Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Unit 02: Addition and Subtraction with Whole Numbers and Decimals (4 days)
Possible Lesson 01 (4 days)
POSSIBLE LESSON 01 (4 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students use base-ten materials and grids as tools to add and subtract whole numbers and decimal numbers to the thousandths place. Students perform whole number
and decimal addition and subtraction computation problems to include perimeter. Students model problems with base-ten blocks and make connections to addition and
subtraction computations.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
5.3
Number, operation, and quantitative reasoning.. The student adds, subtracts, multiplies, and divides to solve meaningful problems.
The student is expected to:
5.3A
Use addition and subtraction to solve problems involving whole numbers and decimals. Readiness Standard
5.4
Number, operation, and quantitative reasoning.. The student estimates to determine reasonable results. The student is expected to:
5.4
Use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and
division problems.
Supporting Standard
5.10
Measurement.. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and
page 1 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
weight/mass to solve problems. The student is expected to:
5.10C
Select and use appropriate units and formulas to measure length, perimeter, area, and volume. Readiness Standard
Underlying Processes and Mathematical Tools TEKS:
5.14
Underlying processes and mathematical tools.. The student applies Grade 5 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
5.14A
Identify the mathematics in everyday situations.
5.14B
Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution
for reasonableness.
5.14C
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.
5.15
Underlying processes and mathematical tools.. The student communicates about Grade 5 mathematics using informal language. The
student is expected to:
5.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
5.15B
Relate informal language to mathematical language and symbols.
5.16
Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to:
5.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
page 2 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Grade5 Mathematics Unit02 PI01
Use appropriate operations to estimate and solve a multi-step real-life situation involving the perimeter of at least 2 rectangular figures (e.g., rectangular and square gardens or
decks, etc.). Create a one-page visual that includes a pictorial representation of the problem situation and a written explanation of the solution process. Record the estimated
and actual perimeters using appropriate units, and justify the reasonableness of the solution.
Sample Performance Indicator:
The Gateway Fencing Company was asked to enclose three gardens with curb siding: a rectangular garden with a length of 270 meters and a
width of 1123.62 meters; a square garden with a side length of 657.955 meters; and a rectangular garden with a width of 35 meters and a length
that is 121.03 meters greater than the width. The company ordered 6,000 meters of curbing. Create a one-page visual that includes: (1) a
pictorial representation of each garden, (2) a written explanation of the solution process with the estimated and actual amount of curbing needed
for each garden, and (3) an analysis and written justification describing if the company ordered too much or too little curbing for all three gardens.
Standard(s): 5.3A ,5.4 , 5.10C ,5.14A ,5.14B ,5.15A ,5.15B , 5.16B
ELPS ELPS.c.1C , ELPS.c.4I , ELPS.c.5G
Key Understanding(s):
Estimation strategies, such as rounding or compatible numbers, can be used to approximate the solution of an addition or a subtraction problem involving whole
numbers and decimals to determine if the actual solution is reasonable by focusing on the meaning of the numbers.
When solving addition and subtraction problems involving whole numbers and decimals, equivalent forms of the numbers may be needed so that digits with the
same place value can be added or subtracted because digits in like places have the same underlying unit amount.
The perimeter of a figure is a linear measure and can be determined by estimating each side length of the figure and expressing the total with appropriate units and
calculated by adding the exact lengths of each side of the figure and expressing the total with appropriate units.
Problem solving with addition and subtraction of whole numbers and decimals involves analyzing the given information, the missing information, and the
question(s); developing a solution plan with strategies; observing and communicating the mathematical ideas through verbal/written descriptions, statements,
and/or equations; and evaluating the solution for reasonableness.
Misconception(s):
Some students may think that when estimating a solution, you add all of the numbers and then estimate the solution, instead of estimating the numbers prior to
page 3 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
computation.
Underdeveloped Concept(s):
Some students may not understand that equivalent forms of decimals are needed to subtract decimal numbers (e.g., 0.5 – 0.47 would be 0.50 – 0.47).
Some students may have difficulty with aligning like places in decimal numbers and may simply align the digits right justified.
Some students may have difficulty visualizing thousandths models in grid format. They may need more experience with various thousandths grids.
Vocabulary of Instruction:
estimate
perimeter
round
Materials:
map pencil (2 colors) (1 set per teacher)
math journal (1 per student)
paper (1 sheet per student)
scissors (1 per student)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Dad’s Day Decimal Problem KEY
Dad’s Day Decimal Problem
Hundredths Grid
page 4 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Thousandths Grids Addition and Subtraction Examples KEY
Thousandths Grids Addition and Subtraction Examples
Connecting Decimal Addition and Subtraction – Notes KEY
Connecting Decimal Addition and Subtraction – Notes
Connecting Decimal Addition and Subtraction Practice KEY
Connecting Decimal Addition and Subtraction Practice
Adding and Subtracting Decimals with Base­Ten Blocks – Notes
Practice Problems KEY
Practice Problems
Place Value Window – Teacher Directions
Place Value Window
Place Value Window Prompts – Teacher Notes
Garden Pathway Problem Solving KEY
Garden Pathway Problem Solving
Garden Club Mileage KEY
Garden Club Mileage
Centimeter Grid Paper
Inch Grid Paper
page 5 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Exploring Perimeters
Perimeter Plans KEY
Perimeter Plans
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Introduction to addition and subtraction of whole numbers and decimals
Engage 1
ATTACHMENTS
Students use experience and reasoning skills to add decimals in a real-life problem situation involving
Teacher Resource: Dad’s Day Decimal
money.
Problem KEY (1 per teacher)
Teacher Resource: Dad’s Day Decimal
Instructional Procedures:
Problem (1 per teacher)
1. Display teacher resource: Dad’s Day Decimal Problem. Read the scenario aloud to students.
Instruct students to solve the problem in their math journal. Encourage students to draw bills and
MATERIALS
coins to justify their work if necessary. Allow time for students to complete the problem. Monitor and
assess students to check for understanding. Facilitate a class discussion about the strategies used
math journal (1 per student)
to solve the problem.
page 6 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Ask:
Notes for Teacher
TEACHER NOTE
What strategies did you use when adding the money? Answers may vary. I estimated by
If math journals are not used or are unavailable,
rounding the price of the items before I added them; etc.
teacher resource: Dad’s Day Decimal
What strategy did you use to determine if you had enough money? Answers may vary. I
Problem may be used to create a handout for
compared the two amounts to see which one was larger; etc.
individual students.
What rule could you use for the addition of decimal numbers? Answers may vary. Make
sure the place values are lined up; If decimal points are lined up, the place values are lined up;
RESEARCH
etc.
According to Marilyn Burns and Robyn Sibley,
journal writing can be a valuable technique to
further develop, and enhance, mathematical
thinking and communication skills in
mathematics.
Topics:
Hundredths and thousandths grid to model addition and subtraction of decimals
ATTACHMENTS
Handout: Hundredths Grid (1 per
student)
Explore/Explain 1
Teacher Resource: Hundredths Grid (1
Students apply knowledge of the hundredths and thousandths grid to model addition and subtraction of
per teacher)
decimals. Students estimate solutions prior to computation to determine if their solution is reasonable.
Teacher Resource: Thousandths Grids
Addition and Subtraction Examples
Instructional Procedures:
1. Distribute handout: Hundredths Grid to each student.
2. Display teacher resource: Hundredths Grid and the numbers 0.64 and 0.29 for the class to see.
KEY (1 per teacher)
Teacher Resource: Thousandths Grids
Addition and Subtraction Examples
(1 per teacher)
page 7 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Ask:
Notes for Teacher
Teacher Resource: Connecting
How could I use a single hundredths grid to add these two numbers? Answers may vary.
Shading part of the grid to show 0.64 and the other part to show 0.29; etc.
Decimal Addition and Subtraction –
Notes KEY (1 per teacher)
Teacher Resource: Connecting
Decimal Addition and Subtraction –
3. Using the displayed teacher resource: Hundredths Grid, demonstrate how to shade 0.64 by using
Notes (1 per teacher)
a colored map pencil and then, using a different colored map pencil, shade 0.29. Model counting all
Teacher Resource: Connecting
the shaded squares to determine how many hundredths are shaded.
Decimal Addition and Subtraction
Practice KEY (1 per teacher)
Handout: Connecting Decimal
Addition and Subtraction Practice (1
per student)
Handout (optional): Adding and
Subtracting Decimals with Base-Ten
4. Facilitate a class discussion about adding 2 decimals on a single hundredths grid.
Blocks – Notes (1 per student)
Teacher Resource (optional): Practice
Ask:
Problems KEY (1 per teacher)
Why are these squares referred to as hundredths? Answers may vary. Because there are
Handout (optional): Practice Problems
100 little squares in the whole; hundredths refer to less than 1 whole; it represents part of a
(1 per student)
whole; etc.
When you added 64 hundredths to 29 hundredths what was the sum? (0.93)
How could you write this as a fraction? (
)
How could you use a single hundredths grid to subtract these two numbers? Answers
MATERIALS
map pencil (2 colors) (1 set per teacher)
may vary. I can shade part of the grid to show 0.64 and then remove 0.29 by crossing out 29 of
page 8 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
the little squares; etc.
TEACHER NOTE
5. Using the displayed teacher resource: Hundredths Grid, demonstrate how to shade 0.64 by using
a colored map pencil and then cross out 29 squares to represent finding the difference between 0.64
For struggling learners, use base-ten blocks to
model the numbers on a place value board and
then make trades as necessary with the base-
and 0.29.
ten blocks.
TEACHER NOTE
Encourage students to always estimate
solutions prior to solving in order to determine if
their solution is reasonable.
6. Facilitate a class discussion about subtracting 2 decimals with a single hundredths grid.
State Resources
Ask:
When you subtracted 29 hundredths from 64 hundredths what was the difference? (0.35)
TEXTEAMS: Rethinking Elementary
How could you write this as a fraction? (
Mathematics Part I: Diffyboxes; Dollar
)
How is adding and subtracting decimal numbers like adding and subtracting whole
Addition and Subtraction; Magic Squares
numbers? Answers may vary. When you add decimals, you are combining the numbers and
when you subtract decimals you are removing or finding the difference, just like with whole
numbers; you have to consider the value of each digit by thinking about what place it is in; etc.
ADDITIONAL PRACTICE
Use handouts (optional): Adding and
Explain to students that the decimal point plays an important role in decimal operations as it
Subtracting Decimals with Base-Ten Blocks
needs to be aligned in order for the decimal numbers to be in the correct place value; decimals
– Notes and/or Practice Problems to further
have decimal points that must be placed in a straight line and whole numbers do not have
facilitate understanding of decimal addition and
page 9 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
decimal points, etc.
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Notes for Teacher
subtraction concepts.
How is adding and subtracting decimal numbers different from adding and subtracting
whole numbers? Answers may vary. When you add and subtract decimals, you are working
with numbers that represent some whole and parts of a whole; decimal addition and subtraction
can be represented on a decimal grid; the answer to decimal addition and subtraction problems
may have a decimal, but the sum or difference to a whole number problem will not; etc.
If the place to the right of the decimal is referred to as tenths and two places to the right
of the decimal is referred to as hundredths, what do you call three places to the right of
the decimal? (thousandths)
How could you model adding and subtracting decimal numbers in the thousandths?
Answers may vary. I could use a thousandths grid and shade it according to the decimal
numbers given; etc.
7. Display teacher resource: Thousandths Grids Addition and Subtraction Examples.
Ask:
What number sentence does each grid represent? (0.255 + 0.245 = 0.500 and 0.500 –
0.070 = 0.430)
What decimal equivalencies could you also record for the sum or difference to these
two problems? (0.50, 0.5 and 0.43)
8. Explain to students that when adding decimal numbers vertically, it is important to remember place
value. Therefore, lining up the decimal is important when using the traditional algorithm for decimal
addition and subtraction computation. Demonstrate how to record the following 2 number sentences.
page 10 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Notes for Teacher
Ask:
Is the role of the zero in decimals the same as the role of the zero in whole numbers?
How do you know? (Yes, it is a place holder, and if there is no value, a zero is “placed” there.)
9. Display teacher resource: Connecting Decimal Addition and Subtraction – Notes to
demonstrate how to connect the shading of the grid to the process of adding and subtracting
decimals. Explain to students that they can use what they already know about addition and
subtraction of whole numbers to add or subtract decimals.
10. Distribute handout: Connecting Decimal Addition and Subtraction Practice to each student for
independent practice or homework.
2
Topics:
Spiraling Review
Decimal place value and addition
Explore/Explain 2
ATTACHMENTS
Students review and apply previous knowledge of decimals to demonstrate understanding with decimal
Teacher Resource: Place Value
place value windows. Students use their knowledge of place value to add and subtract whole numbers
Window – Teacher Directions (1 per
and decimals in problem situations.
teacher
Class Resource: Place Value Window
page 11 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Instructional Procedures:
Notes for Teacher
(1 per student)
Teacher Resource: Place Value
1. Prior to instruction, review the teacher resource: Place Value Windows-Teacher Directions and
create a class resource: Place Value Window for each student and a teacher resource: Place
Value Window for each teacher by copying the “windows” and the number strips on cardstock,
laminating, and cutting apart. Cut out each “window” and make slits along the dotted lines. Cut out
each number strip and slide each one through the slit under each place value.
2. Distribute class resource: Place Value Window to each student.
3. Display teacher resource: Place Value Window and model how to use the windows. Instruct
students to use their class resource: Place Value Window to model values as directed by the
teacher. Monitor and assess students to check for understanding of how to use their “window”.
Ask:
How would you represent “four and fifteen hundredths” with a Place Value Window?
Window (1 per teacher)
Teacher Resource: Place Value
Window Prompts – Teacher Notes (1
per teacher)
Teacher Resource: Garden Pathway
Problem Solving KEY (1 per teacher)
Teacher Resource: Garden Pathway
Problem Solving (1 per teacher)
Teacher Resource: Garden Club
Mileage KEY (1 per teacher)
Handout: Garden Club Mileage (1 per
student)
(4.15)
How would you represent “twenty­three and eighty­four hundredths” with a Place Value
Window? (23.84)
MATERIALS
How would you represent one-tenth more than 23.84 with a Place Value Window?
cardstock (1 sheet per 2 students, 1
(23.94)
sheet per teacher)
How would you represent two-hundredths less than 23.84 with a Place Value Window?
scissors (1 per teacher)
(23.82)
4. Read the prompts from teacher resource: Place Value Window Prompts – Teacher Notes aloud
to students. Instruct students to follow the directions in the prompt and manipulate their class
State Resources
page 12 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Notes for Teacher
resource: Place Value Window to display their response. Allow 10-15 minutes for this activity.
Monitor and assess students to check for understanding.
TEXTEAMS: Rethinking Elementary
Mathematics Part I: Decimal Addition
5. Display teacher resource: Garden Pathway Problem Solving.
6. Instruct students to read and complete the first 3 questions. Allow time for students to complete the
activity. Facilitate a class discussion allowing students to share their responses emphasizing ways
to estimate with decimals including rounding to the nearest whole number or using benchmarks,
such as one-half.
7. Instruct students to use their class resource: Place Value Window to model and solve the fourth
problem. Remind students that if they are not sure where to place the decimal point, they can think
of the numbers as money amounts. Allow time for students to complete the activity. Monitor and
assess students to check for understanding. Facilitate a class discussion about the strategies used
to solve the problem and demonstrate the solution process, if necessary.
8. Distribute handout: Garden Club Mileage to each student. Instruct students to complete the
page 13 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
handout for independent practice or homework.
3
Topics:
Spiraling Review
Addition of whole numbers and decimals
Elaborate 1
ATTACHMENTS
Students apply prior knowledge to estimate and find the perimeter of rectangles using base-ten blocks.
Handout: Centimeter Grid Paper (2 per
Students make connections between the addition and subtraction of whole numbers and decimals to
student)
finding the perimeter of rectangles, without the use of formulas.
Teacher Resource: Centimeter Grid
Paper (1 per teacher)
Instructional Procedures:
Handout: Inch Grid Paper (1 per
student)
1. Distribute handout: Centimeter Grid Paper to each student.
2. Instruct students to create a 6 × 5 rectangle on their handout: Centimeter Grid Paper.
Ask:
Handout: Exploring Perimeters (1 per
student)
Teacher Resource: Perimeter Plans
KEY (1 per teacher)
What is the perimeter of this rectangle? (22 cm). How do you know? Answers may vary. I
Handout: Perimeter Plans (1 per
added the lengths of each side; etc.
student)
Allow time for students to respond and share strategies for finding perimeter. Remind students that
each square is 1 centimeter in length and when naming a measurement, the unit of measure (such
MATERIALS
as cm) must accompany the actual measurement.
math journal (1 per student)
Based on what you have just explained, what is the meaning of the word perimeter?
scissors (1 per student)
(The sum of the distance around the outside of a figure.)
page 14 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
3. Display teacher resource: Centimeter Grid Paper and draw only 1 length and 1 width (semi-
Notes for Teacher
TEACHER NOTE
perimeter) of a rectangle with a length of 8 and a width of 6.
When asked to estimate, students have the
Ask:
choice of using compatible numbers or rounding
the numbers. Rounding numbers have specific
What do you know about rectangles that would help you find the perimeter? Answers
may vary. The opposite sides of a rectangle are equal or have the same length; etc.
What would be a good estimate for the perimeter of the rectangle? Answers may vary. 8
rules, and compatible numbers involve students
finding “friendly numbers” where no specific
rules apply.
is about 10, so 10 + 10 = 20 and 6 + 6 = 12, so the perimeter is about 20 + 12 = 32; or 8 is
about 10 and 6 is about 5, so 10 + 10 = 20 and 5 +5 = 10, so the perimeter is 20 + 10 = 30; etc.
State Resources
4. Instruct students to replicate the displayed semi-perimeter on their handout: Centimeter Grid
Paper, complete the other sides of the rectangle, and calculate its perimeter.
TEXTEAMS: Rethinking Elementary
Ask:
Mathematics Part II: What’s the Perimeter?
What did you do to find the length of the missing sides? Answers may vary. I found the
length of the opposite sides; I doubled the measurement of each side and added them together;
I doubled the length and doubled the width, then added the numbers together; etc.
What rule could you use to find the perimeter of a rectangle? Answers may vary. Add the
lengths of all the sides; multiply the width times 2 and the length times 2; etc.
5. Place students in groups of 3 – 4. Instruct student groups to use their handout: Centimeter Grid
Paper to find the perimeter of their desktop (or math textbook) and record their findings in their math
journal. Allow time for students to complete their measurements. Monitor and assess student
groups to check for understanding. Facilitate a class discussion about the measurements.
Ask:
page 15 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
What was the perimeter of your desktop? Answers may vary.
Did all of the desks have the same desktop perimeter? Why or why not? Answers may
vary.
6. Place students in pairs. Distribute a pair of scissors, handout: Exploring Perimeters, and either
handout: Inch Grid Paper or another copy of handout: Centimeter Grid Paper or to each student.
7. Instruct student pairs to complete handout: Exploring Perimeters. Allow time for student pairs to
complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a
class discussion to debrief student solutions.
8. Distribute handout: Perimeter Plans to each student. Instruct students to complete the handout for
independent practice or homework.
4
Evaluate 1
Instructional Procedures:
MATERIALS
paper (1 sheet per student)
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Performance Indicator(s):
page 16 of 49 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
Notes for Teacher
Grade5 Mathematics Unit02 PI01
Use appropriate operations to estimate and solve a multi-step real-life situation involving the perimeter of
at least 2 rectangular figures (e.g., rectangular and square gardens or decks, etc.). Create a one-page
visual that includes a pictorial representation of the problem situation and a written explanation of the
solution process. Record the estimated and actual perimeters using appropriate units, and justify the
reasonableness of the solution.
Sample Performance Indicator:
The Gateway Fencing Company was asked to enclose three gardens with curb siding:
a rectangular garden with a length of 270 meters and a width of 1123.62 meters; a
square garden with a side length of 657.955 meters; and a rectangular garden with a
width of 35 meters and a length that is 121.03 meters greater than the width. The
company ordered 6,000 meters of curbing. Create a one-page visual that includes:
(1) a pictorial representation of each garden, (2) a written explanation of the solution
process with the estimated and actual amount of curbing needed for each garden,
and (3) an analysis and written justification describing if the company ordered too
much or too little curbing for all three gardens.
Standard(s):5.3A ,5.4 , 5.10C ,5.14A ,5.14B ,5.15A ,5.15B , 5.16B
ELPS ELPS.c.1C , ELPS.c.4I , ELPS.c.5G
03/26/13
page 17 of 49 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 02:
Suggested Duration: 4 days
page 18 of 49 Grade 5
Mathematics
Unit: 02 Lesson: 01
Dad’s Day Decimal Problem KEY
Michelle and her brothers want to get their dad something really special for his
birthday. They have all put their money together and find they have $56.94.
Michelle is looking in the paper and finds the following advertisement:
Do Michelle and her brothers have enough money to buy all three of these items for
their dad’s birthday? Why or why not?
Yes, because 22 + 13 +17 = 52 and 22.39 + 12.99 + 16.55 = 51.93
©2012, TESCCC
03/21/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Dad’s Day Decimal Problem
Michelle and her brothers want to get their dad something really special for his
birthday. They have all put their money together and find they have $56.94.
Michelle is looking in the paper and finds the following advertisement:
Do Michelle and her brothers have enough money to buy all three of these items
for their dad’s birthday? Why or why not?
©2012, TESCCC
03/21/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Hundredths Grids
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Thousandths Grids Addition and Subtraction
Examples KEY
Grid 1: 0.255 + 0.245 = 0.500; 0.50; 0.5
Grid 2: 0.500 – 0.070 = 0.430; 0.43
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Thousandths Grids Addition and Subtraction
Examples
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction – Notes KEY
Addition:
0.35 + 0.28
What do you shade?
How do you record?
1
0.35
0.28
0.6 3
Add the numbers
the same as whole
numbers. Regroup
as needed.
Subtraction:
0.35 – 0.28
What do you shade?
How do you record?
21
0.35
0.28
0.0 7
©2012, TESCCC
05/14/12
Subtract the
numbers the same
as whole numbers.
Regroup as needed.
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction – Notes
Addition:
0.35 + 0.28
What do you shade?
How do you record?
Subtraction:
0.35 – 0.28
What do you shade?
©2012, TESCCC
How do you record?
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction Practice KEY
Shading on grids will vary.
Addition:
0.44 + 0.38 = 0.82
0.57 + 0.09 = 0.66
0.59 + 0.11 = 0.70 or 0.7
Subtraction:
0.44 − 0.38 = 0.06
0.57 − 0.09 = 0.48
0.59 − 0.11 = 0.48
Answers to “created” problems will vary.
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction Practice
Use these decimal numbers to shade the grid and then record the problem with the answer.
Addition:
Decimal
Numbers
Shade it.
Record it.
0.44 and 0.38
0.57 and 0.09
0.59 and 0.11
©2012, TESCCC
04/07/13
page 1 of 4
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction Practice
Subtraction:
Decimal
Numbers
Shade it.
Record it.
Take 0.44
from 0.38
Take 0.57
from 0.09
Take 0.59
from 0.11
©2012, TESCCC
04/07/13
page 2 of 4
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction Practice
Create your own decimal addition problems. Shade the grid and then record the problem with the answer.
Decimal
Numbers
©2012, TESCCC
Shade it.
04/07/13
Record it.
page 3 of 4
Grade 5
Mathematics
Unit: 02 Lesson: 01
Connecting Decimal Addition and Subtraction Practice
Create your own decimal subtraction problems. Shade the grid and then record the problem with the answer.
Decimal
Numbers
©2012, TESCCC
Shade it.
04/07/13
Record it.
page 4 of 4
Grade 5
Mathematics
Unit: 02 Lesson: 01
Adding and Subtracting Decimals with Base-Ten Blocks – Notes
Addition:
Place Value Blocks for Decimals
1 Whole (1.0)
1 Tenth (0.1) 1 Hundredth (0.01)
(1) Put the hundredths together.
Trade if necessary.
1 whole
8 hundredths
4 tenths
Trade 10
hundredths for
1 tenth.
1. 4 8
+ 3. 5 5
3 wholes
5 hundredths
5 tenths
(2) Put the tenths together.
Trade if necessary.
1 whole
1
1 whole
5 tenths
Trade 10 tenths
for 1 whole.
1
1. 4 8
+ 3. 5 5
5. 0 3
©2012, TESCCC
3 wholes
5 tenths
5 wholes
0 tenths
05/14/12
3 hundredths
page 1 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Adding and Subtracting Decimals with Base-Ten Blocks – Notes
Subtraction:
©2012, TESCCC
05/14/12
page 2 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Practice Problems KEY
(1)
(2)
(3)
(4)
(5)
(6)
3.92
3.46
6.30
2.18
0.49
1.34
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Practice Problems
Use the base-ten block diagrams to model the trades.
(1)
2. 5
+ 1. 3
5
7
(2)
1. 6
+ 1. 8
2
4
(3)
2. 7
+ 3. 5
4
6
©2012, TESCCC
05/14/12
page 1 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Practice Problems
(4)
4. 3 6
- 2. 1 8
(5)
2. 2 5
- 1. 7 6
(6)
3. 2 3
- 1. 8 9
©2012, TESCCC
05/14/12
page 2 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Place Value Window - Teacher Directions
O
1
0
1
2
3
4
5
6
7
8
9
©2012, TESCCC
3
2
0
4
1
PLACE
VALUE5 WINDOW
2
4
6
5
3
5
7
6
4
6
8
7
5
7
9
8
6
8
9
7
9
8
9
thousandths
T
hendredths
H
tenths
Run the “windows” and the number strips on cardstock and laminate before cutting out. Then,
cut out each “window” and make slits along the dotted lines. Cut out each number strip and
slide each through the slits under each place value. See sample below. These number strips
slide much easier when laminated.
05/14/12
0
1
2
3
4
5
6
7
8
9
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
O
thousandths
T
hundredths
H
tenths
Place Value Window
•
O
thousandths
T
hundredths
H
tenths
PLACE VALUE WINDOW
•
PLACE VALUE WINDOW
©2012, TESCCC
05/14/12
page 1 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Place Value Window (Number Strips)
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
©2012, TESCCC
05/14/12
page 2 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Place Value Window Prompts – Teacher Notes
“Students, use your Place Value Windows to answer the following decimal addition/subtraction questions.”
Note: It is important to give these prompts verbally to facilitate student understanding of decimal word
vocabulary. By listening and manipulating the “windows,” students’ overall place value understanding should be
enhanced.
(1)
Display 600
What is displayed behind your decimal point? (0’s' nothing, etc.)
What digit is in the tenths place? hundredths place? (0; nothing, etc.)
What is the role of the zeroes in this number? (they are place holders.)
What is the value of the 6? (six hundreds or 600)
How many tens are equivalent to 6 hundreds? (60)
How many ones are equivalent to 6 hundreds? (600)
•
•
•
•
•
•
(2)
Show me 7 tens more than 600. (670)
How do you say this number? (six hundred seventy)
What is displayed behind your decimal point? (0; nothing, etc.)
What digit is in the ones place? (0)
What digit is in the tenths place? hundredths place? thousandths place? (0; nothing, etc.)
What is the role of the zeroes in this number? (they are place holders.)
How many hundreds are there in 670? (6)
What digit is in the tens place? (7)
What is the value of that digit? (7 tens or 70)
How many tens make the number 670? (67)
What digit is in the ones place? (0)
How many ones make the number 670? (670)
•
•
•
•
•
•
•
•
•
•
•
(3)
Show me 9 ones more than 670. (679)
• How do you say this number? (six hundred seventy-nine)
• What is displayed behind your decimal point? (0; nothing, etc.)
• What digit is in the tenths place? hundredths place?, thousandths place? (0; nothing, etc.)
• What is the role of any zeroes in this number? (place holder for decimal places)
• What digit is in the hundreds place? tens place? ones place? (6, 7, 9 respectively)
• What is the value of each of those digits? (6 hundreds or 600, 7 tens or 70, 9 ones or 9),
• How many ones make the number 679? (679)
(4)
Show me 21 hundredths more than 679. (679.21)
• How do you say this number? (six hundred seventy-nine and twenty-one hundredths)
• What is the role of the word “and” in this number? (signifies the decimal point)
• What digit is displayed in the tenths place? (2)
• What is the value of that digit? (2 tenths, 20 hundredths, or 200 thousandths)
• What digit is in the hundredths place? (1)
• What is the value of the 1? (1 hundredth or 10 thousandths)
• How many tenths are in the number 679.21? (6,792)
• How many hundredths are in the number 679.21 (67,921)
• How many thousandths are in the number 679.21 (679,210)
©2012, TESCCC
05/14/12
page 1 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Place Value Window Prompts – Teacher Notes
(5)
Show me 5 thousandths more than 679.21. (679.215)
• How do you say this number? (six hundred seventy-nine and two hundred fifteen thousandths)
• What is the role of the word “and” in this number? (signifies the decimal point)
• What is displayed behind your decimal point? (215 or two hundred fifteen thousandths)
• How many tenths? hundredths, thousandths? (2, 1, and 5 respectively)
(6)
Show me 2 tenths more than 679.215. (679.415)
• How do you say this number? (six hundred seventy-nine and four hundred fifteen thousandths)
(7)
Show me 7 hundredths more than 679.415. (679.485)
• How do you say this number? (six hundred and four hundred eighty-five thousandths)
(8)
Show me 3 thousandths more than 679.415. (679.418)
How do you say this number? (six hundred seventy-nine and four hundred eighteen thousandths)
•
(9)
Show me 110 more than 679.488. (789.488)
• How do you say this number? (seven hundred eighty-nine and four hundred eighty-eight
thousandths)
(10)
Show me 1 more than 789.488 (790.488)
• How did you know to regroup? (Sample answer: Because when I moved the strip in the ones place
up one more, there was a 0 which meant “10” since 9 + 1 = 10)
• How do you say this number? (seven hundred ninety and four hundred eighty-eight thousandths)
(11)
Show me 10 more than 790.488 (800.488)
• How did you know to regroup? (Sample answer: Because when I moved the strip in the tens place
up one more, there was a 0 which meant “100” since 90 + 10 = 100)
• How do you say this number? (eight hundred and four hundred eighty-eight thousandths)
(12)
Show me 2 hundredths more than 800.488 (800.508)
• How did you know to regroup? (Sample answer: Because when I moved the strip in the hundredths
place up two more, there was a 0 which meant “0.1” since 0.08 + 0.02 = 0.10)
• How do you say this number? (eight hundred and five hundred eight thousandths)
(13)
Show me 3 thousandths more than 800.508 (800.511)
• How did you know to regroup? (Sample answer: Because when I moved the strip in the hundredths
place up three more, it would only go up two and then I had to move the strip back to the beginning
to add one more. Which brought the strip to the number “1” 8 thousands + 3 thousands = 11
thousandths.)
• How do you say this number? (eight hundred and five hundred eleven thousandths)
©2012, TESCCC
05/14/12
page 2 of 2
Grade 5
Mathematics
Unit: 02 Lesson: 01
Garden Pathway Problem Solving KEY
START
This diagram shows parts of a garden pathway with the lengths labeled in meters.
4.6 m
2.63 m
3.4 m
(1)
Estimate the total length of this pathway and explain your reasoning.
4.6 m → 5 m; 2.63 → 3 m; 3.4m →3m; 5 + 3 + 3 = 11m
(2)
What is the length of the longest part of the pathway? 4.6 m
(3)
What is the length of the shortest part of the pathway? 2.63 m
(4)
What is the total length of this pathway? How do you know?
10.63 meters; by adding all the lengths together
©2012, TESCCC
04/07/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Garden Pathway Problem Solving
START
This diagram shows parts of a garden pathway with the lengths labeled in meters.
4.6 m
2.63 m
3.4 m
(1)
Estimate the total length of this pathway and explain your reasoning.
(2)
What is the length of the longest part of the pathway?
(3)
What is the length of the longest part of the pathway?
(4)
What is the total length of this pathway? How do you know?
©2012, TESCCC
04/07/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Garden Club Mileage KEY
The map below shows where the Garden clubs are located for a region. Record a number
sentence, then add or subtract the distances necessary to answer the questions. (All distances
are in miles).
Club Flores
8
27
.61
24
.2
Kindly Holly
33.3
0
Pleasant
Petunias
Gorgeous
Geraniums
3
.4
41
.92
5
Amazing
Amaranthus
23
.5 0
8
Lillyville
Rapture
Roses
32.3
41.3
Daring
Daisies
35.73
Mumsford
.2
28
35
46.5
17.2
Berry
01
Nandina 18.
22
.8
River
Willows
.7 5
.9
28
29
27
16.401
Club Carnation
=====================================================
1.
What is the total distance from Club Carnation to Mumsford to Amazing Amarathus to Berry
Nandina? Explain your process.
16.401 + 35.73 + 41.3 = 93.431 miles; Process explanation should include
information about place value and aligning decimal points.
2.
Estimate the total distance from River Willows to Kindly Holly to Lillyville to Daring Daisies
to Rapture Roses? Explain your process.
Answers may vary. 30 + 30 + 30 + 25 = 115 miles; Process explanation should
include information about they chose what numbers to use to estimate with.
3.
List the shortest route from Club Carnation to Pleasant Petunias and record the distance in
miles.
Explain your process.
Club Carnation to Daring Daisies to Lillyville to Berry Nandina to River Willows to
Pleasant Petunias. 28.2 + 32.3 + 18.01 + 17.2 + 41.43 = 137.14 miles; Process
explanation should include info about place value and aligning decimal points.
©2012, TESCCC
04/07/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Garden Club Mileage
The map below shows where the Garden clubs are located for a region. Record a number sentence,
then add or subtract the distances necessary to answer the questions. (All distances are in miles).
Club Flores
8
27
.61
24
.2
Kindly Holly
33.3
0
Pleasant
Petunias
Gorgeous
Geraniums
3
.4
41
.92
5
Amazing
Amaranthus
23
.5 0
8
Lillyville
Rapture
Roses
32.3
41.3
Daring
Daisies
35.73
Mumsford
.2
28
35
46.5
17.2
Berry
01
Nandina 18.
22
.8
River
Willows
.7 5
.9
28
29
27
16.401
Club Carnation
=====================================================
1.
What is the total distance from Club Carnation to Mumsford to Amazing Amarathus to Berry
Nandina? Explain your process.
2.
Estimate the total distance from River Willows to Kindly Holly to Lillyville to Daring Daisies to
Rapture Roses? Explain your process.
3.
List the shortest route from Club Carnation to Pleasant Petunias and record the distance in miles.
Explain your process.
©2012, TESCCC
04/07/13
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Centimeter Grid
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Inch Grid Paper
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Exploring Perimeters
Step 1
Each partner needs to cut out 3 (centimeter or inch) grid paper rectangles of different size,
taking care to cut along the lines (carefully cutting along the lines).
Step 2
Spread out each of the 6 rectangles created and imagine that you need to make frames for the
rectangles. You need to know the perimeter. Without calculating, estimate the perimeter of each
rectangle and record your estimates in the table below.
Estimated Perimeter
Actual Perimeter
Rectangle A
Rectangle B
Rectangle C
Rectangle D
Rectangle E
Rectangle F
Step 3
Use your perimeter estimates to order the rectangles from least to greatest and record them on
the line below. Calculate the actual perimeters of the rectangles and record in the table above.
Make any adjustments to the order if needed, then record the actual perimeters from least to
greatest.
Estimate: Least -------------------------------------------------------------------→Greatest
Actual: ________
________
________
________
________
________
Step 4
Summarize how to find perimeter.
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Perimeter Plans KEY
The diagram below shows the drawings for two decks a builder plans to construct.
8 ft
Lower Deck
Upper Deck
8 ft
4 ft
17 ft.
(1)
Estimate the perimeters of each model and explain your reasoning.
Possible Answer: Lower Deck 20 + 20 + 10 + 10 = 60 feet if rounding
15 + 15 + 10 + 10 = 50 feet or 30 + 16 = 46 feet if using compatible numbers
Possible Answer: Upper Deck 10 + 10 + 4 + 4 = 28 feet if rounding
8 + 8 + 5 + 5 = 26 feet if using compatible numbers
(2)
Calculate the actual perimeters of each deck and their combined perimeters. Show your
work.
Lower Deck 17 + 17 + 8 + 8 = 50 feet;
Upper Deck 8 + 8 + 4 + 4 = 24 feet
50 + 24 = 74 feet
(3)
What is the difference between the perimeters of the two decks? How do you know?
26 ft because 50 – 24 = 26 feet
The diagram below shows the sizes of two photos a magazine editor plans to use.
(4)
Estimate the perimeter of each photo above and explain your reasoning.
Possible Answer: Photo A: 3 + 4 + 3 + 4 = 14 cm; Photo B: 1 + 1 + 3 + 3 = 8 cm
(5)
What is the perimeter of each photo above? Explain your process.
Photo A: 3.7 + 3.7 + 2.5 + 2.5 = 12.4 cm
Photo B: 1.3 + 1.3 + 2.5 + 2.5 = 7.6 cm
Sample Answer: Aligned decimals to add opposite sides
(6)
How much larger is the perimeter of Photo A than Photo B? How do you know?
12.4 – 7.6 = 4.8 cm
Sample Answer: Aligned decimals to find the difference between the two
perimeters.
©2012, TESCCC
05/14/12
page 1 of 1
Grade 5
Mathematics
Unit: 02 Lesson: 01
Perimeter Plans
The diagram below shows the drawings for two decks a builder plans to construct.
8 ft
Lower Deck
Upper Deck
8 ft
4 ft
17 ft.
(1)
Estimate the perimeters of each model and explain your reasoning.
(2)
Calculate the actual perimeters of each deck and their combined perimeters. Show your
work.
(3)
What is the difference between the perimeters of the two decks? How do you know?
The diagram below shows the sizes of two photos a magazine editor plans to use.
(4)
Estimate the perimeter of each photo above and explain your reasoning.
(5)
What is the perimeter of each photo above? Explain your process.
Photo A:
Photo B:
(6)
How much larger is the perimeter of Photo A than Photo B? How do you know?
©2012, TESCCC
05/14/12
page 1 of 1