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N a m e Operations and Algebraic Thinking3 .0A .1 ,3 .0A .3

Lesson 1

Hands On; Mode l

MultiplicationeHelpHomework Helper [O Need help? connectED.mcgraw-hill.com

Gina put 3 scoops of frozen yogurt ineach bowl. There are 6 bowls. How

many scoops of frozen yogurt are there?

DThe model shows the totalnumber of scoops.

There are 6 bowls, and each has3 scoops. There are 6 groups of 3.

Use repeated addition to find the total.

3 + 3 + 3 + 3 + 3 + 3 = 1 8

There are 18 scoops of frozen yogurt. (•:) (•:)P r a c t i c eDraw a model to find the total number.

1- 2 groups of 8 equals 2. 5 groups of 7 equals

3 . 6 X 4 = 4 . 4 X 8 =

Lesson 1 My Homework 197

Describe each set of equal groups.

5 .

+ + +

g r o u p s o f =

/StJx

+ +

groups of

7 . 6 X 5 =

groups of

M a t h e m a t i c a l

8 . 3 X 4 =

groups of

Problem Solvingticalrg^PRACTICE Model Math Complete each number sentence.

9- Paulina played 3 soccer games on Saturday. She drank 1 juicebox during each soccer game. How many juice boxes didshe drink?

+ + juice boxes10. Daniel, Jamie, Molly, and Corey each have 4 books from the

library. How many books do they have in all?

+ + library books

Vocab

Vocabulary Check11. Choose the correct word(s) to complete the sentence below,

equa l g roups mu l t ip l i ca t ion

Yo u c a n u s e

objects in

to find the total number of

198 Chapter 4 Understand Multiplication

Homework Helper QDani will put 2 forks at each of the8 table settings. How many forksdoes she need in al l?

Find 8 groups of 2.Write an addition sentence toshow the equal groups.2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 1 6

Write a multiplicationsentence to show 8 groups of 2.

Lesson 2

Multiplication asRepeated Addition

Need help? gJconnectED.mcgraw-hUI.com

8 X 2 = Find the unknown.

8 x 2 = 1 6

So, 8 groups of 2 is 16. The unknown is 16 forks.

P r a c t i c eWrite an addition sentence and a multiplication sentence for each.

1 .

a2 .

6 + 6 + + +

X -

+ + +

X =


r Problem SolvingDraw a picture to find the total. Write a multiplication sentence.3- 7 groups of 1 green grape 4. 9 groups of 2 square crackers

X = X


5. PRACTICE w Model Math How many buttons doesLeonora have altogether if she has 4 bags of buttons andeach bag has 10 buttons?

Multiply to find the unknown product.6 . 8 X 3 = B 7 - 4 x 3 = B

T h e u n k n o w n i s . T h e u n k n o w n i s

I Vocab

Vocabulary CheckUse the correct word(s) and the number sentence 6 x 8 = 48 to solve.

equal groups repeated addition multiply factors product8. The number 48 is the

9_ The symbol x tells you to

10. The numbers 6 and 8 are the

11 . 8 H " 8 + 8 H " 8 H ~ 8 ~ I ~ 8 — 4 8 s h o w s

1 2 . 6 x 8 m e a n s 6 o f 8 .

Te s t P r a c t i c e13. Sam is washing windows. There are 5 windows in each of

7 rooms. How many windows does Sam have to wash?

® 2 w i n d o w s ® 3 0 w i n d o w s

(D 12 windows ® 35 windows

204 Need more practice? Download Extra Practice at connectED.mcgraw-hill.com

N a m e Operations and Algebraic Thinking3.0A.I,3.0A.3,3.0A.5

Lesson 3

Hands On:

Multiply withArrays

Homework Helper eHelp

Q Need help? connectED.mcgraw-hill.comJames discovered that a sheet of stampsis in an array. The stamps are arrangedin 6 equal rows of 3.

Write an addition sentence to show equal rows.

3 + 3 + 3 + 3 + 3 + 3 = 1 8

Write a multiplication sentence torepresent the array.

E l l

r o w s

6

n u m b e r i ne a c h r o w

X

t o t a l

1 8 wtJames turns the sheet of stamps theother way. There still are 18 stamps.Only now, there are 3 equal rows of 6.

r o w s

3

n u m b e r i ne a c h r o w t o t a l

1 8X 6 =

This is the Commutative Property of Multiplication.

i 0 1 B Iii S B Q

P r a c t i c eDraw an array to find the product.

1 . 5 X 7 = 2 . 6 X 5


Write an addition sentence and a multiplication sentence toshow equal rows.

3 . 4 .

I Vocab

Vocabulary Check (|5- Draw two arrays to model 2x3 = 6.

Use the arrays to show the meaning ofthe Commutative Property ofMultiplication.

Problem SolvingM a t h e m a t i c a l

6 . PRACTICE Mode l Math Suk i ' s wa te rco lo r se thas 3 rows of paint. There are 8 colors in each row.Write a multiplication sentence to find the totalnumber of colors in the set.

7. A checkerboard has 8 rows, with 8 squares in eachrow. Write a multiplication sentence to find thetotal number of squares.


N a m e

Homework Helper [q

Operations and Aigebraic Thinking3.0A.T, 3.0A.3, 3.0A.5, 3.0A.8

Lesson 4

/ Arrays andMultiplication

i /

Need help? connectED.mcgrawhill.comThe pumpkins in a patch are arranged inrows with an equal number in each row.How many pumpkins are in the patch?

Write an addit ion sentence and a

multiplication sentence to show equal rows.

6 + 6 + 6 = 1 8 3 X 6 = 1 8

The Commutative Property of Multiplication allows you to changethe order of the factors to write another multiplication sentence, 6x3= 18.

There are 18 pumpkins in the pumpkin patch.

P r a c t i c eWrite an addition sentence and a multiplication sentenceto show equal rows.

1 .

G G G G+

X

+

2 - ^'■ ■ ' l M t € I ( i '

« «

(p/'I*, £ £ 1^ £5

+

X

+


Use the Commutative Property of Multiplication to find eachmissing number.

3 - 3 x 2 = 6 x 3 = 6 4 . 6 x 4 = 2 4 4 x = 2 4

5 - 8 x 6 = 4 8 6 x 8 = 6 _ 5 x 2 = 1 0 x 5 = 1 0

Problem SolvingDraw an array to solve. Then write two multiplication sentences.

7- Bottles of syrup are arranged in4 rows of 7 bottles each. How manybottles of syrup are there in all?

8. A parking lot has 6 rows of10 spaces. How many parkingspaces are there altogether?

f VocalT

Vocabulary Check (g9. How can you use an array to show the Commutative Property?

Test Pract ice10. Which pair of number sentences represents the

Commutative Property of Multiplication?

© 3 x 6 = 1 8 ; 2 x 9 = 1 8 © 4 x 5 = 2 0 ; 8 x 5 = 4 0® 6 X 7 = 42; 7 X 6 = 42 ® 9 + 11 = 20; 11 + 9 = 20

216 Need more practice? Download Extra Practice at connectED.mcgraw-hill.com

N a m e Operations and Algebraic Thinkingt a

T r t A * T A A T; 3.0A.1. 3.0A.3

Lesson 5

Problem Solving:Make a Table

1 eHelpHomework Helper Q Need help? connectED.mcgraw-hill.comJane's new bike can have hand brakes or foot brakes.The bike can be silver, blue, black, or purple. Howmany possible bikes are there?

U n d e r s t a n dThere are 2 types of brakes: hand brakes or foot brakes.There are 4 color choices: silver, blue, black, or purple.I need to find the number of possible bikes.

P l a nMake a table.

S o l v eThere are 8 possible bikes.

C h e c k

S i l v e r B l u e B l a c k PurpleH a n db r a k e s

Hand/Si lver Hand/Blue

Hand/Black

Hand/Purple

F o o t

b r a k e sFoot/Si lver Foot/Blue Foot/

BlackFoot/Purple

4Multiply 2 types of brakes by 4 color choices. 4x2 = 8

Problem Solving1. Solve the problem by making a table.

Claudio wi l l decorate his bedroom. He canchoose tan, blue, or gray paint and striped orplaid curtains. How many ways can he decoratehis room with different paint and curtains?

t a n . blue, (b) gray, (g)

striped,(s) m

plaid,(p)


Solve each problem by making a table.2- Jimmy has a number cube labeled 1 through 6, and a penny.

How many different ways can the cube and penny land withone roll of the cube and one flip of the penny?

1 2 3 4 5

heads, (h) ■ 1■ 1■ 1■; tails, ■ ■ ■

3- Archie earns $4 each week for doing his chores. How muchmoney will Archie earn in 2 months if there are 4 weeks ineach mon th?

W e e k 2 W e e l i 3 W e e k 4

M o n t h1

M o n t h2 ■ ■

Time to dochores!


4. PRACTICE Identify Structure Abigail has a green, yellow,and purple shirt to match with either a white, black, or red pair ofpants. How many different shirt and pants outfits can she make?

' sh i r t (g )

shirt, (y)

shirt (p)

pants, (w) pants, (b) pants, (r)

■ I H

How many outfits would be possible if Abigail had only 2 shirtsand 2 pair of pants? Explain.

224 Need more practice? Download Extra Practice at gJconnectED.mcgraw-hill.com

N a m e

L e s s o n 6

Use Multiplicationto F indC o m b i n a t i o n s

Homework Helper [q Need help? connectED.mcgraw-hilLcom

Lucia's three dogs have red, purple, blue, green, and orangecollars that they take turns wearing. Find the number ofpossible dog and collar combinations.

Show all of the possible combinationsred

purpleb l u e

g r e e no r a n g e

There are 3 dogs and 5 collar colors.3x5 = 15 possible combinations

P r a c t i c e1. Diana can take 1 pencil and 1 eraser to school. Her choices

are shown. How many different pencil and erasercombinations are there? Complete the tree diagram.Write a multiplication sentence.

P e n c i l C o l o r s

yellow

s q u a r e

C o m b i n a t i o n s

yellow, heart

yellow, staryellow, square

blue,

blue, starblue,

X c o m b i n a t i o n s


2. PRACTICE Identify Structure For a snack, Randy canchoose from peanuts, carrots, or popcorn. He can have water orjuice to drink. How many snack and drink combinations arethere? Complete the tree diagram. Write a multiplication sentence.

S n a c k D r i n k C o m b i n a t i o n s

c o m b i n a t i o n s

Vocabulary CheckVocab

3. Write the correct vocabulary word(s) in each space to completethe sentence.

c o m b i n a t i o n t r e e d i a g r a m

E a c h b r a n c h o f a s h o w s a p o s s i b l e

of i tems.

Te s t P r a c t i c e4. Amanda bought 4 pairs of shoes and 5 purses. Which number

sentence shows the number of different shoes and pursecombinat ions that Amanda can make?

® 4 + 5 = 9 © 4 + 4 + 4 + 4 = 1 6

@ 5 X 8 = 4 0 © 4 x 5 = 2 0

230 Need more practice? Download Extra Practice at connectED.mcgraw-hUI.com

Use the word bank to complete each sentence.

a r r a y c o m b i n a t i o n C o m m u t a t i v e P r o p e r t ye q u a l g r o u p s f a c t o r m u l t i p l i c a t i o nm u l t i p l i c a t i o n s e n t e n c e m u l t i p l y p r o d u c ttree diagram

1. An arrangement of objects into rows of equal length andcolumns of equal length is a(n)

2- The answer to a multiplication problem is the

3 - i s t h e o p e r a t i o n o f t w o n u m b e r s t h a tcan be thought of as repeated addition.

4. A number multiplied by another number is a

5- You can put equal groups together to

6 . T h e s a y s t h e o r d e r i n w h i c hnumbers are multiplied does not change the product.

7 . A u s e s " b r a n c h e s " t o s h o w a l l

possible combinations.

8 . W h e n y o u m a k e a o f i t e m s , y o u m a k ea new set that has one item from each group.

9 - W h e n y o u h a v e , y o u h a v e t h e s a m enumber of objects in each group.

My Chapter Review 231

Concept Checkc n e c k

Write an addition and a multiplication sentence to showequal rows.1 0 . n - r r r r r

m

+

X

+ +

X

Write two multiplication sentences for each array.1 2 . i 1 I 1 1 3 .

X

X

X

14. Find the possible combinations of one Yogurtyogurt and one topping. Complete thetree diagram. Write a multiplication strawberrysentence to check.

Sundaes

Yogur t Toppingsstrawberry granolapeach s t r a w b e r r i e s

vani l la

X = c o m b i n a t i o n s


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