Saturday, May 30, 2015

How many in this?

I like to put a drawing up and have the students count how many total shapes are found within the shape. 

I usually start with a 4 by 4 square and have the students count the total number of squares.  Usually they say 17 because they see 16 - 1 by 1 squares and 1 large square.  They forget the 2 by 2 and 3 by 3 squares.

Background, Form, Triangle, AbstractThe next time I do it, I have them look at a larger square such as a 5 by 5 or 6 by 6.  Once they have this down, I move to a simple triangle.

If you start with a triangle such the one to the left, it is much easier for them to count.  I sometimes will put a triangle  and ask them how many quadrilaterals do you see?  Be sure to break down the types of quadrilaterals.  There are trapezoids, parallelograms, and rhombus.  This type of problem can challenge them.

Sierpinski Triangle, Chaos, FractalI also like to put triangles like the one to the left with multiple different sized triangles within triangles.  This can take a while to do and students tend to naturally collaborate to make sure they have all the triangles.  Sometimes I will take this a step further and ask them "How do you know you found all the triangles?"  This questions requires them to give an explanation of the process they went through