Rich Learning Tasks

177

For more information visit

www.mathletics.com

Big and Little Rectangles

Questions to facilitate the learning

•

Suppose the length was doubled. How would the width change?

•

Suppose the length was not changed at all. How would the width change?

•

Is it possible that the rectangle’s length could change from 5 cm to 15 cm? Explain.

Scaffolding the learning

•

What does 2

times something mean?

•

Could you change just the length?

What’s the point of this task?

Creating a rectangle with an area 2

times as big as another’s engages students in a number of

mathematical concepts. It might involve using the formula for areas of rectangles. It certainly involves

students in using multiplicative reasoning, recognising that 2

of something is two of it and another half

of it. Students might realise they could leave the length and multiply the width by 2

or leave the width

and multiply the length by 2

or they might change both measures—e.g. multiply the length by 5 and

take half of the width. Since students are asked for at least three possibilities, they will have to use at least

one example where both dimensions are changed. It would be interesting to see if they just guess and test

or use the idea that 2

Students could just use a rectangle with one even dimension so that it could be easily cut in half and

simply copy the rectangle and another half of it, put the pieces together and then figure out the dimensions.

Asking if the first size of the rectangle matters gives students an opportunity to generalise.

Extending the learning

Students might be asked to try to multiply the area by 2

, but make sure the perimeter is multiplied by

a value that is a little less than half.

Measurement