Multiply and Divide with Multiples of 10, 100, and 1,000 and Divide with Multiples of 10, 100, and...

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712 Unit 9 Multiplication and Division

��

Advance PreparationPost the Guide to Solving Number Stories poster (Math Masters, page 406).

Teacher’s Reference Manual, Grades 1– 3 pp. 193 –195

Key Concepts and Skills• Find multiples of 10, 100, and 1,000.

[Number and Numeration Goal 3]

• Compare and order numbers.


• Use multiplication facts to solve problems.

[Operations and Computation Goal 3]

• Solve number sentences involving the

symbols ×, ÷, and =.

[Patterns, Functions, and Algebra Goal 2]

Key ActivitiesChildren make up and solve multiplication

and division number stories about animal

weights. Children find products and quotients

involving multiples of 10, 100, and 1,000.

Ongoing Assessment: Informing Instruction See page 715.

Ongoing Assessment: Recognizing Student Achievement Use journal page 206. [Number and Numeration Goal 3]

MaterialsMath Journal 2, pp. 204–206

Math Masters, p. 406

slate � blank transparency (optional)

Playing Name That NumberStudent Reference Book, pp. 299

and 300

per group: 4 each of number cards

0–10 and 1 each of number cards

11–20 (from the Everything Math

Deck, if available)

Children use two or more operations

to find equivalent names for numbers.

Math Boxes 9�1Math Journal 2, p. 207

Children practice and maintain skills

through Math Box problems.

Home Link 9�1Math Masters, p. 267

Children practice and maintain skills

through Home Link activities.

READINESS

Extending Multiplication Fact PatternsMath Masters, p. 268

per partnership: base-10 blocks (longs, flats,

and big cubes)

Children explore patterns in multiples of 10,

100, and 1,000.

EXTRA PRACTICE

Minute Math +Minute Math ®+, pp. 128 and 131

Children solve number stories involving

multiplication and division.

ELL SUPPORT

Writing Multiplication and Division Number StoriesChildren write multiplication and division

number stories.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Multiply and Divide withMultiples of 10, 100, and 1,000

Objective To guide children as they multiply and divide

with multiples of 10, 100, and 1,000.w

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Lesson 9�1 713

Adult Weights of North American Animals cont.LESSON

9�1

Am

eric

an p

orcu

pine

20 lb

to 4

0 lb

Sea

otte

r48

lb to

99

lb

Pum

a15

0 lb

to 2

30 lb

Whi

te-ta

iled

deer

50 lb

to 4

80 lb

Pilo

t wha

le3,

200

lb to

6,4

00 lb

Atla

ntic

gre

en tu

rtle

250

lb to

450

lb

Wes

t Ind

ian

man

atee

500

lb to

1,1

00 lb

Am

eric

an a

lliga

tor

200

lb to

500

lbG

ray

fox

9 lb

to 1

6 lb Com

mon

dol

phin

200

lb to

300

lbR

ight

wha

le70

,000

lb to

140

,000

lb

Bot

tle-n

osed

dol

phin

350

lb to

430

lb

Gila

mon

ster

2lb

to 4

lb1 2

Gra

y w

hale

45,0

00 lb

to 7

2,00

0 lb

Date Time

Math Journal 2, p. 205

Student Page

Interactive whiteboard-ready

ePresentations are available at

www.everydaymathonline.com to

help you teach the lesson.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, pp. 204 and 205)

According to the Adult Weights of North American Animals poster, a normal weight for a beaver is from 20 to 56 lb. Remind children that the abbreviation for pounds is lb. Any weight within this range is a correct response to the Math Message. Have children briefly share their observations from the poster.

NOTE The word range is used here to mean the series of numbers between

two given numbers. Children should not confuse this meaning with the data

landmark range, which means the difference between the largest (maximum) and

the smallest (minimum) numbers in a set of data. To support English language

learners, write range on the board twice with examples of both meanings.

Ask children to name other animals on the poster and to tell their normal adult weight ranges. Have children give numbers within these ranges. For example, the weight range for an arctic fox is 7 lb to 20 lb. Ask: Could an arctic fox weigh 15 lb? yes 22 lb? no

� Modeling How to Solve WHOLE-CLASS ACTIVITY

Multiplication and Division Number Stories(Math Journal 2, pp. 204 and 205; Math Masters, p. 406)

Explain that the class will solve multiplication and division number stories. Refer children to the Guide for Solving Number Stories poster (Math Masters, page 406) and the animal posters in their journals (Math Journal 2, pages 204 and 205). Write the following problem on the board or transparency. Which animal could weigh 30 times as much as a 50-pound sea otter?

ELL

Getting Started

Math MessageUse journal pages 204 and 205 to find out how much an adult beaver might weigh. Write the answer on your slate. Talk to a partner about information on the map.

Mental Math and ReflexesPose problems like the following. Children answer on their slates:

How much are 7 [30s]? 210

What number is 50 times as much as 6? 300

How many 9s equal 540? 60

How much are 70 [30s]? 2,100

What number is 50 times as much as 60? 3,000

How many 90s make 5,400? 60

How much are 30 [700s]? 21,000

What number is 60 times as much as 500? 30,000

How many 60s make 54,000? 900

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Guide to Solving Number Stories

Name Date Time

1. What do you understand from the story?

� Read the story. What do you want to find out?

� What do you know?

2. What will you do?

� Add?

� Subtract?

� Multiply?

� Divide?

� Draw a picture?

� Make tallies?

� Use counters or base-10 blocks?

� Use a number grid or number line?

� Make a table?

� Draw a diagram?

� Write a number model?

3. Answer the question.

� Solve the problem. Record your work.

� Write the answer with the units.

4. Check.

� Does your answer make sense? How do you know?

EM3MM_G3_U02_036-063.indd 406 12/29/10 5:57 PM


Teaching Aid Master

?30 [50s] = ?

30 [50s] = 1,500

One polar bear weighs as much as 30 sea otters.

1. What do you understand from the story? Think:

● What do you want to find out? Which animal could weigh 30 times as much as the sea otter?

● What information do you know from reading the story? A sea otter weighs 50 lb. There is an animal that weighs about 30 times as much as a sea otter.

2. What could you do to find which animal weighs about 30 times as much as the sea otter? You could multiply 30 times 50 lb and then find an animal that weighs about that much.

● Write a number model to represent the story. Possible number models: ? = 30 × 50; 30 × 50 = ?

NOTE Remind children that they can use either a question mark or a letter for

the unknown quantity in a number model.

3. Answer the question. 30 times 50 lb is 1,500 lb. A polar bear could weigh from 650 to 1,750 lb; and 1,500 lb is in that range.

Allow time for children to write solution strategies on the board and explain them to the class. Possible strategies may include: I added 50 ten times to get 500 and then added 500 three times to get 1,500; I know that 50 × 30 = 1,500 is an extension of the basic fact 5 × 3 = 15; I added 30 fifty times to get 1,500.

4. Does your answer make sense? How do you know? Sample answer: I know that 10 sea otters weigh 500 lb. 30 sea otters would weigh 3 times that amount, about 1,500 lb; which is in the weight range for polar bears.

● Does your answer make the number model true? yes Write a summary number model on the board: 1,500 = 30 × 50.

Write the following problem on the board or transparency: How many 50-pound sea otters together would weigh about 1 ton? (1 ton = 2,000 lb)

1. What do you understand from the story? Think:

● What do you want to find out? The number of 50-pound sea otters whose total weight would be 2,000 lb

● What information do you know from reading the story? A sea otter weighs 50 lb. An unknown number of sea otters weigh 2,000 lb.

2. What could you do to find the number of 50-pound sea otters whose total weight would be 2,000 pounds? Children may think of this problem in terms of multiplication (What number times 50 equals 2,000?) or division (How much is 2,000 divided by 50?).

● Write a number model for the story. Possible number models: ? × 50 = 2,000; 2,000 ÷ 50 = ?

3. Answer the question. 50 times 40 is 2,000, so forty 50-pound sea otters together weigh a ton.


Lesson 9�1 715

Allow time for children to share solution strategies. Possible strategies may include: I know the basic fact 4 × 5 = 20. 40 × 50 = 2,000 and 2,000 ÷ 50 = 40 are extensions of the basic fact. From the first story, I knew that 30 sea otters were 1,500 lb and that 10 sea otters were 500 lb, so I added and found that 40 sea otters weigh 2,000 lb.

4. Does your answer make sense? How do you know? Possible answer: One sea otter weighs 50 lb, so two weigh 100 lb. There are ten 100s in 1,000 and twenty 100s in 2,000, so 40 sea otters weigh 2,000 lb.

● Does your answer make the number model true? yes Write a summary number model on the board: 40 × 50 = 2,000.

� Writing and Solving Number WHOLE-CLASS ACTIVITY

Stories with Multiples of 10, 100, and 1,000(Math Journal 2, pp. 204 and 205)

Use the Adult Weights of North American Animals poster as a basis for multiplication and division number stories. Choose any numbers that fall within the weight ranges. Record the problems on the board.

Suggestions:

● Which animal could weigh about 10 times as much as a 34-pound American porcupine? Harp seal, northern fur seal, American alligator, white-tailed deer, Atlantic green turtle, or black bear

● Which animal could weigh about 30 times as much as a 5-pound snowshoe hare? Puma or white-tailed deer

● How many 300-pound northern fur seals weigh as much as a 6,000-pound pilot whale? 20

● How many 80-pound white-tailed deer weigh as much as a 560-pound black bear? 7

Invite children to tell their own multiplication and division number stories for the class to solve.

Ongoing Assessment: Informing Instruction

Watch for children who tell addition or subtraction number stories. Accept and

solve these types of problems, but continue to model multiplication and division

number stories, emphasizing that multiplication is a way to find the total number

of things when equal groups are put together.

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Adjusting the Activity Pose problems that require two

steps. Suggestion:

Which animal could weigh about 1,000 times

as much as the combined weight of a

75-pound sea otter and a 45-pound sea

otter? Right whale

AUDITORY � KINESTHETIC � TACTILE � VISUAL


Links to the Future

Date Time

Multiples of 10, 100, and 1,000LESSON

9 �1

Solve each problem.

1. a. 7 [40s] = 280 b. 7 × 40 = 280

2. a. 6 [70s] = 420 b. 6 × 70 = 420

3. a. 60 [20s] = 1,200 b. 60 × 20 = 1,200

4. How many 50s are in 4,000? 80

5. How many 800s are in 2,400? 3

6. a. How many 3s are in 270? 90 b. 90 × 3 = 270

c. 270 ÷ 3 = 90

7. a. 40 × 300 = 12,000 b. 12,000 ÷ 40 = 300

For Problems 8 through 10, use the information on pages 204 and 205.

8. a. Which animal might weigh about

20 times as much as a 30-pound raccoon? Black bear

b. Can you name two other animals that might

weigh 20 times as much as a 30-pound raccoon?

Northern fur seal and West Indian manatee

9. About how many 200-pound American alligators

weigh about as much as a 3,200-pound

beluga whale? 16 American alligators

10. Which animal might weigh about 100 times as much as

the combined weights of a 15-pound

arctic fox and a 10-pound arctic fox? Beluga whale or walrus

� ��

Try This

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Student Page


Date Time

Math BoxesLESSON

9�1

5. Use bills and coins.

Share $45.90 equally among

3 people.

Each gets $ 15.30 .

Share $49.20 equally among

4 people.

Each gets $ 12.30 .

3. Write equivalent fractions.

1 _ 2 =

1 _ 4 =

2. Put these numbers in order from

smallest to largest.

998,752 750,999

1,000,008 998,752

750,999 1,000,008

1,709,832 1,709,832

4. Pencils cost $1.99 for a package

of 24. Estimate. About how much

do 4 packages cost?

about $8.00

6. Measure the line segment to the

nearest 1 _ 2 inch.

about 1 in.

Draw a line segment that is

1 1 _ 2 inches long.

1. If I wanted to take out a square

about 4 times as often as a circle,

I would put in 20 square(s).

20

19127–30

73 143 144

Sample answers:3

6

3

12

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Student Page

� Finding Products and INDEPENDENTACTIVITY

Quotients Involving Multiples of 10, 100, and 1,000(Math Journal 2, pp. 204–206)

Children complete journal page 206. Circulate and assist as necessary.

Ongoing Assessment: Journal page 206 �Problems 1 and 2Recognizing Student Achievement

Use journal page 206, Problems 1 and 2 to assess children’s progress toward

solving problems involving multiples of 10, 100, and 1,000. Children are making

adequate progress if they are able to complete Problems 1 and 2. Some children

may be able to solve problems involving multiples of 100 and 1,000.


In this lesson, children make up and solve multiplication and division number stories involving multidigit numbers. Many children will use basic facts, multiples of 10, and mental math to solve these problems. However, using and explaining strategies for solving number stories involving multiplication of multidigit whole numbers by a 2-digit whole number is a Grade 4 Goal. Using and explaining strategies for solving number stories involving division of multidigit whole numbers is a Grade 5 Goal.

2 Ongoing Learning & Practice

� Playing Name That Number SMALL-GROUP ACTIVITY

(Student Reference Book, pp. 299 and 300)

Children play Name That Number. They use two or more operations to find equivalent names for numbers. For game instructions, see Lesson 1-6 or pages 299 and 300 in the Student Reference Book.

� Math Boxes 9�1 INDEPENDENTACTIVITY

(Math Journal 2, p. 207)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-3. The skill in Problem 6 previews Unit 10 content.

Writing/Reasoning Have children write an answer to the following: Explain how you solved Problem 4. Sample answer: $1.99 is close to $2.00. I multiplied $2.00 × 4 to get $8.00.

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Name Date Time

Who Am I?HOME LINK

9�1

The problems in this Home Link involve children solving whole-number riddles. Your childwill use place-value concepts, number sense, and computation skills to solve the riddles. Toprovide practice with basic and extended facts, multiplication fact practice is added at thebottom of this Home Link.

Please return this Home Link to school tomorrow.

FamilyNote

In each riddle, I am a different whole number. Use the clues to find out who I am.

1. Clue 1: I am greater than 30 and less than 40. Who am I?Clue 2: The sum of my digits is less than 5.

2. Clue 1: I am greater than 15 and less than 40. Who am I?Clue 2: If you double me, I become

a number that ends in 0.

Clue 3: �15

� of me is equal to 5.

3. Clue 1: I am less than 100. Who am I?Clue 2: The sum of my digits is 4.

Clue 3: Half of me is an odd number.

4. Clue 1: If you multiply me by 2, I become Who am I?a number greater than 20 and less than 40.

Clue 2: If you multiply me by 6, I end in 8.

Clue 3: If you multiply me by 4, I end in 2.

5. Clue 1: Double my tens digit to get Who am I?my ones digit.

Clue 2: Double me and I am less than 50.

Solve.

6. 8 � 7 � 7. 5 � 4 �

80 � 7 � 5 � 40 �

800 � 7 � 50 � 400 � 20,0005,600

200560

2056

Practice

31

25

22

13 or 18

12 or 24


Home Link Master

Lesson 9�1 717

Name Date Time

LESSON

9�1 Extending Multiplication Fact Patterns

Fill in the missing numbers.

1. 1 � 10 � 1 � 100 �

2 � 10 � 2 � 100 �

3 � 10 � 3 � 100 �

4 � 10 � 4 � 100 �

5 � 10 � 5 � 100 �

2. 6 � 100 � 6 � 1,000 �

7 � 100 � 7 � 1,000 �

8 � 100 � 8 � 1,000 �

9 � 100 � 9 � 1,000 �

3. 1 [10] � 1 [100] �

2 [10s] � 2 [100s] �

7 [10s] � 7 [100s] �

5 [10s] � 5 [100s] �

8 [10s] � 8 [100s] �

4. Explain how you can use the patterns above to find the answer to 8 [1,000s].

Sample answer: I know that 8 [1s] are 8. 8 [1,000s] are 1,000times as much, or 8,000. I know that 8 [10s] are 80 and

8 [100s] are 800; so 8 [1,000s] must be 8,000.

5. 10 � 100 � 10 [100s] �

10 � 1,000 � 10 [1,000s] �

Try This

1020304050

100200300400500

6,0007,0008,0009,000

600700800900

1020705080

100200700500800

1,000 1,00010,00010,000


Teaching Master

� Home Link 9�1 INDEPENDENTACTIVITY

(Math Masters, p. 267)

Home Connection Children solve whole-number riddles.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Extending Multiplication 5–15 Min

Fact Patterns(Math Masters, p. 268)

To explore patterns in multiples of 10, 100, and 1,000, have children complete Math Masters, page 268. Children can model the problems with base-10 longs, flats, and big cubes.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Minute Math+ 5–15 Min

To offer children more experience with multiplication and division number stories, see the following pages in Minute Math+:

Number Stories: pp. 128 and 131.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Writing Multiplication and 15–30 Min

Division Number StoriesTo provide language support for multiplication and division, have children write multiplication and division number stories for others to solve. Also provide them

with opportunities to write a paragraph describing how they solved a particular problem. Provide English language learners with feedback on their mathematical writing and offer them multiple opportunities to revise their writing. This activity will support not only their problem-solving efforts, but also their communication skills.

NOTE Remind children to continue to record the sunrise, sunset, and length of

day in their journals on pages 279–281. They should also continue to record the

national high and low temperatures on journal page 175 and then graph the

temperature range on journal page 177.


Copyrig

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Wrig

ht G

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406

Guide to Solving Number Stories

Name Date Time

1. What do you understand from the story?

� Read the story. What do you want to find out?

� What do you know?

2. What will you do?

� Add?

� Subtract?

� Multiply?

� Divide?

� Draw a picture?

� Make tallies?

� Use counters or base-10 blocks?

� Use a number grid or number line?

� Make a table?

� Draw a diagram?

� Write a number model?

3. Answer the question.

� Solve the problem. Record your work.

� Write the answer with the units.

4. Check.

� Does your answer make sense? How do you know?

EM3MM_G3_U02_036-063.indd 406EM3MM_G3_U02_036-063.indd 406 12/29/10 5:57 PM12/29/10 5:57 PM

Multiply and Divide with Multiples of 10, 100, and 1,000 and Divide with Multiples of 10, 100, and...

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