Rich Learning Tasks

120 / 216

116
Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
Circle Patterns
Questions to facilitate the learning
• Describe one of your patterns. What makes it a pattern?
• Which of your patterns grows faster? Do you think it will keep growing faster? Why?
• Could your pattern include the number 10? How?
Scaffolding the learning
• The pattern has to increase. Do you think you want to add, subtract, multiply or divide? Why?
• What did you notice about how the 1st picture and 2nd picture look alike? Different?
• How many rows and columns of dots does the 1st picture have? The 2nd? How could that be helpful in
extending the pattern?
Extending the learning
Students might create different ways to extend the pattern that starts 5, 10, …
What’s the point of this task?
An important notion about patterns is that when no rule is given, there are always many ways to extend
the pattern. In this case, students are asked to use different rules to create increasing patterns that begin
with the terms 2 and 5. By representing the patterns with shapes, the student often can better ‘express’
the rule. When only two terms are provided, students are likely to find it easier to come up with many ideas
than if three terms are given.
Some possibilities include 2, 5, 8, 11, … (adding 3 each time) or 2, 5, 11, 23, … (add the number to itself
and then add 1) or 2, 5, 9, 14, 20, …. (add 1 more each time) or 2, 5, 8, 12, 16, 21, 26, … (add the same
amount twice, then 1 more twice, then 1 more twice), etc.
Some students might focus on the visual to help them add to the pattern: e.g. noticing that the 2nd term
was created by repeating the first term and putting a circle between the original and the copy. This might
lead to this as the third term:
Pattern