Inspired by NCETM and Jan Parry, my Year 9 second set today explored some of the relationships between area and algebra. The starter gave them this image:
But rather than ask for the area of the shaded space, I asked for three different calculations that would give the area of the shaded space. Collectively the class managed to arrive at 13x15 - 8x5; 13x7 + 8x8; and 15x8 + 7x5. Once we understood this idea, we moved on to this image:
We talked about the similarities and differences between this shape and the starter image, and then worked through the same questions about finding different expressions for the area of the shape and then showing that these areas are all equivalent.
After a little independent work we then looked at a different link between area and algebra. The shot below explains:
But rather than ask for the area of the shaded space, I asked for three different calculations that would give the area of the shaded space. Collectively the class managed to arrive at 13x15 - 8x5; 13x7 + 8x8; and 15x8 + 7x5. Once we understood this idea, we moved on to this image:
We talked about the similarities and differences between this shape and the starter image, and then worked through the same questions about finding different expressions for the area of the shape and then showing that these areas are all equivalent.
After a little independent work we then looked at a different link between area and algebra. The shot below explains:
We used the polydron (see earlier blog) to explore this shape (importantly here making the link between 2a + 2b and 2(a+b)) and then other shapes, building shapes that give expressions like 2(5a+3b). The pupils really enjoyed getting hands on with algebra and being able to physically build expressions.
The link here gives the whole lesson, it is definitely worth a look.
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