Perimeter Part 2: Overlearning

In part 1 I discussed “seeing” perimeters.

The tasks in this post are designed to hone in on notation, without getting into properties of shapes. Dashes denoting equal lengths is isolated to begin with, and exaggerated to really hammer home how much information is implicit in mathematical diagrams.

In the following questions, pupils made links to their work on number bonds (mentioned here). Some pupils found groups of 10cm (either a group of one and two dashes, or a group of one, two and three dashes) and then counted their groups, whereas others added all their one dashes up first etc.

Discussing these alternate strategies helped pupils be more flexible in their thinking and make explicit the commutativity of addition applies to lengths as much as abstract numbers.

The next page repeats this format with subtractions to find missing lengths when given perimeters.

For some reason, kids really love a question that looks like a total beast but is basically the same thing.

The next question is really nice in that pupils had to be wary of the 10m in the bottom right as it’s the only edge that long.

These questions are all hexagons with perimeter 60cm and the shortest side is 3cm, but each one has a different answer. At first, I gave this out with just the written information and unlabelled diagrams, but found it too overloading.

After the task, pupils are amazed how much you can delete from the question and it still make sense. This led to a great teaching point around how in diagrams we consider them not to scale, but assume any lengths shown smaller than others are so.

I really loved these questions from @giftedHKO on twitter (found here amongst so much amazing maths) and wanted to make some that were accessible for my year 7s (no circles for us just yet!).

To start with, we looked at when we could and couldn’t find a perimeter from given information.

This was followed with some practice.

In this task, the answers have some prompts for discussion around strategies for certain questions that relate to seeing.

Similarly, a lot of pupils are fewmin when they don’t spot that the question below can be answered without any decimal calculations, as half of the perimeter is highlighted.

This explicit discussion around strategies that are flexible to approach different questions lays the groundwork for the last two pages of questions.

In this final question, while I’m tempted to crack out simultaneous equations, this can be done using addition, subtraction, number bonds to 5 and a bit of spatial reasoning.

(All resources and solutions are linked at the top of the post.)

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