Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Teacher Background Information:
Multiplication
Explore multiplication of decimals by using problems in a context and by returning to a model that was successful with multiplying whole numbers—the area
model. Use a scenario such as this one:
A gardener has 1.5m2 of her garden where she can plant flowers. She decides to plant bluebells on an area
that’s 0.6 of the garden. On how many total square meters did she plant bluebells?
Student solution using a grid diagram to model the problem.
Each large square represents 1 square meter with each row of 10 small squares as 0.1 of a square meter and each small square
as 0.01 of a square meter. The shaded section shows 0.6 m2 + 0.3 m2 = 0.9m2. Notice that this is a proportional model, allowing
students to “see” the values of the factors.
Estimation should play a significant role in developing a multiplication algorithm. As a beginning, consider this problem:
The farmer fills each jug with 3.7 liters of cider. If you
buy 4 jugs, how many liters of cider is that?
Begin with an estimate. Is it more than 12 liters? What is the most it could be? Could it be 16 liters? Once an estimate of the result is decided on, let students use
their own methods for determining an exact answer. Many will use repeated addition: 3.7 + 3.7 + 3.7 + 3.7. Others may begin by multiplying 3 * 4 and then adding
up 0.7 four times. Eventually, students will agree on the exact result of 14.8 liters. Explore other problems involving whole-number multipliers. Multipliers such as
3.5 or 8.25 that involve common fractional parts—here, one-half and one-fourth—are also reasonable.
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Teacher Background Information:
Division
Division can be approached in a manner exactly parallel to multiplication. In fact, the best approach to a division estimate generally comes from thinking about
multiplication rather than division. Consider the following problem:
The trip to Washington was 282.5 miles. It took exactly 4.5 hours
to drive. What was the average miles per hour?
To make an estimate of this quotient, think about what times 4 or 5 is close to 280. You might think 60 * 4.5 = 240 + 30 = 270. So maybe about 61 or 62 miles per
hour.
Addition & Subtraction
Jessica and MacKenna each timed their own quarter-mile run with a
stopwatch. Jessica says that she ran the quarter mile in 74.5
seconds. MacKenna was more accurate in her timing, reporting that
she ran the quarter mile in 81.34 seconds. Who ran it the fastest
and how much faster was she?
Students who understand decimal numeration should be able to tell approximately what the difference is—close to 7 seconds. Then they should be challenged to
figure out the exact difference. The estimate will help them avoid the common error of lining up the 5 under the 4. A variety of student strategies are possible. For
example, students might note that 74.5 and 7 is 81.5 and then figure out how much extra that is. Others may count on from 74.5 by adding 0.5 and then 6 more
seconds to get to 81 seconds and then add on the remaining 0.34 second. These and other strategies will eventually confront the difference between the 0.5 and
0.34. Students can resolve this issue by returning to their understanding of place value. Similar story problems for addition and subtraction, some involving
different numbers of decimal places, will help develop students’ understanding. Always require an estimate prior to computation.
Process Standards to Emphasize with Instruction of 5.AT.5:
5.PS.1: Make sense of problems and persevere in solving them.
5.PS.2: Reason abstractly and quantitatively.
5.PS.3: Construct a viable argument and critique the reasoning of others.
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Lesson Plans/Print Activities:
Web-based Practice:
Math Expressions Resources:
*Unit 3, Lesson 4:
*Unit 7, Lesson 7, 13, 18, 19, 20

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-doverview Measurement Word Problems with Whole Number and Decimal
Multiplication

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-hoverview Measurement Word Problems with Multi-Digit Division

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-foverview Multiplication with Fractions and Decimals as Scaling and Word
Problems

https://grade5commoncoremath.wikispaces.hcpss.org/file/view/5.NBT.3_5.N
BT.7_MakingCentsofDecimals.pdf/457250150/5.NBT.3_5.NBT.7_MakingCents
ofDecimals.pdf Georgia DOE Lesson Plan

https://grade5commoncoremath.wikispaces.hcpss.org/file/view/5.NBT.7_Roa
dTrip.pdf/457250434/5.NBT.7_RoadTrip.pdf In this task, students determine
fuel costs for a trip through the Southeast of the United States.

http://illuminations.nctm.org/Lesson.aspx?id=3649 Welcome to the Aquarium:
Planning a Classroom Aquarium to practice decimal operations
Indianapolis Public Schools

https://learnzillion.com/lessonsets/189-adding-and-subtractingdecimals-to-hundredths Learnzillion Lessons

https://learnzillion.com/student/lessons/2503 Solve Real-World
problems with multi-digit decimals.

https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5tharith-operations Khan Academy: 5th Grade Arithmetic Operations:
adding decimals, subtracting decimals, multiplication and
decimals, dividing decimals

http://www.khanacademy.org/math/cc-fourth-grade-math/cc-4thmeasurement-topic Khan Academy: Word problems with units.
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank:
Part 1:
Mrs. Potter bought 6 boxes of clay for an art project. If each box of clay weighs 17.4 ounces, how many ounces of clay did the teacher buy? Explain your answer
using pictures, numbers, and/or words.
Part 2:
If the clay is shared equally among the 18 students in the class, how many ounces of clay will each student get? Explain your answer using pictures, numbers,
and/or words.
Part 3:
After her students begin the project, Mrs. Potter realizes that each student needs 8.7 ounces of clay. How many more boxes of clay does Mrs. Potter need to buy?
Explain your answer using pictures, numbers, and/or words.
Part 4:
Explain your strategy to all 3 parts in writing. Make sure to use pictures and/or numbers to justify your reasoning.
[North Carolina Dept. of Public Instruction]
John is purchasing a piece of canvas on which to paint a self-portrait. The canvas is 4.4 feet wide and 2.05 feet long. In order to determine how much paint he
needs for his background color, John wants to know the area of his canvas. What is the area of the canvas?
In order to frame the canvas, John needs to know the perimeter of the canvas. What is its perimeter?
John decides the canvas is too big, so he cuts it in half. What are the new area and perimeter of his canvas?
[North Carolina Dept. of Public Instruction]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
[NAEP 2007]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
[NAEP 2003]
[NAEP 2011]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
Item
yogurt
pretzels
cheese cubes
bagel
fruit drink
peanuts
Cost
$0.95 each
$2.50 per bag
$2.19 per bag
$0.89 each
$1.85 each
$2.55 per bag
[NAEP 2011]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
Color
Color A
Color B
Color C
Amount
311.25 mL
150.17 mL
90.4 mL
1. How many milliliters of the solution will be made? Show your calculations.
2. Jenny made more than one batch of the solution and has a total of 1,103.64 mL of the solution. She wants to pour the solution into application bottles so that
there is one application per bottle. Each application bottle holds 135 mL of solution.
a. How many application bottles can Jenny fill completely? Explain your reasoning.
b. How many milliliters will be left after as many application bottles as possible have been completely filled with the solution Jenny made? Show how you found
your answer.
3. Jenny has a recipe for a different hair-coloring solution that makes 575.48 mL in one batch. Jenny is going to ship this hair-coloring solution in single-application
bottles to her other salons. Each shipping box can hold 16 application bottles, which hold 135 mL each.
a. How many batches of the solution will Jenny need to make to completely fill 16 single-application bottles? Explain your reasoning.
b. How many liters of the solution will be packed into one box? Show your calculations.
[www.louisianabelieves.com]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
a. Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why?
b. Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans and then scale reads 12.0 grams. How much would you expect 1 jellybean to
weigh? Why?
c. Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads 312.4 grams. How much would you expect 1,000 pink erasers to
weigh? Why?
[www.illustrativemathematics.com]
a. Jessa has 23 one-dollar bills that she wants to divide equally between her 5 children.
i.
How much money will each receive? How much money will Jessa have left over?
ii.
Jessa exchanged the remaining one-dollar bills for dimes. If she divides the money equally between her 5 children, how much money will each child get?
b. A website has games available to purchase for $5 each. If Lita has $23, how many games can she purchase? Explain.
c. A jug holds 5 gallons of water. How many jugs can Mark fill with 23 gallons of water? Explain.
d. A class of 23 children will take a field trip. Each car can take 5 children. How many cars are needed to take all the children on the field trip? Explain.
e. Write a division problem for 31 ÷ 4 where the answer is a mixed number. Show how to solve your problem.
[www.illustrativemathematics.com]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
The Tasty Deli uses 6.5 pounds of ham each day.
a. How many ounces of ham will be used in three weeks? Use equations or pictures to show how you found your answer.
b. Each ham sandwich the deli sells uses 13 ounces of ham. How many sandwiches can the deli make in three weeks? Show your work or explain your reasoning.
The deli manager pays $1.59 per pound for turkey and $1.75 per pound for beef. Write an expression that shows how to calculate the amount of money the deli
manager will spend if he buys 9 pounds of beef and 15 pounds of turkey. Use the expression you wrote to find the total amount the manager will spend.
[www.louisianabelieves.com]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.AT.5
Standard:
5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money
in decimal notation (e.g. by using equations to represent the problem).
Item Bank (continued):
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum & Instruction