There was a resource I used to use years ago around ‘nibbled’ perimeters. “Move the end on one across and add two to the top and bottom to complete the rectangle.” “You’d add four lines on and then off the double line inside.” “You’d add three lines on and then take off the one on the inside.” Showing pupils some maths and asking them to explain it is powerful AfL for us as teachers to see where kids are at with communicating maths through a speech, a precursor of writing it down.įor the above conditions I had the following responses: “Year 7, some people might look at this and think that four squares will have a perimeter of 10 units, but watch this!”įollowing with this up with reasoning around why adding a square in a line is a definite way to increase the perimeter by two helps train pupils out of that ‘there’s always just a right or wrong answer in maths’, and brings in increasing conditions for mathematical knowledge. No matter what the level of mathematics in lesson (the above screenshot and the one below were taken from our year 7 nurture group) conjecture and argument have a place.Īgain, the aim is not to catch pupils out with the 4 squares also having a perimeter of 8, but was presented in a way that is a big sneaky secret. Even in the task below, it took a lot of modelling and using the visualiser to get them to look at individual line segments rather than the number of lines in the shape. Secondly, pupils really struggled divorcing the number of squares (we’re avoiding the word area here) from the perimeter. (Similarly, Pilot V Board Master Chisel Tip Medium Refillable pens? No contest. This post, and the subsequent post, address two approaches I’ve taken.įirstly, I can’t recommend projecting a square excel spreadsheet on the board with border shading enough for a quick and dirty square whiteboard. In this task, the answers have some prompts for discussion around strategies for certain questions that relate to seeing.Separating perimeter from area has a whole host of benefits in allaying misconceptions around dimensional differences between lengths and areas, but this often means that reasoning and teaching to greater depth with perimeter exclusively can be more challenging. To start with, we looked at when we could and couldn’t find a perimeter from given information. I really loved these questions from 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!). 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. At first, I gave this out with just the written information and unlabelled diagrams, but found it too overloading.Īfter the task, pupils are amazed how much you can delete from the question and it still make sense. These questions are all hexagons with perimeter 60cm and the shortest side is 3cm, but each one has a different answer. 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. The next page repeats this format with subtractions to find missing lengths when given perimeters.įor some reason, kids really love a question that looks like a total beast but is basically the same thing. 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.ĭiscussing 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. In the following questions, pupils made links to their work on number bonds (mentioned here).
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