2. Encouraging pupils to ask questions

Investigations in which pupils have opportunities to discover facts by themselves or in small groups are effective ways of working in mathematics. Key Resource: Using investigations in the classroom [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]   will help you look at different approaches to investigation. By asking pupils to make up their own simple questions you can improve their investigatory powers. This part explores number charts in a different way to extend pupils’ thinking about number and pattern.

Case Study 2: Moving around the number chart

Mrs Mudenda wanted to develop her pupils’ confidence in their mathematical thinking. She made many copies of a 100-square number chart, divided her class into pairs and gave a chart to each pair. She then asked the following questions for the pairs to solve using their charts:

How can you move from 10 to 15? E.g. move right 5 squares.

How can you move from 10 to 35? E.g. move right 5 squares and down 2 squares; or down 2 squares and right 5 squares.

She discussed with the class the possible ways of moving from 10 to 35 on the chart and helped pupils understand that there are sometimes many ways to answer a question in mathematics.

Mrs Mudenda then asked the pupils to make up ten similar questions each and take turns with their partner to answer them with the help of the number square. She asked her more able pupils to try to write the sums down.

Activity 2: Addition and subtraction from number charts

Before the lesson, prepare some number charts (see Resource 1). Also, do the activities yourself and find out how many different ways there are of answering each question.

Ask the pupils to go into pairs and hand out a chart to each pair. Now ask them to investigate questions such as:

How many ways can I move from ‘21’ to ‘34’ on the chart?

Go round the class, listening to their reasoning and making notes. Different pairs may give different answers, for example: ‘I will go down 1 and along 3’ or ‘I will go along 3 and down 1’.

Next, ask your pupils to each make up five similar questions, moving from one square to any other, and ask their partner to solve each of these in at least two ways.

Finally, you could extend this work by asking the pupils to agree with their partner, ‘what is happening to the tens and units with each move?’ e.g. moving from 19 to 47 is going down 3 rows, (adding 30), and moving left 2 columns (removing 2). This is the same as adding 28.

1. Using number charts in groups

3. Simple investigations