Bring along a rod to start angling
Have you any suggestions on how I could start the lesson with a novel idea? I wonder what you would think of me holding a fishing rod at an angle sitting on a desk? Do you think this is a bit corny?
The fishing rod is fine, but don't have a hook on the end. Pupils need to understand that there are many types of angles. I wonder what they think the relevance of a fishing rod is for the lesson? I'll bet they guess measuring. Having familiar or interesting objects linked to your lesson starter can bring lessons to life. The numeracy strategy says that Year 4 pupils should in particular be able to use, read and write "turn", "rotate", "whole turn", "half a turn", "quarter turn", "angle", "right angle", "straight line", "degree".
In Year 5, the vocabulary is extended to acute and obtuse angles and protractor. Make sure you know what the pupils should know from Year 4, particularly the language and that there are 360 degrees in a circle. Have the words on some pieces of card to put up on the wall as you mention them.
A great activity pupils really enjoy is having to guess the angle. This can be used to revise the words from Year 4 as well as to introduce new ones.
Cut out two circles from different coloured pieces of card. Make a cut from the circumference to the centre in each, then thread the cards together.
Each pupil has their own angle machine. Ask them to show you 90 degrees, 45 degrees and so forth, revising Year 4. Then talk about acute angles and obtuse angles, putting word cards on the wall.
Ask them to show you an obtuse angle, an acute angle, a straight angle and so on. The blue shows an obtuse angle in the first turn and an acute angle (marked) in the second. Finally, you can show some angles and ask them to use their digit cards to tell you how big they think the angle is. Is it acute or obtuse?
In some envelopes or small plastic bags have a matching exercise using the angle name and a picture of the angle - perhaps 10 pairs. Tell them not to open them until they are told to.
Finish the lesson by having a "thought shower" on what different kinds of angles there are. There are obvious angles: those made with two lines and a pivot or point, such as when a pair of scissors are opened or the angle the fishing line makes with the rod. Then there are the angles where there is only one obvious line and a pivot, such as a window or door opening - there is an imaginary line somewhere on the door and an open gap with another imaginary line. Lastly, there are the angles that appear to have no lines, such as a wheel or doorknob - in the first activity you created the line with the two different colours making this easy to see.
Discuss with the class where they might find the different kinds of angles.
Perhaps for homework they could bring in a picture from real life of each of the angles so that they can create a poster of angles on the wall.
I don't know how long your lesson is, but it does need detailed planning.
These are only suggestions, and to have a successful lesson you need to personalise it.
For a fuller understanding of the development of the concept of angle I suggest you read the paper by Paul White and Michael Mitchelmore: "Teaching Materials Angles by Abstraction from Physical Activities with Concrete" http:dlibrary.acu.edu.aumaths_educpaulwhiteTeachingangles.pdf
* I have been discussing the language used in maths with Professor Chris Budd from Bath University, and he sent me this: "When a top spins, its polhode rolls along the herpolhode lying in the invariant plane. This piece of gibberish is central to the design of stable satellites... and hence to good TV reception from satellite TV. (Incidentally, another application of quadratic equations.)" Also... "With respect to the problem of the shift of the sine wave that you mentioned in your column of March 11, you might find it interesting to know that the process of shifting sine waves to and fro is very important in the communications industry, and is the key idea behind FM radio."