Extending Transformations

All four transformations (Translation, Reflection, Rotation, Enlargement) with Year 10. It feels like one of those topics that we cover in Year 8, they mostly grasp some of the skills but then forget the details (e.g. to specify the centre of rotation). That’s OK, I reckon. But it does imply that the time in Year 8 is better spent mastering the more tricky skills like reflecting in 45 degree lines than answering GCSE style questions, e.g doing translations using vectors.  These sheets are an old favourite which are great for practising those skills.

I was a bit surprised how long my middle set took to get to grips with it. Inevitably there were some who finished quickly because they found it easier to visualise than others. I was a bit stumped for how to extend it. A quick conversation in the maths office gave me the idea of multiple translations. Of course! Do, say, a reflection followed by a rotation. And then what is the single transformation that has the same effect?

I created a simple extension question:

The shape ABCD has coordinates (-1,1) (-3,1)
(-3,4) and (-1,5) respectively. It is reflected in the line y = x to produce shape A’B’C’D’ and then rotated 900 anticlockwise about (2,2) to create A’’B’’C’’D’’.

What are the coordinates of each of the points A’’, B’’, C’’, D’’ after these TWO transformations?

Describe fully the single transformation which would map ABCD onto A’’B’’C’’D’’.

This document can easily be printed and chopped. I used this geogebra file to create it.Screen Shot 2015-03-25 at 18.47.35

It’s easy to create more questions like this by moving the points of the original shape and changing the transformations in the Geogebra file.

Extension Arithmetic

Here is a mixture of arithmetic questions to ponder with solutions (or here as a pdf in case the Equation editor in Word messes things up).   They are all non-calc although that’s not immediately obvious when you look at them. I used this today with second set Year 9 and they seemed to appreciate that they achieved more than they originally thought they would when I put them all up at once.

Here is an example:

Screen Shot 2015-04-20 at 20.19.32