I like these little tricks and students seem to enjoy them too, I usually start with a simple one like: I think of a number, add 3, double it, subtract 6 and halve it. If they quickly work out that my answer will always get back to my start number, we then look at why. We look at writing the calculations out without calculating but just simplifying if possible
So if they used 4…
4 ( i think of a number)
4+3 (add 3)
4+4+3+3 (double it)
4+4+3+3-6 = 4+4 (subtract 6)
4 (Halve it)
When you compare each student they can see the variables and the constants. They can start to generalise. The student work below is an example of using values and then generalising. I asked how he got from add 6 to halve it and he said that 7 x 2 + 6 is 7 + 3 because you only have one 7 when you have 7 x 2 and half of 6 is 3. After working through these a few students asked if they could try and make their own up. So next lesson we hope to try and write some expressions and put words to them. The students noticed how my tricks always came back to the original number or a specific number and they want to try and make their own versions of these.
I was thinking that next lesson
What i hope is for them to write the words to my expressions and then get them to work using numbers or letters if they prefer to create a series of slightly altered expressions of their own.
I want to display the slide above and ask them to explain what they notice to be the same and what changes. What they notice has to apply to all 3 examples. They could write out an example of their own if it helps.