Minds On
Examine the following pattern groups
For each of the groups, decide which one does not belong.
There can be more than one answer. As long as you can justify your answer, you are not wrong!
Record your ideas using a voice recorder, speech-to-text, or writing tool.
Example #1
Example #2
The second example includes 4 different patterns. Each includes different geometric patterns.
The first is a growing pattern with 3 items. Item 1 has 1 circle, item 2 has 3 circles that form a triangle, and item 3 has 6 circles that form a triangle.
The second growing pattern has 3 items. Item 1 has a circle surrounded by 4 sets of 2 squares forming a t. Item 2 has 1 circle surrounded by 4 sets of 3 squares forming a t. Item 3 has 1 circle surrounded by 4 sets of 4 squares forming a t.
The third pattern is a growing pattern with 3 items. Item 1 has 1 circle in the middle with 1 circle on each corner forming an X. Item 2 has 1 circle in the middle with 3 circles on each corner forming an X. Item 3 has 1 circle in the middle with 5 circles on each corner forming an X.
The fourth pattern is a shrinking one with 3 items. Item 1 has a square in the middle with 4 squares on each corner forming an X. Item 2 has a square in the middle with 3 squares on each corner forming an X. Item 3 has a square in the middle with 2 squares on each corner forming an X.
Example #3
Reflect
Now, that you've explored the sets of patterns reflect on the following questions.
- Were there similarities in the patterns that did not belong?
- How did you choose which pattern did not belong?
Action
Growing and shrinking patterns
A growing pattern is a type of extending pattern where something is added to each term and each term gets longer.
A shrinking pattern is an extending pattern where each term gets smaller as the pattern extends. Something is taken away from each term.
Growing and shrinking patterns can be numerical and non-numerical. They can use shapes, pictures, and objects.
Task 1: What comes next?
Examine the patterns.
For each pattern, determine if it is a growing or shrinking pattern. Complete the next 3 terms. Identify the pattern rule if there is one.
Record your patterns using a method of your choice.
Be prepared to identify the different strategies that were used to determine the pattern rules and extend the patterns.
Pattern #1:
100, 200, 400, 800…
- Is the pattern growing or shrinking?
- What are the next 3 terms?
- What is the pattern rule?
Pattern #2:
First term has 10 squares, second term has 8 squares and third term has 6 squares.
Description
A pattern with 3 terms. The first term is 2 columns with 5 squares each. The second term is 5 squares in the left column and 3 squares in the right column. The third term is 5 squares in the left column and 1 square in the right column.
- Is the pattern growing or shrinking?
- What are the next 3 terms?
- What is the pattern rule?
Press ‘Patterns’ to access the details of patterns #1 and #2.
For pattern #1 :
- It is a growing pattern.
- The next 3 terms are : 1,600, 3,200, 6,400.
- Pattern Rule is : Start at 100 and double the number each time.
For pattern #2 :
- It is a shrinking pattern.
- The next 3 terms are : 4, 2, 0.
- Pattern Rule is : Start with 10 squares (5 rows of 2) and remove two squares from the right column, starting at the top, each time.
Task 2: Creating growing and shrinking patterns
Create any growing pattern. Next, create any shrinking pattern. Record your patterns digitally, orally or in print. You may wish to use the digital tools suggested in Task 1.
Answer the following questions:
- How do you know these are patterns?
- How can you distinguish between a growing and shrinking pattern?
- What would the 10th term in the pattern be? How do you know?
Task 3: Tables of values
Tables of values include the term number and the term value.
- The term number refers to the position of a term in the pattern.
- The term value refers to the number of elements in each pattern.
Example: 3, 6, 9, 12, 15, 18
Number 3 is the term value and is the first term number of the pattern.
| Term Number | Term Value |
|---|---|
|
1 |
3 |
|
2 |
6 |
|
3 |
9 |
|
4 |
12 |
|
5 |
15 |
|
6 |
18 |
Examine the following Table of Values to determine a pattern rule. Fill in the table with the next 3 term values in the pattern in your notebook or using the following activity document.
Press the ‘Activity’ button to access Table of Values.
After you have filled out the table, you may press ‘Answer’ to access the solution to check your answers.
| Term Number | Term Value |
|---|---|
|
1 |
4 |
|
2 |
10 |
|
3 |
16 |
|
4 |
22 |
|
5 |
28 |
|
6 |
34 |
|
7 |
40 |
|
8 |
46 |
|
9 |
52 |
Pattern rule: Start at 4 and add 6 each time.
Task 4: Word problems
Let’s explore extending a pattern using the pattern rule.
- If the pattern rule is “start at 5 and add 3 every time,” what will the 10th term be?
You may wish to start by building a model of this pattern, for example:
Term 1 has a row of 2 green blocks with a row of 3 purple blocks stacked above. Term 2 has a row of 2 green blocks and 2 rows of 3 purple blocks stacked above. There are 6 purple blocks in total. Term 3 has a row of 2 green blocks and 3 rows of 3 purple blocks stacked above. There are 9 purple blocks in total.
Complete the Table of Values #2 in your notebook or using the following fillable activity document.
| Term number | Term value |
|---|---|
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 |
Press the ‘Activity’ button to access Table of Values #2.
After you have filled out the table, you may press ‘Answer’ to access the solution to check your answers.
Answer| Term Number | Term Value |
|---|---|
|
1 |
5 |
|
2 |
8 |
|
3 |
11 |
|
4 |
14 |
|
5 |
17 |
|
6 |
20 |
|
7 |
23 |
|
8 |
26 |
|
9 |
29 |
|
10 |
32 |
Now that you’ve completed the table answer the following question:
- What would the term value of the 20th term be?
To figure this out we can determine a rule that relates the term number to the term value.
If we multiply the term number by 3 and add 2, we get the term value.
Let’s try it:
Don’t forget to apply the rules for order of operations (BEDMAS).
Term number × 3 + 2 = Term Value
So, for the 20th term it would be: 20 × 3 + 2 = 62
The 20th term would be 62.
Time to try on your own
Now try some on your own! Record your work using a method of your choice.
Identify the pattern rule and find the term value.
Use a table of values, math tools, or another organizer to support your thinking.
Select the correct answer.
Consolidation
Task 1: Creating patterns
Student Success
Think-Pair-Share
Record your answers digitally, orally, or in print.
Create your own growing or shrinking pattern by using any method of your choice (for example, using shapes, numbers.) Create at least 3 or 4 terms.
- Identify what type of pattern it is (i.e. growing or shrinking)
- Create and fill in a table of values for the pattern
- Identify the pattern rule
- Add in the next 3 terms
- Identify what the 10th, 20th, and 50th term would be. Show your work
If possible, trade your pattern with a partner and extend their pattern.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Task 2: Think about your learning
Reflect on following questions:
- What is important to consider when determining if a pattern is a growing or shrinking pattern?
- What do you need to consider when identifying a pattern rule? Explain how it is different in a table of values.
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.
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