multiplication fact power and shortcuts€¦ · shortcut square numbers materials math journal 1,...

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266 Unit 4 Multiplication and Division

Advance Preparation

Teacher’s Reference Manual, Grades 1–3 pp. 195–198, 199

Key Concepts and Skills• Practice multiplication facts.

[Operations and Computation Goal 3]

• Identify patterns in skip counting by 2s,

5s, and 10s.

[Patterns, Functions, and Algebra Goal 1]

• Use arrays to represent turn-around

multiplication facts.


• Use the Commutative Property of

Multiplication (the turn-around rule), the

Multiplicative Identity, and the Zero

Property of Multiplication to generate

multiplication facts.


Key ActivitiesChildren discuss multiplication facts and the

importance of fact power. They also review

multiplication shortcuts and play Beat the

Calculator (Multiplication).

Key Vocabularyfactor � product � fact power � turn-around

shortcut � square numbers

MaterialsMath Journal 1, p. 156

Student Reference Book, p. 279

Home Link 4�4

Math Masters, p. 95; p. 446 (optional)

transparency of Math Masters, p. 95

(optional) � calculator � slate � per group of

3 children: calculator

Solving Multidigit Subtraction ProblemsMath Journal 1, p. 88

number grid (optional) � base-10

blocks (optional)

Children solve multidigit subtraction

problems.

Math Boxes 4�5Math Journal 1, p. 89

Children practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 5. [Measurement and Reference Frames

Goal 2]

Home Link 4�5Math Masters, p. 96

Children practice and maintain skills

through Home Link activities.

READINESS

Building Facts on a GeoboardMath Masters, p. 97

geoboard � rubber bands

Children use an array model to find products

for basic facts.

ENRICHMENTCreating Fact Shortcutspaper

Children create and explain their own

fact shortcuts.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Multiplication FactPower and Shortcuts

Objectives To discuss multiplication facts and the importance

of fact power; and to review fact shortcuts.o

��

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 4�5 267

2 × 3 = 6

18 = 9 * 2

5 • 4 = 20

3 × 8

24

Different multiplication formats

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Multiplication facts are products of two 1-digit numbers. Have children call out multiplication facts, with or without the products, while you write them on the board. Use both horizontal formats (with the product to the left and the right) and vertical formats. Tell children that the symbols * and • are sometimes used to show multiplication.

The numbers being multiplied are factors. The result of multiplication is the product. To support English language learners, label some of the facts written on the board with the words factor and product. Encourage children to use this vocabulary, but do not insist on it.

� Reviewing the Importance WHOLE-CLASSDISCUSSION

of Fact PowerAsk children to name some good and some bad habits. A habit is an automatic behavior that comes from doing something over and over again. Developing basic number-fact reflexes is developing a good habit. In Everyday Mathematics, fact habits are referred to as fact power. Stress to children that they need to learn the multiplication and division facts so that they can solve multidigit multiplication and division problems.

� Reviewing Shortcuts for WHOLE-CLASS ACTIVITY

Multiplication Facts(Math Masters, p. 95)

Algebraic Thinking Tell children they will review shortcuts that will help them develop a good habit—knowing the multiplication facts by heart.

ELL

Getting Started

Math Message7 × 4 = 28 is a multiplication fact. Write 5 other multiplication facts.

Home Link 4�4 Follow-Up Have partners describe to each other how they solved one of the problems.

Mental Math and Reflexes Children count from 1 to 30, clapping at the intervals described below.

every 5th number 1, 2, 3, 4, 5 (clap), 6, 7, 8, 9, 10 (clap), 11, 12, 13, 14, 15 (clap), and so on to 30

every 3rd number 1, 2, 3 (clap), 4, 5, 6 (clap), 7, 8, 9 (clap), and so on to 30

every 4th number 1, 2, 3, 4 (clap), 5, 6, 7, 8 (clap), 9, 10, 11, 12 (clap), and so on to 30

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Adjusting the Activity


4 × 3 = 12 and 3 × 4 = 12

LESSON

4�5

Name Date Time

4 � 3 Grid

Math Masters, p. 95

Teaching Master

The Turn-around Shortcut� Illustrate the turn-around shortcut (Commutative Property

of Multiplication) by writing several fact phrases for small numbers, such as 4 × 3, on the board. Pair each fact with its turn around, or commutative partner—4 × 3 and 3 × 4. The order of the factors does not change the product, so if you know 3 × 4 = 12, you also know 4 × 3 = 12.

� Include square numbers, such as 3 × 3 and 5 × 5, and point out that the turn-around fact for a square number is the same as the original fact.

� Then have children use Math Masters, page 95 to make arrays for the facts you suggest.

� Children write number models under each array.

The arrays that children draw represent the multiplication turn-around facts, similar in principle to the addition turn-around facts. You may wish to use an overhead of the master to model building arrays.

� Ask: What number models made square arrays? Sample answers: 3 × 3 = 9 and 5 × 5 = 25

� Ask: What is the pattern of these number models? The factors are the same.

� Ask: How can you know if a number model will make a square array? If the number model has two identical factors, it will make a square array.

The Multiplication by 1 ShortcutIf 1 is multiplied by any number, or any number is multiplied by 1, the product is that number (Multiplicative Identity).

Tell a few times 1 and 1 times number stories, and have children tell some. For example:

● There are 8 flowers in a pot. You have 1 pot. How many flowers do you have? 1 × 8 = 8; 8 × 1 = 8. You have 8 flowers.

● There is 1 ring in each box. You have 6 boxes. How many rings do you have? 1 × 6 = 6; 6 × 1 = 6. You have 6 rings.

As you review the number stories, record the number models on the

board so that children will be able to see the patterns for the shortcut.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

The Multiplication by 0 ShortcutIf 0 is multiplied by any number, or any number is multiplied by 0, the product is 0 (Zero Property of Multiplication).

Tell a few times 0 and 0 times number stories, and have children tell some, including some with larger numbers. For example:

● There are 10 cookies in a box. You have 0 boxes. How many cookies do you have? 0 × 10 = 0; 10 × 0 = 0. You have 0 cookies.

ELL

NOTE It is not expected that children

use formal terms for the properties of

multiplication. It is important for them to

know, however, that order does not matter

when multiplying factors, that multiplying any

number by 1 results in a product that is that

number, and that multiplying any number by

0 results in a product of 0.


Lesson 4�5 269

The Caller draws a 10 and a 7. The Callersays, “10 times 7.” The Brain and the Calculatoreach solve the problem. The Caller decides who gotthe answer first

107

Beat the Calculator (Multiplication)

Materials � number cards 1–10 (4 of each)� 1 calculator

Players 3Skill Mental multiplication skillsObject of the game To multiply numbers without acalculator faster than a player using one.

Directions

1. One player is the “Caller.” A second player is the“Calculator.” The third player is the “Brain.”

2. Shuffle the cards and place them number-side downon the table.

3. The Caller draws 2 cards from the number deck andasks for the product of the numbers.

4. The Calculator solves the problem with a calculator.The Brain solves it without a calculator. The Callerdecides who got the answer first.

5. The Caller continues to draw 2 cards at a time from thenumber deck and ask for the product of the numbers.

6. Players trade roles every 10 turns or so.

Games

Student Reference Book, p. 279

Student Page

The Caller draws a 10 and a 7. The Callersays, “10 times 7.” The Brain and the Calculatoreach solve the problem. The Caller decides who gotthe answer first.

107

Beat the Calculator (Multiplication)

Materials � number cards 1–10 (4 of each)� 1 calculator

Players 3Skill Mental multiplication skillsObject of the game To multiply numbers without acalculator faster than a player using one.

Directions

1. One player is the “Caller.” A second player is the“Calculator.” The third player is the “Brain.”

2. Shuffle the cards and place them number-side downon the table.

3. The Caller draws 2 cards from the number deck andasks for the product of the numbers.

4. The Calculator solves the problem with a calculator.The Brain solves it without a calculator. The Callerdecides who got the answer first.

5. The Caller continues to draw 2 cards at a time from thenumber deck and ask for the product of the numbers.

6. Players trade roles every 10 turns or so.

Games● There are 0 cookies per box. You have 10 boxes. How many

cookies do you have? 10 × 0 = 0; 0 × 10 = 0. You have 0 cookies.

The Familiar Facts ShortcutTell children that the 2s, 5s, and 10s facts are simply counts by 2s, 5s, and 10s—remind them of the Mental Math and Reflexes exercise. Have the class recite in unison the 2s, 5s, and 10s facts in order. Point out the following patterns:

� The products of 2s and 10s facts are always even numbers. (The products of 4s, 6s, and 8s facts are also always even.)

� The products of 5s facts always end in 0 or 5.

� The products of 10s facts always end in 0.

Additional Strategies with Familiar Facts� 4 times any number can always be decomposed into 2 equal

addends. 4 × 7 can be thought of as 2 × 7 = 14 and 2 × 7 = 14. To find the product of 4 × 7, the two products can be added together. 14 + 14 = 28, so 4 × 7 = 28.

� Break one factor into easy addends. For example, 6 × 7 can be thought of as 6 × 5 = 30 and 6 × 2 = 12. The two products, 30 and 12, can be added together to find the product of 6 × 7. 30 + 12 = 42, so 6 × 7 = 42.

� Taking the Fact WHOLE-CLASS ACTIVITY

Power Challenge

Divide the class into two groups. Pose a multiplication fact problem. Children in one group use calculators to find the product. Children in the other group find the product without using calculators.

Repeat the activity with other multiplication facts. Mix easy and hard facts, so that children in each group can get the product first some of the time. Children are generally surprised to find that fact power can indeed beat the calculator.

NOTE This activity makes the point that for many easy problems, mental

calculation is quicker than using a calculator. Over time, children should develop

good judgment about when to estimate and when to use calculators, calculate

mentally, or use paper and pencil.

� Playing Beat the Calculator SMALL-GROUP ACTIVITY

(Multiplication)(Student Reference Book, p. 279;

Math Journal 1, p. 156; Math Masters, p. 446)

Have children examine the Fact Power Table on journal page 156. The unshaded facts include the 0s, 1s, and 10s facts as well as the facts from Activity Sheets 1 and 2. The shaded facts are from Activity Sheets 3 and 4.

Adjusting the Activity Use the minute hand on the clock face to practice the 5s facts. When the minute hand is on the 8, the time is 40

minutes past the hour: 5 × 8 = 40. When the minute hand is on the 2, the time is 10

minutes past the hour: 2 × 5 = 10. Pose other clock facts.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

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Subtraction StrategiesLESSON

4� 5

Date Time

Make a ballpark estimate. Write a number model to show your estimate. Choose at least two problems to solve using the counting-up method. You may choose any method you wish to solve the other problems.

63 192

1. Ballpark estimate: 2. Ballpark estimate: 3. Ballpark estimate:

487�129358

93�4746

226�13492

4. Ballpark estimate: 5. Ballpark estimate: 6. Ballpark estimate:

515�367148

724�396328

361�248113

Estimates vary.

Math Journal 1, p. 88

Student Page

5. Draw a 2 � 4 rectangle.

Number model: � �

Area: square units8842

3. Solve. Fill in the oval for the bestanswer.4 rows of chairs6 chairs in each rowHow many chairs in all?

10 chairs 12 chairs

24 chairs 20 chairs

Date Time

89

2. Maximum numberof points scored:

Minimum numberof points scored:

Range of points scored:

20 points

5 points

25 points

4. Fill in the number grid.

6. Which is more?

$3.45 or $3.09?

$0.34 or $0.09?

$14.50 or $14.55?

$30.15 or $31.05? $31.05$14.55

$0.34$3.45

1. Use the dots to show a 3 � 6array.

What is the number model?

� � 1863

Math BoxesLESSON

4� 5

64 65 7986 87

7–9

154–156 36

A B C DPlayers

0

5

10

15

20

25

30

Poin

ts

Game Points

66 67

2,946

2,9572,967

2,9762,9862,9963,006

�

Math Journal 1, p. 89

Student Page

Explain to children that they will use the Fact Power Table during Beat the Calculator games to record the facts they get correct while playing the role of the Brain. When children have earned 3 check marks for a fact, they write the product in the table. The page will become a cumulative record of their progress toward multiplication fact power.

Divide the class into groups of three to play Beat the Calculator. If necessary, review the directions on page 279 in the Student Reference Book.

Have children follow the steps below to record their wins on their Fact Power Table.

1. The Caller selects a problem at random from the Fact Power Table on journal page 156.

2. The Brain finds the product without a calculator. The Calculator finds the product using a calculator.

3. The Caller determines whether the Brain or the Calculator got the product first.

4. If the Brain beats the Calculator and announces the correct product, the Caller makes a check mark in the box for that fact on the Brain’s Fact Power Table. Once a fact has three check marks, the Brain writes the product in that box to indicate that the fact has been mastered.

5. You might wish to pass out Beat the Calculator triangles (Math Masters, page 446) to assist with assigning roles to players.

NOTE Playing this game frequently will help develop children’s automaticity with

multiplication facts. Remind children to use their copy of the Fact Power Table on

journal page 156 as a record sheet during Beat the Calculator games.

2 Ongoing Learning & Practice

� Solving Multidigit Subtraction INDEPENDENTACTIVITY

Problems(Math Journal 1, p. 88)

Children use counting-up, trade-first, or other methods of their choice to solve multidigit subtraction problems. Encourage children to use the number grid, base-10 blocks, or other manipulatives as needed.

� Math Boxes 4�5 INDEPENDENTACTIVITY

(Math Journal 1, p. 89)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-7. The skill in Problem 6 previews Unit 5 content.


97

LESSON

4�5

For each problem:

Use a rubber band to make each

rectangle on a geoboard.

Draw the rectangle onto this record

sheet.

Record the number of pins inside the

rubber band as the answer to the

problem.

1. 3 � 3 � pins

3. 3 � 2 � pins

Make up problems of your own.

5. � � pins

6

9

Example

2 � 4 � pins

2. 4 � 3 � pins

4. 4 � 4 � pins

6. � � pins

16

12

8

Answers

vary.

Answers

vary.

Building Facts on a Geoboard

Name Date Time

Math Masters, p. 97

Teaching Master

Lesson 4�5 271

Name Date Time

Multiplication-Fact ShortcutsHOME LINK

4�5

Your child is learning the basic multiplication facts. Listen to your child explain multiplication-fact shortcuts as he or she works the problems. Review some 1s, 2s, 5s, and 10smultiplication facts (facts like 1 � 3 � ?, ? � 2 � 4, 5 � 5 � ?, and 10 � 4 � ?).

Please return this Home Link to school tomorrow.

FamilyNote

Tell someone at home about multiplication-fact shortcuts.

The turn-around rule: 3 � 4 � 12 helps me know 4 � 3 � 12.

1. 2 � 5 � and 5 � 2 �

2. � 5 � 3 and � 3 � 5

3. 10 � 2 � and 2 � 10 �

If 1 is multiplied by any number, the product is that number.

The same is true if any number is multiplied by 1.

4. � 1 � 9 and � 9 � 1

5. 1 � 90 � and 90 � 1 �

6. 365 � 1 � and 1 � 365 �

If 0 is multiplied by any number, the product is 0.

The same is true if any number is multiplied by 0.

7. 0 � 12 � and 12 � 0 �

8. 99 � 0 � and 0 � 99 �

9. � 9,365 � 0 and � 0 � 9,365

Think about counting by 2s, 5s, and 10s.

10. 11. 12. 13. 14. 15. 10

� 5

5

� 3

2

� 7

9

� 2

5

� 4

10

� 2

00

00

00

365365

9090

99

2020

1515

1010

20 20 18 14 15 50

56

Math Masters, p. 96

Home Link Master

Ongoing Assessment: Math Boxes

Problem 5 �Recognizing Student Achievement

Use Math Boxes, Problem 5 to assess children’s progress toward finding the

area of rectangular shapes. Children are making adequate progress if they are

able to draw the rectangle and find the area. Some children might be able to

write the number model for the area.

[Measurement and Reference Frames Goal 2]

� Home Link 4�5 INDEPENDENTACTIVITY

(Math Masters, p. 96)

Home Connection Children tell someone at home about the multiplication fact shortcuts for turn-around facts and for the 0s, 1s, 2s, 5s, and 10s facts.

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Building Facts 5–15 Min

on a Geoboard(Math Masters, p. 97)

To provide experience with multiplication facts using a concrete model, have children use rubber bands on a geoboard to find products for basic facts. Children record

their work on Math Masters, page 97. When they have finished, briefly review which of the facts might be easiest to remember.

ENRICHMENT PARTNER ACTIVITY

� Creating Fact 15–30 Min

ShortcutsTo further explore fact shortcuts, have children write their own fact shortcut for facts they already know. They explain their shortcut on paper and include an example. Possible shortcuts:

� If I know 2 times a number, adding one more of that number would be 3 times the number.

� If I know 2 times a number, doubling the answer would be 4 times the number.

� If I know 10 times a number, I can subtract the number once and have 9 times the number.

The children’s shortcuts make a wonderful classroom resource. Consider binding them into a class book.


multiplication fact power and shortcuts€¦ · shortcut square numbers materials math journal 1,...

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