Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Unit 07:
Fractions (17 days)
Possible Lesson 01 (7 days)
Possible Lesson 02 (5 days)
Possible Lesson 03 (5 days)
POSSIBLE LESSON 03 (5 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 fraction strips to model and create pictorial representations of addition and subtraction situations involving fractions. The resulting sums and differences are
evaluated to determine if they can be simplified or renamed.
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:
5.3E
Model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures,
words, and numbers. Supporting 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:
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
5.14A
Identify the mathematics in everyday situations.
5.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
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):
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Grade5 Mathematics Unit07 PI03
Estimate fractional values, using benchmarks, to determine a reasonable answer to a real-life situation. Determine the actual solution to a real-life situation involving fractional
values, and justify the solution by comparing it to the estimated solution. Label your solution with appropriate units.
Sample Performance Indicator:
Jerry is building a fence around a triangular garden as shown below.
Use benchmarks to estimate the amount of fencing that Jerry should purchase. Then, determine the exact amount of fencing needed to enclose the garden justifying all steps of
the solution process. Does your estimate allow for enough fencing? If your estimate was not enough, how much more fencing will he need? If your estimate was enough, how
much fencing will be left over? Justify your reasoning and label all answers appropriately.
Standard(s): 5.3E , 5.14A , 5.14D , 5.15A , 5.15B , 5.16B
ELPS ELPS.c.1E , ELPS.c.5F
Key Understanding(s):
Real-life situations involving whole numbers and fractions can be estimated by comparing each fraction to the nearest whole number and then finding the sum or
difference of the estimated whole numbers or comparing each fractional part to 0,
, or 1 and then finding the sum or difference of the whole numbers and/or
fractions.
Real-life situations involving fractions can be estimated and the approximation can be used to justify if the actual solution is reasonable.
When adding or subtracting fractions with like denominators, the resulting numerator reflects the number of parts of the common denominator.
The value of two fractional quantities involving like denominators in addition or subtraction situations can be solved and justified using a variety of methods such as
concrete objects, pictorial models, and algebraic methods.
Misconception(s):
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Some students may think that when you add two fractions, you add the two numerators together and then you add two denominators together.
Some students may think that you round only the fractional part of the mixed number and think that the rounded fraction part is the answer, forgetting to include
the whole number part(s) of the mixed numbers when rounding mixed numbers.
Some students may think you add the whole numbers only and completely disregard the fractions, or vice versa, when adding mixed numbers.
Vocabulary of Instruction:
common denominator
Materials List:
dry-erase marker (1 per student)
Fraction Strips (1 set per student, 1 set per teacher) (previously created)
math journal (1 per student)
whiteboard (student sized) (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.
Rainfall Problem KEY
Rainfall Problem
Fraction Addition Notes and Practice KEY
Fraction Addition Notes and Practice
Invitation Problem KEY
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Unit 07:
Suggested Duration: 5 days
Invitation Problem
Cupcake Problem KEY
Cupcake Problem
Fraction Subtraction Notes and Practice KEY
Fraction Subtraction Notes and Practice
Picturing Addition and Subtraction of Like Fractions KEY
Picturing Addition and Subtraction of Like Fractions
Fraction Estimation Number Line KEY
Fraction Estimation Number Line
Fraction Estimation Notes and Practice KEY
Fraction Estimation Notes and Practice
Estimating Fraction Sums Notes and Practice KEY
Estimating Fraction Sums Notes and Practice
Estimating Fraction Differences Notes and Practice KEY
Estimating Fraction Differences Notes and Practice
Fraction Sum/Difference Estimation Evaluation KEY
Fraction Sum/Difference Estimation Evaluation
Career Choices Graph KEY
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Career Choices Graph
I Like This Egg Best Data Table
I Like This Egg Best Blank Graph
I Like This Egg Best Evaluation KEY
I Like This Egg Best Evaluation
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
Common denominators
Engage 1
Students use logic and reasoning skills to discuss the meaning of a common denominator.
MATERIALS
math journal (1 per student)
Instructional Procedures:
1. Display the words “like,” “common,” and “common denominator” for the class to see. Instruct
students to record the terms and definitions for “like” and “common” in their math journal.
Ask:
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Unit 07:
Suggested Duration: 5 days
Notes for Teacher
How would you define the words “like” and “common”? Answers may vary. Like –
similar or alike, Common – sharing something; etc.
What is meant by the terms “like or common denominators”? Answers may vary. The
denominators are the same; etc.
Explain to students that the terms “like denominators and common denominators” describe
denominators that are the same.
2. Facilitate a class discussion about situations in which students have added or subtracted
fractions.
Ask:
When have you ever needed to add or subtract fractions? Answers may vary. When
using money; buying produce or candy; etc.
How does adding and subtracting fractions differ from adding and subtracting whole
numbers? Answers may vary. When we add and subtract fractions, we are adding parts of
whole numbers; we do not have to worry about the numerator and denominator when we add or
subtract whole numbers; etc.
Topics:
Modeling addition of fractions using fraction strips
ATTACHMENTS
Teacher Resource: Rainfall Problem KEY
(1 per teacher)
Explore/Explain 1
Handout (optional): Rainfall Problem (1
Students use fraction strips to model addition of fractions.
per student)
Teacher Resource: Rainfall Problem (1
page 7 of 67 Grade 5/Mathematics
Unit 07:
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Enhanced Instructional Transition Guide
Suggested
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Notes for Teacher
Instructional Procedures:
per teacher)
1. Distribute a set of Fraction Strips, whiteboard, and dry-erase marker to each student. Instruct
students to select the “one whole” strip and predict the number of strips that can be placed
underneath it without extending or overlapping. Allow time for students to complete the activity.
Teacher Resource: Fraction Addition
Notes and Practice KEY (1 per teacher)
Handout: Fraction Addition Notes and
Practice (1 per student)
2. Using a set of Fraction Strips, demonstrate this process for the class to see.
Ask:
How many
The five
MATERIALS
strips were you able to place under the one whole? (5)
Fraction Strips (1 set per student, 1 set per
teacher) (previously created in Unit 07
strips represent what fraction? ( )
Lesson 01 Explore/Explain 1)
What kind of a fraction is
? How do you know? (Improper, because the numerator is
dry-erase marker (1 per student)
equal to the denominator.)
What whole number is equal to
whiteboard (student sized) (1 per student)
? How do you know? (1) Answers may vary.
5 divided by 5, which is equal to 1; the fraction strip model shows that
means
math journal (1 per student)
is equal to; if a whole
is cut into 5 parts and you have all five, it’s the same as a whole; etc.
TEACHER NOTE
For students who may think that when you add
3. Instruct students to use their set of Fraction Strips to create as many addition equations as
possible to show how many fifths are in
whiteboard or in their math journal.
, and record their models and equations on their
two fractions, you add the two numerators
together and then you add the two denominators
together, provide opportunities for additional
practice with fraction strips and similar addition
page 8 of 67 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 07:
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Suggested Instructional Procedures
Notes for Teacher
problems until they see that when adding like
fractions, the sum of the numerators is always
written over the original denominator.
TEACHER NOTE
Remind students that they do not need to limit themselves to 2 addends.
Students should understand why fractions with
like denominators can be added by adding only
Allow time for students to create several addition sentences. (There should be 5 x 4 x 3 x 2 x 1,
possible addition equations.) Monitor and assess students to check for understanding. Facilitate
a class discussion about the activity.
Ask:
the numerators. Because like fractions have
denominators that name the same fractional part,
the numerators count identical units. When adding
fractions, the denominators are left alone because
they identify the parts that are being combined,
How many addition sentences did you find? Answers may vary. There are several ways to
and just the numerators are added.
create this addition sentence; etc.
Do you notice a pattern in the numerators and denominators of the addition
TEACHER NOTE
sentences you created? Explain. (yes) Answers may vary. The numerator is the sum of the
It may be necessary for students to simplify
numerators’ addends and the denominator stays the same; etc.
several times to begin to look for the greatest
Why doesn’t the denominator change when adding these like fractions? Answers may
divisor. Allow students time to discover this
vary. The denominator represents the number of parts the whole is divided into and the whole
concept.
is divided into the same number of parts: 5; You are adding one-fifth pieces together, so one
one-fifth piece and 4 more one-fifth pieces gives you five one-fifth pieces, etc.
4. Display the table and first question from teacher resource: Rainfall Problem.
Ex:
TEACHER NOTE
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5. Place students in pairs. Instruct student pairs to solve the problem situation and record their
solution process on their whiteboard or in their math journal. Remind students that they may use
their set of Fraction Strips, if needed. Allow time for students to complete the activity. Monitor and
assess students to check for understanding. Facilitate a class discussion to debrief student
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
Some students struggle with the term “reduced”
when referring to fractions. Using the term
“simplify” instead of “reduced” may prevent some
misconceptions.
solutions.
Ask:
Which fraction pieces could you use to model this problem? (eighths and the one whole)
What would your model look like?
Can you simplify
? How do you know? (Yes, four-eighths can be simplified to one-half.)
Answers may vary. I know this because both the numerator and denominator of the fraction
are even and therefore divisible by 2; both the numerator and denominator are divisible by 4;
etc.
Could you use your fraction strips to prove that you have the sum of the fractions in
simplest form? Explain. (yes) Answers may vary. I could find a fraction strip that is
equivalent to the sum of the strips we have now; etc.
6. Instruct students to find one strip from their set of Fraction Strips that has one piece equivalent to
page 10 of 67 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
the sum of the four one-eighth strips, and to line that strip up underneath the others as proof that
they have simplified the fraction correctly. Allow time for students to complete the activity. Monitor
and assess students to check for understanding.
7. Display the second question from the displayed teacher resource: Rainfall Problem. Instruct
student pairs to solve the problem situation and record their solution process on their whiteboard
or in their math journal. Remind students that they may use their set of Fraction Strips, if needed.
Allow time for students to complete the activity. Monitor and assess students to check for
understanding. Facilitate a class discussion to debrief student solutions.
Ask:
Would you use the same fraction strips to model this problem? Explain. (yes) Answers
may vary. All of the rainfall amounts are in eighths of an inch; etc.
What would your model look like?
How is this addition model different from the previous addition model? Answers may
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Unit 07:
Suggested Duration: 5 days
Notes for Teacher
vary. The number of eighth pieces is greater than the one whole strip; the model shows that
the sum of the fractions results in an improper fraction or a mixed number because the pieces
are more than 8; etc.
What mixed number is equivalent to this improper fraction? (
)
8. Display the third question from the displayed teacher resource: Rainfall Problem. Instruct
student pairs to solve the problem situation and record their solution process on their whiteboard
or in their math journal. Remind students that they may use their set of Fraction Strips, if needed.
Allow time for students to complete the activity. Monitor and assess students to check for
understanding. Facilitate a class discussion to debrief student solutions.
Ask:
How does this last question change your model? Answers may vary. It will have one more
eighth strip added; etc.
How many eighths of rainfall does your model show? (10)
What is the equivalent mixed number for this improper fraction? (
)
Can the fraction in this mixed number be simplified? How do you know? (yes) Answers
page 12 of 67 Grade 5/Mathematics
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Enhanced Instructional Transition Guide
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Notes for Teacher
may vary. Both the numerator and the denominator are even and therefore divisible by 2; a
one-fourth fraction strip is equivalent to the two one-eighth strips; etc.
9. Instruct students to use their set of Fraction Strips to show that
is equivalent to . Allow time
for students to complete the activity. Monitor and assess students to check for understanding.
Facilitate a class discussion to debrief student solutions.
What is the simplified equivalent mixed number for this improper fraction? (
)
10. Distribute handout: Fraction Addition Notes and Practice to each student as independent
practice or homework.
2
Topics:
Spiraling Review
Modeling subtraction of fractions using fraction strips
Explore/Explain 2
Students use fraction strips to model subtraction of fractions.
ATTACHMENTS
Teacher Resource: Invitation Problem
KEY (1 per teacher)
Instructional Procedures:
Teacher Resource: Invitation Problem (1
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Suggested Instructional Procedures
1. Facilitate a class discussion to debrief and discuss the previously assigned handout: Fraction
Addition Notes and Practice.
by folding the strip so only 5 one-eighth pieces show.
Teacher Resource: Cupcake Problem
Teacher Resource: Cupcake Problem (1
per teacher)
Teacher Resource: Fraction Subtraction
Ask:
How could you use this strip to represent
per teacher)
KEY (1 per teacher)
2. Distribute a set of Fraction Strips to each student. Instruct students to use their set of Fraction
Strips to model
Notes for Teacher
Notes and Practice KEY (1 per teacher)
minus
? Answers may vary. I could remove
Handout: Fraction Subtraction Notes and
Practice (1 per student)
or cover two of the eighth strips to represent taking them away; etc.
Teacher Resource (optional): Picturing
Addition and Subtraction of Like
3. Instruct students to cover two of the eighth strips on their Fraction Strip model.
Ask:
How many one-eighth pieces are left? (3)
What do they represent? (The difference between five one-eighth pieces and two one-eighth
Fractions KEY (1 per teacher)
Handout (optional): Picturing Addition
and Subtraction of Like Fractions (1 per
student)
pieces.)
Instruct students to record the fraction subtraction problem they have just modeled in their math
journals.
MATERIALS
Fraction Strips (1 set per student, 1 set per
teacher) (previously created)
math journal (1 per student)
whiteboard (student sized) (1 per student)
dry erase marker (1 per student)
Explain to students the importance of drawing the entire whole, even the portion not used in the
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Suggested Instructional Procedures
problem situation. It is just another reminder that they are working with parts of a whole even if
they are not using all of the parts.
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
TEACHER NOTE
For students who struggle with adding and/or
4. Display teacher resource: Invitation Problem.
subtracting fractions, the use of a part-part-whole
5. Place students in pairs. Instruct student pairs to use their Fraction Strips to solve the problem
box may help. Example:
situation and record their solution process on their whiteboard or in their math journal. Allow time
for students to complete the activity. Monitor and assess students to check for understanding.
Facilitate a class discussion to debrief student solutions.
Ask:
page 15 of 67 Enhanced Instructional Transition Guide
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Which fraction strips did you use? Explain. Answers may vary. The whole strip and the
one-sixth strip because the fraction of the sheet of paper used was four-sixths.
How many of the sixth strips represent the whole sheet of paper? (6)
How many of the sixth strips represent the fraction of the paper that was used? (4)
Notes for Teacher
Using a part-part-whole box can help organize
information in the problem and allow students to
see all of the fractions. You can see that
of the
How many parts are left? (2) What fraction of the sheet of paper was left? ( )
cupcakes have been eaten because (5 out of 12) +
Is this fraction in simplest form? Explain. (no) Answers may vary. Both the numerator and
(3 out of 12) is (8 out of 12). Therefore, 4 out of 12
denominator are even numbers which means 2 is a factor; because there is one fraction strip
or
equal to two-sixths; etc.
What is this fraction in simplest form? (
of the cupcakes remain because 12 – 8 =
4. The parts must add up to the whole.
)
State Resources
MSTAR Math Academy 5-6: Addition &
Subtraction of Fractions Activities A, B, C,
6. Display teacher resource: Cupcake Problem. Instruct student pairs to use their Fraction Strips
E, & F
to solve the problem situation. Allow time for students to complete the activity. Monitor and
TEXTEAMS: Rethinking Elementary
assess students to check for understanding. Facilitate a class discussion to debrief student
Mathematics Part I: Wipe Out ONE! Task
solutions.
Card
Ask:
page 16 of 67 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
Which fraction strips did you use? Explain. Answers may vary. The whole strip and the
ADDITIONAL PRACTICE
strips because the fraction of the cupcakes eaten is expressed in twelfths; etc.
How many of the twelfths strips represent the total amount of cupcakes? (12)
How did you determine the fraction of cupcakes she ate all together? (added the two
fractional amounts eaten:
and
equals
)
Handout (optional): Picturing Addition and
Subtraction of Like Fractions may be used as
additional practice.
Was this sum in simplest form? How do you know? (No; because the numerator and
denominator of
are both even and therefore divisible by 2; both 8 and 12 are divisible by
4; The simplest form of
is
; etc.)
How can you determine the fraction of cupcakes remaining? (Cover or cross off 8 of the
one-twelfth pieces.)
How many pieces are left? (4)
What is the fraction of cupcakes that remain? (
)
Is this fraction in simplest form? Explain. (no) Answers may vary. Both the numerator and
denominator are even numbers, which means 2 is a factor; four can be used to simplify the
fraction; etc.
7. Demonstrate this process for the class to see, using 2 as a factor.
÷ =
Ask:
Is this fraction in its simplest form? Explain. (no) Answers may vary. There is a fraction
page 17 of 67 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
strip equal to two-sixths; Two is a factor of 2 and 6; etc.
8. Demonstrate this process for the class to see, using 2 as a factor.
÷ =
Ask:
Is this fraction in its simplest form? Explain. (Yes, because the numerator is 1.)
Explain to students that using 2 as a factor helped simplify
. However, if 4 was used instead of
2, it would only take 1 step instead of 2 steps.
9. Display the following for the class to see.
÷ =
Ask:
What do you notice about the two numerators in the problem? (They are the same or
they are both fours.)
10. Explain to students that when simplifying fractions, it is helpful to look at the numerator to see if
the numerator is a factor of the denominator. For example, the numerator is 4 in the fraction
and 12 is a multiple of 4.
Ask:
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Unit 07:
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Suggested Instructional Procedures
Notes for Teacher
What is this fraction in simplest form? ( )
11. Distribute handout: Fraction Subtraction Notes and Practice to each student as independent
practice or homework.
3
Topics:
Spiraling Review
Estimating fraction sums and differences
Explore/Explain 3
Students use prior knowledge and models to estimate fraction sums and differences.
ATTACHMENTS
Teacher Resource: Fraction Estimation
Number Line KEY (1 per teacher)
Instructional Procedures:
1. Facilitate a class discussion to debrief and discuss the previously assigned handout: Fraction
Subtraction Notes and Practice.
2. Display teacher resource: Fraction Estimation Number Line. Explain to students that a number
line is useful when estimating to determine whether fractions are closer to 0, , or 1.
Teacher Resource: Fraction Estimation
Number Line (1 per teacher)
Handout: Fraction Estimation Number
Line (1 per student)
Teacher Resource: Fraction Estimation
Notes and Practice KEY (1 per teacher)
Handout: Fraction Estimation Notes and
3. Display the following fractions for the class to see:
Practice (1 per student)
Teacher Resource: Estimating Fraction
Sums Notes and Practice KEY (1 per
4. Distribute handout: Fraction Estimation Number Line to each student. Place students in pairs.
teacher)
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Enhanced Instructional Transition Guide
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Notes for Teacher
Instruct student pairs to determine whether each of the displayed fractions is closer to 0,
, or 1.
Notes and Practice (1 per student)
Remind students that they do not have to find the actual placement of each fraction on the
number line; however, they should write each fraction under the 0,
Handout: Estimating Fraction Sums
Teacher Resource: Estimating Fraction
, or 1 on their handout to
Differences Notes and Practice KEY (1
show which benchmark each fraction is closer to. Encourage students to use the fraction number
per teacher)
line rules to determine the connection between a fraction’s place on the number line and the
Handout: Estimating Fraction
relationship of its numerator to its denominator. Allow time for students to determine where each
Differences Notes and Practice (1 per
fraction belongs. Monitor and assess student pairs to check for understanding. Facilitate a class
student)
discussion to debrief student solutions.
Ask:
MATERIALS
How is estimating with fractions like estimating with whole numbers? Answers may
math journal (1 per student)
vary. With whole numbers and with fractions, you are always trying to determine how close or
far away the number is from the given benchmarks; etc.
How is estimating with fractions different than estimating with whole numbers?
Answers may vary. The benchmarks are different; with these fractions the benchmarks are 0,
, or 1, whereas with whole numbers, the benchmarks can be any set of whole numbers
TEACHER NOTE
Some students may think you add the whole
numbers only and will completely disregard the
depending on the place value to which you are estimating. With fractions you have to look at
fractions or vice versa when adding mixed
the numerator and denominator and with whole numbers, you compare the place value of the
numbers. Other students may add the mixed
digits in the numbers; etc.
numbers and then count each fraction as one
whole without considering how close or far away
When you estimate with mixed numbers, could you use the same rules as with
fractions? Explain. Answers may vary. Yes and no; You can use the rules for the fraction
,
from one each fractional part actually is. These
students will need to work with a number line more
but the benchmarks would change since you are no longer looking for numbers close to 0.
to further the concept of fraction estimation.
With mixed numbers, the whole numbers under consideration would dictate the benchmarks
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
to be used; etc.
5. Display the mixed number
for the class to see.
Ask:
Between which 2 whole numbers does this mixed number fall? (between 4 and 5)
If you were to make a number line from 4 to 5, where would 4
fall? (halfway between
the 4 and the 5)
6. Draw a number line to show the whole numbers 4 and 5, and record
in the middle of the
number line. Instruct students to replicate the model in their math journal.
7. Instruct students to consider the benchmarks on the number line to determine which is the
closest benchmark to
.
Ask:
Is the numerator (2) much less than half the denominator (5)? (No, half of 5 is 2.5, so it
is fairly close to half.)
Is the value of the numerator about the same as the value of the denominator?
Explain. (No, 2 is not about the same as 5.)
Is the numerator about half the denominator? (Yes, 2 is close to 2.5.)
page 21 of 67 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
Explain to students that by asking yourself the “fraction rounding rules,” the closest benchmark
can be found. For example in the fraction
which means
Which is
is closest to
closest to,
, the numerator 2 is about half of the denominator 5,
.
or 5? (
)
8. Distribute handout: Fraction Estimation Notes and Practice to each student. Instruct students
to complete the handout independently. Allow time for students to complete the activity. Monitor
and assess students to check for understanding. Facilitate a class discussion to debrief student
solutions, if time allows.
9. Distribute handout: Estimating Fraction Sums Notes and Practice to each student.
10. Display teacher resource: Estimating Fraction Sums Notes and Practice. Facilitate a class
discussion about how to estimate fraction sums.
11. Instruct students to complete handout: Estimating Fraction Differences Notes and Practice
as independent practice or homework.
4 – 5
Topics:
Spiraling Review
Applying addition and subtraction of fractions in real-life problem situations
Elaborate 1
Students use prior knowledge and models to add and subtract fractions in real-life problem situations.
ATTACHMENTS
Teacher Resource: Fraction
Sum/Difference Estimation Evaluation
page 22 of 67 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Suggested Instructional Procedures
Instructional Procedures:
1. Facilitate a class discussion to debrief and discuss the previously assigned handout: Estimating
Fraction Differences Notes and Practice.
2. Distribute handout: Fraction Sum/Difference Estimation Evaluation to each student. Instruct
Notes for Teacher
KEY (1 per teacher)
Handout: Fraction Sum/Difference
Estimation Evaluation (1 per student)
Teacher Resource: Career Choices
Graph KEY (1 per teacher)
students to complete the handout. Allow time for students to complete the activity. Monitor and
Teacher Resource: Career Choices
assess students to check for understanding. Facilitate a class discussion to debrief student
Graph (1 per teacher)
solutions.
Handout: I Like This Egg Best Data
3. Display teacher resource: Career Choices Graph. Place students in pairs. Instruct student pairs
to record their solution process for each problem in their math journal. Allow time for students to
complete the activity. Monitor and assess students to check for understanding. Facilitate a class
discussion to debrief student solutions.
Ask:
Table (1 per student)
Teacher Resource: I Like This Egg Best
Data Table (1 per teacher)
Handout: I Like This Egg Best Blank
Graph (1 per student)
Teacher Resource: I Like This Egg Best
Why is it important to know the total student responses for the class? Answers may
Evaluation KEY (1 per teacher)
vary. The total responses represent the whole class, and if we know the total, we’ll know “out
Handout: I Like This Egg Best Evaluation
of how many” when we are considering the parts; etc.
(1 per student)
What part of the fraction does the total student responses represent? (the denominator)
What part of the graph might the numerator represent? (the number of students who
chose a particular career)
What operation does the word “or” indicate when asking which fraction of the class
MATERIALS
math journal (1 per student)
want to be doctors or lawyers? (addition)
4. Display teacher resource: I Like This Egg Best Data Table. Explain to students that they will be
using this table to gather class data on the type of eggs the students in the class like best. Name
TEACHER NOTE
Students are introduced to bar graphs in Grade 2
page 23 of 67 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
the possible choices and explain that each student can only choose and vote for one choice.
(2.11A). Having students use class data to create
Instruct students to raise their hands when the type of egg they like best is called out. Announce
a graph and describe the fractional amounts
each type of egg and record the number of students who prefer that type of egg. There is always a
generated is merely an instructional reminder of
possibility that some students will not like any type of egg listed; these students will fall under the
the myriad of ways fractions can be used. In this
“no opinion” category.
case, it is used to describe meaningful, real-life
5. Distribute handout: I Like This Egg Best Data Table to each student. Instruct students to record
classroom data.
the class data in the table.
6. Distribute handout: I Like This Egg Best Blank Graph to each student. Instruct student pairs to
create a bar graph in the space provided using the class data. Remind students that bar graphs
can be either vertical or horizontal. Monitor and assess students to check for understanding.
7. Distribute handout: I Like This Egg Best Evaluation to each student. Instruct students to use
the data from their handout: I Like This Egg Best Data Table to independently complete the
handout. Remind students that the “Fraction Process” column should show the operation used to
page 24 of 67 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
find their answer, as well as any simplifying that may need to be done. Allow time for students to
complete the activity. Monitor and assess students to check for understanding. Facilitate a class
discussion to debrief student solutions, as needed.
5
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Performance Indicator(s):
page 25 of 67 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
Notes for Teacher
Grade5 Mathematics Unit07 PI03
Estimate fractional values, using benchmarks, to determine a reasonable answer to a real-life situation.
Determine the actual solution to a real-life situation involving fractional values, and justify the solution by
comparing it to the estimated solution. Label your solution with appropriate units.
Sample Performance Indicator:
Jerry is building a fence around a triangular garden as shown below.
Use benchmarks to estimate the amount of fencing that Jerry should purchase. Then, determine the
exact amount of fencing needed to enclose the garden justifying all steps of the solution process. Does
your estimate allow for enough fencing? If your estimate was not enough, how much more fencing will
he need? If your estimate was enough, how much fencing will be left over? Justify your reasoning and
label all answers appropriately.
Standard(s): 5.3E , 5.14A , 5.14D , 5.15A , 5.15B , 5.16B
ELPS ELPS.c.1E , ELPS.c.5F
04/12/13
page 26 of 67 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 07:
Suggested Duration: 5 days
page 27 of 67 Grade 5
Mathematics
Unit: 07 Lesson: 03
Rainfall Problem KEY
For a science project, Megan recorded the amount of
rainfall each day. She used the table below to collect
the information:
Rainfall
(in inches)
Day
1
8
3
8
5
8
1
8
Sunday
Monday
Tuesday
Wednesday
 How much rain fell on Sunday and Monday?
1 + 3 = 4 = 1 inch of rainfall
8
8
8
2
 How much rain fell on Sunday, Monday, and Tuesday?
1 + 3 + 5 = 9 = 11
8
8
8
8
8
inches of rainfall
 How much rain fell on all four days?
1 + 3 + 5 + 1
10
2
1 inches of rainfall
=
8
8
8
8
8 = 18 = 14
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Rainfall Problem
For a science project, Megan recorded the amount of
rainfall each day. She used the table below to collect
the information:
Rainfall
(in inches)
Day
1
8
3
8
5
8
1
8
Sunday
Monday
Tuesday
Wednesday
 How much rain fell on Sunday and Monday?
 How much rain fell on Sunday, Monday, and Tuesday?
 How much rain fell on all four days?
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Addition Notes and Practice KEY
You can use models to add fractions.
1
5
Add and .
8
8
(1)
Use the denominators to
determine how many equal
parts the model should be spit
into. Model by shading one of
the eighths.
1
8
(2)
Add five-eighths by shading
5 more of the parts.
(3)
Write the sum in simplest form.
1
5
6
+
=
8
8
8
3
2
6
=
÷
4
2
8
3
1
of an hour at the beginning of practice and
of an hour at the
6
6
end of practice. How long did Kayla’s tennis team spend running drills at practice?
Kayla’s tennis team ran drills for
(1)
Use the model below to help you add the fractions. Explain your model.
3
6
+
1
6
=
4
6
Sample answer: I can divide the rectangle into 6 equal parts and shade 3 and then 1 of the
parts to model the problem.
(2)
Show how to write the sum in simplest form.
4
2
2
÷
=
6
2
3
(3)
How long did Kayla’s tennis team spend running drills at practice?
2
of an hour
3
©2012, TESCCC
04/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Addition Notes and Practice KEY
There were 10 bowling pins standing before Paul took his turn. He knocked down three pins on his
first turn and then five pins on his second turn. What fraction of the pins did Paul knock down in his
two turns?
(1)
Use the model below to help you add the fractions. Explain your model.
3
10
+
5
10
=
8
10
I can divide the rectangle into 10 equal parts and shade 3 and then 5 of the parts to model
the problem.
(2)
Show how to write the sum in simplest form.
4
8
2
÷
=
10
2
5
(3)
What fraction of the pins did Paul knock down in his two turns?
4
of the pins
5
======================================================================
3
Jake swims every day. One day he swam
of a mile in ten minutes. On the second day, he swam
7
the same distance in 11 minutes. On the third day, he swam the same distance in 10.5 minutes.
How far did Jake swim altogether?
(1)
Use the model below to help you add the fractions. Explain your model.
3
7
+
3
7
+
3
7
=
9
7
I can divide the rectangle into 7 equal parts and shade 3 and then 3 more of the part. Then, I
only have one part left of the whole and need to add two more equal parts to make 3 more
sevenths.
(2)
Show how to write the sum as a mixed number.
9 = 1 2 of a mile
7
7
(3)
How far did Jake swim on all three days all together?
1 2 of a mile
7
©2012, TESCCC
04/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Addition Notes and Practice
You can use models to add fractions.
1
5
Add and .
8
8
(1)
Use the denominators to
determine how many equal
parts the model should be spit
into. Model by shading one of
the eighths.
1
8
(2)
Add five-eighths by shading
5 more of the parts.
(3)
Write the sum in simplest form.
1
6
5
=
+
8
8
8
3
2
6
=
÷
4
2
8
3
1
of an hour at the beginning of practice and
of an hour at the
6
6
end of practice. How long did Kayla’s tennis team spend running drills at practice?
Kayla’s tennis team ran drills for
(1)
Use the model below to help you add the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the sum in simplest form.
(3)
How long did Kayla’s tennis team spend running drills at practice?
©2012, TESCCC
04/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Addition Notes and Practice
There were 10 bowling pins standing before Paul took his turn. He knocked down three pins on
his first turn and then five pins on his second turn. What fraction of the pins did Paul knock down
in his two turns?
(1)
Use the model below to help you add the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the sum in simplest form.
(3)
What fraction of the pins did Paul knock down in his two turns?
=======================================================================
3
Jake swims every day. One day he swam
of a mile in ten minutes. On the second day he swam
7
the same distance in 11 minutes. On the third day he swam the same distance in 10.5 minutes.
How far did Jake swim altogether?
(1)
Use the model below to help you add the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the sum as a mixed number.
(3)
How far did Jake swim on all three days all together?
©2012, TESCCC
04/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Invitation Problem KEY
Martha folded a sheet of paper
into six sections to create
invitations for a sleepover. She
cut out 4 of the sections to
decorate and send to friends.
What fraction of the paper did
Martha not use for the invitations?
Draw a representation and justify
your answer.
Representations may vary.
Martha used four out of the six sections of paper for
invitations leaving two out of the six sections not
used for invitations.
2 1
or
6 3
of the sheet of paper not
used.
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Invitation Problem
Martha folded a sheet of paper
into six sections to create
invitations for a sleepover. She
cut out 4 of the sections to
decorate and send to friends.
What fraction of the paper did
Martha not use for the invitations?
Draw a representation and justify
your answer.
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Cupcake Problem KEY
Jen ate 5 of her cupcakes on
12
Monday and 3 of her cupcakes on
12
Tuesday.
 What fraction of her cupcakes did
she eat all together?
One whole
1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12
5
12
+
3
8 4
2
12 = 12 ÷ 4 = 3
 What fraction of her cupcakes
remains?
One whole
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
4
1
12 - 8 = 4
÷
=
12 12
12
4
3
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Cupcake Problem
Jen ate 5 of her cupcakes on
12
Monday and 3 of her cupcakes on
12
Tuesday.
 What fraction of her cupcakes did
she eat all together?
 What fraction of her cupcakes
remains?
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Subtraction Notes and Practice KEY
You can use models to subtract fractions.
3
5
Subtract 8 from 8 .
(1)
Use the denominators to
determine how many equal
parts the model should be split
into. Model by shading five of
the eighths.
5
8
(2)
Subtract three-eighths by
crossing out 3 of the shaded
parts.
5
8
3
2
=
8
8
(3)
Write the difference in simplest
form.
2
2
1
÷
=
8
2
4
4
2
of the pieces one day and
of the puzzle
6
6
pieces the next day. How much more of the puzzle did Shondra do on the first day than on the
second day?
Shondra is working on a puzzle. She placed
(1)
Use the model below to help you subtract the fractions. Explain your model.
4
2
2
=
6
6
6
I can divide the rectangle into 6 equal parts and shade 4 of them. Then I cross out 2
parts to model the problem.
(2)
Show how to write the difference in simplest form.
2
2
1
÷
=
6
2
3
(3)
How much more of the puzzle did Shondra do on the first day than on the second day?
1 more of the puzzle
3
©2012, TESCCC
09/15/12
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Subtraction Notes and Practice KEY
Stan had a glass filled with
3
1
cup of apple juice. He drank
cup of the juice. How much juice
4
4
was left in Stan’s glass?
(1)
Use the model below to help you subtract the fractions. Explain your model.
3
1
2
=
4
4
4
I can divide the rectangle into 4 equal parts and shade 3 of them and then cross out 1
part to model the problem.
(2)
Show how to write the difference in simplest form.
2
2
1
÷
=
4
2
2
(3) How much juice was left in Stan’s glass?
1
cup
2
======================================================================
7
2
Cassie’s mom left
of a peach pie for Cassie and her dad. Cassie ate
of the pie and her
8
8
3
dad ate
of the pie. How much pie was left after Cassie and her dad ate?
8
(1)
Use the model below to help you subtract the fractions. Explain your model.
7
8
-
2
8
-
3
8
=
2
8
I can divide the rectangle into 8 equal parts and shade 7. Then I cross out 2 parts and
then 3 parts to model the problem.
(2)
Show how to write the difference in simplest form.
2
2
1
÷
=
8
2
4
(3)
How much pie was left after Cassie and her dad ate?
1 pie
4
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Subtraction Notes and Practice
You can use models to subtract fractions.
3
5
Subtract 8 from 8 .
(1)
Use the denominators to
determine how many equal
parts the model should be split
into. Model by shading five of
the eighths.
5
8
(2)
Subtract three-eighths by
crossing out 3 of the shaded
parts.
5
8
3
2
=
8
8
(3)
Write the difference in simplest
form.
2
2
1
÷
=
8
2
4
4
2
of the pieces one day and
of the puzzles
6
6
pieces the next day. How much more of the puzzle did Shondra do on the first day than on the
second day?
Shondra is working on a puzzle. She placed
(1)
Use the model below to help you subtract the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the difference in simplest form.
(3)
How much more of the puzzle did Shondra do on the first day than on the second day?
©2012, TESCCC
02/26/13
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Subtraction Notes and Practice
Stan had a glass filled with
3
1
cup of apple juice. He drank
cup of the juice. How much juice
4
4
was left in Stan’s glass?
(1)
Use the model below to help you subtract the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the difference in simplest form.
(3)
How much juice was left in Stan’s glass?
======================================================================
2
7
of a peach pie for Cassie and her dad. Cassie ate
of the pie and her
Cassie’s mom left
8
8
3
of the pie. How much pie was left after Cassie and her dad ate?
dad ate
8
(1)
Use the model below to help you subtract the fractions. Explain your model.
_________________________________________________________________________
_________________________________________________________________________
(2)
Show how to write the difference in simplest form.
(3)
How much pie was left after Cassie and her dad ate?
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Picturing Addition and Subtraction of Like
Fractions KEY
Fill in the spaces and shadein the correct answers.
Example:
1 fourth
+
2 fourths
=
3 fourths
3 eighths
+
2 eighths
=
5 eighths
2 sixths
+
3 sixths
=
5 sixths
4 twelfths
+
3 twelfths
=
7 twelfths
6 ninths
+
1 ninth
=
7 ninths
(1)
(2)
(3)
(4)
Fill in the blanks and write in the fraction or mixed number for your answer.
Example:
(5)
2 tenths
+ 5 tenths
=
7 tenths =
(6)
3 fifths
+ 3 fifths
=
6 fifths
(7)
6 eighths - 3 eighths
=
3 eighths =
(8)
9 ninths -
=
6 ninths
©2012, TESCCC
9
2
= 1
7
7
4 sevenths + 5 sevenths = _9_ sevenths =
3 ninths
09/15/12
=
=
7
10
6 = 11
5
5
3
8
6
9
=
2
3
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Picturing Addition and Subtraction of Like
Fractions
Fill in the spaces and shade in the correct answers.
Example:
1 fourth
+
2 fourths
=
3 fourths
(1)
+
=
+
=
+
=
+
=
(2)
(3)
(4)
Fill in the blanks and write in the fraction or mixed number for your answer.
Example:
4 sevenths + 5 sevenths = _9_ sevenths =
(5)
2 tenths
+ 5 tenths
= ___ tenths =
(6)
3 fifths
+ 3 fifths
= ___ fifths
(7)
6 eighths - 3 eighths
=
(8)
9 ninths -
= ___ ninths
©2012, TESCCC
3 ninths
9
2
= 1
7
7
=
___ eighths =
09/15/12
=
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Number Line KEY
1
2
0
A fraction is close to 0 when
the numerator is much less
than half the denominator.
1
5
2
11
©2012, TESCCC
2
15
1
A fraction is close to y when
the numerator is about half
the denominator.
5
11
4
7
9
20
09/15/12
A fraction is close to 1 when
the values of the numerator
and the denominator are
about the same.
9
10
17
19
6
7
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Number Line
0
A fraction is close to 0 when
the numerator is much less
than half the denominator.
©2012, TESCCC
1
2
A fraction is close to y when
the numerator is about half
the denominator.
09/15/12
1
A fraction is close to 1 when
the values of the numerator
and the denominator are
about the same.
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Notes and Practice KEY
A number line is helpful when estimating whether fractions are closer to 0,
Find
1,
2
or 1.
4
4
1
on the number line. Is
closer to 0, , or 1?
10
10
2
1
2
4
10
0
1
4
1
is closer to . One-half is a good estimate for four-tenths.
10
2
Comparing numerators and denominators is another helpful way to estimate whether
1
fractions are closer to 0,
, or 1.
2
Rule
Example
A fraction is closer to 0 when the numerator is much less than
the denominator.
1
7
A fraction is closer to 1 when the numerator is about the same
as the denominator.
6
7
A fraction is closer to one-half when the numerator is about
half the denominator.
3
7
Practice:
Use either a number line or fraction rounding rules to determine whether each fraction is
1
closer to 0, 1, or .
2
(1)
8
1
is closest to
11
2
(4)
12
is closest to 1
15
©2012, TESCCC
(2)
(3)
2
is closest to
9
0
(5)
4
is closest to
5
1
(6)
7
is closest to
8
09/15/12
1
2
is closest to
12
0
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Notes and Practice KEY
(7)
Mr. Sutton wants a new bookshelf for his classroom that is at least
custodian has a board that is
1
yard long. The
2
9
yard long. Is this board long enough? How do you
16
know?
Yes, because the numerator (9) in 9 is more than half the denominator (8) which
16
makes this fraction a little bit greater than 1 .
2
(8)
(9)
5
1
The class aquarium was
full after vacation. Jack said that it was about
full. Karen
8
2
said it was almost full. Whose estimate is closer to the amount of water in the
aquarium? How do you know?
5
Jack’s estimate is closer because
full is closer to 1 full than to full. I know
8
2
because four-eighths is equivalent to one-half and eight-eighths is equivalent to one
whole.
Lucky has to put each insect she has caught into a cage that is as close as possible
1
1
to the length of the insect. She has cages that are inch, 1 inch, 1 inches, and 2
2
2
inches long. For each insect, write which cage size she should use and explain how
you know.
Insect
Length
(in inches)
Size of Cage
Needed
How I Know
Answers may vary.
Ladybug
1
4
1 inch
2
1 inch is closest to the cage choice of 1
4
2
inch because half an inch is equivalent to
2.
4
Housefly
3
4
1 inch
3 is closest to the cage choice of 1 inch.
4
Honeybee
30
32
1 inch
5
13
1 1 inch
2
Beetle
1
Praying
Mantis
9
1
11
©2012, TESCCC
2 inches
30 is closest to the cage choice of 1 inch
32
because 32 is one whole.
32
5
1
is closest to the cage choice of 1 1 inch
2
13
because half of thirteen is 6.5, which is
close to 5.
1
9
is closest to the cage choice of 2
11
inches.
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Notes and Practice
A number line is helpful when estimating whether fractions are closer to 0, 1 , or 1.
2
Find
4
4
1
on the number line. Is
closer to 0, , or 1?
10
10
2
1
2
4
10
0
1
4
1
is closer to . One-half is a good estimate for four-tenths.
10
2
Comparing numerators and denominators is another helpful way to estimate whether
1
fractions are closer to 0, , or 1.
2
Rule
Example
A fraction is closer to 0 when the numerator is much less than
the denominator.
1
7
A fraction is closer to 1 when the numerator is about the same
as the denominator.
6
7
A fraction is closer to one-half when the numerator is about
half the denominator.
3
7
Practice:
Use either a number line or fraction rounding rules to determine whether each fraction is
1
closer to 0, 1, or .
2
(1)
8
is closest to
11
(4)
12
is closest to
15
©2012, TESCCC
(2)
(3)
2
is closest to
9
(5)
4
is closest to
5
(6)
7
is closest to
8
09/15/12
2
is closest to
12
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Estimation Notes and Practice
(7)
Mr. Sutton wants a new bookshelf for his classroom that is at least
custodian has a board that is
1
yard long. The
2
9
yard long. Is this board long enough? How do you
16
know?
(8)
(9)
5
1
full after vacation. Jack said that it was about
full.
8
2
Karen said it was almost full. Whose estimate is closer to the amount of water in the
aquarium? How do you know?
The class aquarium was
Lucky has to put each insect she has caught into a cage that is as close as possible to
1
1
the length of the insect. She has cages that are inch, 1 inch, 1 inches, and 2
2
2
inches long. For each insect, write which cage size she should use and explain how
you know.
Insect
Length
(in inches)
Ladybug
1
4
Housefly
3
4
Honeybee
30
32
Beetle
1
5
13
Grasshopper
1
9
11
©2012, TESCCC
Size of Cage
Needed
09/15/12
How I Know
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Sums Notes and Practice KEY
Estimate 2
1
5
+3 .
8
8
Think:
1
8
Think:
is less than
1
2
2
So, round 2 1 down to 2.
8
Estimate:
So, 2
1
+
8
2
+
3
5 is greater than 1
2
8
5
8
So, round 3 5 Up to 4.
8
4=6
1
5
+ 3 is about 6.
8
8
Practice:
Round each mixed number to the nearest whole number and estimate the sum.
(1)
8
(2)
9
4
+ 3
16
16
9
©2012, TESCCC
+
3
3
= 12
(3)
2
7
+ 4
6
7
3
+
5
09/15/12
4
=
8
9
4
+ 2
10
10
5
+
2
=
7
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Sums Notes and Practice KEY
Round each mixed number to the nearest whole number and estimate the sum.
(4)
8
(5)
2
3
+ 8 = 8 + 9 = 17
5
5
(7)
4
1
4
+ 1 = 5+2=7
6
6
(8)
8
2
+ 3 =5+3=8
9
9
(10)
5
(6)
6
7
1
2
+ 2 = 7 + 3 = 10
3
3
(9)
4
5
+ 1 =7+2=9
6
6
14
1
3
+ 3 = 14 + 4 = 18
5
5
4
7
miles on Monday and 2
miles on Tuesday. About how
10
10
many miles did she walk in all? Show your work.
Constance walked 1
1 + 3 = 4 miles
(11)
3
3
hours on homework and 2 hours watching a movie. About how
4
4
much time did Danny spend on these two activities?
Danny spent 1
2 + 3 = 5 hours
(12)
2
2
cups of juice and 2 cups of ginger ale. About how many
3
3
cups of juice and ginger ale are needed for this recipe? Show your work.
A punch recipe calls for 8
9 + 3 = 12 cups
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Sums Notes and Practice
Estimate 2
1
5
+3 .
8
8
Think:
1
8
Think:
is less than
1
2
2
So, round 2 1 down to 2.
8
Estimate:
So, 2
1
+
8
2
5
8
3
+
5 is greater than 1
2
8
So, round 3 5 Up to 4.
8
4=6
1
5
+ 3 is about 6.
8
8
Practice:
Round each mixed number to the nearest whole number and estimate the sum.
(1)
8
(2)
9
4
+ 3
16
16
+
©2012, TESCCC
3
=
(3)
2
7
+ 4
6
7
+
09/15/12
4
=
9
4
+ 2
10
10
+
=
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Sums Notes and Practice
Round each mixed number to the nearest whole number and estimate the sum.
(4)
8
(5)
2
3
+ 8 =
5
5
(7)
4
5
(6)
1
4
+ 1 =
6
6
(8)
8
2
+ 3 =
9
9
6
7
1
2
+ 2 =
3
3
(9)
4
5
+ 1 =
6
6
14
1
3
+ 3 =
5
5
4
7
miles on Monday and 2
miles on Tuesday. About how
10
10
many miles did she walk in all? Show your work.
(10)
Constance walked 1
(11)
Danny spent 1
(12)
A punch recipe calls for 8
3
3
hours on homework and 2 hours watching a movie. About how
4
4
much time did Danny spend on these two activities?
2
2
cups of juice and 2 cups of ginger ale. About how many
3
3
cups of juice and ginger ale are needed for this recipe? Show your work.
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Differences Notes and Practice KEY
Estimate 3
9
1
 1 .
10
10
Think:
Think:
9 is greater than
10
1
2
3
9
So, round 3
up to 4.
10
Estimate:
So, 3
9
10
4
1
-
1
10
1
10
is less than
1
2
1
So, round 110 down to 1.
1=3
9
1
 1
is about 3.
10
10
Practice:
Round each mixed number to the nearest whole number and estimate the difference.
(1)
4
(2)
7
9
5
©2012, TESCCC
1
4
9
1
(3)
4
=
4
6
7
5
2
3
7
2
09/15/12
5
=
3
5
8
6
2
7
8
3
=
3
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Differences Notes and Practice KEY
Round each mixed number to the nearest whole number and estimate the difference.
(4)
8
(5)
3
1
- 8 = 9–8=1
5
5
(7)
4
1
4
- 1 = 5–2=3
6
6
(8)
2
2
- 1 = 4–1=3
9
9
(10)
5
(6)
6
7
2
2
- 2 = 8–3=5
3
3
(9)
5
1
- 1 = 7–1=6
6
6
14
2
3
- 5 = 14 – 6 = 8
5
5
3
7
miles on Monday and 2
miles on Tuesday. About how
10
10
many more miles did she walk on Tuesday than on Monday? Show your work.
Constance walked 1
3–1=2
(11)
3
3
hours on homework and 2 hours watching a movie. About how
4
4
many more hours did Danny spend watching a movie than doing his homework? Show
your work.
Danny spent 1
3–2=1
(12)
2
2
cups of juice and 2 cups of ginger ale. About how many
3
3
more cups of juice than ginger ale are needed for this recipe? Show your work.
A punch recipe calls for 8
9–3=6
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Differences Notes and Practice
Estimate 3
9
1
 1 .
10
10
Think:
9
10
Think:
is greater than 1
2
So, round 3
3
9
up to 4.
10
Estimate:
So, 3
9
10
4
1
-
1
10
1
10
is less than
1
2
1
So, round 110 down to 1.
1=3
9
1
 1
is about 3.
10
10
Practice:
Round each mixed number to the nearest whole number and estimate the difference.
(1)
4
(2)
7
9
1
4
9
4
(3)
6
7
2
3
7
=
©2012, TESCCC
5
=
09/15/12
5
8
2
7
8
=
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Estimating Fraction Differences Notes and Practice
Round each mixed number to the nearest whole number and estimate the difference.
(4)
8
(5)
3
1
- 8 =
5
5
(7)
4
5
(6)
1
4
- 1 =
6
6
7
(8)
2
2
- 1 =
9
9
6
2
2
- 2 =
3
3
(9)
5
1
- 1 =
6
6
14
2
3
- 5 =
5
5
3
7
miles on Monday and 2
miles on Tuesday. About how
10
10
many more miles did she walk on Tuesday than on Monday? Show your work.
(10)
Constance walked 1
(11)
Danny spent 1
(12)
A punch recipe calls for 8
3
3
hours on homework and 2 hours watching a movie. About how
4
4
many more hours did Danny spend watching a movie than doing his homework? Show
your work.
2
2
cups of juice and 2 cups of ginger ale. About how many
3
3
more cups of juice than ginger ale are needed for this recipe? Show your work.
©2012, TESCCC
09/15/12
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Sum/Difference Estimation Evaluation KEY
Read and complete the table below for each problem situation.
(1)
3
3
hours one day and 2 hours the next day. Estimate the total number
4
4
of hours he works on both days combined.
Ryan works 1
Mixed Numbers Used
1
3
4
+
2
Estimate
3
4
2 + 3 = 5 hours
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
(2)
5
7
years experience as a musician. Lawana has 5 years experience
8
8
as a musician. About how many more years experience does Lawana have than
Fernando?
Fernando has 4
Mixed Numbers Used
5
7
8
4
Estimate
5
8
6  5 = 1 year
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
(3)
3
The length of a glass covering for a painting is 14 inches long, and the length of the
5
1
painting is 11 inches long. About how much longer is the glass covering than the
5
painting?
Mixed Numbers Used
14
3
5
11
Estimate
1
5
15  11 = 4 inches
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
©2012, TESCCC
4/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Sum/Difference Estimation Evaluation KEY
(4)
8
7
foot long submarine sandwich and a 2
foot long relish tray
12
12
end-to-end on a picnic table. About how long does the picnic table need to be for these
items to fit?
A caterer put a 6
Mixed Numbers Used
6
8
+
12
2
Estimate
7
12
7 + 3 = 10 foot long
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
(5)
9
Carrie is making cookies for the school bake sale. If she uses 1
pounds of flour per
16
batch, about how much flour will she need if she makes 3 batches?
Mixed Numbers Used
1
9
+
16
1
9
+
16
1
Estimate
9
16
2 + 2 + 2 = 6 pounds
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
(6)
Jerry is building a border around his patio shown below. About how much border
should he buy to make sure he has enough?
8
1 yd
8
6
10
7
yd
8
Mixed Numbers Used
10
7
8
+
8
1
8
+
7
yd
8
Estimate
67
11 + 8 + 7 = 26 yards
8
Explain your estimate: Answers may vary, but could include using a number line or
1
finding how close or far away each fraction in the mixed number was from
.
2
©2012, TESCCC
4/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Sum/Difference Estimation Evaluation
Read and complete the table below for each problem situation.
(1)
3
3
hours one day and 2 hours the next day. Estimate the total number
4
4
of hours he works on both days combined.
Ryan works 1
Mixed Numbers Used
Estimate
Explain your estimate:
(2)
7
5
years experience as a musician. Lawana has 5 years experience
8
8
as a musician. About how many more years experience does Lawana have than
Fernando?
Fernando has 4
Mixed Numbers Used
Estimate
Explain your estimate:
(3)
3
The length of a glass covering for a painting is 14 inches long, and the length of the
5
1
painting is 11 inches long. About how much longer is the glass covering than the
5
painting?
Mixed Numbers Used
Estimate
Explain your estimate:
©2012, TESCCC
04/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Fraction Sum/Difference Estimation Evaluation
(4)
8
7
foot long submarine sandwich and a 2
foot long relish tray
12
12
end-to-end on a picnic table. About how long does the picnic table need to be for these
items to fit?
A caterer put a 6
Mixed Numbers Used
Estimate
Explain your estimate:
(5)
9
Carrie is making cookies for the school bake sale. If she uses 1
pounds of flour per
16
batch, about how much flour will she need if she makes 3 batches?
Mixed Numbers Used
Estimate
Explain your estimate:
(6)
Jerry is building a border around his patio shown below. About how much border
should he buy to make sure he has enough?
8
1 yd
8
6
10
7
yd
8
7
yd
8
Mixed Numbers Used
Estimate
Explain your estimate:
©2012, TESCCC
04/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 07 Lesson: 03
Career Choices Graph KEY
This graph shows the career choices of some of the students in a class.
Career Choices
Lawyer
Professions
Teacher
Scientist
TV Reporter
Firefighter
Doctor
1
2
3
4
5
6
Number of Students
(1)
How many student responses were there for this class? 20
(2)
What fraction of the class wants to be:
5
1
=
20
4
·
doctors?
·
teachers or firefighters?
·
5
1
=
20
4
6
3
TV reporters or firefighters?
=
20
10
·
scientists or doctors?
·
TV reporters, firefighters,
lawyers, or teachers?
10
1
=
20
2
10
1
=
20
2
(3)
Write a fraction that shows how many more students chose being a teacher or scientist
than those who chose being a firefighter. Show your work.
3
8
8
6
2
3
5
2
÷
=
+
and
=
=
20
20
20
2
10
20
20 20
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
Career Choices Graph
This graph shows the career choices of some of the students in a class.
Career Choices
Lawyer
Professions
Teacher
Scientist
TV Reporter
Firefighter
Doctor
1
2
3
4
5
6
Number of Students
(1)
How many student responses were there for this class?
(2)
What fraction of the class wants to be:
(3)

doctors?

teachers or firefighters?

TV reporters or firefighters?

scientists or doctors?

TV reporters, firefighters, lawyers, or teachers?
Write a fraction that shows how many more students chose being a teacher or scientist
than those who chose being a firefighter. Show your work.
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
I Like This Egg Best Data Table
Type of Egg
Number of Students
Fried
Scrambled
Hard-Boiled
Chocolate
No Opinion
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
I Like This Egg Best Blank Graph
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
I Like This Egg Best Evaluation KEY
Answers may vary depending on class responses.
Use the class graph created to answer the following questions.
(1)
How many student responses were there for our class?
What fraction of the class prefers the following types of eggs?
Type of Egg
Fraction
(2)
Fried
(3)
Scrambled
(4)
Hard-Boiled
(5)
Chocolate
(6)
No opinion
What fraction of the class prefers the following types of eggs?
Sample answer based on Sample Graph in Teacher Notes:
Type of Egg
Fraction Process
(7)
3
8
8
5
4
2
=
+
and
÷
=
Fried or Scrambled
20
20
20 20
4
5
(8)
Scrambled or Hard-Boiled
(9)
Hard-Boiled or Chocolate
(10)
Fried or Chocolate
(11)
(12)
No opinion
Write a fraction that shows how many more students prefer chocolate eggs than those
who have no opinion. Show your work.
Sample answer based on Sample Graph in Teacher Notes:
7 2
5
5 5 1
and
=
÷ =
20 20 20
20 5 4
©2012, TESCCC
09/15/12
page 1 of 1
Grade 5
Mathematics
Unit: 07 Lesson: 03
I Like This Egg Best Evaluation
Use the class graph created to answer the following questions.
(1)
How many student responses were there for our class?
What fraction of the class prefers the following types of eggs?
Type of Egg
Fraction
(2)
Fried
(3)
Scrambled
(4)
Hard-Boiled
(5)
Chocolate
(6)
No opinion
What fraction of the class prefers the following types of eggs?
Type of Egg
Fraction Process
(7)
Fried or Scrambled
(8)
(9)
Scrambled or Hard-Boiled
Hard-Boiled or Chocolate
(10)
Fried or Chocolate
(11)
(12)
No opinion
Write a fraction that shows how many more students prefer chocolate eggs than those
who have no opinion. Show your work.
©2012, TESCCC
09/15/12
page 1 of 1