Friday, October 10, 2014

Visual Thinking: Using our eyes as well as our minds

One way to help capture student interest, and to create better access to math is to express mathematical ideas by using images or visual representations.  In Algebra classes, we have been exploring visual patterns as one lens to identify and study linear, quadratic, and even cubic patterns.

If this image shows steps 1, 2, and 3, how many squares would you predict in step 43? 

These patterns are easy for many students to approach.  Even though they present the same ideas as an equation or a table of values, for many kids, they are much less intimidating.  They also help to cement understanding by asking students to express ideas in multiple ways.

Dividing these shapes up into sections helps us to see the x term, the x squared term, and the constant term in this trinomial pattern.

...and if you think that these are a way to water down the math, try to figure out how many penguins are in the nth term of this friendly looking, but difficult pattern!
The patterns shown here come from a site put together by master teacher Fawn Nguyen.  Check out some more of the patterns she's accumulated, and work with your kids to try to create a general rule for the nth term HERE.

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