Minds On
Growing patterns
Student Success
Think-Pair-Share
A pattern is predictable, which means we know what comes next based on what we have already identified. Take a minute to think about the following question: “What is a growing pattern?” Record your thoughts using a method of your choice and, if possible, share them with a partner.
Press the ‘Hint’ button to access a description of a growing pattern.
A growing pattern is a pattern that gets bigger from term to term. For example, these are both growing patterns:
0, 00, 000, 0000
3, 5, 7, 9
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Examine the following pattern. Keep in mind that each step of a growing pattern is called a term. There are four terms to the pattern you are about to examine.
Record answers to the following questions, using a method of your choice.
- How would you describe this pattern?
- What is the pattern rule?
- How would you describe the next term? The tenth term? How do you know?
Student Tips
Growing pattern types
The following anchor chart shows examples of many different types of growing patterns. Take some time to examine the following anchor chart and compare them with the growing pattern you just worked with. What do you notice?
This is an anchor chart titled “Growing Patterns: Keep Going Up/Growing Bigger.” The chart shows 3 examples of growing patterns. The first growing pattern is made up of circles. Term 1 has 2 circles. Term 2 has 4 circles. Term 3 has 6 circles, and Term 4 has 8 circles. Each term value in the pattern is equal to the number of circles it has. The rule of this growing pattern example is “start at 2 and add two each time.”
The next growing pattern example is made up of triangles. Term 1 has a single triangle. In each term that follows, a new triangle is added and connected to one side of the previous triangle. Each term value is equal to the number of unconnected sides of its triangles. Term 1 is 3, Term 2 is 5, Term 3 is 7, Term 4 is 9, and Term 5 is 11. The rule is, “start at 3, add 2 each time.”
The final growing pattern example is made up of squares. Term 1 has 1 square. In each term that follows, 2 squares are added and stacked like a pyramid. Term 2 has 3 squares. Term 3 has 5 squares, and Term 4 has 7 squares. Term 5 is blank. Can you complete the pattern? The rule is, “start at 1, add 2 each time.”
At the bottom of the anchor chart there is a template for creating your own rule. It reads, “Start at (blank). Add (blank) each time.”
Action
Growing patterns and term numbers
Writing pattern rules
When working with patterns and trying to find the pattern, it is helpful to clearly indicate how the pattern is increasing by labelling the difference between one term value and the next.
Examine the following pattern:
A pattern represented by numbers, from left to right: 7, 12, 17, 22, 27.
The pattern rule is, “start at seven, add five each time.” The rule or difference of how the pattern is increasing is represented by adding +5 between each term value and in written terms.
Solving pattern rules
Task one
For this task, you will find the pattern rule and extend the pattern for various examples of growing patterns. Complete the following fillable and printable document Growing Patterns Chart. You can also complete this activity in your notebook or using the method of your choice. You can include pictures, images, or words to help explain your thinking.
| Pattern | The Pattern Rule | Extend the pattern. What will the fourth term be? |
Extend the pattern. What will the tenth term be? |
|---|---|---|---|
| 13, 17, 21, | |||
|
0 0 0 |
Press the 'Activity' button to access Growing Patterns Chart.
Task two
For this task, complete and extend the following patterns and describe the pattern rule.
You may use the following Hundred Chart or another tool, such as a number line, counters, or any material of choice, to help support your understanding.
Complete the Unfinished Patterns in your notebook or using the following fillable and printable document. If you would like, you can use speech-to-text or audio recording tools to record your thoughts.
A. Start at 11 and add 10
| 11 |
B. (Blank) and add 6.
| 13 |
C. Start at 72 and subtract
| 72 | 63 | 45 | 36 |
| 28 | 35 | 56 | 63 |
Press the 'Activity' button to access Unfinished Patterns.
Student tips
Pattern rules
This is an example of a pattern and its pattern rule.
Multiple operations
Growing patterns can be formed with more than one operation. Explore the following pattern on the number line, then answer the following questions using a method of your choice.
- What do you notice?
- What kind of pattern is shown? Describe the pattern.
Press the ‘Hint’ button to reveal a suggested answer.
Now, try completing the following number patterns.
You may use the following Number Line or another tool, such as a hundred chart, counters, or any material of choice, to help support your understanding.
Complete the Rhombus Number Patterns in your notebook or using the following fillable and printable document. If you would like, you can use speech-to-text or audio recording tools to record your thoughts.
- What are the next three terms in this pattern? What is the pattern rule?
- Select a number between 1 and 12 then apply the pattern rule below and record the first 5
terms:
- add 5, subtract 2
- subtract 1, add 5
Press the 'Activity' button to access Rhombus Number Patterns.
Consolidation
Create your own growing pattern
Your task is to create a growing pattern using materials of your choice (numbers, blocks, manipulatives, pictures, etc.) Use the following steps to complete the activity. Record your thoughts digitally, orally or in print.
- A growing pattern can be made using shapes, numbers, or letters. What elements will you include?
- The pattern rule indicates how a growing pattern will change. What is your pattern rule?
- Show at least the first four terms of your pattern.
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.