculators available
H interpreting bar graphs
H explaining and recording observations using technology
Recommended Timing
Advance Preparation See Supplement Activity 12 Advance Preparation notes on page 67.
Note If you have the capacity to project the computer
screen, you can conduct this activity with your whole
class at the same time. If not, plan to work with small
groups, as time allows.
Anytime after Supplement Activity 12 (May be used to
replace Unit Five, Session 14.)
Instructions for The 6-4-2 Spinner
1. Review with the class the procedures for getting to the Spinners feature on the Virtual Manipulatives
web site introduced in Activity 12.
2. When you get to Spinners click the Change Spinner button. That will take you to the Spinner Regions
screen. Work with input from the class to set up the regions so there are 6 yellow, 4 green, and 2 red,
and then click Apply.
3. Give students a moment to examine the spinner. Then ask them to pair-share what fraction of the
spinner is occupied by each color. If they’re not sure about the green and the red regions, have them
count out 6 yellow, 4 green, and 2 red color tiles. Can they form a 2-by-6 rectangle that will help them
determine the fractions?
Green
Red
Yellow
Y Y Y G G R
Y Y Y G G R
Bridges in Mathematics, Grade 5 • 73
Texas Supplement
Activity 13 The 6-4-2 Spinner (cont.)
Students Oh yeah! This is like when we did the tile experiment in the Number Corner.
It’s easy to see that half is yellow on the spinner. I wasn’t sure about the green, but 4 is 1⁄3 of 12, and
2 is 1⁄6 of 12.
It’s kind of like the egg carton fractions too. I remember 2 ⁄12 is the same as 1⁄6 and 4 ⁄12 is the same as
1
⁄3 when I look at the tiles.
4. Now click on the Record Results button so the bar graph is visible. Ask students to make conjectures
about the results of spinning the spinner 12 times. Chances are, some will believe that you’ll get 6 yellows, 4 greens, and 2 reds. Others may know that the experimental results will probably not match the
theoretical probabilities exactly, especially given such a small number of spins.
5. After a bit of discussion, change the number of spins on the spinner screen to read 12 instead of 1 and
have a volunteer click the Spin button. What happens?
Students Cool! It did all 12 spins really fast!
It came out 7 yellow, 3 green, and 2 red. That’s not too far away from 6, 4, and 2.
Do it again!
6. Click the Clear button on the bar graph screen. Then repeat step 5 six more times as a volunteer records the results.
Trial 1: 7 Y, 3 G, 2 R
Trial 2: 4 Y, 6 G, 2 R
Trial 3: 8 Y, 4 G, 0 R
Trial 4: 8 Y, 1 G, 3 R
Trial 5: 6 Y, 4 G, 2 R
Trial 6: 4 Y, 4 G, 4 R
Trial 7: 8 Y, 2 G, 2 R
7. Discuss the results of the 7 trials with the class. What do they notice?
Students It hardly ever matches 6, 4, 2. It only did that once.
It went kind of backwards on Trial 4. It got 4, 6, 2 on that one.
Trial 2 was weird because the spinner never landed on red at all.
I think Trial 6 was pretty strange too because they all came out the same.
It seems like almost anything can happen, but I bet we’ll never get 0 yellows.
8. Now ask students to speculate about what would happen if you set the number of spins at 30 instead
of 12. Although half the spinner is yellow, a third is green and a sixth is red. Will these fractions be reflected in the experimental data? Some students may be fairly convinced by now that the experimental
results won’t match the theoretical probabilities, while others may assert that with a larger number of
spins, the experimental results might be closer. Press the issue by asking students to consider the probable results of increasing the number of spins to 60, 120, 240, and 480.
Students I think the more spins you do, the closer you’ll get to half of them coming out yellow, a
third green, and a sixth red.
I think it doesn’t matter. Sometimes you’ll get an exact match, but most of the time it’ll be way off
like it was with 12 spins.
74 • Bridges in Mathematics, Grade 5
Texas Supplement
Activity 13 The 6-4-2 Spinner (cont.)
9. Ask students to pair up or assign partners. Explain that you’re going to have them continue this experiment on their own. Give each pair a copy of The 6-4-2 Spinner sheets. Review the instructions with
the class and clarify them as needed.
10. Ask student pairs to complete question 1 right now and to finish the rest of the assignment when
they have access to one of the computers in your classroom or in the lab.
Extensions
• When all the pairs have completed their sheets, ask the class to discuss their findings. Does increasing the number of spins produce data that is closer to the theoretical probabilities?
INDEPENDENT WORKSHEET
See “Make & Test Your Own Spinner” on pages 135–137 in the Independent Worksheet section of this
Supplement for another probability experiment that enables students to use experimental results to
make predictions.
Bridges in Mathematics, Grade 5 • 75
Texas Supplement Blackline Run a class set.
NAME
DATE
The 6-4-2 Spinner page 1 of 3
1
Computers make it possible to collect a lot of data very quickly and easily. You’re
going to use a virtual 6-4-2 spinner to find out what happens as you increase the
number of spins from 30 to 480. To start, fill in the chart below to show the number of times you would land on each color if you always got exactly half yellow,
one-third green, and one-sixth red. The first row is done for you.
Number of Spins
30 spins
1
2
of the Number
15
1
3
of the Number
10
1
6
of the Number
5
60 spins
120 spins
240 spins
480 spins
2
•
•
•
•
Follow the steps below to set up your 6-4-2 spinner.
Go to the Virtual Manipulatives web site at
http://nlvm.usu.edu/en/nav/vlibrary.html
Click on Data Analysis & Probability.
Click on Spinners.
When you get to Spinners, click the Change Spinner button. That will take
you to the Spinner Regions screen. Set up the regions so there are 6 yellow, 4
blue, and 2 green, and then click Apply.
3
Click the Record Results button on the spinner screen, and drag the 2 screens
apart so you can see your spinner and the bar graph at the same time. On the
spinner screen, change the number of spins from 1 to 30 spins.
76 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
NAME
DATE
The 6-4-2 Spinner page 2 of 3
4
Click the Spin button and watch what happens. Record the outcome on the
chart below. Then click the Clear button on the bar graph screen and start over.
Repeat this 6 more times. Be sure to click the Clear button after each trial.
SPINS
30
Yellow
Green
Red
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6
Trial 7
5
Compare the data you just collected with the class data for 12 spins. Do you
think taking a larger number of spins makes it more likely that you’ll get closer
to spinning 12 yellow, 13 green, and 16 red? Explain your answer.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 77
Texas Supplement Blackline Run a class set.
NAME
DATE
The 6-4-2 Spinner page 3 of 3
6
Now test your hypothesis. Repeat step 4 for 60 spins, 120 spins, 240 spins, and
480 spins. Record all your results on the charts below.
SPINS
60
Yellow
Green
SPINS
Red
120
Trial 1
Trial 1
Trial 2
Trial 2
Trial 3
Trial 3
Trial 4
Trial 4
Trial 5
Trial 5
Trial 6
Trial 6
Trial 7
Trial 7
SPINS
240
Yellow
Green
Yellow
Green
Red
SPINS
Red
480
Trial 1
Trial 1
Trial 2
Trial 2
Trial 3
Trial 3
Trial 4
Trial 4
Trial 5
Trial 5
Trial 6
Trial 6
Trial 7
Trial 7
Yellow
Green
Red
7
What do you think now? Does increasing the number of spins make it more
likely that you’ll get closer to spinning 12 yellow, 13 green, and 16 red? Explain your
answer.
78 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Activity 14
ACTIVITY
Patterns, Relationships & Algebraic Thinking The Carnival
Overview
You’ll need
Students practice writing equations and drawing diagrams to go with a variety of problem situations. Then
they select equations and diagrams that best represent a
problem situation.
H The Carnival (page 81, 1 copy on a transparency)
Skills & Concepts
H piece of paper to mask parts of the overhead
H selecting diagrams to represent meaningful problem
situations
H Student Math Journals
H More Carnival Problems (pages 82–84, 1 copy on a
transparency, plus a class set)
H overhead pens
H selecting equations to represent meaningful problem
situations
Recommended Timing
Anytime after Unit Seven, Session 14 (May be used to
replace Unit Seven, Session 15.)
Instructions for The Carnival
1. Place the top portion of The Carnival overhead on display, keeping the other 3 problems covered for
now. Read the problem with the class, and ask students to give the thumbs-up sign when they have the
answer. Invite a couple of volunteers to share and explain their solutions.
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Carnival
1 There’s a big carnival every year in our town. It’s opening tonight. It costs
$5.00 to get in and $1 for every ride ticket you buy. How much does it cost to get
in and buy 12 ride tickets?
2 Miguel is going with his friend, Corey. Miguel is planning to buy 16 ride tickets. Which equation could be used to find x, the amount of money he’ll need to
get in and buy ride tickets?
Gabe It’s $17.00 because you have to pay $5.00 to get in and $1.00 for each ticket. If you get 12 ticka x = $5.00 + (16 × $1.00)
ets, that’s $12.00. Five more
dollars makes 17 in all.
b
x = $5.00 × (16 × $1.00)
c
x = $16.00 – $5.00
3
Corey has $27.00 to spend on admission and tickets. How many tickets will
Alyssa I said the same thing.
I just went 12 + 5 because I knew it was a dollar for every ride ticket.
d x = (16 × $1.00) ÷ $5.00
in your journal
to show. Use
letter x to
he be able
to buy? Write an
equation
2. Have students get out their math
journals.
Ask
them
to write
antheequation
to show the amount of
stand for the number of tickets Corey will be able to buy.
money it would take to get in and buy 12 ride tickets. Have them pair-share their responses and then
call on volunteers to read theirs to the class. Record the suggested equations at the overhead.
4
Miguel’s favorite ride is the Teacup. Some of the cups hold 2 people. Others
hold 4 people. There are 9 cups in all, and when the ride is full, it holds 24 people.
Which diagram best represents this problem? Why?
3. Explain that sometimes people use a variable, such as the letter x, to represent part of an equation.
a
b
for the total amount of money in this problem?
How would you write the equation
if you used x to stand
Discuss this with the class and record their ideas at the overhead.
c
d
Bridges in Mathematics, Grade 5 • 79
Texas Supplement
Activity 14 The Carnival (cont.)
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
The Carnival
1
There’s a big carnival every year in our town. It’s opening tonight. It costs
$5.00 to get in and $1 for every ride ticket you buy. How much does it cost to get
in and buy 12 ride tickets?
$5.00 + $12.00 = $17.00
$5.00 + $12.00 = x
$5.00 + (12 x $1.00) = $17.00
x = $5.00 + (12 x $1.00)
2 Miguel is going with his friend, Corey. Miguel is planning to buy 16 ride tickets. Which equation could be used to find x, the amount of money he’ll need to
get in and buy ride tickets?
4. Reveal each of the other 3 problems one by one. In each case, have students respond in their journals
a x = $5.00 + (16 × $1.00)
and pair-share their responses before
asking volunteers to share their thinking with the class. Press stub
x = $5.00 × (16 × $1.00)
The
Carnival
dents to explain how they made ctheir
selections
in problems 2 and 4, and why some of the other choices
x = $16.00
– $5.00
d
x
=
(16
×
$1.00)
÷
$5.00
1 There’smarked
a big carnival every
year in copy
our town. It’s
opening tonight.
It costs reference. Some of your studon’t work. (The answers have been
on
the
below
for
your
$5.00
to get
and $1
every
ticket you
HowHow
much
doestickets
it costwill
to get
3
Corey
hasin$27.00
tofor
spend
onride
admission
andbuy.
tickets.
many
in
and
buy
12
ride
tickets?
he be able toto
buy?
Write an equation
dents may have other valid responses
problem
3.)in your journal to show. Use the letter x to
Texas Grade Five Supplement Blackline Run 1 copy on a transparency.
be able+to
stand
for the
number
of tickets Corey will$5.00
(12buy.
x $1.00) = $17.00
$5.00
+ $12.00
= $17.00
x = $5.00 + (12 x $1.00)
$5.00 + $12.00
=x
x = $27.00
- $5.00
2 Miguel is going with his friend, Corey. Miguel is planning to buy 16 ride tickcould
to find
x, the
amount
money
he’ll Others
need to
ets.
Which equation
4 Miguel’s
favorite ride
is be
theused
Teacup.
Some
of the
cups of
hold
2 people.
buy There
ride tickets?
get
holdin4 and
people.
are 9 cups in all, and when the ride is full, it holds 24 people.
diagram
best×represents
this problem? Why?
Which
a x = $5.00
+ (16
$1.00)
ba x = $5.00 × (16 × $1.00)
c x = $16.00 – $5.00
b
d x = (16 × $1.00) ÷ $5.00
3c Corey has $27.00 to spend on admissiondand tickets. How many tickets will
he be able to buy? Write an equation in your journal to show. Use the letter x to
stand for the number of tickets Corey will be able to buy.
x = $27.00 - $5.00
4
Miguel’s favorite ride is the Teacup. Some of the cups hold 2 people. Others
hold 4 people. There are 9 cups in all, and when the ride is full, it holds 24 people.
Which diagram best represents this problem? Why?
a
b
c
d
5. Ask students to use the information in problem 4, including diagram c to solve the following problem:
How many of the teacups seat 2 people, and how many seat 4 people?
6. Give students each a copy of More Carnival Problems. Review the sheets with the class. When students understand what to do, have them go to work. Encourage them to share and compare strategies
and solutions as they work.
7. Reconvene the class as time allows to discuss solutions and strategies for some or all of the problems.
INDEPENDENT WORKSHEET
See “Padre’s Pizza” and “Choosing Sketches & Diagrams” on pages 149–155 in the Independent Worksheet
section of this Supplement for more practice selecting equations and diagrams to represent meaningful
problem situations.
80 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Run 1 copy on a transparency.
The Carnival
1
There’s a big carnival every year in our town. It’s opening tonight. It costs
$5.00 to get in and $1 for every ride ticket you buy. How much does it cost to get
in and buy 12 ride tickets?
2
Miguel is going with his friend, Corey. Miguel is planning to buy 16 ride tickets. Which equation could be used to find x, the amount of money he’ll need to
get in and buy ride tickets?

x = $5.00 + (16 × $1.00)

x = $5.00 × (16 × $1.00)

x = $16.00 – $5.00

x = (16 × $1.00) ÷ $5.00
3
Corey has $27.00 to spend on admission and tickets. How many tickets will
he be able to buy? Write an equation in your journal to show. Use the letter x to
stand for the number of tickets Corey will be able to buy.
4
Miguel’s favorite ride is the Teacup. Some of the cups hold 2 people. Others
hold 4 people. There are 9 cups in all, and when the ride is full, it holds 24 people.
Which diagram best represents this problem? Why?




© The Math Learning Center
Bridges in Mathematics, Grade 5 • 81
Texas Supplement Blackline Run a class set plus 1 copy on a transparency.
NAME
DATE
More Carnival Problems page 1 of 3
1
Each of the seats on the giant ferris wheel holds 3 people. There are 26 seats in
all. Which equation could be used to find x, the number of people riding when the
ferris wheel is full?
x + 26 = 3
3 ÷ 26 = x


3 × 26 = x
x – 3 = 26


2
After they rode on the Teacup, Miguel and Corey wanted to go on the Yoyo. In
order to get there, they had to walk past the Whip. It is three times as far from
the Teacup to the Whip as it is from the Whip to the Yoyo. It is 840 yards from
the Teacup to the Yoyo. How far is it from the Teacup to the Whip?
a
Which diagram below best shows this problem?
Teacup
Whip
YoYo
Teacup
Whip
840 yards
840 yards

Teacup
Whip
840 yards

b
YoYo

YoYo
Teacup
Whip
YoYo
420 yards

Use the diagram you picked to help solve the problem. Show all of your work.
82 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Run a class set plus 1 copy on a transparency.
NAME
DATE
More Carnival Problems page 2 of 3
3
a
Some of the rides take 2 tickets and some of them take 3 tickets.
If Marisa had 17 tickets and used all of them, how many 2-ticket and 3-ticket
rides did she take?
5 two-ticket rides and 4 three-ticket rides
10 two-ticket rides and 7 three-ticket rides
3 two-ticket rides and 3 three-ticket rides
4 two-ticket rides and 3 three-ticket rides


b


Use numbers, words, and/or labeled sketches to explain your answer to part a.
4
Darius has 9 rides tickets. His sister Deja has 3 more ride tickets than Darius.
Their friend Camila has twice as many ride tickets as Deja.
a
Which equation could be used to find x, the number of tickets Camila has?
(9 + 3) × 2 = x

b
9×3=x

(9 + 3) ÷ 2 = x

9×3÷2=x

Use numbers, words, and/or labeled sketches to explain your answer to part a.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 83
Texas Supplement Blackline Run a class set plus 1 copy on a transparency.
NAME
DATE
More Carnival Problems page 3 of 3
5
There is a bumper-car ride for little kids next to the hotdog stand. The fence
around the ride is a hexagon with 2 long sides that are equal and 4 short sides
that are equal.
a
Which diagram below best shows the fence around the bumper car ride?
9 feet
10 feet
10 feet
9 feet
10 feet
18 feet
10 feet
9 feet
10 feet
10 feet

15 feet
10 feet
18 feet

9 feet
9 feet
7 feet

b
Use the diagram you picked to write and solve an equation for the perimeter
of the fence.
84 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement
Grade 5 Activity Blackline Answer Keys
ANSWER KEY
Activity 2
4 cm
Factor Riddles, pages 14 and 15
1
2
3
4
5
9
6
20
(challenge) 15
Riddles will vary.
4 × 2 = 8 sq. cm
2 cm
2 cm
6 cm
6 × 4 = 24 sq. cm
4 cm
6 cm
Activity 6
P = 24 cm
A = 32 sq. cm
Hexarights, Perimeter = 24 cm, page 36
Here are some examples of hexrights with a perimeter of 24 cm. The closer the hexaright gets to being
a square, the larger its area. The largest possible area
is 35 sq cm if you’re working on grid paper. If you’re
working on blank paper and using fractions as well
as whole numbers, there are an infinite number of
hexarights between 35 and 36 sq. cm in area.
5 cm
1 cm
5 × 1 = 5 sq. cm
6 cm
5 × 6 = 30 sq. cm
5 cm
6 cm
2 cm
P = 24 cm
A = 35 sq. cm
2×4=
8 sq. cm
4 cm
Activity 11
6 cm
4 cm
6 × 2 = 12 sq. cm
2 cm
6 cm
P = 24 cm
A = 20 sq. cm
3 cm
Transforming Figures, page 64
Note: original figure is gray; sample response figures
are shown in white
1 Responses will vary. Examples:
12
11
10
3 × 3 = 9 sq. cm
3 cm
9
8
3 cm
6 cm
7
6
5
6 × 3 = 18 sq. cm
3 cm
4
3
2
6 cm
P = 24 cm
A = 27 sq. cm
1
0
1
2
3
4
5
6
7
8
9
10 11 12
Bridges in Mathematics, Grade 5 • 85
Texas Supplement
ANSWER KEY
Activity 11 (cont.)
Activity 14
Transforming Figures, page 64
More Carnival Problems, pages 82–84
Note: original figure is gray; sample response figures
are shown in white
2 Responses will vary. Examples:
1 3 × 26 = x
2 a
Teacup
Whip
12
YoYo
840 yards
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
b
3 a
b
4 a
b
5 a
630 yards; explanations will vary.
4 two-ticket rides and 3 three-ticket rides
Explanations will vary.
(9 + 3) × 2 = x
Explanations will vary.
9 feet
3 Responses will vary. Examples:
9 feet
18 feet
9 feet
12
11
18 feet
10
9
b Perimeter = 72 feet; equations will vary.
Example: (2 × 18) + (4 × 9) = 72 feet
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
4 Responses will vary. Examples:
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
Name that Transformation, page 65
1
2
3
4
rotation
reflection
rotation
translation
86 • Bridges in Mathematics, Grade 5
Texas Supplement
Grade 5 Independent Worksheets Grouped by Skill
NUMBER, OPERATION & QUANTITATIVE REASONING
(ESTIMATION TO SOLVE ADDITION & SUBTRACTION PROBLEMS)
Activity
Name
Independent Worksheet 1
Independent Worksheet 2
Recommended Timing
Using Compatible Numbers to
Estimate Answers
Anytime during the school
year
Are These Answers
Anytime during the school
year
Reasonable?
Independent Worksheet 3
Travel Miles
Anytime during the school
year
TEKS Addressed
TEKS 5.4A (5) Use strategies, including compatible numbers, to estimate solutions to addition
problems.
TEKS 5.4A (6) Use strategies, including compatible numbers, to estimate solutions to subtraction problems
NUMBER, OPERATION & QUANTITATIVE REASONING (COMMON FACTORS)
Independent Worksheet 4
Factor Trees & Common Factors
Anytime after Supplement
Activity 2
Independent Worksheet 5
More Factor Riddles
Anytime after Supplement
Activity 2
TEKS 5.3D Identify common factors of a set of
whole numbers
MEASUREMENT (AREA & PERIMETER)
Independent Worksheet 6
Area & Perimeter Review
Anytime after Supplement
Activities 3–5
Independent Worksheet 7
Measuring Rectangles
Anytime after Supplement
Activities 3–5
TEKS 5.10B (1) Connect models for perimeter
with their respective formulas
TEKS 5.10B (2) Connect models for area with
their respective formulas
TEKS 5.10C (2) Select appropriate units to measure perimeter
TEKS 5.10C (3) Select appropriate units to
measure area
TEKS 5.10C (6) Use appropriate units to measure
perimeter
TEKS 5.10C (7) Use appropriate units to measure
area
TEKS 5.10C (10) Select formulas to measure
perimeter
TEKS 5.10C (11) Select formulas to measure area
TEKS 5.10C (14) Use formulas to measure perimeter
TEKS 5.10C (15) Use formulas to measure area
MEASUREMENT (VOLUME)
Independent Worksheet 8
Volume Review
Anytime after Supplement
Activities 7 & 8
Independent Worksheet 9
The Camping Trip
Anytime after Supplement
Activities 7 & 8
TEKS 5.10B (3) Connect models for volume with
their respective formulas
TEKS 5.10C (4) Select appropriate units to measure volume
TEKS 5.10C (12) Select formulas to measure volume
TEKS 5.10C (16) Use formulas to measure volume
GEOMETRY & SPATIAL REASONING (3-DIMENSIONAL FIGURES)
Independent Worksheet 10
Nets & 3-D Figures
Anytime after Supplement
Activities 9 & 10
TEKS 5.7A (4) Identify essential attributes including parallel parts of 3D geometric figures
TEKS 5.7A (5) Identify essential attributes including perpendicular parts of 3D geometric figures
TEKS 5.7A (6) Identify essential attributes including congruent parts of 3D geometric figures
Bridges in Mathematics, Grade 5 • 87
Texas Supplement
Grade 5 Independent Worksheets Grouped by Skill (cont.)
GEOMETRY & SPATIAL REASONING (TRANSFORMATIONS)
Activity
Name
Recommended Timing
Independent Worksheet 11
Transforming Figures, Part 1
Anytime after Supplement
Activity 11
Independent Worksheet 12
Transforming Figures, Part 2
Anytime after Supplement
Activity 11
TEKS Addressed
TEKS 5.8A (1) Sketch the results of translations
on a Quadrant 1 coordinate grid
TEKS 5.8A (2) Sketch the results of rotations on a
Quadrant 1 coordinate grid
TEKS 5.8A (3) Sketch the results of reflections
on a Quadrant 1 coordinate grid
TEKS 5.8B Identify the transformation that generates one figure from the other when given two
congruent figures on a Quadrant 1 coordinate grid
NUMBER, OPERATION & QUANTITATIVE REASONING
(ESTIMATION TO SOLVE MULTIPLICATION & DIVISION PROBLEMS)
Independent Worksheet 13
Using Compatible Numbers to
Multiply & Divide
Anytime after Unit Four, Session 9
Independent Worksheet 14
More Multiplication & Division
with Compatible Numbers
Anytime after Unit Four, Ses-
Independent Worksheet 15
Reasonable Estimates in Multiplication & Division
Anytime after Unit Four, Session 9
sion 9
TEKS 5.4A (7) Use strategies, including compatible numbers, to estimate solutions to multiplication problems
TEKS 5.4A (8) Use strategies, including compatible numbers, to estimate solutions to division
problems
PROBABILITY & STATISTICS (USING EXPERIMENTAL RESULTS TO MAKE PREDICTIONS)
Independent Worksheet 16
Make & Test Your Own Spinner
Anytime after Supplement
Activities 12 & 13
TEKS 5.12B Use experimental results to make
predictions
TEKS 5.15A (5) Explain observations using
technology
TEKS 5.15A (10) Record observations using
technology
NUMBER, OPERATION & QUANTITATIVE REASONING (PLACE VALUE TO 999 BILLION)
Independent Worksheet 17
Tons of Rice
Anytime after Unit Seven,
Session 8
Independent Worksheet 18
Inches to the Moon & Other
Very Large Numbers
Anytime after Unit Seven,
Session 8
Independent Worksheet 19
More Very Large Numbers
Anytime after Unit Seven,
Session 8
TEKS 5.1A (1) Use place value to read whole
numbers through 999,999,999,999
TEKS 5.1A (2) Use place value to write whole
numbers through 999,999,999,999
TEKS 5.1A (3) Use place value to compare
whole numbers through 999,999,999,999
TEKS 5.1A (4) Use place value to order whole
numbers through 999,999,999,999
PATTERNS, RELATIONSHIPS & ALGEBRAIC THINKING (DIAGRAMS & EQUATIONS)
Independent Worksheet 20
Padre’s Pizza
Anytime after Supplement
Activity 14
Independent Worksheet 21
Choosing Equations & Dia-
Anytime after Supplement
Activity 14
grams
88 • Bridges in Mathematics, Grade 5
TEKS 5.6A (2) Select from diagrams to represent
meaningful problem situations
TEKS 5.6A (3) Select from equations such as
y = 5 + 3 to represent meaningful problem
situations
Texas Supplement Blackline Use anytime during the school year.
NAME
DATE
Independent Worksheet 1
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Using Compatible Numbers to
Estimate Answers
Mathematicians sometimes estimate answers to addition and subtraction problems by using compatible numbers. Compatible numbers are numbers that work
well together. If a pair of numbers is easy to add or subtract, those numbers are
friendly or compatible. For example:
Tonio collects sports cards. He has 17 football cards and 26 baseball cards. About how many
cards does he have in all? About how many more baseball than football cards does he have?
17 is close to 15
26 is close to 25
15 + 25 = 40, so he has about 40 cards in all.
25 – 15 = 10, so he has about 10 more baseball than football cards.
1
Use compatible numbers to estimate the answer to each problem below. To use
this estimation strategy, change the actual numbers to compatible numbers. The
first two are done for you.
addition example
397 + 198
subtraction example
252 – 126
400
397 is close to _______.
250
252 is close to _______.
200
198 is close to _______.
125
126 is close to _______.
200 = _______,
600
400
_______
+ _______
250
125 = _______,
125
_______
– _______
600
so the answer is about _______.
125
so the answer is about _______.
a
b
149 + 148
481 – 138
149 is close to _______.
481 is close to _______.
148 is close to _______.
138 is close to _______.
_______ + _______ = _______,
_______ – _______ = _______,
so the answer is about _______.
so the answer is about _______.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 89
Texas Supplement Blackline
Independent Worksheet 1 Using Compatible Numbers to Estimate Answers (cont.)
c
529 + 398
d
652 – 249
529 is close to _______.
652 is close to _______.
398 is close to _______.
249 is close to _______.
_______ + _______ = _______,
_______ – _______ = _______,
so the answer is about _______.
so the answer is about _______.
2
Use compatible numbers to estimate the answer to each problem below. Show
your work.
a
Sam and Sara are on vacation with their mom. They live in Seattle, Washington, and they’re driving to Disneyland in California. The first day, they drove 172
miles to Portland, Oregon, and stopped for lunch. After they’d gone another 128
miles, they stopped for gas. About how many miles had they driven so far?
b
They stopped in Ashland, Oregon to spend the night. It cost them $74.99, including tax, to stay in a motel. Dinner cost $24.97 for the three of them. Breakfast
the next morning cost $14.99. About how much money did they spend while they
were in Ashland?
c
After breakfast, their mom said, “We’re going to stop near Sacramento for
lunch. That’s 295 miles from here.” When they stopped for gas that morning they
still had 147 miles left to go. About how many miles had they driven so far?
90 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 1 Using Compatible Numbers to Estimate Answers (cont.)
d
Sam and Sara took $7.00 into the store at the gas station to buy snacks. They
got some juice for $2.99 and a bag of pretzels for $1.49. Then Sara said, “Hey look!
Let’s get 3 oranges too. They only cost 49¢ each.” About how much change did
they get back after they paid for the juice, pretzels, and oranges?
e
When they got back into the car their mom said, “The odometer on our car
said 28,103 miles when we started. Now it says 28,601 miles. About how far have
we driven so far?”( An odometer tells us how far we have driven altogether.)
f
Sara looked at the map and said, “We have 424 miles left to go until we get to
Disneyland.” Her mom said, “We’re going to stop for lunch near Merced, which is
127 miles from here. About how much farther will we have to go after that?”
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 91
Texas Supplement
92 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime during the school year.
NAME
DATE
Independent Worksheet 2
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Are These Answers Reasonable?
Compatible numbers are numbers that work well together. If a pair of numbers is
easy to add or subtract, those numbers are friendly or compatible. You can check
to see if answers to problems are reasonable by changing the actual numbers to
compatible numbers.
Use compatible numbers to decide whether or not the answer to each problem
below is reasonable or not. Be sure to explain your answer each time
Question
Is this answer reasonable? Why or why not?
example
Ty used a calculator to add
598 and 349. Here’s the answer he got:
It’s not reasonable because 598 is close to 600
and 349 is close to 350. 600 + 350 = 950,
so 795 is way off.
1
Abby used a calculator to add 203, 449,
and 152. Here’s the answer she got:
2
Miguel used a calculator to find
the difference between 1,203 and 598.
Here’s the answer he got:
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 93
Texas Supplement Blackline
Independent Worksheet 2 Are These Answers Reasonable? (cont.)
Question
Is this answer reasonable? Why or why not?
3
Keiko used a calculator to add 749
and 498. Then she subtracted 649.
Here’s the final answer she got:
4
Mr. Gordon went to the store to buy
some fruit. Here’s his sales slip.
Thriftee Mart
$1.99
Peaches
Grapes
$2.03
Apples
$1.49
Bananas
$1.52
Total
$9.28
5
Mrs. Chan went to an office supply
store in Oregon where there is no sales
tax. She bought 6 boxes of markers for
$3.99 a box, 1 box of pencil grips for
$4.99, 10 boxes of pencils for $.99 each,
and an electric pencil sharpener for
$13.99. She gave the lady at the check
stand three 20-dollar bills and got back
$7.18 in change.
94 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 2 Are These Answers Reasonable? (cont.)
6
We have 4 elementary schools in our town, 2 middle schools, and 1 high
school. The chart below shows how many students there are at each school.
Name of School
Number of Students
King Elementary
514
Lincoln Elementary
413
Garfield Elementary
226
Adams Elementary
399
Madison Middle School
598
Jefferson Middle School
603
Grant High School
1,012
a
The town newsletter said that there are 32 more students at King and Lincoln
than there are at Garfield and Adams. Is this a reasonable statement? Why or
why not?
b
My brother said that if you add the number of students at both the middle
schools, there are about 200 more kids at the middle schools than there are at the
high school. Is this a reasonable estimate? Why or why not?
c
About how many students are there in all 7 schools put together? Use compatible numbers to help make your estimate. Show your work below.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 95
Texas Supplement
96 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime during the school year.
NAME
DATE
Independent Worksheet 3
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Travel Miles
Compatible numbers are numbers that work well together. If a pair of numbers
is easy to add or subtract, those numbers are friendly or compatible. When you’re
solving problems, you can check to see if your answers are reasonable by changing the actual numbers to compatible numbers.
The chart below shows the travel miles between several cities in the U.S.
U.S. Cities
Denver
Denver
Houston
875 miles
Nashville
Philadelphia
1,858 miles
1,023 miles
1,575 miles
956 miles
960 miles
663 miles
1,336 miles
1,647 miles
686 miles
992 miles
2,887 miles
681 miles
1,969 miles
Houston
875 miles
Orlando
1,858 miles
960 miles
Nashville
1,023 miles
663 miles
686 miles
Philadelphia 1,575 miles
1,336 miles
992 miles
San
Francisco
1,647 miles
2,887 miles 1,969 miles
956 miles
San
Francisco
Orlando
681 miles
2,526 miles
2,526 miles
Use the information on the chart to sove the problems on the following pages.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 97
98 • Bridges in Mathematics, Grade 5
Mrs. Polanco has to fly from San
Francisco to Denver and back home
again in October. She has to fly
from San Francisco to Orlando and
back home again in November. How
much farther does she have to fly
in November than in October?
b
Anna’s family lives in Houston.
They’re trying to decide whether
to go to Nashville or Orlando for
a vacation next summer. Which
city is farther from Houston? How
much farther is it?
a
Mr. Buck and Ms.
Penny both live in Houston and
work for a video game company.
On Monday, Mr. Buck flew to Orlando and Ms. Penny flew to San
Francisco for business meetings.
How much farther did Ms. Penny
travel than Mr. Buck?
example
Question
5
1
1,647
– 960
687
Ms. Penny traveled 687 miles
farther than Mr. Buck.
My Work
1,650 – 950 = 700. My answer is 687, and
that’s really close to 700.
My answer is reasonable because 1,647 is
close to 1,650 and 960 is close to 950.
My answer is reasonable because
Use the chart of travel miles on the previous page to solve the problems below. For each one, show your
work. Then use compatible numbers to explain why your answer is reasonable The first one is done for you.
1
Independent Worksheet 3 Travel Miles (cont)
Texas Supplement Blackline
© The Math Learning Center
© The Math Learning Center
My Work
My answer is reasonable because
Plan an imaginary trip. You can start in any city you want and fly to as many places as you want, but your
travel miles have to total between 9,000 and 10,000 miles, including the return trip to your starting city. Show
your travel plan on the back of this page and prove that your mileage isn’t less than 9,000 or more than 10,000
miles in all.
2
The Houston Astros are flying
from Houston to San Francisco to
play a baseball game with the Giants on Friday. Next, they’re flying from San Francisco to Denver
to play a game with the Colorado
Rockies. After that, they have to
fly from Denver to Philadelphia to
play the Phillies. Then they’re flying from Philadelphia back home
to Houston. How many miles do
they have to travel in all?
d
How much arther is it to fly
from San Francisco to Philadephia
and back, than to fly from Denver
to Houston to Orlando and then
back to Denver?
c
Question
Independent Worksheet 3 Travel Miles (cont)
Texas Supplement Blackline
Bridges in Mathematics, Grade 5 • 99
Texas Supplement
100 • Bridges in Mathematics, Grade 5
© The Math Learning Center
DATE
1
12 and 20
20 and 28
example
Numbers
2
6
12 = 2 x 2 x 3
2
12
3
12 = 2 x 6
12 = 4 x 3
12 = 1 x 12
Factor Tree and Factor Pairs
2
10
20 = 2 x 2 x 5
2
20
5
20 = 2 x 10
20 = 4 x 5
20 = 1 x 20
Factor Tree and Factor Pairs
Find the common factors of each pair of numbers below. To do this:
• Make a factor tree and list the factor pairs for each number.
• Make a Venn Diagram to show their common factors.
Number, Operation & Quantitative Reasoning Factor Trees & Common Factors
INDEPENDENT WORKSHEET
Independent Worksheet 4
NAME
3
1
2
4
5
Common Factors
Factors of 28
20
10
Factors of 20
Common Factors
12
Factors of 20
6
Factors of 12
Venn Diagram
Texas Supplement Blackline Use after Supplement Activity 2.
Bridges in Mathematics, Grade 5 • 101
32 and 40
24 and 54
100 and 120
2
3
4
Numbers
Factor Tree and Factor Pairs
DATE
Factor Tree and Factor Pairs
Independent Worksheet 4 Factor Trees & Common Factors (cont.)
NAME
102 • Bridges in Mathematics, Grade 5
Factors of 40
Factors of 54
Common Factors
Factors of 100 Factors of 120
Common Factors
Factors of 24
Common Factors
Factors of 32
Venn Diagram
Texas Supplement Blackline
© The Math Learning Center
Texas Supplement Blackline Use after Supplement Activity 2.
NAME
DATE
Independent Worksheet 5
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning More Factor Riddles
Solve the factor riddles below. Show your work. You can use a calculator to help if
you like.
Factor Riddle
Solution
1
I am a common factor of 24 and 60.
I am an even number. I am divisible
by 3 and 4. What number am I?
2
I am an odd number. I am a common factor of 54 and 63. When you
multiply me by 2, you get a number
greater than 10. What number am I?
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 103
Texas Supplement Blackline
Independent Worksheet 5 More Factor Riddles (continued)
Factor Riddle
Solution
3
I am a common factor of 80 and
120. I am greater than 5. I am divisible
by 4. I am also divisible by 10. What
number am I?
4
I am an odd number. I am a common factor of 120 and 150. I am not
prime. What number am I?
104 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activities 3–5.
NAME
DATE
Independent Worksheet 6
INDEPENDENT WORKSHEET
Measurement Area & Perimeter Review
Perimeter is the distance all the way around a figure. Perimeter is measured in
linear units like centimeters, meters, inches, feet, and yards.
Area is the amount of surface a figure covers. Area is measured in square units like
square centimeters, square meters, square inches, square feet, and square yards.
Area
Perimeter
1
Use the centimeter side of your ruler to measure the dimensions (the length and
width) of each rectangle on the next page. Then find its area and perimeter using
the formulas below. Show your work.
Perimeter = (2 × the width) + (2 × the length) or P = (2 × w) + (2 × l)
Area = length × width or A = l × w
example
12 cm
3 cm
36 sq. cm
Perimeter: (2 x 3) + (2 x 12) = 30 cm
Area: 12 x 3 = 36 sq. cm
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 105
Texas Supplement Blackline
Independent Worksheet 6 Area & Perimeter Review (cont.)
a
b
Perimeter:
Perimeter:
Area:
Area:
c
d
Perimeter:
Perimeter:
Area:
Area:
2
Jamie says you only need to measure one side of a square to find its perimeter.
Do you agree with her? Why or why not? Use numbers, labeled sketches, and
words to explain your answer.
106 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 6 Area & Perimeter Review (cont.)
3
Hector says you have to measure
the length of every side of this figure
to find its perimeter. Do you agree
with him? Why or why not? Use numbers, labeled sketches, and words to
explain your answer.
5
Mr. Hunter is trying to find the distance from one end of his whiteboard
to the other. Mr. Hunt is measuring:
whiteboard

the board’s area

the board’s length

the board’s perimeter
6
Which of these situations is about
perimeter?

determining the number of tiles
needed to cover a floor
4
Which equation shows how to find
the perimeter of this rectangle?
8 ft.

determining how many feet of fencing
is needed to surround a rectangular yard

determining the width of a table
7

3 × 8 = 24 ft.
Beckett and his mom are going to
paint the living room. They need to
measure the room so they know how
much paint to buy. They should measure the wall in:

(2 × 3) + 8 = 14 ft.

square centimeters

(2 × 3) + (2 × 8) = 22 ft.

square feet

4 + 8 = 12 ft.

square inches

square miles
3 ft.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 107
Texas Supplement Blackline
Independent Worksheet 6 Area & Perimeter Review (cont.)
8
This rectangle has an area of 45 square feet. What is the missing measure?
Show your work.
? ft.
5 ft.
45 sq. ft.
9
Tom wants to find the area of his school’s basketball court. Which formula
should he use? (circle one)
A=l+w
A=l×w
A=l–w
A = (2 × w) + (2 × l)
10
Alexandra and her dad build a deck in their backyard. It had an area of 48
square feet and a perimeter of 28 feet. Circle the drawing that shows the deck
they built. Use numbers, labeled sketches, and words to explain your answer.
6 ft.
9 ft.
12 ft.
8 ft.
5 ft.
108 • Bridges in Mathematics, Grade 5
4 ft.
© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activities 3–5.
NAME
DATE
Independent Worksheet 7
INDEPENDENT WORKSHEET
Measurement Measuring Rectangles
1a
Which formula shows how to find the area of this rectangle?
6 ft.
4 ft.
Area = (2 × width) + (2 × length)
A = 2w + 2l

b
Area = length + width
A=l+w

Area = length × width
A=l×w

Use the formula you selected to find the area of the rectangle. Show your work.
2a
Which formula shows how to find the perimeter of this rectangle?
8 cm
2 cm
Perimeter = (3 × width) + (3 × length)
P = 3w + 3l
Perimeter = length + width
P=l+w
Perimeter = length × width
P=l×w
Perimeter = (2 × width) + (2 × length)
P = 2w + 2l


© The Math Learning Center


Bridges in Mathematics, Grade 5 • 109
Texas Supplement Blackline
Indpendent Worksheet 7 Measuring Rectangles (cont.)
b
Use the formula you selected to find the perimeter of the rectangle. Show your
work.
3a
Which formula shows how to find the area of this rectangle?
4 meters
3 meters
Area = length ÷ width
A=l÷w
Area = length – width
A=l–w
Area = length × width
A=l×w
Area = length + width
A=l+w




b
Use the formula you selected to find the area of the rectangle. Show your
work.
110 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Indpendent Worksheet 7 Measuring Rectangles (cont.)
4a
Which formula shows how to find the perimeter of this rectangle?
40 ft.
20 ft.
Perimeter = (2 × width) + (2 × length)
P = 2w + 2l
Perimeter = length × width
P=l×w
Perimeter = length × width × height
P=l×w×h
Perimeter = (2 × width) – length
P = 2w – l




b
Use the formula you selected to find the perimeter of the rectangle. Show your
work.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 111
Texas Supplement
112 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Supplement Activities 7 and 8.
NAME
DATE
Independent Worksheet 8
INDEPENDENT WORKSHEET
Measurement Volume Review
Volume is the measure of the space inside a 3-dimensional object. Volume is measured in cubes of a given size, such as cubic centimeters, cubic inches and cubic feet.
1
Each of the rectangular solids below was built with centimeter cubes. Label each
with its dimensions (length, width, and height) and find the volume. Show your work.
example
a
3 cm
4 cm
2 cm
Volume 4 x 2 x 3 = 24 cubic cm (or cm3)
Volume
b
Volume
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 113
Texas Supplement Blackline
Independent Worksheet 8 Volume Review (cont.)
2
Use the centimeter side of your ruler to measure the dimensions of each rectangular solid below. Then find its area and perimeter. Show your work.
example
a
2 cm
3 cm
4 cm
Volume 4 x 3 x 2 = 24 cubic cm (or cm3)
Volume
b
Volume
114 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 8 Volume Review (cont.)
3
Miguel says you only need to measure one edge of a cube to find its volume. Do you agree with him? Why or
why not? Use numbers, labeled sketches, and words to explain your answer.
5
Brandon is going on a fishing trip
with his family. He wants to find
the volume of the family’s ice chest.
Which expression should he use?
2 ft.
2 ft.
3 ft.
4
Mia has already measured the dimensions of this packing box. Help her
find the volume. Show your work.

2×3

3×2×2

3+2+2

(3 × 2) – 2
6
Jeff’s little brother is trying to find out
how many alphabet blocks will fit into a
shoebox. He is measuring:
6 in.
4 in.
© The Math Learning Center
8 in.

the volume of the shoebox

the area of the shoebox

the length of the shoebox
Bridges in Mathematics, Grade 5 • 115
Texas Supplement Blackline
Independent Worksheet 8 Volume Review (cont.)
7
Which of these situations is about
volume?

determining the amount of fencing
it takes to go around a square garden

determining how many tiles it will
take to cover the kitchen floor
CHALLENGE
10
The volume of this cube is 125 cubic inches. What is the length of each
edge? Show your work.

determining how many rectangular
containers of food will fit into a freezer
8
Vanesa wants to find the volume
of her lunchbox. Which of these units
should she use?

cubic feet

cubic inches

cubic yards
9
The volume of this rectangular solid is 40 cubic feet. What is its height?
Show your work.
?
5 ft.
2 ft.
116 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activities 7 and 8.
NAME
DATE
Independent Worksheet 9
INDEPENDENT WORKSHEET
Measurement The Camping Trip
The Gomez family is going on a camping trip next week. There are 4 people in the
family: Mr. and Mrs. Gomez and the 11-year-old twins, Ramon and Dora. Help them
do some planning for their trip. Circle the correct answer to each question below.
1
Mrs. Gomez wants to cut a piece of rope that’s long enough to dry the family’s
laundry on every day. Which of these units should she use to measure the rope?
inches
feet
yards
miles
2
Mr. Gomez wants to figure out how far they’ll have to drive to get to the campsite. He already knows that it will take about a day to get there. Which of these
units should he use?
inches
feet
yards
miles
3
The shoelaces on Ramon’s tennis shoes are almost worn out. He has to measure
them so he gets the right length at the store. Which of these units should he use?
millimeters
centimeters
meters
kilometers
4
Mrs. Gomez says it’s going to be a 3-minute walk from their tent to the lake.
Dora wants to measure the distance when they get there. Which of these units
should she use?
millimeters
centimeters
meters
kilometers
5
Ramon wants to find the area of his sleeping bag to see how much room he’ll
have in the family’s tent. Which of these units should he use?
square inches
© The Math Learning Center
square feet
square yards
square miles
Bridges in Mathematics, Grade 5 • 117
Texas Supplement Blackline
Indpendent Worksheet 9 The Camping Trip (cont.)
6
Which formula should Ramon use to find the area of his sleeping bag?
Area = Length + Width
Area = Length × Width
Area = Length ÷ Width
7
Dora says when they get there, she’s going to measure the area of their campsite. Mrs. Gomez says the campsite is big enough for their car, their tent, their
picnic table and chairs, and their campfire, with a little room left over. Which of
these units should she use?
square inches
8
square feet
square yards
square miles
Which formula should Dora use to find the area of the campsite?
A = (2 × l ) + (2 × w )
A = (3 × l ) – (2 × w )
A=l×w
9
Mr. Gomez wants to find the volume of the family car trunk so he’ll know how
much luggage will fit back there. Which of these units should he use?
cubic inches
cubic feet
cubic yards
10
Ramon wants to measure the volume of a shoebox to find out how many CD’s
he can fit into it for the trip. Which of these units should he use?
cubic inches
cubic feet
cubic yards
11
Dora is going to collect tiny pebbles at the lake. She wants to measure the volume of a metal band-aid box to keep them in. Which of these units should she use?
cubic centimeters
118 • Bridges in Mathematics, Grade 5
cubic meters
cubic kilometers
© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activities 9 and 10.
NAME
DATE
Independent Worksheet 10
INDEPENDENT WORKSHEET
Geometry and Spatial Reasoning Nets & 3-D Figures
1
Predict the 3-dimensional figure each net on the next 2 pages represents. Record your predictions on the chart below.
Net
z
Prediction
cube
Actual 3-D Figure
cube
a
b
c
d
e
2
a
Before you cut them out, follow the instructions below for each of the nets:
Mark the congruent faces with a red dot. If there are 2 different sets of congruent faces, like 4 congruent rectangles and 2 congruent squares on one net, mark
the second set with blue dots.
b
Trace in purple along the lines between any pairs of faces you think will be
perpendicular when you cut out the net and make the figure.
c
Lightly color in each pair of faces you think will be parallel when you cut out
the net and make the figure. Use a different color for each pair.
3
After you’ve made all the predictions listed above, cut out each net along the
heavy outline, fold it on the dotted lines, and tape it together to form a 3-dimensional figure.
4
On the chart above, write in the actual 3-dimensional figure each net represents.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 119
Texas Supplement Blackline
Independent Worksheet 10 Nets & 3-D Figures (cont.)
example
z
e
a
120 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 10 Nets & 3-D Figures (cont.)
c
b
d
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 121
Texas Supplement
122 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Supplement Activity 11.
NAME
DATE
Independent Worksheet 11
INDEPENDENT WORKSHEET
Geometry & Spatial Reasoning Transforming Figures, part 1
Sketch the results of each transformation on the grids below.
1
2 Translate this figure.
Reflect this figure.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
3
1
2
3
4
5
6
7
8
9
10 11 12
0
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
© The Math Learning Center
5
6
2
3
4
5
6
7
8
9
10 11 12
4 Rotate this figure.
Rotate this figure.
12
0
1
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
Bridges in Mathematics, Grade 5 • 123
Texas Supplement Blackline
Independent Worksheet 11 Transforming Figures, part 1 (cont.)
For each pair of figures below, select the transformation that takes the gray figure
to the white figure.
5
6
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
translation
7
5
6
7
8
9
rotation

10 11 12
reflection


0
8
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
translation

3
4
5
6
7
rotation

124 • Bridges in Mathematics, Grade 5
8
9
10 11 12
reflection

2
3
4
translation
12
0
1
0
2
translation

6
7
8
9
rotation

1
5
reflection

3
4
5
6
7
rotation

10 11 12

8
9
10 11 12
reflection

© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activity 11.
NAME
DATE
Independent Worksheet 12
INDEPENDENT WORKSHEET
Geometry & Spatial Reasoning Transforming Figures, part 2
Sketch the results of each transformation on the grids below.
1
2 Reflect this figure in a different way.
Reflect this figure.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
3
1
2
3
4
5
6
7
8
9
10 11 12
0
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
© The Math Learning Center
5
6
2
3
4
5
6
7
8
9
10 11 12
4 Translate this figure.
Rotate this figure.
12
0
1
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
Bridges in Mathematics, Grade 5 • 125
Texas Supplement Blackline
Independent Worksheet 12 Transforming Figures, part 2 (cont.)
5
Circle the grid that shows only a translation.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
8
9
10 11 12
0
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
126 • Bridges in Mathematics, Grade 5
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10 11 12
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 12 Transforming Figures, part 2 (cont.)
6
Circle the grid that shows only a reflection.
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
8
9
10 11 12
0
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
© The Math Learning Center
5
6
7
8
9
10 11 12
0
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10 11 12
Bridges in Mathematics, Grade 5 • 127
Texas Supplement
128 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Unit Four, Session 9.
NAME
DATE
Independent Worksheet 13
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Using Compatible Numbers to
Multiply & Divide
Mathematicians sometimes estimate answers to multiplication and division problems by using compatible numbers. Compatible numbers are numbers that work
well together.
example 1
A page in my chapter
book has 12 words in each line and
32 lines on the page. About how many
words on the whole page? Change 12
and 32 to nearby numbers that are
easier to multiply in your head.
example 2
Mr. Gomez had 396 crayons left over at the end of the year. He’s
putting them in bags to send home with
the kids. He has 20 students in his class.
About how many crayons will each student get? Change 396 to a nearby number that is easier to divide by 20.
12 is close to 10
396 is close to 400.
32 is close to 30
10 x 30 = 300, so the page has about 300 words. 20 is already a friendly number. You don’t always
have to change both numbers.
400 ÷ 20 = 20, so each student will get about
20 crayons.
1
Choose a chapter book from your classroom. Turn to a page in the middle of
the book. About how many words do you think there are on the page? To find out,
count the number of words in one line. Next, count the number of lines on the
page. Record the information:
Words in one line _______________
Lines on the page ________________
2
Use compatible numbers to estimate the number of words on the page. Show
your work.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 129
Texas Supplement Blackline
Independent Worksheet 13 Using Compatible Numbers to Multiply & Divide (cont.)
3
All the fourth and fifth graders at King School are going on a field trip with
their teachers and some parent helpers. In all, there will be 197 people. The bus
company plans to use 4 buses. Estimate how many people will ride in each bus.
Use compatible numbers to help you. Show your work.
4
Use compatible numbers to estimate the answer to each problem below. To use
this estimation strategy, change the actual numbers to nearby numbers that are
compatible. The first two are done for you.
multiplication example
21 × 19
division example
249 ÷ 24
20
21 is close to _______.
250
249 is close to _______.
20
19 is close to _______.
25
24 is close to _______.
400
20 × _______
20
_______
= _______,
10
250 ÷ _______
25
_______
= _______,
400
so the answer is about _______.
10
so the answer is about _______.
a
b
32 × 29
153 ÷ 9
32 is close to _______.
153 is close to _______.
29 is close to _______.
9 is close to _______.
_______ × _______ = _______,
_______ ÷ _______ = _______,
so the answer is about _______.
so the answer is about _______.
c
d
49 × 19
119 ÷ 9
49 is close to _______.
119 is close to _______.
19 is close to _______.
9 is close to _______.
_______ × _______ = _______,
_______ ÷ _______ = _______,
so the answer is about _______.
so the answer is about _______.
130 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Unit Four, Session 9.
NAME
DATE
Independent Worksheet 14
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning More Multiplication &
Division with Compatible Numbers
1
Which 2 numbers in the box could you multiply to come closest to 600? Circle
them. Show your thinking.
39
47
5
62
87
11
5
26
2
Estimate the answers to the following multiplication problems. Use compatible
numbers to help. Show your work. The first one is done for you.
example
31 × 28
a
39 × 22
c
48 × 18
30
31 is close to _____.
30
28 is close to _____.
900
30 = _____,
30 × _____
_____
900
so the answer is about _____.
b
84 × 11
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 131
Texas Supplement Blackline
Independent Worksheet 14 More Multiplication & Division with Compatible Numbers (cont.)
3
Estimate the answers to the following division problems. Use compatible numbers to help you. Show your work.
a
About how much does each can of sugar-free soda cost if a case of 24 costs $5.99?
b
9 scouts want to split a bag of 262 peanuts equally. About how many peanuts
will each of the scouts get?
c
The scouts in Lincoln City collected 594 cans of food Now they’re going to put
the cans into bags to take to the Food Bank. If they put 21 cans in each bag, about
how many bags of food can they make?
132 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Unit Four, Session 9.
NAME
DATE
Independent Worksheet 15
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Reasonable Estimates in
Multiplication & Division
1
Fill in the bubble in front of the answer that gives a reasonable estimate for
each problem. (Hint: Try using compatible numbers to help.) To the right of the
problem, use words, numbers and/or pictures to explain why you think it is a
reasonable estimate. The first one is done for you.
example
19
× 22
a
28
× 21

229
19 is close to 20. 22 is close to 20.

400

290
20 x 20 =400, so 400 is the

500

400
best estimate.

600

500

700
c
206 ÷ 19 =
b
26
×9

180

10

260

16

300

20

540

26
d
598 ÷ 18 =
e
994 ÷ 19 =

18

40

21

45

25

50

30

60
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 133
Texas Supplement Blackline
Independent Worksheet 15 Reasonable Estimates in Multiplication & Division (cont.)
2
Brianna has $9.00. Baseball trading cards cost $0.49 each. She estimates that
she will be able to buy about 27 cards with her money. Is this a reasonable estimate? Use words, numbers and/or pictures to explain your answer.
134 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Supplement Activities 12 and 13..
NAME
DATE
Independent Worksheet 16
INDEPENDENT WORKSHEET
Probability & Statistics Make & Test Your Own Spinner
•
•
•
•
Go to the Virtual Manipulatives web site at:
http://nlvm.usu.edu/en/nav/vlibrary.html
Click on Data Analysis & Probability.
Click on Spinners.
When you get to Spinners click the Change Spinner button. That will take you
to the Spinner Regions screen. Choose 3 different colors. Then decide how
many regions you want for each color. The number of regions has to add up to
exactly 12. For instance, you may decide to have 4 purple, 4 red, and 4 orange.
Or maybe you’ll choose 7 green, 3 blue, and 2 yellow. It’s up to you. Click Apply.
1
Tell what fraction of the spinner turned out to be each color. (Hint: Look back
at the Spinner Regions screen. Remember that the number of regions you assigned was 12 in all. You can also use the color tile to help figure it out.)
a
My spinner is __________ __________.
(fraction)
(color)
b
My spinner is __________ __________.
(fraction)
(color)
c
My spinner is __________ __________.
(fraction)
(color)
2
What color do you think the arrow will land on if you spin the spinner 1 time?
Explain your answer.
3
Click the Spin button once What color did the arrow land on? ___________
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 135
Texas Supplement Blackline
Independent Worksheet 16 Make & Test Your Own Spinner (cont.)
4
Which color do you think will come up most often if you make 100 spins? Why?
5
Which color do you think will come up least often if you make 100 spins? Why?
6
About how many times do you think you’ll get each color if you spin the spinner 100 times? Explain your answers.
a
I think I’ll get _____________ about _____________ times because:
b
I think I’ll get _____________ about _____________ times because:
c
I think I’ll get _____________ about _____________ times because:
7
Click the Record Results button on the spinner screen, and drag the 2 screens
apart so you can see your spinner and the bar graph at the same time On the
spinner screen, change the number of spins from 1 to 100 spins.
136 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 16 Make & Test Your Own Spinner (cont.)
8
Click the Spin button and watch what happens. Record the outcome on the
chart below. Then click the Clear button on the bar graph screen and start over.
Do the experiment 10 times and record the data on the chart. Be sure to click the
Clear button after each set.
Color:
9
Color:
Color:
List at least 3 different observations about your data.
10
How well did your results match what you thought was going to happen?
Why do you think this experiment turned out the way it did?
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 137
Texas Supplement
138 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Unit Seven, Session 8.
NAME
DATE
Independent Worksheet 17
INDEPENDENT WORKSHEET
Number, Operations & Quantitative Reasoning Tons of Rice
In the story of the King’s Chessboard, the king was furious when he found out he
would have to give a wise man 274,877,906,944 tons of rice to keep his promise.
You can use place value to help understand this number.
274,877,906,944 tons
hundreds
thousands
millions
billions
If you were to read this number to someone over the phone, you’d say,
“Two hundred seventy-four billion,
eight hundred seventy-seven million,
nine hundred six thousand,
nine hundred forty-four.”
Solve problems 1–4 below to get some idea of just how big this number really is
and why the king was so furious.
1
In July 2007, the world’s population
was estimated to be 6,602,224,175. Label this number with its place values,
just like the example above.
6,602,224,175 people
© The Math Learning Center
2
Write the number 6,602,224,175 out
in words, the way you’d read it over the
phone.
Bridges in Mathematics, Grade 5 • 139
Texas Supplement Blackline
Independent Worksheet 17 Tons of Rice (cont.)
3
If you rounded 274,877,906,944 to the nearest billion, it would be 275 billion. If
you rounded 6,602,224,175 to the nearest billion it would be:
4
If you said 6,602,224,175 rounded to the nearest billion is 7 billion, you’re right.
Divide 275 billion by 7 billion to estimate how many tons of rice each person on
earth would get if the king kept his promise. Show your work.
5
The chart below shows the estimated populations of some different countries
around the world in 2006. Use the information to solve the problems below.
a
Name of Country
Estimated Population in 2006
Brazil
188,078,227
China
1,313,973,713
India
1,095,351,995
Pakistan
165,803,560
United States
298,444,215
Which country on the chart had the largest population? ____________________
Which had the smallest? ____________________
b
Compare the populations of some of these countries by writing the numbers
and putting a greater than (>) or less than (<) sign between them.
The United States and Pakistan
India and China
298,444,215 > 165,803,560
Brazil and Pakistan
140 • Bridges in Mathematics, Grade 5
The United States and Brazil
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 17 Tons of Rice (cont.)
c
Write the populations of the 5 countries in order from least to greatest on the
lines below. Write the name of each country below its population number. Use abbreviations if you need to.
______________ < ______________ < ______________ < ______________ < ______________
______________
______________
______________
______________
______________
CHALLENGE
6
Go online to find out what the estimated population of the world is right now.
Record the answer here:
The population of the world on ____________________ is ____________________.
(month, day, year)
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 141
Texas Supplement
142 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Unit Seven, Session 8.
NAME
DATE
Independent Worksheet 18
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning Inches to the Moon & Other
Very Large Numbers
Did you know that it’s 15,133,979,520 inches from the earth to the moon? That’s
fifteen billion, one hundred thirty-three million, nine hundred seventy-nine
thousand, five hundred twenty inches!
1
Here’s a chart that shows the place value of every digit in the number
15,133,979,520. Use the information on the chart to answer questions a–e below.
100
Billions
a
b
c
d
e
10
Billions
Billions
100
Millions
10
Millions
Millions
100
Thousands
10
Thousands
Thousands
Hundreds
Tens
Ones
1
5
1
3
3
9
7
9
5
2
0
The digit in the millions place is _________.
The digit in the ten billions place is _________.
The digit in the hundred thousands place is _________.
The digit in the ten billions place is _________.
Are there any hundred billions in this number? If so, how many?_________
2
If you could measure the distance around the earth with a giant tape measure,
how many inches would it be? This chart shows the answer. Use the information
on the chart to answer questions a–d.
100
Billions
10
Billions
Billions
100
Millions
10
Millions
Millions
100
Thousands
10
Thousands
Thousands
Hundreds
Tens
Ones
1
5
7
7
7
2
7
3
6
0
a
How far is it around the world in inches? Write the number here with the commas
placed correctly.
b
Now write the number out in words, the way you’d read to someone over the phone.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 143
Texas Supplement Blackline
Independent Worksheet 18 Inches to the Moon & Other Very Large Numbers (cont.)
c
Are there any ten billions in this number? If so, how many?_________
d
The digit in the ten thousands place is _________.
3
Which is greater, the distance around the earth or the distance to the moon?
Write the numbers on the lines below. Then put a greater than (>) or less than (<)
symbol between them to compare the two.
4
___________________________
___________________________
Distance to the Moon (inches)
Distance around the earth (inches)
Complete the chart to write and name 4 other very large numbers.
Number
a
735,658,902,456
b
c
Sixty-five billion, nine hundred forty-three million,
three hundred twenty-seven thousand, one hundred
seventy-six
34,586,113,042
d
e
Number Name Written Out in Words
Four hundred thirty-nine billion, five hundred sixty-two
million, three hundred twenty-nine thousand, two hundred
fifty-one
Write the 4 numbers in order from least to greatest on the lines below.
______________ < ______________ < ______________ < ______________
144 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline Use anytime after Unit Seven, Session 8.
NAME
DATE
Independent Worksheet 19
INDEPENDENT WORKSHEET
Number, Operation & Quantitative Reasoning (Place Value) More Very Large
Numbers
According to many sources, there are about 100,000,000,000 stars in the Milky
Way. That’s 100 billion! You can use place value to help understand this number.
100,000,000,000 stars
hundreds
thousands
millions
billions
Here’s another way to look at the number.
100
Billions
10
Billions
Billions
100
Millions
10
Millions
Millions
100
Thousands
10
Thousands
Thousands
Hundreds
Tens
Ones
1
0
0
0
0
0
0
0
0
0
0
0
Use this information to help answer the questions on this sheet and the next.
76,000,000 people attended major
league baseball games in 2006. How is
this number written out in words?
2

Seventy-six thousand
a

Seventy-six billion

Seventy-six million

Seventy-six trillion
1
On June 2, 2007, the population of China was estimated to be
1,321,345,816.
The digit in the ten thousands place
is ________.
b
The digit in the ten millions place
is ________.
c
The digit in the thousands place is
________.
d
The digit in the hundred millions
place is ________.
e
Are there any billions in this number? If so, how many? ________
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 145
Texas Supplement Blackline
Independent Worksheet 19 More Very Large Numbers (cont.)
3
In 1986, a fast food restaurant advertised that it had sold more than sixty billion hamburgers. Which number shows this amount?

60,000

600,000,000,000

6,000,000

60,000,000,000
4
Pluto is approximately 5,893,000,000 kilometers from the sun. Which is true?

Pluto is more than 50 billion kilometers from the sun.

Pluto is less than 500,000 million kilometers from the sun.

Pluto is almost 6 billion kilometers from the sun.

Pluto is about 60 billion kilometers from the sun.
5
The chart below shows the estimated populations of some different countries
around the world in 2006. Use the information to solve the problems below.
Name of Country
Estimated Population in 2006
Bangladesh
147,365,352
Japan
127,463,611
Mexico
107,449,525
Philippines
89,468,677
Russia
142,893,540
a
Which country on the chart had the largest population? ___________________
b
Which had the smallest? ____________________
146 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 19 More Very Large Numbers (cont.)
c
Write the populations of the 5 countries in order from least to greatest on the
lines below. Write the name of each country below its population number. Use abbreviations if you need to.
______________ < ______________ < ______________ < ______________ < ______________
______________
______________
______________
______________
______________
6
Alani multiplied 11,000 by 63,360 to find out how many inches wide the Pacific
Ocean is. Her calculator isn’t working well. What place value doesn’t show up?
(circle one)
Millions
© The Math Learning Center
Hundred thousands
Ten millions
Billions
Bridges in Mathematics, Grade 5 • 147
Texas Supplement
148 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Supplement Activity 14.
NAME
DATE
Independent Worksheet 20
INDEPENDENT WORKSHEET
Algebraic Thinking Padre’s Pizza
1
It costs $9.50 for a large pizza with cheese at Padre’s Pizza. Each extra topping
is $1.00.
a
Which equation could be used to find y, the amount of money it would cost for
a large pizza with 4 extra toppings?
y = $9.50 – $4.00
y = $9.50 × (4 × $1.00)
y = $9.50 + (4 × $1.00)
y = (4 × $1.00) ÷ $9.50




b
Explain your answer to part a. Why did you choose this equation instead of
the others?
2
It’s Ty’s birthday. For his party, his mom bought 4 large pizzas with a total of 9
extra toppings.
a
Which equation could be used to find y, the amount of money she had to pay?
y = $9.50 + (9 × $1.00)
y = (4 × $9.50) + (4 × $1.00)
y = $9.50 – (9 × $1.00)
y = (4 × $9.50) + (9 × $1.00)




b
Explain your answer to part a. Why did you choose this equation instead of
the others?
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 149
Texas Supplement Blackline
Independent Worksheet 20 Padre’s Pizza (cont.)
3
The marching band went to Padre’s after the Friday night football game They
ordered 7 large pizzas with 3 extra toppings each and 4 large pizzas with 4 extra
toppings each.
a
Which equation could be used to find t, the total number of extra toppings?
t = (7 × 3) + (4 × 4)
t=7×3×4×4
t = (7 + 3) × (4 + 4)
t=7+3+4+4




b
Use the equation you picked to solve the problem. How many extra toppings
did they order in all? Show your work.
c
How much did they have to pay for all the pizzas they ordered? Show all your
work.
4
The cook at Padre’s Pizza has 12 pizzas lined up for a special order. She put
cheese and sausage on all of them. She added pineapple to every second pizza
and olives to every third pizza.
a
Which pizzas in the line will have all 4 toppings (cheese, sausage, pineapple, and
olives)? Circle the diagram you could use to solve this problem.
P
PC
PO
PC
T
P
PC
O
P
PC
T
PO
PC
P
PC
OT
C
CS
CP
CS
O
C
CS
P
C
CS
O
CP
CS
C
CS
PO
CS
CS
P
CS
O
CS
P
CS
CS
PO
CS
CS
P
CS
O
CS
P
CS
CS
PO
150 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 20 Padre’s Pizza (cont.)
b
Which of the 12 pizzas got all 4 toppings?
5
The boy’s basketball team came into Padre’s on Wednesday night after practice. Half the boys on this team also play soccer, 14 play baseball, and 18 are in
the school band. The remaining 3 boys aren’t in any other activities. No one is in
more than 2 activities.
a
How many boys are there on the basketball team? Circle the diagram that will
give you the most help solving this problem.
3
3
3
b
Use the diagram you picked to help solve the problem. Show all of your work.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 151
Texas Supplement
152 • Bridges in Mathematics, Grade 5
Texas Supplement Blackline Use anytime after Supplement Activity 14.
NAME
DATE
Independent Worksheet 21
INDEPENDENT WORKSHEET
Algebraic Thinking Choosing Equations & Diagrams
Select the diagram and equation that best represent each problem situation below.
1
There are 5 rows of 6 desks in the classroom. Today, 3 of the desks are empty.
How many students are in class today?
a
Which diagram below best shows this problem?




b
If x represents the number of students in class, which equation could be used
to solve the problem?
5+3 +6=x

(5 × 6) – 3 = x

(5 × 3) + 6 = x

(5 × 6) + 3 = x

c
Explain your answer to part b. Why did you choose this equation instead of the
others?
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 153
Texas Supplement Blackline
Independent Worksheet 21 Choosing Diagrams & Sketches (cont.)
2
A pentagon has three longer sides that are all the same length and two shorter
sides that are both the same length.
a
Which diagram shows the pentagon described above?
a
b
b
a
b
a
a
b
a
b
d
c
e

a
b
c


a
a
a
a
a

Which equation could be used to find the perimeter of the pentagon?
P=5×a

P=3+a+2+b

P = (2 × a) + (2 × b) P = (3 × a) + (2 × b)


3
Destiny is having a party. She wants to get two cookies for each of the 8 people, including herself, who will be at the party. If each cookie costs 50¢, how
much money will she spend on cookies?
a
Which diagram below best shows this problem?
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢




b
Explain your answer to part a. Why did you choose this diagram instead of the
others?
154 • Bridges in Mathematics, Grade 5
© The Math Learning Center
Texas Supplement Blackline
Independent Worksheet 21 Choosing Diagrams & Sketches (cont.)
c
If x represents the amount of money Destiny is going to spend, which equation
could be used to solve the problem?
(2 + 8) × 0.50 = x (2 × 8) × 1.00 = x


(2 × 8) – 0.50 = x

(2 × 8) × 0.50 = x

4
There are 4 bikes, 2 skateboards, and a tricycle in Milo’s garage How many
wheels are there altogether?
a
Which diagram below best shows this problem?




b
If x represents the number of wheels in Milo’s garage, which equation could be
used to solve the problem?
2 × (4 + 2 + 1) = x (2 + 4 + 3) × 2 = x 2 × 4 × 3 = x (4 × 2) + (2 × 4) + 3 = x




c
Explain your answer to part b. Why did you choose this equation instead of the
others?
5
There are some bikes and trikes on the playground. There are 36 wheels in all,
and 15 bikes and trikes. How many bikes are there? How many trikes are there?
Draw a diagram and write an equation to solve this problem. Show your work.
Use the back of the page if you need more room.
© The Math Learning Center
Bridges in Mathematics, Grade 5 • 155
Texas Supplement
156 • Bridges in Mathematics, Grade 5
Texas Supplement
Grade 5 Independent Worksheet Answer Keys
ANSWER KEYS
Independent Worksheet 1
Using Compatible Numbers to Estimate
Answers, pages 89–91
1
a
b
c
d
2 a
b
c
d
e
f
Responses will vary. Example:
149 is close to 150 and 148 is close to 150.
150 + 150 = 300, so the answer is about 300.
Responses will vary. Example:
481 is close to 480 and 138 is close to 140.
280 – 140 = 140, so the answer is about 140.
Responses will vary. Example:
529 is close to 525 and 398 is close to 400.
525 + 400 = 925, so the answer is about 925.
Responses will vary. Example:
652 is close to 650 and 249 is close to 250.
650 – 250 = 400, so the answer is about 400.
About 300 miles
About $115.00
About 150 miles
About $1.00
About 500 miles
About 300 miles
Independent Worksheet 2
Are These Answers Reasonable?, pages 93–95
1
Yes. Example:
203 is close to 200. 449 is close to 450. 152 is close to 150.
200 + 450 + 150 = 800, which is really close to 804.
2 No. Example:
1,203 is close to 1,200 and 598 is close to 600.
1,200 – 600 = 600, so 713 is more than 100 off.
3 Yes. Example:
749 is close to 750, and 498 is almost 500. 750 + 500
= 1,250. 649 is close to 650, and 1,250 – 650 = 600,
which is really close to 598.
4 No. Example:
$1.99 and $2.03 are both close to $2.00, so that’s $4.00
in all. $1.49 and $1.52 are both close to $1.50, so that’s
another $3.00. $4.00 + $3.00 = $7.00. so $9.28 is
way off.
5 Yes. Example:
It’s about $24 for the markers, $5 for the pencil grips,
$10 for the pencils, and $14 for the pencil sharpener.
That’s $53 in all. $60 – $53 = $7, which is really close
to $7.18.
6 a No. Explanations will vary.
b Yes. Explanations will vary.
c There are 3,765 students in all. Estimates
will vary.
Independent Worksheet 3
Travel Miles, pages 97–99
1
a
Orlando is 297 miles farther than Nashville
from Houston. Explanations will vary.
b 3,862 miles farther. Explanations will vary.
c It’s 1,359 miles farther to fly from San Francisco to Philadelphia and back.
d 5,514 miles. Explanations will vary.
2 Responses will vary.
Independent Worksheet 4
Factor Trees & Common Factors, pages 101 and
102
1
2
3
4
1, 2, and 4
1, 2, 4, and 8
1, 2, 3, and 6
1, 2, 4, 5, 10, and 20
Independent Worksheet 5
More Factor Riddles, pages 103 and 104
1
2
3
4
12
9
40
15
Bridges in Mathematics, Grade 5 • 157
Texas Supplement
ANSWER KEY
Independent Worksheet 6
Area and Perimeter Review, pages 105–108
1
2
3
4
5
6
7
8
9
10
a Perimeter = 14 cm; Area = 12 sq cm
b Perimeter = 22 cm; Area = 30 sq cm
c Perimeter = 20 cm; Area = 21 sq cm
d Perimeter = 20 cm; Area = 24 sq cm
Responses will vary.
Responses will vary.
(2 × 3) + (2 × 8) = 22 ft.
the board’s length
determining how many feet of fencing is
needed to surround a rectangular yard
square feet
9 feet; explanations will vary
A=l×w
the 8 ft × 6 ft rectangle; explanations will vary
Independent Worksheet 7
Measuring Rectangles, pages 109–111
1
a
b
2 a
b
3 a
b
4 a
Area = length × width, A = l × w
6 ft × 4 ft = 24 sq ft
Perimeter = (2 × width) + (2 × length)
(2 × 2 cm) + (2 × 8 cm) = 20 cm
Area = length × width, A = l × w
3 m × 4 m = 12 sq meters
Perimeter = (2 × width) + (2 × length),
P = 2w + 2l
b (2 × 20 ft) + (2 × 40 ft) = 120 ft
8 cubic inches
9 4 ft.
10 (challenge) 5 inches
Independent Worksheet 9
The Camping Trip, pages 117 and 118
1
2
3
4
5
6
7
8
9
10
11
feet
miles
centimeters
meters
square inches
Area = length × width
square feet
A=l×w
cubic feet
cubic inches
cubic centimeters
Independent Worksheet 10
Nets & 3-D Figures, pages 119–121
1 Predictions will vary.
2
a
b
Independent Worksheet 8
Volume Review, pages 113–116
1
2
3
4
5
6
7
a 30 cm3
b 54 cm3
a 32 cm3
b 96 cm3
Responses will vary
192 cm3
(3 × 2 × 2)
the volume of the shoebox
determining how many rectangular containers of
food will fit into a freezer
158 • Bridges in Mathematics, Grade 5
c
d
e
Texas Supplement
ANSWER KEY
Independent Worksheet 10 (cont.)
Nets & 3-D Figures, pages 119–121
4 a
b
c
d
e
4 Responses will vary. Example:
12
triangular prism
square pyramid
triangular prism
rectangular prism
triangular pyramid
11
10
9
8
7
6
5
4
3
Independent Worksheet 11
2
1
0
Transforming Figures, Part 1, pages 123 and 124
1
Responses will vary. Example:
12
11
10
9
8
5
6
7
8
1
2
3
4
5
6
7
8
9
10 11 12
rotation
translation
reflection
reflection
7
6
Independent Worksheet 12
5
4
Transforming Figures, Part 2, pages 125–127
3
2
1
1
0
1
2
3
4
5
6
7
8
9
10 11 12
Responses will vary. Example:
12
11
10
9
2 Responses will vary. Example:
12
8
7
6
11
5
10
4
9
3
8
2
7
1
6
5
0
1
2
3
4
5
6
7
8
9
10 11 12
4
3
2 Responses will vary. Example:
2
1
0
12
1
2
3
4
5
6
7
8
9
10 11 12
11
10
9
3 Responses will vary. Example:
12
8
7
6
11
5
10
4
9
3
8
2
7
1
6
5
0
1
2
3
4
5
6
7
8
9
10 11 12
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
Bridges in Mathematics, Grade 5 • 159
Texas Supplement
ANSWER KEY
Independent Worksheet 12 (cont.)
Independent Worksheet 13
Transforming Figures, Part 2, pages 125–127
Using Compatible Numbers to Multiply & Divide,
pages 129 and 130
3 Responses will vary. Example:
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
4 Responses will vary. Example:
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
1 Answers will vary.
2 Answers will vary.
3 Answers will vary. Example:
197 is close to 200 and 200 ÷ 4 = 50; about 50 people
will ride each bus.
4 a Answers will vary. Example:
32 is close to 30. 29 is close to 30. 30 x 30 = 900, so
the answer is about 900.
b Answers will vary. Example:
153 is close to 150. 9 is close to 10. 150 ÷ 10 = 15
so the answer is about 15.
c Answers will vary. Example:
49 is close to 50. 19 is close to 20. 50 x 20 = 1,000,
so the answer is about 1,000.
d Answers will vary. Example:
119 is close to 120. 9 is close to 10. 120 ÷ 10 = 12,
so the answer is about 12.
10 11 12
Independent Worksheet 14
5
More Multiplication & Division with Compatible
Numbers, pages 131 and 132
12
11
10
1
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10 11 12
6
12
11
10
9
8
7
6
5
4
3
2
1
0
160 • Bridges in Mathematics, Grade 5
62 and 11; explanations will vary. Example:
62 × 11 will come closest to 600 because 62 is close to
60 and 11 is close to 10. 60 x 10 = 600
2 a Answers will vary. Example:
39 × 22 is close to 40 × 20, so the answer is
about 800.
b Answers will vary. Example:
84 × 11 is close to 84 × 10, so the answer is
about 840.
c Answers will vary. Eaxmple:
48 × 18 is close to 50 × 20, so the answer is
about 1,000.
3 a Answers will vary. Example:
$5.99 ÷ 24 is close to $6.00 ÷ 25, so each can of
soda costs about 24¢.
b Answers will vary. Example:
262 ÷ 9 is close to 260 ÷ 10, so they’ll each get
about 26 peanuts.
Texas Supplement
ANSWER KEY
Independent Worksheet 14 (cont.)
Independent Worksheet 18
More Multiplication & Division with Compatible
Numbers, pages 131 and 132
Inches to the Moon and Other Very Large
Numbers, pages 143 and 144
c
Answers will vary. Example:
594 ÷ 21 is close to 600 ÷ 20, so the answer is
about 30 bags of food.
1
a
b
c
d
e
2 a
b
Answers to all the problems on this worksheet will
vary.
3
1
9
1
No
1,577,727,360 inches
One billion, five hundred seventy-seven, seven
hundred twenty-seven, three hundred sixty
inches
c No
d 2
3 15,133,979,520 inches > 1,577, 727,360 inches
4 a seven hundred thirty-five billion, six hundred
fifty-eight million, nine hundred two thousand,four
hundred fifty-six
b 65,943,327,176;
c thirty-four billion, five hundred eighty-six million,
one hundred thirteen thousand, forty-two
d 439,562,329, 251
e 34,586,113,042 < 65,943,327,176 <
439,562,329, 251 < 735,658,902,456
Independent Worksheet 17
Independent Worksheet 19
Tons of Rice, pages 139–141
More Very Large Numbers, pages 145–147
1 Billions, millions, thousands, hundreds
2 Six billion, six hundred two million, two hundred
twenty-four thousand, one hundred seventy-five
3 7 billion
4 About 40 tons of rice; explanations will vary
5 a China; Pakistan
b India and China: 1,095,351,995 < 1,313,973,713;
Brazil and Pakistan: 188,078,227 > 165,803,560;
The United States and Brazil: 298,444,215 >
188,078,227
c 165,803,560 < 188,078,227 < 298,444,215 <
1,095,351,995 < 1,313,973,713; Pakistan, Brazil,
United States, India, China
6 Responses will vary.
1 Seventy-six million
2 a 4
b 2
c 5
d 3
e Yes, 1
3 60,000,000,000
4 Pluto is almost 6 billion kilometers from the sun.
5 a Bangladesh
b Philippines
c 89,468,677 < 107,449,525 < 127,463,611 <
142,893,540 < 147,365,352; Philippines, Mexico,
Japan, Russia, Bangladesh
6 Ten millions
Independent Worksheet 15
Reasonable Estimates in Multiplication &
Division, pages 133 and 134
1
a 600
b 260
c 10
d 30
e 50
2 Answers will vary, but it’s not a reasonable estimate. If the cards cost 50¢ each and she bought
just 24, she’d need $12.00.
Independent Worksheet 16
Make & Test Your Own Spinner, pages 135–137
Bridges in Mathematics, Grade 5 • 161
Texas Supplement
ANSWER KEY
Independent Worksheet 20
Padre’s Pizzas, pages 149–151
1
a
b
2 a
b
3 a
b
c
4 a
4 a
$9.50 × (4 × $1.00)
Explanations will vary.
y = (4 × $9.50) + (9 × $1.00)
Explanations will vary.
t = (7 × 3) + (4 × 4)
37 extra toppings; explanations will vary.
$141. 50; explanations will vary.
CS
CS
P
CS
O
CS
P
CS
CS
PO
CS
CS
P
CS
O
CS
P
CS
b (4 × 2) + (2 × 4) + 3 = x
c Explanations will vary.
5 9 bikes and 6 trikes. Diagrams and equations will
vary.
CS
PO
b The sixth and the twelfth pizza
5 a
3
b There are 24 boys on the basketball team.
Student work will vary.
Independent Worksheet 21
Choosing Equations and Diagrams, pages XX-XX
1
a
b (5 × 6) – 3 = x
c Explanations will vary.
2 a
a
b
a
b
a
b P = (3 × a) + (2 × b)
3 a
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
0.50¢
b Explanations will vary.
c (2 × 8) × 0.50 = x
162 • Bridges in Mathematics, Grade 5
Bridges
Unit 6, Sessions 13–18
Unit 6, page 919, Home Connection 54
Unit 6, page 928, Home Connection 55
Unit 6, page 976–977, Work Place 6D
(5.1) (B) use place value to read, write,
compare, and order decimals through the
thousandths place
Unit 4, Session 17
Unit 4, pages 616–617, Home Connection 37
Unit 6, Sessions 8–9
Unit 6, pages 870–871, Home Connection 51
Unit 6, Session 11
Unit 6, pages 889–890, Home Connection 52
Unit 6, pages 897–900, Work Place 6B
Unit 4, Session 19
Unit 6, Sessions 9, 12, 24
Unit 6, page 871, Home Connection 51
Unit 6, pages 889–890, Home Connection 52
Unit 6, Sessions 15–18
Unit 6, page 928, Home Connection 55
Unit 6, page 959, Home Connection 57
(5.2) (B) generate a mixed number equivalent to a
given improper fraction or generate an improper
fraction equivalent to a given mixed number
(5.2) (C) compare two fractional quantities in
problem-solving situations using a variety of
methods, including common denominators
(5.2) (D) use models to relate decimals to
fractions that name tenths, hundredths, and
thousandths.
November Calendar Grid
April Computational Fluency
April Computational Fluency
November Calendar Grid
February Calendar Grid
March Computational Fluency
November Computational Fluency
April Calendar Collector
Number Corner
GRADE 5
(5.2) (A) generate a fraction equivalent to a
given fraction such as 1 ⁄ 2 and 3 ⁄6 or 4 ⁄12 and 1 ⁄ 3
Fractions & Decimals
Unit 2, Session 1
Unit 6, Session 13
Unit 7, Session 8
(5.1) (A) use place value to read, write, compare, and order whole numbers through the
999,999,999,99
Numbers To 999,999,999,999
NUMBER, OPERATION & QUANTITATIVE REASONING
TEKS
Bridges Grade 5 TEKS Correlations
Independent Worksheet 17
Independent Worksheet 18
Independent Worksheet 19
Texas Supplement
Texas Supplement
Bridges in Mathematics, Grade 5 • 163
164 • Bridges in Mathematics, Grade 5
Unit 6, Session 10
Unit 4, Sessions 11–12, 13, 18–19, 22
Unit 4, pages 643–644, Home Connection 39
Unit 6, Sessions 10–11
Unit 6, Sessions 889–890, Home Connection 52
Unit 6, pages 897–900, Work Place 6B
(5.3) (D) identify common factors of a set of
whole numbers
(5.3) (E) model situations using addition and/
or subtraction involving fractions with like de-
(5.4) (A) use strategies, including rounding
and compatible numbers to estimate solutions
to addition, subtraction, multiplication, and
division problems
Computational Estimation
Unit 2, Sessions 8, 14–15
Unit 4, Sessions 2–3, 6
Unit 4, page 523, Home Connection 30
Unit 6, Session 19
Unit 2, Sessions 13, 16
Unit 4, Sessions 4, 9
Unit 6, Sessions 4–5
(5.3) (C) use division to solve problems involving whole numbers (no more than two-digit
divisors and three-digit dividends without
technology), including interpreting the remainder within a given context
nominators using concrete objects, pictures,
words, and numbers.
Unit 2, Sessions 5–6, 11
Unit 6, Sessions 1–3
Unit 6, pages 828–829, Home Connection 48
Unit 6, page 908, Home Connection 53
November Computational Fluency
April Calendar Collector
March Computational Fluency
April Computational Fluency
February Calendar Grid
April Problem Solving
November Calendar Grid
March Computational Fluency
April Calendar Collector
Number Corner
GRADE 5
Unit 6, Sessions 5, 19
Unit 6, page 959, Home Connection 57
Unit 6, pages 976–977, Work Place 6D, Challenge Version
Unit 6, page 983, Home Connection 59
Unit 1, Sessions 11, 13
Unit 2, Sessions 9, 17
Unit 5, Session 11
Bridges
(5.3) (B) use multiplication to solve problems
involving whole numbers (no more than three
digits times two digits without technology)
(5.3) (A) use addition and subtraction to solve
problems involving whole numbers and decimals
Computation
TEKS
Bridges Grade 5 TEKS Correlations (cont.)
Independent Worksheet 1
Independent Worksheet 2
Independent Worksheet 3
Independent Worksheet 13
Independent Worksheet 14
Independent Worksheet 15
Activity 1
Activity 2
Independent Worksheet 4
Independent Worksheet 5
Texas Supplement
Texas Supplement
Bridges
Activity 11
Independent Worksheet 11
Independent Worksheet 12
Activity 6
Activity 7
Activity 9
Activity 10
Independent Worksheet 10
(5.8) (B) identify the transformation that generates
one figure from the other when given two congruent figures on a Quadrant I coordinate grid
December Calendar Grid
Activity 14
Independent Worksheet 20
Independent Worksheet 21
Activity 11
Independent Worksheet 11
Independent Worksheet 12
Unit 1, Session 1
Unit 3, Sessions 1–2, 10–11, 13–14, 18–19
Unit 3, page 374–375, Home Connection 22
Unit 3, page 410, Challenge
Unit 3, pages 465, Home Connection 28
September Problem Solving
Activity 1
Activity 2
Independent Worksheet 4
Independent Worksheet 5
Texas Supplement
(5.8) (A) sketch the results of translations,
rotations, and reflections on a Quadrant I
coordinate grid
Transformations
(5.7) (A) identify essential attributes including
parallel, perpendicular, and congruent parts of
two- and three-dimensional geometric figures
2- & 3-Dimensional Figures
GEOMETRY & SPATIAL REASONING
(5.6) (A) select from and use diagrams and
equations such as y = 5 + 3 to represent
meaningful problem situations
Unit 1, Session 15–16
Unit 3, Session 6
Unit 3, page 388, Home Connection 23
Unit 4, Session 9
Unit 6, Sessions 2, 4
Unit 7, Sessions 4, 9–13
Unit 7, page 1087, Home Connection 64
March Problem Solving
Unit 1, Session 9–10, 20
Unit 1, page 82, Home Connection 5
(5.5) (B) identify prime and composite numbers using concrete objects, pictorial models,
and patterns in factor pairs
Diagrams & Equations
December Calendar Collector
January Calendar Collector
March Calendar Collector
Unit 7, Sessions 4–7, 9
Number Corner
(5.5) (A) describe the relationship between
sets of data in graphic organizers such as lists,
tables, charts, and diagrams
Patterns & Functions
PATTERNS, RELATIONSHIPS & ALGEBRAIC THINKING
TEKS
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Texas Supplement
Bridges in Mathematics, Grade 5 • 165
166 • Bridges in Mathematics, Grade 5
Unit 2, pages 297–298, Home Connection 18
(5.10) (C10 and C14) select and use formulas to
measure perimeter
(5.10) (B2) connect models for area with their
respective formulas
Unit 2, Sessions 2–3, 5
Unit 3, Sessions 3–4
Unit 2, pages 297–298, Home Connection 18
(5.10) (C2 and C6) select and use appropriate
units to measure perimeter
Area
Unit 2, pages 297–298, Home Connection 18
Unit 4, Session 8
Unit 4, page 561, Work Place 4C
Unit 7, Session 8
Unit 1, Session 17
Unit 3, Sessions 16–17
Unit 3, page 454, Home Connection 27
Unit 7, Sessions 4–5
Bridges
(5.10) (B1) connect models for perimeter with
their respective formulas
Perimeter
(5.10) (A) perform simple conversions within
the same measurement system (SI (metric) or
customary)
Conversions
MEASUREMENT
(5.9) (A) locate and name points on a coordinate grid using ordered pairs of whole
numbers
Coordinate Grids
TEKS
Number Corner Student Book, page 123
Number Corner Student Book, page 123
November Calendar Collector
Number Corner Student Book, page 123
October Computational Fluency
March Calendar Grid
Number Corner
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Activity 3
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Activity 4
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Activity 4
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Activity 4
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Texas Supplement
Texas Supplement
(5.10) (C1 and C5) select and use appropriate
units to measure length
Length
Unit 1, Session 1
Unit 2, page 178, Home Connection 11
Unit 2, page 311, Home Connection 19
Unit 4, pages 635–636, Work Place 4F
Unit 6, Session 18
Unit 8, Sessions 2, 4
April Calendar Grid
January Calendar Grid
April Calendar Grid
(5.10) (C4 and C8) select and use appropriate
units to measure volume
(5.10) (C12 and C16) select and use formulas to
measure volume
April Calendar Grid
Number Corner
(5.10) (B3) connect models for volume with
their respective formulas
Unit 3, Session 20
Unit 3, page 479, Home Connection 29
Unit 2, Sessions 2–3, 7–8
Unit 2, pages 297–298, Home Connection 18
(5.10) (C11 and C 15) select and use formulas
to measure area
Volume
Unit 2, Sessions 2, 4
Unit 2, pages 297–298, Home Connection 18
Unit 4, page 608, Home Connection 36
Bridges
(5.10) (C3 and C7) select and use appropriate
units to measure area
Area (cont.)
TEKS
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Independent Worksheet 9
Activity 7
Activity 8
Independent Worksheet 8
Activity 7
Activity 8
Independent Worksheet 8
Independent Worksheet 9
Activity 7
Activity 8
Independent Worksheet 8
Independent Worksheet 9
Activity 3
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Independent Worksheet 9
Activity 3
Activity 5
Activity 6
Independent Worksheet 6
Independent Worksheet 7
Independent Worksheet 9
Texas Supplement
Texas Supplement
Bridges in Mathematics, Grade 5 • 167
168 • Bridges in Mathematics, Grade 5
Unit 6, Session 10–11
(5.11) (B) solve problems involving elapsed time
Unit 5, Sessions 7, 11
(5.12) (C) list all possible outcomes of a probability experiment such as tossing a coin
Unit 7, Session 7
Unit 1, Session 18–19
Unit 1, page 129, Home Connection 9
Unit 5, Sessions 4–5
Unit 5, pages 700–701, Home Connection 41
Unit 8, Sessions 6, 8
Unit 8, pages 1207–1208, Home Connection 70
Unit 1, Session 2
Unit 5, Sessions 1–4, 18
(5.13) (A) use tables of related number pairs to
make line graphs
(5.13) (B) describe characteristics of data presented in tables and graphs including median,
mode, and range
(5.13) (C) graph a given set of data using an
appropriate graphical representation such as a
picture or line graph
February Calendar Collector
March Calendar Collector
September Calendar Collector
December Calendar Collector
January Calendar Collector
October Calendar Collector
March Calendar Collector
December Calendar Collector
January Calendar Collector
September Calendar Collector
Unit 5, Sessions 14–16
Unit 5, page 754, Home Connection 44
(5.12) (B) use experimental results to make
predictions
Graphing
September Calendar Collector
February Calendar Collector
Unit 5, Sessions 6, 8, 16
September Calendar Collector
February Calendar Collector
March Calendar Collector
January Calendar Collector, Week 1
January Calendar Collector, Week 2
Number Corner
(5.12) (A) use fractions to describe the results
of an experiment
Probability
PROBABILITY & STATISTICS
Unit 6, Session 19
Unit 8, Session 2
Unit 1, Session 1
Unit 4, pages 635–636, Work Place 4F
Unit 6, Session 18
Bridges
(5.11) (A) solve problems involving changes in
temperature
Time & Temperature
(5.10) (C9 and C13) select and use formulas to
measure length
Length (cont.)
TEKS
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Activity 12
Activity 13
Independent Worksheet 16
Texas Supplement
Texas Supplement
Bridges
Communication (cont.)
(5.15) (A) explain and record observations
using objects, words, pictures, numbers, and
technology
Communication
Unit 1, Sessions 5–7, 10, 12
Unit 2, Sessions 5, 16
Unit 3, Sessions 1, 11, 13–14
Unit 4, Sessions 9–11, 15, 17
Unit 5, Sessions 9, 15–16
Unit 6, Sessions 3, 7, 17, 20–21
Unit 7, Sessions 4, 6–7
Unit 8, Sessions 1, 4
Unit 1, Session 10
Unit 2, Session 13
Unit 3, Session 11
Unit 4, pages 562–564, Work Place 4D
December Calendar Grid
January Calendar Collector
March Calendar Collector
Unit 6, Session 17
nipulatives, and technology to solve problems
(5.14) (D) use tools such as real objects, ma-
September Problem Solving
January Problem Solving
April Problem Solving
May Problem Solving
January Calendar Collector
January Calendar Grid
March Calendar Collector
September–February Problem Solving
April Problem Solving
Unit 2, Sessions 11, 15
Unit 4, Session 19
Unit 6, Session 4, 19
Number Corner
(5.14) (C) select or develop an appropriate
problem-solving plan or strategy, including
drawing a picture, looking for a pattern, systematic guessing and checking, acting it out,
making a table, working a simpler problem, or
working backwards to solve a problem
(5.14) (B) solve problems that incorporate
understanding the problem, making a plan,
carrying out the plan, and evaluating the solution for reasonableness
Problem Solving
(5.14) (A) identify mathematics in everyday
situations
Connections
UNDERLYING PROCESSES & MATHEMATICAL TOOLS
TEKS
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Activity 12
Activity 13
Independent Worksheet 16
Activity 12
Activity 13
Independent Worksheet 16
Texas Supplement
Texas Supplement
Bridges in Mathematics, Grade 5 • 169
170 • Bridges in Mathematics, Grade 5
Unit 1, Sessions 15–16
Unit 3, Session 2
Unit 5, Sessions 10
Unit 7, Sessions 9
(5.16) (A) make generalizations from patterns
or sets of examples and non-examples
(5.16) (B) justify why an answer is reasonable
and explain the solution process
Unit 1, Session 6
Unit 4, Session 19
Unit 6, Sessions 19
Unit 1, Sessions 8, 12, 15
Unit 3, Sessions 6, 17
Unit 5, Session 6
Unit 6, Session 20
Unit 7, Sessions 2, 9
(5.15) (B) relate informal language to mathematical language and symbols
Representation
Bridges
TEKS
September–May Problem Solving
Number Corner Student Book, pages 155–158,
165–169, 173–176
Number Corner
GRADE 5
Bridges Grade 5 TEKS Correlations (cont.)
Texas Supplement
Texas Supplement