Home-School
Connection
Name
Use Operations with Whole
Numbers to Solve Problems
Topic
11
Dear Family,
Your child is learning to apply his or her understanding of the four operations (addition,
subtraction, multiplication, and division) to solve two-step word problems. Your child will
learn to use letters to represent unknown quantities and solve for these quantities. Use
the problem below to discuss with your child how to solve two-step word problems.
Jonah has $120. He buys 4 games that are $9 each. How much money does he
have left?
m = money left after buying games
Write an equation showing the amount
$120 - 4 × $9 = m
of money minus the number of games
multiplied by the cost of each game.
Start reading the equation from the left
$120 - (4 × $9) = m
and do any multiplication or division as
you move to the right.
Then, start back from the left and do any
$120 - $36 = m
addition or subtraction.
m = $84
Jonah has $84 left.
Here is an activity you can complete with your child.
Writing and Solving Word Problems
Materials paper and pencil
Take turns with your child saying and writing two-step word problems using different operations.
Have your child write the related equations and identify the correct operations to use.
Observe Your Child
Use an incorrect operation to answer one of the word problems. Then ask your child to explain
why the answer is incorrect.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
De la escuela al hogar
(en español)
Nombre
Usar operaciones con números
enteros para resolver problemas
Tema
11
Estimada familia:
Su niño(a) está aprendiendo a usar lo que aprendió sobre las cuatro operaciones
(suma, resta, multiplicación y división) para resolver problemas verbales de dos pasos.
Aprenderá a usar letras para representar y hallar cantidades desconocidas. Use el
siguiente problema para hablar con su niño(a) sobre cómo resolver problemas verbales de
dos pasos.
Juan tiene $120. Compra 4 juegos que cuestan $9 cada uno. ¿Cuánto dinero
le queda?
d = dinero que queda después de comprar juegos
Escribe una ecuación que muestre
$120 - 4 × $9 = d
cuánto dinero queda después de
comprar los juegos.
Empieza a leer la ecuación desde el lado
$120 - (4 × $9) = d
izquierdo y resuelve las multiplicaciones
o divisiones que haya hacia la derecha.
Luego, vuelve al lado izquierdo y resuelve
$120 - $36 = d
las sumas o restas que haya.
d = $84
A Juan le quedan $84.
Pruebe esta actividad con su niño(a).
Escribir y resolver problemas verbales
Materiales papel y lápiz
Túrnese con su niño(a) para decir y escribir problemas verbales de dos pasos con distintas
operaciones. Pida a su niño(a) que escriba las ecuaciones relacionadas e identifique las
operaciones que debe usar.
Observe a su niño(a)
Use una operación incorrecta para resolver uno de los problemas verbales y pida a su niño(a) que
explique por qué la respuesta es incorrecta.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Reteach to Build
Understanding
Name
11-1
Vocabulary
1. You can draw a bar diagram to help solve 2-step problems. A letter can be
used to stand for the unknown quantity.
Complete the equation for each unknown quantity in each bar diagram.
185
p
124
t
32
25
Write an equation using subtraction.
Write an equation using addition.
t=
p=
-
+
2. Jared has $ 236. He spends $ 153 paying bills. Jared will earn $ 76
next week. How much money will Jared have next week?
Step 1: Find and answer the hidden question.
Hidden question: How much money does Jared have after paying bills?
Complete the bar diagram. Then write and solve an equation.
m=
$236
-
m=
m
Jared has
after he pays bills.
Money left
after paying
bills
3. Step 2: Use the answer to the hidden question to answer the original question.
Original question: How much money will Jared have next week?
Complete the bar diagram. Then write and
solve an equation.
s=
s
Money next week
+
s=
Jared will have
next week.
On the Back!
4. Draw bar diagrams and write equations to solve. Aaron has
996 baseball cards. He sells 333 of them. Then, he buys 165 baseball
cards. How many baseball cards does Aaron have now?
R 11•1
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Reteach to Build
Understanding
Name
11-2
Vocabulary
1. A product is the answer to a multiplication problem.
A quotient is the answer to a division problem.
Write a multiplication equation for the bar diagram.
×b=
The product is
40
.
b
b
b
b
b
Write a division equation for the bar diagram.
,b=
The quotient is
.
2. Complete the bar diagrams and write equations to solve. Use
letters to represent unknown quantities.
Jill is in charge of scheduling fields for the youth soccer leagues. There
are 4 leagues with 6 teams in each league. An equal number of teams will
play on each of 3 fields. How many teams will play on each field?
Step 1: Find and answer the hidden question.
Hidden question: How many
There are
leagues. There are
t = 4 × 6
t=
There are
teams in all.
are there in all?
teams in each league.
t
Teams in all
Step 2: Use the answer to the hidden question to answer the original question.
Original question: How many teams will play on each field?
There are
teams in all.
There are
fields.
f = 24 , 3
f=
f
teams will play on each field.
f
f
Teams on
each field
On the Back!
3. Draw bar diagrams and write equations to solve. Use letters to
represent unknown quantities.
A pack of 8 sports drinks costs $ 5. How much would it cost to buy 72 sports drinks?
R 11•2
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Math and Science
Activity
Name
11-2
Golf Ball Flight
Did You Know? The golf ball has undergone many
changes in the 600 years since it was first used in the
1400s. The first golf balls were made of wood. Leather golf
balls stuffed with feathers soon replaced these. Engineers
first introduced the dimples on golf balls in the early
1900s to help reduce drag. The dimples allow the ball to
travel a longer distance when hit.
Lucien and Tina are doing an experiment to see how different
golf clubs might change the distance golf balls travel. The
table shows the costs of packages of golf balls they can buy
for the experiment.
Golf Ball Sale
Number of
Packages
➊ Lucien wants to know the cost per package of golf balls
if he buys 8 packages. Which operation will he use?
Total Cost
5
$20
8
$24
12
$36
➋ Complete the bar diagram to find the cost per
package if Lucien buys 8 packages.
c
c
c
c
c
c
c
c
➌ Tina says that she can save $2 per package if she buys 12 packages instead of
8 packages. Is she correct? Explain.
➍Extension The store introduces a new sale on 20 packages of golf balls for $40.
Is this a better deal than buying 8 or 12 packages of golf balls?
Math and Science Activity
11•2
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Reteach to Build
Understanding
Name
11-3
Vocabulary
1. Some problems need more than one operation to solve. Operations are addition,
subtraction, multiplication, and division.
You need to know which operation to do first. Follow these rules.
• Read the equation from the left side and do any multiplication or division as
you move to the right.
• Start back on the left side and do any addition or subtraction.
Solve this equation:$135 - $6 × 7 = p
Multiply first. $135 - $6 × 7 = p
Then subtract.
$135 -
$135 -
= p
=p
=p
2. Amanda has $ 268 in her savings account. She adds $ 60 to it each
week for 8 weeks. How much money does she have after 8 weeks?
Let s = the amount of money Amanda has after 8 weeks.
Write an equation: $ 268
8=s
$ 60
Using the rules above, draw parentheses to show which operation
is done first. Then solve.
$ 268 + $ 60 × 8 = s
$ 268 +
=s
=s
After 8 weeks, Amanda has
.
On the Back!
3. Write equations to solve. Use a letter to represent the unknown
quantity.
Sally bought a dress for $ 82. She also bought 2 pairs of shoes for
$ 40 each. How much money did Sally spend?
R 11•3
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Reteach to Build
Understanding
Name
11-4
Vocabulary
1. When you critique reasoning, you explain why someone’s thinking is correct or
incorrect. Estimation can help you critique reasoning.
Estimate 54 + 42 by rounding.
54 is about
.
42 is about
50 + 40 =
.
Is the estimate less than or greater than the actual sum?
Estimate 27 + 35 by rounding.
27 is about
.
35 is about
30 + 40 =
.
Is the estimate less than or greater than the actual sum?
2. Jessica has $ 75. She works 6 hours at $ 8 an hour at her job. Jessica
wants to buy a bicycle for $ 129. Can Jessica buy the bicycle?
Abby solved the problem. Her work is shown below.
$8 × 6 = $48, which is about $ 50.
Jessica has $ 75, which is about $ 80.
$50 + $80 = $130, so Jessica can buy the bicycle.
Critique Abby’s reasoning.
Abby rounds $ 48 to $ 50. This estimate is rounded
.
Abby rounds $ 75 to $ 80. This estimate is rounded
.
the actual amount.
The estimate will be
3. Find the actual answer.
$8 × 6 =
$75 +
Abby’s conclusion is
=
because the actual
.
amount Jessica will have is less than
On the Back!
4. The park had 425 visitors on Friday. It had 289 visitors on Saturday
and 126 visitors on Sunday.
Eva says there were more visitors on Friday than on Saturday and
Sunday combined because 289 + 126 is about 300 + 100 = 400,
and 400 6 425. Critique Eva’s reasoning. Tell if she is correct or
incorrect. Explain your thinking.
R 11•4
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3
Math and Science
Activity
Name
11-4
Cost of Materials
Building Project
Materials
Did You Know? Engineers perform math calculations
to create their desired product. They may work
towards many goals, such as using the least amount
of materials, spending the least amount of money, or
using the least amount of space.
Material
The Grade 3 team is building structures using the materials
shown in the table. Each team is given 145 points. Kendra’s
team buys 30 gumdrops. She needs to know if they have
enough points left to buy 30 toothpicks. Kendra says her
team has enough points.
Cost
toothpick
2 points
gumdrop
3 points
cotton ball
4 points
rubber band
5 points
fabric strip
7 points
tin foil
9 points
Kendra’s work
30 × 3 = 90
The team has used 90 points.
145 is about 150. 150 − 90 = 60 and 30 × 2 = 60
30 toothpicks cost 60 points.
The team has enough points to buy 30 toothpicks.
➊ What is Kendra’s argument? How does she support it?
➋ Extension Critique Kendra’s reasoning.
Math and Science Activity
11•4
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3