This is just about some ideas for angles we’ve been using in the department.

**Polygons: angles as turn**

We’ve been trying to demonstrate to the pupils what it actually means to say the sum of the angles in a triangle is 180 degrees. On a straight line it is easy to demonstrate the half-turn, and remain faithful to the idea that angles are a measure of turn.

I find that the activity of tearing the corners from a triangle and arranging them on a line doesn’t seem to stick. I suspect it also reinforces the idea of a line more than the idea of a half-turn.

Using a board pen or, in my case, a small toy bird, we’ve tried this instead. Because it is small-scale, I’ve used an anthropomorphised key…

It starts facing forward. At each vertex, it turns. Upon returning to its original position, it is facing the opposite direction. It has completed a half turn đ

It then extends nicely to quadrilaterals (it is facing the same way), then pentagons (a turn and a half – facing backwards) and so on. It allows the pupils to see that not only does the number of triangles increase (the standard and much-loved way of showing progression in polygons), but also that each time they increase by a half-turn.

**Vertically opposite angles**

We were finding it tricky to help pupils spot vertically opposite angle when there were more than two intersecting lines. One pupil* suggested that they position their rulers to rotate around the point of intersection, turning to hide the one being focused on. The one that is revealed has the same turn, so must be equal. They are the vertically opposite angles. Here are two examples of her suggestion:

It is obviously easier if a finger is placed at the point of intersection, as it is easier for the ruler to rotate. The limits of one-handed camera phone filming!

Lastly, another pupil had a good suggestion to help with spotting vertically opposite angles. If each separate line segment is highlighted (and there are no non-straight lines!), then the ones ‘trapped’ between the same colour-pair will be vertically opposite to each other:

This works better than just giving highlighters, as the additional rule of ‘trapped between the same colours’ gives them a little more to hang onto!

If you have tips to make it easier to spot alternate angles than ‘a Z shape’…please tell me!

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(I’ve partly made a fussÂ of this way of modellingÂ because the pupilÂ is a solid fourth quartile kid. It’s been really exciting to hear her come up with her own ideas for demonstrating what she understands. I plan on showing her this video tomorrow)