How Do Patterns Grow?

Step 1:
Using manipulatives such as snap cubes, model a growing pattern such as the one shown below. Have students use snap cubes to copy the growing pattern.

Have students expand the pattern to the next level.

Class discussion:

• How many red cubes are in the next level?
• How many blue clues are in the next level?
• What's does the next level look like?
• How many total cubes are in the next level?
• Describe the pattern. Tell about the number of red cubes and the number of blue cubes in each level. Tell about the total number of cubes in each level.

Step 2:
Now model the following growing pattern and have students copy it.

Class discussion:

• How is this growing pattern like the previous one?
  (red and blue cubes, each time the number increases)
• How is this growing pattern different from the previous one?
  (The first growing pattern only increased numerically and expanded at one end, while this one also increases numerically and expands in two places.)
• How many red cubes are in the next level?
• How many blue cubes are in the next level?
• How many total cubes are in the next level?
• What's would the next level look like?

Let's keep a count of the cubes in a chart for levels 1–4. The first level has been done for you.

• Describe number patterns in the chart.
• Use your patterns to predict the number of red cubes in level 5.
• Use your patterns to predict the number of blue cubes in level 5.
• Use your patterns to predict the number of total cubes in level 5.

Continue asking students to predict the next sets of number cubes in subsequent levels. Have them verify their predictions by building the levels with the cubes.

Step 3:
Have students work in pairs to create their own growing patterns. One student creates a growing pattern and the other describes the pattern. Students record their patterns in a chart such as the one above. Then they switch roles.