Q I teach a Year 6 class and we have been preparing for their key stage 2 national tests. I noticed that they find it really difficult to draw reflections of shapes when the mirror line is at an angle. We have done work with mirrors and folding paper, but there are still a few who cannot get the image right.
A Page 107 of the framework states: Year 6 pupils should "sketch the reflection of a simple shape in a mirror line touching it at one point, where the edges of the shape are not necessarily parallel or perpendicular to the mirror line".
I will show you how I suggest you progress on the second shape in the diagram below. This could be done in class on an OHP.
Begin by moving the page so that the mirror is displayed vertically in front of the class.
Label each corner in alphabetical order going clockwise or anticlockwise.
Explain that a line drawn between a point on the shape to its image point would be a straight line going through the mirror at a right angle. Also, that the image is always the same distance from the mirror on the opposite side as the object is from the mirror. Demonstrating this with a mirror helps in understanding this idea of distance.
Demonstrate how a ruler can be used to determine (approximately) the length of a straight line at right angles to the mirror (in this case, from point C) by aligning the large subdivision mark for centimetres with the mirror line (this is because these lines are already at right angles to the edge of the mirror). See the diagram below. Some pupils find this idea difficult.
Draw the line, then measure the perpendicular distance of the point on the object to the mirror - in this case, 2cm - and then measure 2cm the other side of the mirror and mark this as the image point C1 of C.
Invite a pupil to select another point. Use the ruler to show the ray from this point that is at right angles to the mirror.
Draw this line through the mirror.
Next, ask the same pupil to measure the distance from the object point, say C, to the mirror (in this case, 2cm). Now measure the same distance on the other side of the mirror line. Mark this point with a small cross and mark it C1.
Do the same for each of the points, getting different members of the class to demonstrate the reflection point for each point of the shape.
When all the reflection points have been marked, join them up in alphabetical order with a ruler.
Now the paper can be put in its original position.
Ask pupils to draw a diagonal line across a piece of paper and write the first letter of their name on one side of the diagonal, using straight lines where possible. Get them to draw the reflection using the same construction. Although the framework doesn't say "construct", the reflection is much easier to sketch when the pupil knows how to create the image.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.
Email your questions to Mathagony Aunt at firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX