So, I thought, lets put the array thing together with some shapes that we need to find the area of.

I constructed the following set of shape outlines:

Then I asked the kids to find the biggest one and the smallest one. Fortunately I had made the sides of all the shapes whole centimetres, suggesting to the kids that they could use Base 10 blocks to work out the area of each shape.

(Just to be tricky, I made the task a bit ambiguous - there are several shapes that all have the same area - some are big and some are small. I wanted to see what conversation would come out of that.)

And here's what they did:

So we can put the Base 10 blocks onto the shapes to find how many cover it.

This one looks really big - it's soooo long!

Might need to use some units and well as tens.

Hmm, several of these are 24 square cms.

But why are they hanging over edge of the shape? asks the teacher.

Well, there's 2 hanging over so it must be 8 long (10 - 2 = 8) so 3 x 8 = 24! says the student.

And same again! 10 - 4 = 6.

So 4 x 6 = 24.

Smart kids! It's easier (less fiddly) to use the 10 blocks than getting all the units blocks out.

And yes, they were doing multiplication and arrays and area all in one go.

Hi Bruce,

ReplyDeleteI love the idea of modeling through base-ten blocks because of the foundation built for multiplication with double-digit factors. This allows for building partial products conceptually from the ground up.

What if we cut the rods in half and made them "base-five" and students had to write an expression to represent it. 8 * 3 could be (5*3) + (3*3).

My wheels are spinning...I'll be back when it clears up a bit.

Cheers,

Graham