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224 Unit 3 Visual Patterns, Number Patterns, and Counting

Key Concepts and Skills• Count forward and backward by 1s, 2s, 3s,

5s, and 10s from a given number.  

[Number and Numeration Goal 1]

• Find the missing numbers in a Frames-

and-Arrows problem given the rule.  

[Patterns, Functions, and Algebra Goal 1]

• Identify rules in Frames-and-Arrows

problems. 

[Patterns, Functions, and Algebra Goal 1]

• Create Frames-and-Arrows problems.  

[Patterns, Functions, and Algebra Goal 1]

Key ActivitiesChildren complete Frames-and-Arrows

diagrams in which a sequence of numbers

is given and they are to find the rule.

Ongoing Assessment: Informing Instruction See page 225.

Ongoing Assessment: Recognizing Student Achievement Use journal page 43. [Patterns, Functions, and Algebra Goal 1]

MaterialsMath Journal 1, p. 43 and inside back cover

Home Link 3�8

Math Masters, pp. 336A and 336B

transparency of Math Masters, p. 312

(optional)

Practicing Adding on the Number GridMath Masters, p. 76

Children practice adding on a

number grid.

Math Boxes 3�9Math Journal 1, p. 44

Children practice and maintain skills

through Math Box problems.

Home Link 3�9Math Masters, p. 77

Children practice and maintain skills

through Home Link activities.

READINESS

Finding Patterns on the Number Line Math Masters, p. 78; p. 312 (optional)

Children find patterns as they count on a

number line.

ENRICHMENTMaking Frames-and-Arrows Diagrams from Skip-Counting PatternsMath Masters, p. 79

Children skip count on a number grid and

apply those numbers to Frames-and-Arrows.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

�������

More Frames-and-Arrows Problems

Objective To introduce Frames-and-Arrows problems in

which the “arrow rule” is missing.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 3�9 225

Frames Missing Rules

2, 4, 6, 8, 10 Count up by 2s, or add 2

15, 14, 13, 12, 11 Count back by 1s, or subtract 1

3, 6, 9, 12, 15 Count up by 3s, or add 3

15, 13, 11, 9, 7 Count back by 2s, or subtract 2

20, 30, 40, 50, 60 Count up by 10s, or add 10

Suggestions:

Suggestions:

Rules First Missing Frames Frames

Count up by 2s 7, 9 11, 13, 15

Count back by 2s 12, 10 8, 6, 4

Add 3 4, 7 10, 13, 16

- 10 60, 50 40, 30, 20

1 Teaching the Lesson

� Finding the Arrow Rule WHOLE-CLASS ACTIVITY

(Math Masters, p. 312)

Algebraic Thinking On the board, write a set of numbers that represents a simple skip count, such as 5, 10, 15, and 20. Ask children to be detectives and determine how many hops it takes to move from one number to the next. 5 Tell children that today they will be solving mystery problems like this one.

Begin by doing a few problems like those in Lesson 3-8, in which the rule and the first few numbers are given. You can use the suggestions given in the margin. (Write the problems on the board, or use a transparency of Math Masters, page 312.)

When you feel that children are ready, pose the following problem:

1 3 5 7 9Rule

?

Ask children to guess the rule. Answers include “Count up by 2s,” “Add 2,” “2 more,” and “+ 2.” Encourage children to suggest various ways to state the rule.

Continue with other problems in which the rule is missing. (See the second set of suggestions in the margin.) Children should use the number grid on the inside back cover of their journals if they need help figuring out the rule or pattern.

Ongoing Assessment: Informing InstructionWatch for children who have difficulty stating the rule. Encourage them to

determine how many hops there are between two numbers by using the number

grid. Record the number of hops in the rule box. Then help them determine if

they are hopping up or back. Show them how to record this information with a

+ or - sign in the rule box.

Getting Started

Home Link 3�8 Follow-Up Briefly go over the answers.

Mental Math and Reflexes Play Ten-Frame Top-It. See Lesson 2-3 for detailed instructions. Depending on children’s comfort level with ten frames, you may wish to have children write the addition facts for their cards. For example, if a player’s ten-frame card shows 7, the player would write 7 + 3 = 10 or 3 + 7 = 10.

NOTE Once children have determined that

the numbers in the frames increase from left

to right (indicating that you should add), you

may wish to explain that finding the arrow

rule is like finding the unknown number that

makes these number models true.

1 + = 3

3 + = 5

5 + = 7

7 + = 9

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226 Unit 3 Visual Patterns, Number Patterns, and Counting

Math Journal 1, p. 43

Student Page

Adjusting the Activity

NOTE Math Journal 1, page 43, will be used

again for the optional Enrichment activity in

Lesson 3-10.

� Making up Frames-and- WHOLE-CLASS ACTIVITY

Arrows Problems(Math Masters, p. 312)

Algebraic Thinking Ask children to make up their own Frames-and-Arrows problems. Since the simplest problems are those in which the rule and the first number are given, begin with these. Then encourage children to suggest more difficult problems.

Suggest that children make up problems in which the first frame is

empty. This requires counting back to fill in the first frame.

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

� Solving Frames-and- PARTNER ACTIVITY

Arrows Problems(Math Journal 1, p. 43)

Algebraic Thinking Partners work together to solve the problems. Encourage children to help each other and to check each other’s work. They should use a number grid to help them with the more difficult problems.

Ongoing Assessment: Journal

Page 43 �Problem 1Recognizing Student Achievement

Use journal page 43, Problem 1 to assess children’s understanding of Frames

and Arrows. Children are making adequate progress if they are able to

correctly answer Problem 1. Some children may be able to correctly answer

more problems.

[Patterns, Functions and Algebra Goal 1]

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1. Use your number line. Start at 0.

Count up 6.

You end at .

0 + 6 =

2. Record the time.

half-past o’clock

3.

4. Fill in the blanks. 10 , 20 , 30 , , 50 ,

, , 80 , ,

Math Boxes LESSON

3 �9

Date

12 12

3

4567

8

9

1011

15Rule

Count by 5s

66

7

2520 30 35

4060 70 90 100

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Math Journal 1, p. 44

Student Page

Today we worked with Frames-and-Arrows diagrams in which the rule was missing. You may want to refer back to the Family Note for Lesson 3-8 and review the Frames-and-Arrows routine.

Please return this Home Link to school tomorrow.

Family Note

HOME LINK

3�9

Name Date

Find the Rule

Show someone at home how to find the rules.Then write each rule. 1.

2.

3.

gg

77

3 5 7 9 11

Rule

Add 2

5 10 15 20 25

Rule

Add 5

18 15 12 9 6

Rule

Subtract 3

Practice

4. Circle the winning card in Top-It.

18 12

Sample answers given for Problems 1–3.

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Math Masters, p. 77

Home Link Master

Lesson 3�9 227

LESSON

3�9

Name Date

Adding on the Number Grid

py

gg

p

1. Start at 25. Count up 3. Where do you end up?

28 25 + 3 =

2. Start at 19. Count up 6. Where do you end up?

25 19 + 6 = 25 3. Start at 38. Count up 2. Where do you end up?

40 38 + 2 = 40 4. Start at 57. Count up 10. Where do you end up?

67 57 + 10 = 67

5. 29 + 20 = 49 6. 25 + 15 = 40

28

01 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 70

Try This

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Math Masters, p. 76

Teaching Master

2 Ongoing Learning & Practice

� Practicing Adding on the INDEPENDENTACTIVITY

Number Grid(Math Masters, p. 76)

Use Math Masters, page 76 to provide additional practice adding on the number grid.

� Math Boxes 3�9 INDEPENDENTACTIVITY

(Math Journal 1, p. 44)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 3-11. The skills in Problem 4 preview Unit 4 content.

� Home Link 3�9 INDEPENDENTACTIVITY

(Math Masters, p. 77)

Home Connection Children find the missing rules in Frames-and-Arrows problems.

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228 Unit 3 Visual Patterns, Number Patterns, and Counting

Math Masters, p. 78

Teaching Master

Math Masters, p. 79

Teaching Master

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Finding Patterns on the 5–15 Min

Number Line(Math Masters, p. 78)

Algebraic Thinking To provide children with a visual model for how to find the rule in Frames-and-Arrows sequences, have children count on a number line. Children complete Math Masters, page 78. When children have finished the page, share ideas on how to solve the problems and discuss which problem was the most difficult. Consider having children state rules for each problem. The rules could be to either add or subtract, depending on which direction children choose to move. Consider recording the problems as Frames-and-Arrows diagrams on Math Masters, page 312. Have children read the number of hops for each number line. For example, “There were three hops between the numbers on this number line.”

ENRICHMENT INDEPENDENTACTIVITY

� Making Frames-and-Arrows 5–15 Min

Diagrams from Skip-Counting Patterns(Math Masters, p. 79)

Algebraic Thinking To further explore Frames-and-Arrows diagrams, have children complete Frames-and-Arrows diagrams for patterns on the number grid. Have children fill in each number-grid section on Math Masters, page 79 with a series of consecutive numbers. Invite them to shade a skip-counting pattern on the number-grid section. Challenge them to transfer their skip counting pattern into a Frames-and-Arrows diagram. Encourage children to repeat the process with a different section of the number grid.

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