Mathematics Pacing Resource Document
5.AT.2
Standard: 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike
denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to
estimate mentally and assess whether the answer is reasonable.
Teacher Background Information: Benchmark fractions help students know the value of fractions. Students need to know where fractions fall on a number line
using benchmark fractions. Benchmark fractions are 1/4., 1/2, and 3/4 and 1. Students need to know that one whole is represented by fractions like 3/3, 4/4,
etc. When comparing fractions, students need to say the fraction is close to zero, one-half, or one whole. Understanding this also helps when estimating sums
and differences. Students should be able to explain that 3/4 + 2/3 is more than one whole because both fractions are more than one-half. Essential vocabulary
for this standard includes: benchmark fraction, addition, subtraction, sum, and difference
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Resources:
o Unit 5: Lesson 5,20
o Unit 9: Lesson 6

https://www.engageny.org/resource/grade-5-mathematics-module-3topic-d-lesson-13 Use fraction benchmark numbers to assess
reasonableness of addition and subtraction equations.
https://www.engageny.org/resource/grade-5-mathematics-module-3topic-d-lesson-14 Strategize to solve multi-term problems.


https://www.engageny.org/resource/grade-5-mathematics-module-3topic-d-lesson-15 Solve multi-step word problems; assess reasonableness
of solutions using benchmark numbers.

https://www.engageny.org/resource/grade-5-mathematics-module-3topic-d-lesson-16 Explore part to whole relationships.

https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit4Framewor
kSE.pdf Adding, Subtracting, Multiplying, and Dividing Fractions
Indianapolis Public Schools

http://www.khanacademy.org/math/cc-fifth-grade-math/cc-5thfractions-topic Adding and subtracting fraction word problems

http://www.mathplayground.com/wpdatabase/Fractions1_1.htm
Fraction online quiz-word problems

http://www.softschools.com/quizzes/math/add_and_subtract_mix
ed_numbers_word_problems/quiz5100.html online quiz

http://illuminations.nctm.org/Activity.aspx?id=3519 Fraction
models

http://www.ixl.com/math/grade-7/add-subtract-multiply-anddivide-fractions-and-mixed-numbers-word-problems Online quiz
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.2
Item Bank:
1
2
of the cookies. Ryan ate of the cookies. How many cookies were left? [Delaware Dept. of Education]
6
3
D. 6 Answer: D
1) Monica and Ryan shared 36 cookies. Monica ate
A. 12
B. 29
C. 4
2) Amy, Elizabeth, Katie, Gretchen, and Deb love chocolate. One afternoon at a meeting, each of them brought their own large candy bar. Each candy bar was
the same size. Throughout the meeting, all of the ladies munched on their candy bars. At the end of the meeting, everyone was moaning and groaning about
having stomach aches.
Here is a list of what the ladies consumed:
 Amy: two-sixths of her candy bar
 Elizabeth: two-thirds of her candy bar
 Katie: three-fourths of her candy bar
 Gretchen: one-half of her candy bar
 Deb: one-third of her candy bar
a. Determine which of the ladies ate the most chocolate. ___________________________ Katie
b. Who ate the least? ___________________________ Deb and Amy
c. How much chocolate did they eat all together? ___________________________ two and seven-twelfths candy bars.
[Delaware Dept. of Education]
2
1
gallon of honey. The last two hives yielded gallon each.
3
4
a. How many gallons of honey did Lila collect in all? Draw a diagram to support your answer. one and one-sixth gallons of honey
3
b. After using some of the honey she collected for baking, Lila found that she only had gallon of honey left. How many gallons of honey did she use for
4
baking? Explain your answer using a diagram, numbers, and words. five-twelfths of a gallon of honey
3) Lila collected the honey from 3 of her beehives. From the first hive she collected
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.2
Item Bank:
3
gallon of honey, Lila decided to bake some loaves of bread and several batches of cookies for her school bake sale. The bread needed
4
1
1
gallon of honey and the cookies needed gallon. How much honey, in gallons, was left over? Explain your answer using a diagram, numbers, and words.
6
4
one-third gallon of honey
1
1
d. Lila decided to make more baked goods for the bake sale. She used lb less flour to make bread than to make cookies. She used lb more flour to make
8
4
1
cookies than to make brownies. If she used lb of flour to make the bread, how much flour, in pounds, did she use to make the brownies? Explain your
2
answer using a diagram, numbers, and words. three-eighths pound of flour
c. With the remaining
[www.engageny.org] Visual models for Question 3 may be found at https://www.engageny.org/resource/grade-5-mathematics-module-3. Click on “Grade 5
Mathematics Module 3: Mid-Module Assessment”
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.3
Standard: 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations
to represent the problem).
Teacher Background Information: The student will: demonstrate understanding that multiplying by a unit fraction 1/n is the same as dividing by the whole
number n; express multiplicative comparisons in two ways; multiply a whole number by a unit fraction to produce a whole number; represent improper
fractions and mixed numbers, convert between improper fractions and mixed numbers, apply the terms improper fraction and mixed number.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Resources:
o Unit 9: Lesson 1
o Unit 5: Lesson 6

http://www.ixl.com/math/grade-7/add-subtract-multiplyand-divide-fractions-and-mixed-numbers-word-problems
Online quiz

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-flesson-21 Explain the size of the product, and relate fraction and decimal
equivalence to multiplying a fraction by 1.

http://www.iq.poquoson.org/5math/5mathwordprobmultf
rac.htm Online quiz


https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-flesson-22 Compare the size of the product to the size of the factors.
http://www.math-play.com/Fractions-Jeopardy/fractionsjeopardy.html Fraction Jeopardy

http://www.superteachertools.com/jeopardy/usergames/F
eb201006/game1265756453.php Fraction word problem
Jeopardy

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-flesson-23 Compare the size of the product to the size of the factors.

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-flesson-24 Solve word problems using fraction and decimal multiplication.

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-elesson-16 Solve word problems using tape diagrams and fraction-by-fraction
multiplication.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.3
Item Bank:
3
of a 20-mile trail on Saturday. How many miles did she run on Saturday? [Delaware Dept. of Education] Answer: C
4
A. 5 miles
B. 10 miles
C. 15 miles
D. 19 miles
1) Connie ran
2) On Sunday, Travis bought the carton of eggs pictured below. [Delaware Dept. of Education]
1
of the eggs in the carton.
4
2
 On Tuesday, Travis used of the eggs that remained in the carton after Monday.
3
Which picture represents the number of eggs remaining in the carton after Travis used eggs on Tuesday? Answer: C

On Monday, Travis used
A.
B.
Indianapolis Public Schools
C.
D.
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.3
Item Bank:
3) Illustrative Mathematics performance task To Multiply or Not to Multiply https://www.illustrativemathematics.org/illustrations/609
4) Illustrative Mathematics performance task Half of a Recipe https://www.illustrativemathematics.org/illustrations/296
3
pounds of food and packaging. Jared can carry 4 full shopping bags into his house on one trip. How much food can Jared carry
4
in one trip? [Howard County Public Schools, Maryland] Answer: 23 pounds of food
5) A full shopping bag holds 5
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Teacher Background Information: Math Expressions Teacher Resource: pp. 865L-865M: Fraction Division Methods and The Meaning of Fraction Division.
The student will: recognize the inverse relationship between multiplication and division and apply it to fractional amounts; Divide a fraction by another fraction
with no visual aids; unsimplify to divide fractions that are not evenly divisible.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Resources:
o Unit 9: Lesson 10
o Unit 9: Lesson 11
o Unit 9: Lesson 12

https://www.engageny.org/resource/grade-5-mathematics-module-6topic-e-lesson-21 Multi-Step Word Problems Lessons (Lessons 21-26)

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-g-overview (Lessons 25-31)

https://www.illustrativemathematics.org/illustrations/1196 Illustrative
Math Task

https://grade5commoncoremath.wikispaces.hcpss.org/file/view/Dividing
_with_Unit_Fractions_GA_5nf7.pdf/407299828/Dividing_with_Unit_Fract
ions_GA_5nf7.pdf Dividing Unit Fractions Lessons

http://fractionbars.com/CommonCore/Gd5Les/CCSSDiv5_NF_7aGd5.pdf
Division of unit fractions by whole numbers lesson.

http://www.mathsolutions.com/documents/Fifth_Grade_Lesson.pdf
Math Solutions Lesson
Indianapolis Public Schools

https://learnzillion.com/student/lessons/3788 Divide whole
numbers by unit fractions and unit fractions by whole numbers:
LZ3788, LZ3787, LZ3786

http://www.basic-mathematics.com/dividing-fractions-wordproblems.html Online examples

http://www.homeschoolmath.net/online/problem_solving.php List
of problem solving websites
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
1) A farmer mows one-fifth of an acre each day. If his property has three acres, how many days will it take to mow it all? [Delaware Dept. of Education]
A. 3 days
B. 5 days
C. 8 days
D. 15 days Answer: D
1
a bag of licorice to share with her friends. She decided to share the
8
contents of the licorice bag equally with her teammates Sara and Jessica. How much of the licorice bag will each girl receive?
1
[Delaware Dept. of Education (modified)] Answer:
of the original bag of licorice
24
2) Tara had a great soccer game! After the soccer game, the coach awarded Tara
3)


3 pineapples
1
1 serving = pineapple
2
1
would be the method of solution.
2
[NAEP, 2005, Grade 8 Mathematics Assessment] Sample Answer: Samantha has 3 pineapples. She figures that each person will eat half of a pineapple. How
many people can Samantha serve with the 3 pineapples?
Given the information above, write a mathematics word problem for which 3 ÷
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
4) Students are running in a relay race. Each team will run a total of 2 miles. Each member of a team will run
1
of a mile. How many students will a team need
5
to complete a race? Choose the correct number. You may use the number line to help find your answer.
[Smarter Balanced sample items] Answer: 10 students
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.3
Standard: 5.C.3: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated
multiplication.
Teacher Background Information: The identity property of multiplication tells us that a number x 1 has a product equal to the number (itself). For example, 4 x
1 = 4. So when we multiply by a fraction that is less than 1 our product has to be less than the number we are multiplying the fraction by. For example, 4 x 1/3 =
1 1/3. The product (1 1/3) is less than the original factor 4 because the second factor (1/3) is less than 1. Conversely, when we multiply a number by a number
greater than 1 (including fractions/mixed numbers) our product is greater than the original factor. For example, 4 x 5/4 = 5. The product (5) is greater than the
first factor (4) because the second product is greater than 1.
Lesson Plans/Print Activities:
Web-based Practice:

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-f-lesson21 Explain the size of the product, and relate fraction and decimal equivalence to
multiplying a fraction by 1.

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-f-lesson22 Compare the size of the product to the size of the factors.

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-f-lesson23 Compare the size of the product to the size of the factors.

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-f-lesson24 Solve word problems using fraction and decimal multiplication.

https://grade5commoncoremath.wikispaces.hcpss.org/file/view/reasoning_with_fra
ctions_GA_5NF5.pdf/406449176/reasoning_with_fractions_GA_5NF5.pdf
Constructing Task-Reasoning with fractions.

http://fractionbars.com/CommonCore/Gd5Les/CCSSMulti5_NF_5aGd.pdf
Comparing sizes of products by comparing the sizes of factors.
Indianapolis Public Schools

https://learnzillion.com/lessonsets/387-interpretmultiplication-as-scaling Learnzillion scaling lessons

http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1
.html?open.instructions Virtual manipulative
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.3
Item Bank:
1) Jackson claims that multiplication always makes a number bigger. He gave the following examples:
 If I take 6, and I multiply it by 4, I get 24, which is bigger than 6.
1
2
1
1
 If I take and I multiply it by 2 (whole number), I get or which is bigger than .
4
4
2
4
Jackson’s reasoning is incorrect. Give an example that proves he is wrong, and explain his mistake using pictures, words, or numbers.
[www.engageny.org] Answer: The first example Jackson used proved his point, but the second example did not. He didn’t compare the product (
the factors (
1
) to both of
2
1
1
1
and 2). is bigger than , but it isn’t bigger than 2.
4
2
4
2) Circle the greater value. DO NOT calculate to find your answer. Choose 1 item and explain how you know which value is greater.
[Howard County Public Schools, Maryland] Answer: a) first choice; b) first choice; c) second choice; d) second choice; e) first choice
Explanations should include knowledge that multiplying a proper fraction times a second factor results in a product that is smaller in value than the second
factor.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.3
Item Bank:
3)
[PARCC online practice test] Answers: a) less than; b) greater than; c) greater than (“equal to” is also a choice)
4)
[Delaware Dept. of Education] Answers: a. Yes; b. No; c. No
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.4
Standard: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers.
Teacher Background Information:
In order to add and subtract two fractions with unlike denominators, students must understand how to find equivalent fractions. They need to know that the
same fraction can be named in many different ways. Essential vocabulary for this standard includes: mixed numbers, improper fraction, equivalent fraction,
addend, sum, difference, numerator, and denominator
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions: Unit 5: Lessons 3-16


https://www.engageny.org/resource/grade-5-mathematics-module-3
o Topic A Lessons 1 & 2 Equivalent Fractions
o Topic B Lessons 3 – 7 Making like units pictorially
o Topic C Lessons 8 – 12 Making like units numerically
o Topic D Lessons 13 – 16 Further application
http://www.math-play.com/FractionsJeopardy/fractions-jeopardy.html Adding fractions
jeopardy

http://www.mathplayground.com/fractions_add.html
Adding fractions game

http://www.math-play.com/adding-and-subtractingfractions-game.html Adding and subtracting fractions
online game

http://www.math-play.com/math-fractions-games.html
Math fractions game

http://www.funbrain.com/fractop/ Brainpop game

http://www.khanacademy.org/math/arithmetic/fractions adding and subtracting
fractions with unlike denominators

http://www.oercommons.org/courses/domino-fractions/view Domino Fractions

http://schools.nyc.gov/NR/rdonlyres/D0A70F2D-1133-418C-B68F95E6D714F357/0/NYCDOEG5MathStuffedwithPizza_Final.pdf In this unit students
will develop and expand the concept of rational numbers by using several
interpretations and different types of physical models.

http://www.k-5mathteachingresources.com/supportfiles/mixednumberswithsumof5nf1.pdf Lesson seed

http://www.k-5mathteachingresources.com/supportfiles/mixednumberswithdifference5nf1.pdf Lesson Seed
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.4
Item Bank:
3
5
miles. The next day he ran 6 miles. How many total miles did Scott run?
4
8
3
D. 12
[Delaware Dept. of Education] Answer: C
4
1) Scott ran in a two-day race. The first day he ran 5
A. 11
3
8
B. 11
2
3
C. 12
3
8
2) The table below shows the length of ribbon, in yards, needed to make different art projects.
Susan has 4 yards of ribbon and wants to make as many different art projects as possible. Which art projects can Susan make that will use exactly 4 yards of
ribbon altogether? Show your work.
[Delaware Dept. of Education] Sample Answer: one flower, one costume, and one picture frame
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.4
Item Bank:
3) Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a
1
2
different recipe for their perfect s’more. Nick likes to use of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly of a
2
5
chocolate bar.
a. What fraction of a chocolate bar will Nick and Tasha use in total if they each eat one s’more?
b. Nick wants to cut one chocolate bar into pieces of equal size so that he and Tasha can make their s’mores. How many pieces should he cut the chocolate bar
into so that each person will get the right amount of chocolate to make their perfect s’more?
c. After Nick cuts the chocolate bar into pieces of equal size, how many pieces of the chocolate bar should he get? How many pieces of the chocolate bar should
he give to Tasha?
9
[www.illustrativemathematics.org] Answers: a)
of a chocolate bar; b) ten pieces; c) 5 pieces for Nick and 4 pieces for Tasha
10
4) Alex is training for his school's Jog-A-Thon and needs to run at least 1 mile per day. If Alex runs to his grandma's house, which is
to his friend Justin's house, which is
5
of a mile away, and then
8
1
of a mile away, will he have trained enough for the day?
2
[www.illustrativemathematics.org] Answer: Yes, Alex has run more than 1 mile that day. After running to his grandma’s house, he only needs
meet his goal. Since Justin’s house is more than
Indianapolis Public Schools
3
of a mile to
8
3
1
4
away ( is the same as ), he will surpass his goal.
2
8
8
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Multiplication of a fraction by a whole number, such as 1/4 x 8 can be interpreted as one-fourth of 8 pies. If 8 pies are divided into 4 equal groups, each group
has 2 pies. If students struggle with this remind that the multiplication sign can be read as pf so the problem would read, What is 1/4 of 8?
The multiplication of a whole number by a fraction, such as 8 x 1/4 can be interpreted as repeated addition, 8 groups of one-fourth. When multiplying a fraction
to fraction, the algorithm is easily taught by saying multiply numerators and multiply the denominators. This will not help students understand this conceptually
prior to teaching the algorithm, multiplication of fractions can be shown by the area model for multiplication.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Lessons:
o Unit 9: Lessons 1-5

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-c-overview Multiplication of a Whole Number by a Fraction

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-e-overview Multiplication of a Fraction by a Fraction

http://www.shodor.org/interactivate/activities/FractionQuiz/ Online
quiz
http://www.k-5mathteachingresources.com/supportfiles/multiplyingfractionsbydividingrectangles5.nf4a.pdf Multiplication of
fractions. Lesson seed

http://www.math-play.com/Multiplying-FractionsMillionaire/Multiplying-Fractions-Millionaire.html Multiplication of
fractions millionaire game
http://www.cpalms.org/Public/PreviewResource/Preview/27870
Modeling Fraction Multiplication

http://www.arcademics.com/games/snow-sprint/snow-sprint.html
Multiplication of fractions game





http://www.khanacademy.org/math/arithmetic/fractions/multiplyin
g_fractions/v/multiplying-fractions-and-whole-numbers Multiplying
fractions lessons
Understand multiplication of fractions by whole numbers
LZ2696, LZ2971, LZ3026, LZ2927, LZ2938, LZ2939, LZ3076
http://www.cpalms.org/Public/PreviewResource/Preview/38419
Multiplying fractions with an area model
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Item Bank:
1) Makayla said, "I can represent 3 ×
2
2
with 3 rectangles each of length ."
3
3
2
2
2
2
× 3 can be thought of as of 3. Is 3 copies of the same as of 3?”
3
3
3
3
2
a. Draw a diagram to represent of 3.
3
2 2
b. Explain why your picture and Makayla’s picture together show that 3 × = × 3.
3 3
Connor said, “I know that
c. What property of multiplication do these pictures illustrate?
[www.illustrativemathematics.org] Solution at https://www.illustrativemathematics.org/illustrations/321
2) What is 2/3 of 15 marbles?
A. 10 marbles
B. 9 marbles
Indianapolis Public Schools
C. 8 marbles
D. 5 marbles
[NAEP 1990 Grade 12] Answer: A
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Item Bank:
3) Gregory is installing tile on a rectangular floor.

He is using square tiles.

The length of a side of each tile is

1
foot.
2
The area of the floor is 22 square feet.

The width of the floor is 4 feet.
Use the grid to model the rectangular floor that Gregory is installing.
What is the length, in feet, of the floor? ________________ feet
[Delaware Dept. of Education] Answer: 5
1
feet
2
4) Illustrative Mathematics task Folding Strips of Paper https://www.illustrativemathematics.org/illustrations/965
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.6
Standard: 5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain
why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction
equivalence, a/b = (n × a)/(n × b), to the effect of multiplying a/b by 1.
Teacher Background Information: The identity property of multiplication tells us that a number x 1 has a product equal to the number (itself). For example, 4 x
1 = 4. So when we multiply by a fraction that is less than 1 our product has to be less than the number we are multiplying the fraction by. For example, 4 x 1/3 =
1 1/3. The product (1 1/3) is less than the original factor 4 because the second factor (1/3) is less than 1. Conversely, when we multiply a number by a number
greater than 1 (including fractions/mixed numbers) our product is greater than the original factor. For example, 4 x 5/4 = 5. The product (5) is greater than the
first factor (4) because the second product is greater than 1.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Lessons:
o Unit 9: Lessons 1-3

https://learnzillion.com/lessonsets/387-interpret-multiplication-asscaling Learnzillion videos

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-e-lesson-14 Multiply unit fractions by non-unit fractions.

http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html?open.i
nstructions Virtual Manipulative

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-f-lesson-21 Explain the size of the product, and relate fraction and
decimal equivalence to multiplying a fraction by 1.

http://www.xpmath.com/forums/arcade.php?do=play&gameid=110
fractions by whole numbers

http://www.mathplayground.com/fractions_fractionof.html Finding
a fraction of a number

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-f-lesson-22 Compare the size of the product to the size of the
factors.

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-f-lesson-23 Compare the size of the product to the size of the
factors.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.6
Item Bank:
1) Jackson claims that multiplication always makes a number bigger. He gave the following examples:
 If I take 6, and I multiply it by 4, I get 24, which is bigger than 6.
1
2
1
1
 If I take and I multiply it by 2 (whole number), I get or which is bigger than .
4
4
2
4
Jackson’s reasoning is incorrect. Give an example that proves he is wrong, and explain his mistake using pictures, words, or numbers.
[www.engageny.org] Answer: The first example Jackson used proved his point, but the second example did not. He didn’t compare the product (
the factors (
1
) to both of
2
1
1
1
and 2). is bigger than , but it isn’t bigger than 2.
4
2
4
2) Circle the greater value. DO NOT calculate to find your answer. Choose 1 item and explain how you know which value is greater.
[Howard County Public Schools, Maryland] Answer: a) first choice; b) first choice; c) second choice; d) second choice; e) first choice
Explanations should include knowledge that multiplying a proper fraction times a second factor results in a product that is smaller in value than the second
factor.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.6
Item Bank:
3)
[PARCC online practice test] Answers: a) less than; b) greater than; c) greater than (“equal to” is also a choice)
4)
[Delaware Dept. of Education] Answers: a. Yes; b. No; c. No
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.7
Standard: 5.C.7 Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number to divide a whole number by a unit
fraction.
Teacher Background Information: The student will: divide a whole number by a whole number to produce a fraction; recognize that dividing a whole number w
by a unit fraction 1/d gives the same result as w x d; recognize that dividing a unit fraction 1/d by a whole number w gives the same result as 1/d x w; recognize
the inverse relationship between multiplication and division and apply it to fractional amounts; divide a fraction or mixed number by another fraction with the
visual support of number lines; divide a fraction by another fraction with no visual aids; unsimplify to divide fractions that are not evenly divisible; recognize that
all division questions can be solved by inverting the dividing factor and multiplying; plan and conduct a systematic investigation to verify a method.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Lessons:
o Unit 9: Lessons 8, 10-12

https://learnzillion.com/student/lessons/3787-divide-a-unitfraction-by-a-whole-number Learnzillion videos

https://www.engageny.org/resource/grade-5-mathematics-module-6topic-e-overview Lessons 21-26

http://www.learner.org/courses/learningmath/number/session9/pa
rt_a/ Models for the multiplication and division of fractions

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-g-overview Lessons 25 -31

http://www.ixl.com/math/grade-6/divide-by-fractions-with-models
Division of fraction models quiz

https://www.illustrativemathematics.org/illustrations/1196
Illustrative Math Task

http://www.visualfractions.com/divide.htm Divide fractions

https://www.illustrativemathematics.org/illustrations/12
Dividing by one-half

https://www.illustrativemathematics.org/illustrations/1120
How many marbles task
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.7
Item Bank:
1) A farmer mows one-fifth of an acre each day. If his property has three acres, how many days will it take to mow it all? [Delaware Dept. of Education]
A. 3 days
B. 5 days
C. 8 days
D. 15 days Answer: D
1
a bag of licorice to share with her friends. She decided to share the
8
contents of the licorice bag equally with her teammates Sara and Jessica. How much of the licorice bag will each girl receive?
1
[Delaware Dept. of Education (modified)] Answer:
of the original bag of licorice
24
2) Tara had a great soccer game! After the soccer game, the coach awarded Tara
3)


3 pineapples
1
1 serving = pineapple
2
1
would be the method of solution.
2
[NAEP, 2005, Grade 8 Mathematics Assessment] Sample Answer: Samantha has 3 pineapples. She figures that each person will eat half of a pineapple. How
many people can Samantha serve with the 3 pineapples?
Given the information above, write a mathematics word problem for which 3 ÷
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.7
Item Bank:
4) Students are running in a relay race. Each team will run a total of 2 miles. Each member of a team will run
1
of a mile. How many students will a team need
5
to complete a race? Choose the correct number. You may use the number line to help find your answer.
[Smarter Balanced sample items] Answer: 10 students
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.1
Standard:
5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.
Teacher Background Information:
The students need to:
1. Understand the greater than, less than, and equal to symbols
2. Be able to draw in interpret number lines showing whole numbers, fractions, and decimals
3. Understand and recognize equivalent decimals and fractions (including mixed numbers)
4. Understand place value names, periods, and visual models
Lesson Plans/Print Activities:
Web-based Practice:
 Math Expressions:
 http://www.brainpop.com/games/battleshipnumberline/ Battleship
o Unit 3: Lessons 1-5
number line game
o Unit 5: Lesson 2
o Unit 7: Lesson 7
 http://studyjams.scholastic.com/studyjams/jams/math/decimalso Unit 7: Lesson 14
percents/place-decimal-number-line.htm Decimals on a number line
o Unit 11: Lesson 10

http://www.khanacademy.org/math/arithmetic/decimals Decimals on a number
line

http://www.khanacademy.org/math/arithmetic/fractions Plotting basic fractions
on a number line.

http://www.insidemathematics.org/common-core-math-tasks/5th-grade/52005%20Fractions.pdf Mars Task

https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-boverview Decimal Fractions and Place Value Patterns

https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-blesson-6 Compare decimal fractions to the thousandths using like units and

http://mathsframe.co.uk/en/resources/resource/266 Click on decimals.

http://www.sheppardsoftware.com/mathgames/fractions/AnimalRescue
AdvancedFractionsNumberLineGame.htm Fractions on a number line
game
express comparisons with >, <, =.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.1
Item Bank:
1) Use the number line below. Write in the blank the letter than best corresponds with the position of the number on the number line.
1
7
________
10
1.3 _________
0.5 _________
0.8 __________
[Indiana Standards Resources Classroom Assessment] Answers: D, C, A, B
2) Illustrative Mathematics task Comparing Decimals on the Number Line https://www.illustrativemathematics.org/illustrations/1802
3) Illustrative Mathematics task Placing Thousandths on the Number Line https://www.illustrativemathematics.org/illustrations/1803
4) If the following numbers were plotted on a number line, which number would be nearest to zero?
5
81
A. 0.29
B. 0.065
C.
D.
[www.cpalms.org] Answer: B
3
100
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.2
Standard: 5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by
whole numbers.
Teacher Background Information:
Fractions as parts of wholes: A fraction such as ¾ represents a whole which has been partitioned into 4 equal parts and 3 of those parts are being considered.
Fractions as parts of a set: Uses a set of objects as a whole (unit). Without mentioning fractions students should have many opportunities to partition sets –
background for both fractions and division.
Fractions as division: This meaning comes from division 3 ÷ 5 and also the partitioning illustration. It is this meaning that needs to be understood to change
fractions to decimal notation.
Lesson Plans/Print Activities:
Web-based Practice:
 Math Expressions:
o Unit 5: Lesson 1
 https://www.mangahigh.com/enus/math_games/number/fractions_percents_and_ratios/use_fracti
ons Read and write proper fractions, interpreting the denominator
 https://learnzillion.com/student/lessons/715 Learnzillion lesson. Fraction
as the parts of a whole
as shares

https://learnzillion.com/student/lessons/3515 Interpret fractions as
division of the numerator.

http://www2.smarttutor.com/player/swf/STA_Fractional_PartSet_
L4_V1_t1a.swf Fractions as part of a set game.

http://www.khanacademy.org/math/arithmetic/fractions

http://www.sheppardsoftware.com/mathgames/fractions/fracTut
1.htm Fraction tutorial
Understanding fractions.

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-b-lesson-2 Interpret a fraction as division.

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-b-lesson-3 Interpret a fraction as division

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-b-lesson-4 Use tape diagrams to model fractions as division.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.2
Item Bank:
1) What fraction of a graham cracker will each person get when 5 graham crackers are divided equally among 8 people? [Indiana Standards Resources 5.1.5]
5
Answer:
of a graham cracker
8
2) In a classroom, there are 12 boys and 16 girls. What fraction of the class is boys? Write your answer in lowest terms.
3
[Indiana Standards Resources 5.1.5 (modified)] Answer: of the class is boys
7
3) Draw a figure that represents one whole if
represents one-fourth. [IPS C& I Dept.] Sample Answer:
4) After a class potluck, Emily has seven equally sized apple pies left, and she wants to divide them into twelve equal portions to give to twelve students who
want to take some pie home.
a. Draw a picture showing how Emily might divide the pies into twelve equal portions. Explain how your picture shows twelve equal portions.
b. What fraction of a pie will each of the twelve students get?
c. Explain how the answer to (b) is related the division problem 7 ÷ 12.
[www.illustrativemathematics.org (modified numbers)]
A solution and visual explanation is available at https://www.illustrativemathematics.org/illustrations/858.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.6
Standard: 5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models).
Teacher Background Information:
Ratios, unit rates, and percents are critical tools for solving real-world problems. The term percent comes from the Latin expression meaning "per hundred". A
percent is also defined as a ratio comparing one number to 100. So 56% is understand as a ration of 56:100 or the fraction 56/100 or the decimal 0.56.
Depending on the context, quantities may be represented as a ratio, fraction, decimal, or percent. Baseball statistics are presented in the decimal form,
measurements are presented as fractions or decimals, and weather data are referred to as percents (40% chance of rain.)
Lesson Plans/Print Activities:
Web-based Practice:
 Math Expressions:
o Unit 11: Lesson 10
 http://www.curriculumsupport.education.nsw.gov.au/countmein/c
hildren_download.html Percent online game
 https://www.engageny.org/resource/grade-6-mathematics-module-1topic-d-lesson-24 Students understand that percents are related to part http://www.sciencekids.co.nz/gamesactivities/math/percentages.h
to-whole ratios and rates where the whole is 100.
tml Percentages online games

https://www.engageny.org/resource/grade-6-mathematics-module-1topic-d-lesson-25 Students write a fraction and a decimal as a percent of a
whole quantity and write a percent of whole quantity as fraction or
decimal

https://www.engageny.org/resource/grade-6-mathematics-module-1topic-d-lesson-26 Students find the percent of a quantity. Given a part
and the percent, students solve problems involving finding the whole.

https://www.engageny.org/resource/grade-6-mathematics-module-1topic-d-lesson-27 Students find the percent of a quantity. Given a part
and the percent, students solve problems involving finding the whole.

https://www.engageny.org/resource/grade-6-mathematics-module-1topic-d-lesson-28 Given a part and the percent, students find the percent
of a quantity and solve problems involving finding the whole.
Indianapolis Public Schools

http://www.shodor.org/interactivate/activities/EstimatorFour/
Estimating percentage game
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.6
Item Bank:
1) On the 10 × 10 grid below, shade in an area that represents 40%.
What fraction of the whole does this shaded part represent?
[Indiana Standards Resources Classroom Assessments] Answer: Check students’ models for correct shading.
40
or other equivalent fraction
100
2) Approximately what percent of the figure below is shaded?
[IPS C& I Dept.] Answer: 25%
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.6
Item Bank:
3) Ms. Hendricks asked her students how they get to school each day. She collected their answers and determined the following results. [Ohio Dept. of
Education]



Half of her students take the bus.
1
of her students walk.
5
The rest of her students ride with their parents.
a. What percent of the students take the bus? 50%
b. What percent of the students walk? Explain how you know that your answer is correct. 20%. One-fifth is equivalent to 20/100, which is equivalent to 20%.
c. What percent of the students ride with their parents? Show or explain how you got your answer. 30%. 70% (the total percent of students who take the bus and
walk) from 100% leaves 30%.
4) Write the decimal 0.75 as a simplified fraction and a percent:
0.75 = ____________ = ____________
3
[Indiana Standards Resources Classroom Assessments] Answer: 0.75 = = 75%
4
Indianapolis Public Schools
Curriculum and Instruction