Lesson 2 Patterns that Repeat

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

Warm-up How Many Do You See: Colorful Tiles

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

pattern of tiles.

Activity 1 Patterns that Repeat

Problem 1

Here is a pattern made by arranging shapes.

pattern of shapes. black triangle, white circle, black triangle, blue square. Patterns repeats three times.

  1. Look for as many features of patterns as you can and describe them to your partner.

  2. What rule might this pattern follow?

  3. Use the rule to extend the pattern so that it repeats one more time.

Problem 2

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

Diagram. Rectangle partitioned into 12 equal sized squares.

  1. Trade your pattern with your partner. Look for as many features of patterns as you can and describe them.

  2. What rule might your partner have followed to create their pattern?

  3. Use the rule to extend their pattern so that it repeats one more time.

Activity 2 Numbered Patterns

Problem 1

Here is the pattern of shapes you saw earlier.
Number the shapes 1 to 12.

pattern of shapes. black triangle, white circle, black triangle, blue square. Patterns repeats three times.

Problem 2

Your teacher will assign you a shape. Write it in every blank space and answer the questions.

  1. What numbers were written for the s?

  2. If you extend the pattern, what numbers will be written for the next two

    s?

  3. What number will the tenth have? Explain or show your reasoning.

  4. Will the 30th shape be a ? Explain or show your reasoning.

Activity 3 Clare’s Pattern

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

  1. Draw the first 10 shapes in Clare’s pattern.

  2. Clare numbered her shapes. What numbers are the first 5 squares?

  3. What rule is the numerical pattern following?

  4. What is the 31st shape in Clare’s pattern? Explain or show your reasoning.

  5. 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.

Practice Problem

Problem 1

Han types the letters a, s, d, f and then repeats them in that order, over and over.

  1. What is the 5th letter Han will type? What about the 10th? The 20th?

  2. If Han numbers the letters he types, starting with 1 for the first a, what numbers will go with the first 6 f’s he types?

  3. What do you notice about the numbers for the f’s?