1. Working in pairs
The concept of ‘square numbers’ can be very abstract. Drawing squares, or making squares with counters can help pupils begin to gain a visual understanding. What numbers of counters do we need to make square shapes (i.e. those with equal numbers of counters in each row, and as many rows as columns)?
You need to plan your lessons to ensure that all pupils are participating. In Activity 1 you will ask your pupils to work in pairs.
Case Study 1: Drawing square numbers
Mrs Baale in South Africa wanted her pupils to do some investigations in pairs with only some guidance from her. She was keen to see if the pupils could investigate square numbers for themselves.
She began the lesson by asking pupils to work in pairs. She drew a square on the board; then she drew a larger square, made up of four smaller squares (see Resource 1: Square numbers). She asked the pupils to draw as many other squares like these as they could in five minutes. She told the class that these numbers were called ‘square numbers’.
Mrs Baale asked the class if they could make more square numbers, and to note the number of little squares needed to make each big square.
By allowing the pupils to work mainly unaided, Mrs Baale felt they would gain confidence and find enjoyment in the lesson. She found that most pairs worked well together.
Activity 1: Making square numbers with objects
Look at the task in Resource 1. Read it through carefully and try the task yourself before doing it with your class.
Encourage each pupil to participate by asking the pairs to choose first one member to be the scribe (the one to draw) and the other the recorder, and then to swap these tasks. In this way, you can make sure each pupil is participating.
You could also give your pupils objects (seeds or small stones) as counters. Ask pairs of pupils to find ‘square numbers’ (those with equal numbers of counters in each row, and as many rows as columns).