# Pattern problems

Pattern problems are a relatively new phenomenon in mathematics education. They can be used both for early algebra in primary school as well as in secondary school. At primary level students reason and come up with a description of how the figure or pattern grows using word formulas. At secondary school level, students can be encouraged to describe the formula for the nth pattern using symbols for the variables.

Two applets from the Freudenthal Institute make it easy to experiment with pattern problems:
Spotting number problems, if you wish to work with given patters
Spotting numbers, if you wish the students to design their own patterns

Introduce a pattern to the class and ask them to look at it first. Then ask them: How do you see the pattern grow?

For the example below we have used the applet Spotting Numbers and coloured in blue the different views students could have on how the pattern grows.

Thereafter students can explore:

• With how many dots does the figure grow?
• What about the 20th or 50th figure?
• How many dots are required?
• How many dots are on the base?
• Can you describe a ‘rule’ for the growth?
• Can you describe a formula for finding the nth figure?

Information on the applets: Spotting numbers and Spotting number problems.

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