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Unit 6

Patterns that Repeat

Lesson 2

Multiplying and Dividing Multi-digit Numbers

Expressions and Equations

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Let’s look at shapes that repeat by a rule and make some predictions about the patterns they create.

Unit 6 ● Lesson 2

Learning

Goal

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Colorful Tiles

Unit 6 ● Lesson 2 ● Warm-up

How many tiles do you see? How do you see them?

What patterns helped you figure out how many tiles there were?

How Many Do You See?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Patterns that Repeat

Unit 6 ● Lesson 2 ● Activity 1

Here is a pattern made by arranging shapes.

Look for as many features of patterns as you can and describe them to your partner.
What rule might this pattern follow?
Use the rule to extend the pattern so that it repeats one more time.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Patterns that Repeat

Unit 6 ● Lesson 2 ● Activity 1

Create a new pattern that uses only a circle and one other shape, and that follows a new rule.

Trade your pattern with your partner. Look for as many features of patterns as you can and describe them.
What rule might your partner have followed to create their pattern?
Use the rule to extend their pattern so that it repeats one more time.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Patterns that Repeat

Unit 6 ● Lesson 2 ● Activity 1

Let’s share some of your patterns.

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Numbered Patterns

Unit 6 ● Lesson 2 ● Activity 2

Here is the pattern of shapes you saw earlier..

Number the shapes 1 to 12.
Your teacher will assign you a shape. Write it in every blank space and answer the questions.

What numbers were written for the ____________________s?
If you extend the pattern, what numbers will be written for the next two _____________________s?
What number will the tenth ____________________ have? Explain or show your reasoning.
Will the 30th shape be a ____________________? Explain or show your reasoning.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Numbered Patterns

Unit 6 ● Lesson 2 ● Activity 2

Let’s look at a classmate’s work.

How are the numerical patterns the same? How are they different?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Clare’s Pattern

Unit 6 ● Lesson 2 ● Activity 3

Clare has in mind a particular arrangement of shapes. Let’s see what her design looks like and make some predictions about it.

Launch

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Clare’s Pattern

Unit 6 ● Lesson 2 ● Activity 3

Clare created a pattern using 3 shapes—a triangle, a circle, and a square—that repeat in that order.

Draw the first 10 shapes in Clare’s pattern.
Clare numbered her shapes. What numbers are the first 5 squares?
What rule is the numerical pattern following?
What is the 31st shape in Clare’s pattern? Explain or show your reasoning.
Clare wants to use 40 shapes in her pattern and the last shape to be a square. Is this possible? Explain or show your reasoning.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Clare’s Pattern

Unit 6 ● Lesson 2 ● Activity 3

Is it possible to answer the last two questions using the numerical pattern that represents triangles?
Is it possible to use the numerical pattern to represent the circles?
Why might you want to use the numerical pattern that represents the squares?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Patterns that Repeat

Unit 6 ● Lesson 2

Today we explored patterns created by shapes that repeat according to a rule. When we numbered the shapes, we created a numerical pattern.

Here are some numerical patterns we saw in this lesson. How would you find the 50th number in each pattern, without listing all 50 numbers?

1, 3, 5, 7, 9

2, 6, 10, 14, 18

4, 8, 12, 16, 20

Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Happy Faces

Unit 6 ● Lesson 2

Diego created a pattern with smiley faces.

Extend Diego’s pattern by drawing the next 5 shapes.
If Diego numbered the smiley faces, what numbers would he write for the first 5 large smiley faces?
Will the 42nd smiley face be a large one or a small one? Explain or show your reasoning.

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.