1. I asked everyone to draw a rectangle on cm squared paper whose dimensions were 2. As part of this I asked them to explain what ‘dimensions’ meant so everyone used w and h for width and height of their rectangle.

2. Next I asked them to calculate the area and perimeter of their rectangles, referring these measures as A and P. This brought about misconceptions about how to calculate the perimeter of a rectangle when different children explained their methods. Having sorted out which of their three methods was correct we moved on.

3. Now each child had a rectangle with four pieces of information: w, h, A and P.

4. I asked them to make a sketch of their own rectangle on plain (non-squared) sugar paper showing just two of the four pieces of information, i.e. h and A or w and P or A and P, together with their name. So for example Lily drew her rectangle and wrote w = 6 and A = 30.

5. Everyone stuck their piece of sugar paper around the classroom walls and everyone then had to work out the two missing pieces of information from a selection of the data around the room.

Thus each child engaged with doing and undoing. A further key pedagogic issue was how their collective pieces of sugar paper formed a ‘worksheet’ which they collectively had ownership of. This was a far more powerful aspect of their learning by contrast to any worksheet I might have given them to do. ]]>

Thanks Mike, students creating their own questions is a lovely idea, I hadn’t given much thought to the idea of ownership. I often use this with some restraints (eg form an equation with solution greater than 500 or a negative, solution), at some stage this will usually involve me sharing my “teacher trick” of starting with the solution and building up. For me this is about the idea of doing and undoing that leads to more fluency of manipulations.

Cheers, Sam

]]>Thanks Danny, I wasn’t aware that I was presenting a reason for solving equations in lesson 4, but see now that students possible think I am. Rather I wanted to mixed with prior topics studies (area and angles) and reinforce this idea of equations as statements, so going from the geometric statement “interior angles in a pentagon sum to 540 degrees” to an algebraic statement “x + x + 30 + 3x + x + 3x = 540”. If you have any ideas for activities / investigations I would love to hear.

Hope your well,

Sam

]]>I think the initial approach is a good idea, and hopefully will give students the opportunity to become aware of the equivalence of e.g. 3x and x+x+x… and also perhaps reveal an awareness of some of the x’s being ‘duplicated’ on both sides, which might later suggest a method for solving equations (subtracting x’s from both sides).

Perhaps some subtraction or multiplication between the boxes might be interesting here too as an opportunity for generalisation? [i.e. does the method you are using to fill in the boxes still hold for these other operations?] But perhaps this would over-complicate, or take the focus away from the awarenesses you wish to ‘force’.

I can see you have tried to introduce a ‘reason’ why we (students) might want to solve such equations in lesson 4, but they are still sort of ‘arbitrary’ questions. I wonder if there is some kind of investigation (perhaps starting with one of the geometric examples and extending/generalising it) that would achieve this whilst at the same time require the use of some other mathematical skills such as conjecturing. generalising, and so on?

D

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