## Tuesday, 15 November 2011

### Increasing Patterns

Sometimes the students amaze me with their ability to really learn a new concept.  Today, increasing patterns was introduced.  In the Mathematics program of Studies, students in Grade Two must demonstrate an understanding of increasing patterns by describing, reproducing, extending and creating both non-numerical and numerical patterns.

I told the students about a little caterpillar who on his first day out of the egg, had a head, one body part and two legs.  After eating all day long, he slept and the next day he had two body parts and four legs.  This continues until the caterpillar has four body parts and eight legs.  I then asked what he would look like on the sixth day AND they got it!  They recognized that as his body increases by one part, his legs increased by two!  They were they sent off to create their own increasing patterns.  It didn't happen instantly for all of them, but with support and explanation as well as visits to others' desks, they eventually were quite successful.

This work looks easy but would you believe that the students are actually building pre-algebra skills?
Think in terms of x and y and other unknowns.  Here is the number example to go with the example above.  Each day, the creature increases by 3 legs.  How many legs would the creature have on the 7th day?  The students need to extend the pattern, in their head, recognizing the relationship between the upper number and the lower number.  This is a 1 to 3 relationship.  As the top number increased by one, the lower number increased by 3.

In this example (cool that they started to make the patterns both in horizontal and vertical planes) the yellow hexagons increase by twos, as the red quadrilaterals increase by ones.  It is an inverse relationship if you put the yellows in the top spot on the grid and the red on the bottom.

How do the red quadrilaterals and the green triangles relate to each other in this example?

Here's a true challenge.  Can you find the first part of the pattern?  Where does it start to increase?  What colour increases and by how much?  How would you create a chart for this one?  What might look like child's play is truly work!
The best part was how excited they were when I brought out the camera!  They really LOVE to see their ideas showcased on our classroom blog!