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112 Unit 2 Adding and Subtracting Whole Numbers

Advance Preparation

Teacher’s Reference Manual, Grades 1–3 pp. 18, 19, 209–215

“What’s My Rule?”Objective To provide opportunities to review and solve

“What’s My Rule?” problems.

��������

Key Concepts and Skills• Use basic facts to compute extended facts. 

[Operations and Computation Goal 1]

• Describe rules for patterns and use them

to solve problems. 

[Patterns, Functions, and Algebra Goal 1]

• Describe rules and patterns in “What’s My

Rule?” tables; use them to solve addition

and subtraction problems. 

[Patterns, Functions, and Algebra Goal 1]

Key ActivitiesChildren discuss problems in which one

quantity depends on another. They illustrate

this kind of relationship between pairs of

numbers with a function machine and

“What’s My Rule?” tables. They solve

“What’s My Rule?” problems.

Ongoing Assessment: Informing Instruction See page 114.

Ongoing Assessment: Recognizing Student Achievement Use journal page 34. [Patterns, Functions, and Algebra Goal 1]

Key Vocabularyfunction machine � input � rule � output �

“What’s My Rule?”

MaterialsMath Journal 1, p. 34

Home Link 2�2

transparency of Math Masters, p. 41

(optional)

Playing Fact GamesStudent Reference Book, pp. 278 or

310 and 311

Beat the Calculator

per group: 4 each of number cards

0–9 (from the Everything Math Deck, if

available), calculator

Subtraction Top-It

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 maintain and/or practice basic

fact fluency.

Math Boxes 2�3Math Journal 1, p. 35

Children practice and maintain skills

through Math Box problems.

Home Link 2�3Math Masters, p. 42

Children practice and maintain skills

through Home Link activities.

READINESS

Acting Out a Function Machinecardboard box � counters

Children act out a function machine.

ENRICHMENTCreating “What’s My Rule?” TablesMath Masters, p. 41

Children work together to make up their

own “What’s My Rule?” tables.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Algebraic Thinking Draw or display a function machine and “What’s My Rule?” table. Ask children to imagine that the function machine works like this:

● A number (the input) is dropped into the machine.

● The machine changes the number according to a rule.

● A new number (the output) comes out the other end.

The rule for the Math Message problem is Double the number. Write the word Double in the function machine. Point out the “What’s My Rule?” table that you have displayed. Discuss the 8 in the in column and the 16 in the out column. Explain to children that numbers in the in column represent the number of bacteria now. Corresponding numbers in the out column represent the number of bacteria 20 minutes from now.

Review the answers to the Math Message problem by posing questions in the following manner:

● If 50 is dropped into the function machine, which number will come out? 100 Enter the appropriate numbers in the in and out columns. Repeat with the other numbers in the problem.

Lesson 2�3 113

Getting Started

Math Message Some bacteria double in number every 20 minutes. Use this information to complete the table.

Home Link 2�2 Follow-Up Go over answers as necessary. Review the idea that basic facts can be used to solve problems with larger numbers.

Mental Math and Reflexes Pose “What’s My Rule?” riddles. Ask children to say a number. Apply a secret rule and tell them the new number. For example, a child might say 48. Apply the rule “Add 10” and tell the new number, 58. Continue as above until most children know the secret rule. Then you say a number and ask children to apply the rule and tell you the new number.

Secret rules: Add 10; Subtract 10

Secret rules: Add 5; Subtract 5

Secret rules: Add 8; Subtract 8

Rule

out

in

Double

in out

8 16

50 100

200 400

75 150

150 300

Unit

bacteria

Now 20 min later

8 16

50 100

200 400

75 150

150 300

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114 Unit 2 Adding and Subtracting Whole Numbers

Date Time

Fill in the blanks.

1. 2.

3. 4.

Rule

out

in

Subtract 50

Rule

out

in

Add 8

Rule

out

in

Subtract 30

in out

100 5050 070 20150 100200 150

in out

60 30

80 50

130 100

230 200

30 0

Rule

out

in

Add 9

Answers vary. Answers vary.

Answers vary.

Answers vary. Answers vary.

Answers vary.

in out

14 23

34 43

44 53

64 73

94 103

in out

5 13

15 23

35 43

65 73

85 93

5. 6.

Rule

out

in

Rule

out

in

Add 7

in out

6 13

9 165 124 11

11 18

in out

35 20

60 45

20 550 35

46 31

“What’s My Rule?”LESSON

2�3

Subtract 15

� �

Math Journal 1, p. 34

Student Page

� Reviewing Variations of the WHOLE-CLASS ACTIVITY

“What’s My Rule?” Routine(Math Masters, p. 41)

Algebraic Thinking If you made a transparency of Math Masters, page 41, you can demonstrate each type of “What’s My Rule?” table on the overhead. Otherwise, draw the tables on the board. In the Math Message problem, the rule and sample inputs are known, and the outputs must be determined. (See Type 1 in the margin.)

� In a second type of “What’s My Rule?” problem, the rule and sample outputs are known, but the inputs must be determined. (See Type 2 in the margin.)

� In a third type of “What’s My Rule?” problem, the inputs and outputs are known, and the rule must be determined. (See Type 3 in the margin.)

� In a fourth type of “What’s My Rule?” problem, some inputs and outputs are known; missing numbers and the rule must be determined. (See Type 4 in the margin.) To find the rule in problems like these, children should use the pairs in which both in and out numbers are given. Then, after the rule is discovered, children can use the rule to fill in the missing in and out numbers. Pose problems like the fourth type to the class.

� In a fifth type of “What’s My Rule?’’ problem, rules are often stated as simple commands to perform a specific operation, such as Add 5. However, rules may also be stated in a con-text—“Mark is 4 years younger than his sister, Susie” or as in the Math Message—“Some bacteria double in number every 20 minutes.” (See Type 5 in the margin.) Encourage children to supply both types of rules.

� Completing “What’s My Rule?” PARTNER ACTIVITY

Tables(Math Journal 1, p. 34; Math Masters, p. 41)

Algebraic Thinking Children may work in partnerships or independently to complete the journal page. Note that the last row in each table is left blank. Encourage children

to create difficult problems. Math Masters, page 41 may be used to provide additional practice with “What’s My Rule?” tables.

Ongoing Assessment: Informing Instruction

Watch for children who have difficulty finding the missing in numbers. Have them

check their work by reading the number sentence formed by the in number, the

rule, and the out number.

PROBLEMBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMMOOOOOOOOOOBBBBBBBLBLBLBLBBLBLLLLBLPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROROOPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELELEELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBB ELEELEMMMMMMMMMOOOOOOOOOBLBLBLBLBLBLBLBLBLBLROOOROROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINVINNNVINVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOLOLOLOLOLOLOLOOOO VVVVVLLLLLLLLLLVVVVVVVVVOSSOSOSOSOSOSOSOSOSOSOSOSOSOOOOOSOOSOSOSOSOSOSOSOSOSOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

in out

13 4

10 1

17 8

18 9

in out

7 12

10 15

21 26

45 50

in out

10 20

20 30

30 40

50 60

Rule

Subtract 9

Rule

Add 5

Rule

Add 10

Type 1 Type 2 Type 3

in out

13 9

23 19

43 39

53 49

in out

45 25

30 10

100 80

52 32

RuleMark is 4 years younger than his sister Susie

Rule

Subtract 20

Type 4 Type 5

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Name Date Time

“What’s My Rule?”HOME LINK

2�3

You can find an explanation of function machines and “What’s My Rule?” tables on pages202–204 in the Student Reference Book. Ask your child to explain how they work. Help your child fill in all the missing parts for these problems.

Please return this Home Link to school tomorrow.

FamilyNote

202 204

Practice facts and fact extensions. Complete the “What’s My Rule?”problems. Make up problems of your own for the last table.

1.

3.

2.

4.

Rule

out

in

Subtract 7

in out

14 77 012 515 810 321 14

Rule

out

in

Add 9

in out

7 169 18

37 4677 86

49 58

Rule

out

in

Add 30

in out

70 100

20 5030 60

90 120

50 80

Rule

out

in in out

Answers vary.

Answers vary.

Answers vary.

Math Masters, p. 42

Home Link Master

5. What time is it?

What time willit be in 20minutes?

How many minutes until 5:15?

40 min

4:55

4:35

3. Write the numbers that are 100more and 100 less than each givennumber.

100 more 100 less

614

994

2,462

3,965 3,8654,0652,3622,5628941,094514714

Date Time

2. Fill in the missing numbers.

4. You spent $7.88 at the store. Yougave the cashier a $10 bill. Howmuch change should you receive?

$2.12

6. Measure the line segment to thenearest �

12� inch.

inches2

1. Put these numbers in order fromsmallest to largest.

32,764

8,596

32,199

85,096 85,09632,76432,1998,596

20

143–145

1,072 1,073 1,074 1,0751,082 1,083 1,084

1,0941,104

1,114

1,0851,095

12 12

3

4567

8

9

1011

7 8

Math BoxesLESSON

2�3

18 19

�12�

Math Journal 1, p. 35

Student Page

Lesson 2�3 115

Ongoing Assessment: Journal

Page 34 �Recognizing Student Achievement

Use journal page 34, Problems 1 and 2, to assess children’s ability to write and

use rules for functions involving addition and subtraction. Children are making

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

may be able to complete the remaining problems involving missing rules and

numbers.

[Patterns, Functions, and Algebra Goal 1]

2 Ongoing Learning & Practice

� Playing Fact Games SMALL-GROUP ACTIVITY

(Student Reference Book, pp. 278

or 310 and 311)

Have children play either Beat the Calculator (Addition) or Subtraction Top-It to maintain and/or practice basic fact fluency. Review the rules for these two games in the Student Reference Book (page 278 for Beat the Calculator and pages 310 and 311 for Subtraction Top-It).

Continue to provide children with opportunities to play fact games regularly.

� Math Boxes 2�3 INDEPENDENTACTIVITY

(Math Journal 1, p. 35)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-1. The skill in Problem 6 previews Unit 3 content.

Writing/Reasoning Have children write an answer to the following: Explain your strategy for Problem 4. Sample answer: I counted up $0.12 from $7.88 to get to $8.00. From $8.00 to $10.00 is $2.00. The change is $2.00 + $0.12 or $2.12.

� Home Link 2�3 INDEPENDENTACTIVITY

(Math Masters, p. 42)

Home Connection Children practice facts and fact extensions in the “What’s My Rule?” format. “What’s My Rule?” may not be familiar to parents, so you might want to send home the Student Reference Book.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMLEBLELEBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBLBLBLBLBLBLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMMOOOOOOOOOOBBBLBLBLBBLBBBBLROOORORORORORORORORORORORO LELELLEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNVINVINVINNVINVINVINVINV GGGGGGGGGGGGOLOOOLOOOLOOLOO VVINVINLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINGGGGGGGGGGGOOLOLOLOLOLLOOOOLVVVVVLLLLLLLLLLVVVVVVVVVOOSOSOSOOSOSOSOSOSOSOOSOSOSOOOSOOOOSOSOSOSOSOSOSOSOOSOSOOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING

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116 Unit 2 Adding and Subtracting Whole Numbers

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Acting Out a Function Machine 5–15 Min

Algebraic Thinking To explore function machines using a concrete model, use a cardboard box without a lid to demonstrate how a function machine works.

Draw a picture of an Everyday Mathematics function machine on one side of the box. Place 15 counters inside the box. To begin the demonstration, put 3 counters into the machine. Take 6 counters out of the machine. Repeat with additional numbers of counters (4 and 8, 5 and 10). Then ask children how the machine is changing the number of counters each time. Children should try to state the rule the machine is using. (In the example, the machine doubles the number.) Repeat with other rules (for example, +4, –2). As children understand the process, have them serve as the rule makers.

ENRICHMENT

PARTNER ACTIVITY

� Creating “What’s My Rule?” 15–30 Min

Tables(Math Masters, p. 41)

To provide further exploration of “What’s My Rule?” problems, have children create their own “What’s My Rule?” tables. Encourage them to use negative numbers,

larger numbers, or rules stated in a context (such as Type 5 in the margin on page 114.) To support English language learners, have children read their rules. Consider having them state their rules in different ways. For example, “My rule is to add 2. Plus 2 is another way to say my rule.”

ELL

Math Masters, p. 41

Teaching Master

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