Essential Question?

Unlock the ProblemUnlock the Problem

140 30

total number of large beads

a

total number of small beads

total number of beads Shaniqua buys

13 13 13 13 13 5 bracelets with 13 beads

d total number of beads Shaniqua uses

s 65

beads used

170

beads left

total number of beads Shaniqua buys

Name

How can you represent and solve multi-step problems using equations?

Algebraic Reasoning—5.4.B

MATHEMATICAL PROCESSES5.1.B, 5.1.D

Represent and Solve Multi-Step Problems8.4

• Underline the important information.Shaniqua buys 140 small beads and 30 large beads to

make bracelets. She makes 5 bracelets. She uses

13 beads on each bracelet. How many beads does

Shaniqua have left?

Example 1 Use multiple single-step equations.

STEP 1 Find the total number of beads Shaniqua buys. 140 + 30 = a

_ = a

STEP 2 Find the total number of beads Shaniqua uses to make 5 bracelets. 5 × 13 = d

_ = d

STEP 3 Find the total number of beads Shaniqua has left. 170 – 65 = s

_ = s

So, Shaniqua has _ beads left.

Module 8 341

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

14 141414 14 14 14 14

b

15 151515 15 15

p

n

15

10

15 15 7 7

shells givenaway shells left

total numberof shells

Mathematical ProcessesMath Talk

Try This! Sometimes you can use one multi-step equation to

solve a problem.

Miguel sorts his seashell collection into boxes. He has 3 boxes with

15 periwinkle shells in each box. He has 2 boxes with 7 clamshells

in each box. He gives his little brother 10 shells. How many shells

does he have now?

3 × 15 + 2 × 7 – 10 = n

_ + _ – _ = n

_ – _ = n

_ = n

Example 2Meagan has two card-collection books. The first book has 8 cards on

each of 14 pages. The second book has 6 cards on each of 15 pages.

Which of the two books has more cards?

STEP 1 Solve the equation b ÷ 8 = 14 to find the number of cards in the first book.

Write a related multiplication equation.

14 × _ = b b = _

STEP 2 Solve the equation p ÷ 6 = 15 to find the number of cards in the second book.

Write a related multiplication equation.

15 × _ = p p = _

STEP 3 Compare the number of cards in each book.

The first book has _ cards.

The second book has _ cards.

Since _ > _, the _ book has more cards.

Explain why you can use a related multiplication to solve

a division problem.

342

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Problem SolvingProblem Solving

Share and ShowShare and Show

Write MathWrite Math Show Your Work

Name

Use equations to solve.

3. Multi-Step A florist makes 4 floral arrangements that

are exactly the same. He uses 4 bunches of 8 tulips and

2 bunches of 10 daisies. How many flowers, f, are in each

arrangement?

4. Multi-Step Francois is rolling coins.

He has 3 rolls of 40 quarters. He has 8 rolls of 50 dimes.

He exchanges 2 rolls of dimes for 1 roll of quarters.

How many coins, c, does Francois have?

5. Multi-Step Elsa has 4 trays of

15 sedimentary rocks. She has 6 trays

of 12 metamorphic rocks. She gives away

5 sedimentary rocks for 7 metamorphic

rocks. How many rocks, r, does she have?

6. Analyze Murial alternates her exercise. She runs 5 miles

each day for 3 days and walks 4 miles each day for 2 days

in one week. She rides her bike 8 miles each day for

4 days the next week. How many more miles, m, does

Murial travel during the second week than the first week?

Use equations to solve each multi-step problem.

1. A caterer is making 3 trays of 24 sandwiches

and 2 trays of 30 sandwiches. She receives an

order for 35 sandwiches. How many sandwiches,

s, does the caterer have left?

2. A baseball league has a total of 156 players.

The players are divided into 12 equal teams.

Each team has 3 coaches. All players and coaches

receive 2 jerseys. How many jerseys, j, will each

team receive?

Module 8 • Lesson 4 343

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Daily Assessment TaskDaily Assessment Task

Mathematical ProcessesM

TEXAS Test Prep 10. The cost of 3 pizzas is shared equally by 6 people. Each pizza costs $9.

Each person contributes $5. Which equation could be used to find, m,

the amount of money left?

A 3 × 9 – 6 × 5 = m C 6 × 5 – 3 × 9 = m

B 9 ÷ 3 – 6 × 5 = m D 3 × 9 + 5 × 6 = m

Fill in the bubble completely to show your answer.

7. Apply A volunteer took 3 cups and 7 quarts of a large bowl of soup

home from a cooking class.. How much soup did this volunteer take?

(Hint: There are 4 cups in a quart.)

A 31 cups

B 37 cups

C 31 quarts

D 42 quarts

8. What is the first step in solving the equation 4 + 10 × 3 – 2 = n?

A Find 4 + 10.

B Find 3 – 2.

C Find 10 × 3.

D Subtract n.

9. Multi-Step Evelyn has 4 boxes with 8 pieces of sidewalk chalk in each

box. She has 3 boxes with 9 stickers in each box. She gets 5 more pieces

of sidewalk chalk from her brother. If she places everything into a bin,

how many items does she place in the bin?

A 24

B 55

C 64

D 72

344

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Problem SolvingProblem Solving

Homeworkand Practice

Name

Use equations to solve.

1. Last week, Mary picked 4 baskets of 8 tomatoes

from her garden. This week, she picked 3 baskets

of 13 tomatoes. How many more tomatoes, t, does Mary pick this week than last week?

2. A costume designer sews 4 rows of 16 beads

on a princess costume, 5 rows of 15 beads on a

butterfly costume, and 3 rows of 17 beads on a

ballerina costume. How many more beads, b, are

sewn on the costume with the most beads than

are sewn on the costume with the least number

of beads?

3. Venancio needs to paint 8 game boards for the

carnival. Each game board is divided into

12 parts. He paints 5 parts of 8 game boards

yellow, 3 parts of 6 game boards red, 2 parts of

7 game boards green, and 15 parts purple. How

many more parts, p, does Venancio have left

to paint?

4. Mr. Gates buys frozen yogurt bars for the grade

5 picnic. He buys 3 packages of 12 strawberry

yogurt bars and 6 packages of 8 banana yogurt

bars. He gives an equal number of frozen yogurt

bars to each of 3 classes. How many frozen

yogurt bars, y, does each class get?

5. Rusty has a cap collection. He has 2 shelves with

9 football team caps on each shelf. He has

3 shelves with 11 baseball caps on each shelf. He

gives his best friend 2 football caps and

3 baseball caps. How many caps, c, does Rusty

have now?

6. Erin pays $3 for each of 4 headbands and $2 for

each of 5 barrettes. How much more money, m,

does Erin pay for all the headbands than for all

the barrettes?

Algebraic Reasoning—5.4.BMATHEMATICAL PROCESSES 5.1.B, 5.1.D

Represent and Solve Multi-Step Problems8.4

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 8 • Lesson 4 345

TEXAS Test PrepLesson CheckLesson Check

7. Marty is using balloons to decorate for a

party. She has 3 groups of 5 pink balloons and

4 groups of 3 yellow balloons. She also has

6 white balloons. Which equation could be

used to find, b, the total number of balloons?

A 3 × 5 + 4 × 3 = b

B 3 + 5 + 4 + 3 + 6 = b

C 3 × 5 + 4 × 3 + 6 = b

D 3 × 5 × 4 × 3 = b

8. For the bake sale, 6 people each bake two

dozen oatmeal cookies. Each person eats

2 cookies and then delivers the remaining

cookies to the bake sale. Which equation

could be used to find, c, the number of

oatmeal cookies at the bake sale?

A 6 × 2 × 12 − 6 × 2 = c

B 6 × 12 − 6 × 2 = c

C 2 × 12 − 6 × 2 = c

D 6 × 2 − 6 × 2 = c

9. Jasper used 15 inches of blue ribbon, 14 inches

of yellow ribbon, and 3 feet of red ribbon to

decorate his box of cookies. How many inches

of ribbon did Jasper use?

A 65 inches

B 32 inches

C 93 inches

D 29 inches

10 William used 10 ounces of plain milk and

4 pints of chocolate milk when making the

restaurant milkshake recipe. How many

ounces of milk did William use? (Hint: there

are 16 ounces in a pint.)

A 64 ounces

B 40 ounces

C 26 ounces

D 74 ounces

11. Multi-Step Rona has 4 packs of 12 glitter

pens. She has 7 packs of 8 scented pens.

She gives her friend a pack of glitter pens in

exchange for a new pack of scented pens. How

many pens does Rona have now?

A 92

B 104

C 100

D 112

12. Multi-Step Bella has potted plants on her patio.

She has 4 pots with 3 begonia plants in each pot.

She has 3 pots with 8 petunias in each pot. She

plants 7 more zinnia plants in another pot. How

many plants does Bella have on her patio?

A 25

B 43

C 36

D 57

Fill in the bubble completely to show your answer.

346

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

x

15Eric

Margo 5

33 17

g

Name

Module 8 AssessmentConcepts and SkillsConcepts and Skills

1. Which value of n makes the equation, n + 5 = 4 + 4, true? q TEKS 5.4.B

Use the strip diagram to write an equation. Then solve. q TEKS 5.4

2. Eric jogged 15 laps around a track. Margo

jogged 5 laps. How many more laps did

Eric jog than Margo?

Equation: ___ x = _

3. Sadie hit 17 golf balls from her bucket. Then there

were 33 golf balls left in the bucket. How many golf

balls did Sadie have in her bucket before she hit

any golf balls?

Equation: ___ g = _

4. A store sells 8 small, 18 medium, and 20 large

sweatshirts. Each sweatshirt costs $16. How

much money, m, is the store paid for all the

sweatshirts they sell?

5. A caterer makes sandwiches from 8 loaves of

bread. Each loaf makes 10 sandwiches. The

caterer puts 3 ounces of turkey on each

sandwich. How many ounces, z, of turkey

does the caterer use?

6. A train has 34 passengers in each of 3 cars and

28 passengers in each of 4 cars. How many

passengers, p, are on the train?

7. There are 252 students at a school party. They are

seated in groups of 9. Each group gets 3 bags of

popcorn. How many bags of popcorn, p, are used

for the party?

__

Write an equation. Then solve. q TEKS 5.4.B

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 8 347

TEXAS Test PrepFill in the bubble completely to show your answer.

8. Ryanhas5boxeswith8markersineachbox.Hehas7boxeswith10markersineachbox.Hegiveshisfriendoneboxof8markersandoneboxof10markers.Whichequationcanbeusedtofindthetotalnumberofmarkers,m,thatRyanhasleft? q TEKS 5.4.B

A 7×10–5×8–8–10=m

B 8–5×8+10–7×10=m

C 5×8÷7×10–8–10=m

D 5×8+7×10–8–10=m

9. Thorahad$5leftinherpocketafterspending$12onsnacksandsouvenirsonaclasstrip.HowmuchmoneydidThoratakeontheclasstrip?Theequationt–12=5canbeusedtofindt,theamountofmoneyThoratookontheclasstrip. q TEKS 5.4

A $17 C $7

B $14 D $16

10. Studentsearned$368sellingc,calendars.Theyearned$456sellingm,mugs.Thepriceofeachmugandeachcalendaris$8.Theequationc=368÷8representsthenumberofcalendarstheysold.Theequationm=456÷8representsthenumberofmugstheysold.Howmanymoremugsthancalendarsdidstudentssell? q TEKS 5.4.B

A 57

B 103

C 11

D 46

11. Thereare180studentsatsummercamp.Eachcabinhouses12students.Thereare2counselorsforeachcabin.Solvetheequationc=(180÷12)×2tofindthenumberofc,counselors. q TEKS 5.4.B

Recordyouranswerandfillinthebubblesonthegrid.Besuretousethecorrectplacevalue.

.0 0 0 0 0

1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

4 4 4 4 4

5 5 5 5 5

6 6 6 6 6

7 7 7 7 7

8 8 8 8 8

9 9 9 9 9

348

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=B