growing patterns

Zork says: Hey, Gork! Let's show earthlings how this bacteria grow! - Gork says: Are you planning a biological experiment, Zork? -- Zork says: No, Gork! I am planning a math lesson!

Did you know that bacteria, viruses, and every living cell grow in patterns? Mathematicians enjoy investigating growing patterns to understand and describe their growth.

Click on the grade tabs to see different growing pattern activities.

Take a close look at the pattern below:

  • What is happening as the pattern grows from Stage 1 to Stage 4?
    • What is happening with the blue blocks?
    • What is happening with the red blocks?
  • Predict what the blocks will look like in Stage 5.

Complete the table below:

Now complete the table for this other pattern:

Now you can draw graph bars of these patterns. Can you complete the ones below?

  • 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?

Create a different growing pattern using two colours:

  • Build the pattern using cubes
  • Complete the table below for your pattern
  • Draw a bar graph of your pattern. You may use this Square Grid Handout
  • Use words to describe your pattern. What changes? What is constant?

Making changes to your pattern

How would you change the pattern to have the following effects?

  • Make the bar graph steeper.
  • Make the bar graph less steep.
  • Make the bar graph taller.
  • Make the bar graph shorter.
  • Make all the bars the same height.

Watch mathematician Lindi Wahl explaining variables and constants:

Keep exploring growing (or shrinking?) patterns!

Here are some more challenges for you:

  • Can you make a pattern that is shrinking?
  • Can you use 3 colours to build growing patterns?
    • Where only 1 colour is growing
    • Where 2 colours are growing

How bacteria grow

Watch mathematician Lindi Wahl explaining bacteria growing pattern.

Using symbols to express patterns

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.

Can you figure out the expressions for the growing patterns below?

Watch mathematician Lindi Wahl representing patterns through equations:

What did you learn?

  • What did you learn about constants and variables?
  • What surprised you?
  • What math insights did you experience?

Share your learning with others, so they can experience math surprise and insight too.