Finding the Area of a Picture Frame

Once again 4BF joined up with 4RB and @CapitanoAmazing (http://4thgradebigquestions.blogspot.com.au) to explore the exciting world of 2D shapes.

Our recent focus has been on finding the area of a shape.

We started with a look at one of those activities that gives you a picture in a frame and asks you to find the area of the picture - but you only get the dimensions for the frame and the distance from the edge of the frame to the edge of the picture:

This activity was taken from the Mathletics e-book "Length, Area and Perimeter"

Can you work backwards to create your own?

We had been talking a lot about problem solving strategies lately and so the suggestion was made that if we worked backwards, we might create our own similar puzzle.

SO, starting with a picture from a magazine, the kids got busy. 

The initial task was to create a frame that was equal in area to the picture itself. The simplest strategy to do this was found to be trace the outline of the photo onto the coloured paper and then slide the photo across and do it again.

But some students quickly realised that there were problems here. If their photo was very square or very elongated, they were in trouble. To keep it simple, we agreed that they could make their frame from a piece of paper that was four times larger than their photo - and therefore their frame would be three times the area of their photo, with the photo covering 1/4 of the coloured space.

The cutting and pasting was impressive but the most significant dimension of this activity was what the kids wrote about their learning and use of mathematics.

Here's the explanations and reflections the kids produced:

 When explaining this one to me, the student said, "So my picture has an area of  30cm²

and the frame has an area of 88cm²  which is twice the size of....Hey! No it's not!"

Much interesting learning occurred following this reflection.

Two students explaining their calculations

 A bit hard to read but if you zoom your screen in you might be able to read it

Here's what the whole thing looked like..

....and here's a few close-ups of the comments....

And again - the whole picture (above) and the close-ups (below)

So what?

Well, we got to apply the "work backwards" strategy to create our own puzzles.

And we explored area a bit more deeply.

We applied fractions and decimals in our measurements and calculations.

We wrote explanations and reflections on our investigation.

And we got to do some quality cutting and pasting, the life-blood of primary education.

And with five days to go to the end of the school year, they're still working hard in Year 4!