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



Objective To guide children as they multiply and divide with multiples of 10, 100, and 1,000. w

www.everydaymathonline.com

ePresentations

eToolkit

Algorithms Practice

EM Facts Workshop Game™

Teaching the Lesson Key Concepts and Skills • Find multiples of 10, 100, and 1,000.   [Number and Numeration Goal 3]

• Compare and order numbers.  [Number and Numeration Goal 6]

• 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 Activities Children 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.

Family Letters

Assessment Management

Common Core State Standards

Ongoing Learning & Practice 1 2 4 3

Playing Name That Number Student 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 1 

Math Journal 2, p. 207 Children practice and maintain skills through Math Box problems.

Home Link 9 1 

Math Masters, p. 267 Children practice and maintain skills through Home Link activities.

Curriculum Focal Points

Interactive Teacher’s Lesson Guide

Differentiation Options READINESS

Extending Multiplication Fact Patterns Math 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 Stories Children write multiplication and division number stories.

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

Materials Math Journal 2, pp. 204–206 Math Masters, p. 406 slate  blank transparency (optional)

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

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

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Unit 9

Multiplication and Division

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Getting Started Mental Math and Reflexes

Math Message Use 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.

Pose problems like the following. Children answer on their slates: How much are How much are How much are 70 [30s]? 2,100 30 [700s]? 21,000 7 [30s]? 210 What number is 50 times as What number is 50 times as What number is 60 times as much as 60? 3,000 much as 500? 30,000 much as 6? 300 How many 9s equal 540? 60

How many 90s make 5,400? 60

How many 60s make 54,000? 900

1 Teaching the Lesson

Interactive whiteboard-ready ePresentations are available at www.everydaymathonline.com to help you teach the lesson.

 Math Message Follow-Up (Math Journal 2, pp. 204 and 205)

WHOLE-CLASS DISCUSSION ELL

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.

cont.

West Indian manatee 500 lb to 1,100 lb

Atlantic green turtle 250 lb to 450 lb

Pilot whale 3,200 lb to 6,400 lb

Bottle-nosed dolphin 350 lb to 430 lb

Right whale 70,000 lb to 140,000 lb

Gray fox 9 lb to 16 lb

Common dolphin 200 lb to 300 lb

American alligator 200 lb to 500 lb Sea otter 48 lb to 99 lb

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?

Time

Adult Weights of North American Animals

Puma 150 lb to 230 lb

(Math Journal 2, pp. 204 and 205; Math Masters, p. 406)

9 1 䉬

White-tailed deer 50 lb to 480 lb

Multiplication and Division Number Stories

LESSON

Gila monster 1 2 2 lb to 4 lb

WHOLE-CLASS ACTIVITY

Date

American porcupine 20 lb to 40 lb

 Modeling How to Solve

Student Page

Gray whale 45,000 lb to 72,000 lb

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

Math Journal 2, p. 205

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

? 30 [50s] = ?

●

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. 30 [50s] = 1,500

●

One polar bear weighs as much as 30 sea otters.

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. ●

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)

Teaching Aid Master Name

Date

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

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

Time

Guide to Solving Number Stories

●

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.

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?

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?).

 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?

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.

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?

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Unit 9 Multiplication and Division

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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. ●

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

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 Stories with Multiples of 10, 100, and 1,000

WHOLE-CLASS ACTIVITY PROBLEM PRO P RO R OB BLE BL L LE LEM EM SOLVING SO S OL O LV L VIN V IIN NG

(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.

Lesson 9 1 

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Student Page Date

 Finding Products and

Time

LESSON

Multiples of 10, 100, and 1,000

9 1 

Solve each problem.

 

280 420 1,200

1. a. 7 [40s] = 2. a. 6 [70s] = 3. a. 60 [20s] =

4. How many 50s are in 4,000? 5. How many 800s are in 2,400? 6. a. How many 3s are in 270? c. 270 ÷ 3 = 7. a. 40 × 300 =

Quotients Involving Multiples of 10, 100, and 1,000

 

b. 7 × 40 = b. 6 × 70 = b. 60 × 20 =

INDEPENDENT ACTIVITY

280 420 1,200

(Math Journal 2, pp. 204–206)

80 3 90

b.

90 12,000

90

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

× 3 = 270

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

Black bear

20 times as much as a 30-pound raccoon?

Ongoing Assessment: Recognizing Student Achievement

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

Journal page 206 Problems 1 and 2



9. About how many 200-pound American alligators

weigh about as much as a 3,200-pound beluga whale?

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.

16 American alligators

Try This 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

[Number and Numeration Goal 3]

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Links to the Future 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 Student Page

 Playing Name That Number

Time

Date LESSON

91 

Math Boxes

1. If I wanted to take out a square

2.

about 4 times as often as a circle, I would put in

20 square(s).

(Student Reference Book, pp. 299 and 300)

Put these numbers in order from smallest to largest. 998,752 1,000,008 750,999 1,709,832

750,999 998,752 1,000,008 1,709,832

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.

20

3. Write equivalent fractions. 1 _ = 2

3 6

1 _ = 4

3 12

SMALL-GROUP ACTIVITY

4. Pencils cost $1.99 for a package

Sample answers:

of 24. Estimate. About how much do 4 packages cost?

 Math Boxes 9 1

about $8.00



INDEPENDENT ACTIVITY

(Math Journal 2, p. 207) 27–30

5. Use bills and coins.

1 nearest _ 2 inch.

15.30 .

about

Share $49.20 equally among 4 people. Each gets $

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.

6. Measure the line segment to the

Share $45.90 equally among 3 people. Each gets $

191

1

in.

Draw a line segment that is 1 1_ 2 inches long.

12.30 . 73

143 144

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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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Unit 9 Multiplication and Division

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Home Link Master

 Home Link 9 1 

Name

INDEPENDENT ACTIVITY

(Math Masters, p. 267)

Date

HOME LINK

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Family Note

Home Connection Children solve whole-number riddles.

Time

Who Am I? The problems in this Home Link involve children solving whole-number riddles. Your child will use place-value concepts, number sense, and computation skills to solve the riddles. To provide practice with basic and extended facts, multiplication fact practice is added at the bottom of this Home Link. Please return this Home Link to school tomorrow.

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?

2. Clue 1: I am greater than 15 and less than 40.

Who am I?

31

Clue 2: The sum of my digits is less than 5.

25

Clue 2: If you double me, I become a number that ends in 0. 1 ᎏᎏ of me is equal to 5. 5

Clue 3:

3 Differentiation Options

3. Clue 1: I am less than 100.

Who am I?

22

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

READINESS

 Extending Multiplication

PARTNER ACTIVITY

5. Clue 1: Double my tens digit to get

Practice

8⫻7⫽

6.

80 ⫻ 7 ⫽

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.

 Minute Math+

Who am I?

Solve.

(Math Masters, p. 268)

EXTRA PRACTICE

13 or 18

12 or 24

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

5–15 Min

Fact Patterns

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.

800 ⫻ 7 ⫽

56 560 5,600

7.

5⫻4

⫽

5 ⫻ 40 ⫽ 50 ⫻ 400 ⫽

20 200 20,000

Math Masters, p. 267

SMALL-GROUP ACTIVITY 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

 Writing Multiplication and

SMALL-GROUP ACTIVITY

Teaching Master

15–30 Min

Division Number Stories

Name LESSON

91 䉬

To 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.

Date

Extending Multiplication Fact Patterns

Fill in the missing numbers. 1. 1 ⫻ 10 ⫽

2 ⫻ 10 ⫽ 3 ⫻ 10 ⫽ 4 ⫻ 10 ⫽ 5 ⫻ 10 ⫽ 2. 6 ⫻ 100 ⫽

7 ⫻ 100 ⫽ 8 ⫻ 100 ⫽ 9 ⫻ 100 ⫽ 3. 1 [10] ⫽

2 [10s] ⫽ 7 [10s] ⫽ 5 [10s] ⫽

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.

Time

8 [10s] ⫽

10 20 30 40 50 600 700 800 900 10 20 70 50 80

1 ⫻ 100 ⫽ 2 ⫻ 100 ⫽ 3 ⫻ 100 ⫽ 4 ⫻ 100 ⫽ 5 ⫻ 100 ⫽

100 200 300 400 500

6,000 7,000 8 ⫻ 1,000 ⫽ 8,000 9 ⫻ 1,000 ⫽ 9,000 1 [100] ⫽ 100 2 [100s] ⫽ 200 7 [100s] ⫽ 700 5 [100s] ⫽ 500 8 [100s] ⫽ 800 6 ⫻ 1,000 ⫽

7 ⫻ 1,000 ⫽

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 1,000 times 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.

Try This 5. 10 ⫻ 100 ⫽

10 ⫻ 1,000 ⫽

1,000 10,000

10 [100s] ⫽ 10 [1,000s] ⫽

1,000 10,000

Math Masters, p. 268

Lesson 9 1 

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Name

Date

Time

Guide to Solving Number Stories 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?

 Solve the problem. Record your work.  Write the answer with the units.

4. Check.

Copyright © Wright Group/McGraw-Hill

3. Answer the question.

 Does your answer make sense? How do you know?

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