Vary and twist : Inverse proportion

Another ‘vary and twist’. This time on inverse proportion. Download it here.

I have added a section at the top making explicit that students should make an expectation of the answer before working it out, as I think this is where the power of these types of activity come from.

My thinking

  1. A question to start
  2. Does swapping x and y matter? If not, why not?
  3. Doubling x, what happens to y? What you expect?
  4. Doubling y in our initial relationship. Why does this differ in it’s result from doubling x from before?
  5. As above, but for x
  6. What happens if we half the value of x we want? Maybe this should be moved up in the list to question 4.
  7. A multiplication of 10 from the original. Does it hold up to more than halving?
  8. Now we’re finding x not y!
  9. We’ve doubled the y. What happens to x? Does the relationship work both ways?
  10. A decimal answer

As always, feedback would be lovely. I’m not sure I’ve correctly hit the sweet spot between making links and confusing the pupils. I’m also not sure that they flow the way they should.

I guess since I’ve done dividing in a ratio, proportion and inverse I should finish off the module. Expect simplifying a ratio and recipes (which will be a challenge to lay out) to come next.