# Growing Patterns

Grades 1-2: The lyrics of the music video below, performed by grades 1-2 students, are based on parent responses to (a) what did your child share with you, and (b) what did you learn?

Grades 7-9: A similar set of activities may serve as a context for linear relations in grades 7-9.

1. What did you learn?

• What surprised you?
• What else do you want to know?

2. How does the pattern grow?

• What does the pattern grow from Stage 1 to Stage 4?
• How do the blue blocks grow?
• How do the red blocks grow?
• Predict what the pattern will look like in Stage 5.

3. Complete the table below:

4. Complete the table for this pattern:

5. Describe how the 3 growing patterns are similar or different.

• How do the blue numbers/blocks change in each of the patterns?
• How do the red numbers/blocks change in each of the patterns?

6. Complete the table of values for each pattern.

a)

b)

c)

7. Complete the bar graphs.

• How are the bar graphs similar?
• How are they different?
• What makes one graph steeper than the other?
• Is it the red blocks, the blue blocks, or both?

8. Create a different growing pattern using two colours:

• Build the pattern using link cubes or draw it on this Square Grid Handout.
• Complete the table for your pattern
• Draw a bar graph of your pattern on the Square Grid Handout
• Use words to describe your pattern. What changes? What is constant?

9. Watch mathematician Lindi Wahl explain variables and constants.

• What did you learn?

In all the activities so far, you have used blocks, tables, and graphs to express patterns, but the way mathematicians do it is by using symbols.

Look at the example below:

In the following table, we will label the Stage # as “X” and the # of blocks will be “Y”

These are called linear equations because they make a straight line when we graph them.

10. What would be the equations for the growing patterns below?

a)

b)

11. How do bacteria grow differently compared to the patterns above?

12. How may we represent non-linear patterns using equations?

12. How does Lindi Wahl find beautiful about patterns & equations?

13. Investigate growing patterns and their various representations at https://imaginethis.ca/mathncode/sims-growpatt.html

Run the code at https://scratch.mit.edu/projects/964727477/editor

This code represents the pattern shown below.

14. Edit the code to create each of the flowing lists of numbers. Run the code to test your predictions.

15. Go to https://cscircles.cemc.uwaterloo.ca/console

• Enter and run the code below.
• You will see the list of numbers shown on the right.

This code represents the pattern shown below.

16. Edit the code to create each of the flowing lists of numbers. Run the code to test your predictions.

Run the code at https://scratch.mit.edu/projects/556330557/editor.

The Scratch code produces the graph of y = x, as shown below.

17. Alter the code as shown below.

• Describe how the output of the altered code is different from the graph of y = x, shown above.
• Describe the effect of a in the graph of y = ax.

18. Alter the code as shown below.

• Describe how the output of the altered code is different from the graph of y = x.
• Describe the effect of b in the graph of y = x + b.

19. Alter the code as shown below.

Describe how the output of the altered code is different from the graph of y = x.

20. Determine the equation of each plotted relation by altering the code at https://scratch.mit.edu/projects/556330557/editor to match the graph.

21. What did you learn about growing patterns?

• What surprised you?
• What math insights did you experience?
• What else do you want to know?

22. How might you share your learning with others, so they can experience math surprise and insight too?