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Growing Patterns

Grace M. Burton
Location: unknown

Students explore growing patterns. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns differently, this is an opportunity to engage them in communicating about mathematics.

Start this lesson by reading a counting book of your choice. (Ten Black Dots by Donald Crews is especially appropriate, but any book which uses a "count on by 1" strategy will work.) Then ask students to tell what happened in the book. Next, tell the students that in this lesson they will explore patterns that grow according to a rule. Display the following growing pattern (without the numbers):

597 orange dots

Ask, "What will come next in this pattern?" [Students may find this question easier to answer if they copy the pattern onto paper.] Have the students explain how they got the answer. When someone has given the correct answer, write the number of dots in each row. Solicit student responses to add additional rows to this pattern and label them. Ask the students if they know a name for this pattern and the rule they would use to add more rows to the pattern.

Next display the pattern below and tell the students this is called an L pattern. Ask students how each L is changing. After students state the answer, or as a hint, write the number of dots used below each L. Ask several students to state the rule they would use to add more figures to the pattern. Call on students to draw the next three L shapes in the pattern.

597 green dots

Distribute the Growing Pattern Activity Sheet to students.

pdficonGrowing Patterns Activity Sheet 

Have them add three more steps in the pattern and write a number pattern to match the figures. Ask students to share their shape and number patterns, explaining how they identified the pattern.

Assessment Option

Collect students’ Growing Patterns Activity Sheets.


Move on to the last lesson, Looking Back and Moving Forward.

Questions for Students 

1. What will come next in this pattern (first growing pattern)? How do you know?

[There will be 5 dots. I used the counting numbers.]

2. What is a name for this pattern?

[Counting on or counting numbers.]

3. What is the rule?

[You have to add one more to each row.]

4. How many dots are in the first figure of the L pattern? How many are in the second figure? The third?

[The first L figure has 1 dot. The second figure has 3 dots. The third figure has 5 dots.]

5. How is each L changing?

[Each L has two more dots.]

6. What is the rule for the L pattern?

[Add one dot at the top and add one dot at the bottom of the next L.]

7. How many dots in the next three L shapes in the pattern?

[The next L figures will contain 9, 11, and 13 dots.]

8. Have you ever seen this pattern before?

[It is the set of odd numbers.]

9. How long could we continue this pattern?

[We could keep going forever.]

10. What will be the next three figures in the triangle growing pattern (from student activity sheet)?

[They will be 5 triangles, 6 triangles, and 7 triangles.]

11. What number pattern did you use to describe the pattern?

[Possible answers include 1, 2, 3, 4, 5, 6, 7 (number of triangles); 3, 5, 7, 9, 11, 13, 15 (number of sides); 3, 4, 5, 6, 7, 8, 9 (number of vertices/corners). Accept all reasonable answers.]

Teacher Reflection 

  • Were students able to analyze and describe growing patterns? If so, what extension activities are appropriate now?
  • Were students able to write number patterns to match the growing patterns?
  • What other examples of growing patterns could I use in this lesson or for continued practice?
  • Did I encourage students to explain and defend their thinking?

Order, Order


In this lesson students seriate objects and review the meaning of ordinal numbers. They describe orderings in words and in pictures. [This lesson gives you an opportunity to review or teach vocabulary such as before, after, and next.] At the conclusion of the lesson, students make an entry in their portfolios. A Science extension is suggested.


Sorting Time

Students sort objects and symbols and make patterns with sorted objects. They make Venn diagrams and use their sortings to create linear patterns. They extend a pattern created by the teacher. Students will begin identifying pattern cores and reading patterns. A Social Studies connection is suggested as an extension.

What’s Next?

Pre-K-2, 3-5
In this lesson, students make patterns with objects, read patterns and find patterns in the environment. They should be encouraged to classify patterns by type (i.e. AAB, ABC). They continue learning about patterns by extending a given pattern, identifying missing elements in a pattern, and recording a pattern.

Playing With Patterns

Students use objects and symbols to make repeating linear patterns. They extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another. A Physical Education connection is suggested as an extension. This lesson is intended to take two class periods to ensure that all students have multiple opportunities to create original patterns.

More Patterns

Students extend their knowledge of linear patterns by recognizing and discussing familiar patterns. Students make auditory and visual patterns from names. An art activity is suggested as an extension.

Multiple Patterns

Students explore patterns which involve doubling. They use objects and numbers in their exploration and record them using a table.

Exploring Other Number Patterns

Pre-K-2, 3-5
Students make and extend numerical patterns using hundred charts. They also explore functions at an intuitive level. This lesson integrates technology.

Looking Back and Moving Forward

This final lesson reviews the work of the previous lessons. Students explore patterns in additional contexts and record their investigations. Students will rotate through center activities. Teachers may add other centers they feel will benefit the students.

Learning Objectives

Students will:
  • Extend growing patterns.
  • Describe growing patterns.
  • Analyze how growing patterns are created.

NCTM Standards and Expectations

  • Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
  • Analyze how both repeating and growing patterns are generated.

Common Core State Standards – Mathematics

Grade 4, Algebraic Thinking

  • CCSS.Math.Content.4.OA.C.5
    Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule ''Add 3'' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.