Find out if there are enough squares. Given diagrams for the first four figures in a sequence, pupils try to determine the next figure. Individuals find the number of square and triangle pieces of fabric that are required to make patchwork cushions. Working with five terms in each pattern, scholars develop formulas for the number of pieces of fabric, no matter the size of the cushion.

Concepts

arithmetic sequences, sequences, linear equations, quadratic equations, patterns

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Additional Tags

math

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Instructional Ideas

• Provide instruction on how to organize terms from a sequence to make it easier to see the pattern
• Ask classmates to share their thinking with the class and determine good approaches that can be generalized

Classroom Considerations

• Learners at different levels will approach the problem differently and may or may not find the quadratic expression for the number of squares

Pros

• Provides probing questions to verify individuals understand the context
• Contains sample responses and how they are scored

Cons

• None

Common Core

MP1 MP4 MP7 6.EE.B.6 HSF-BF.A.1.a