# 3. Simple investigations

When pupils are confident in moving around the number chart, they can begin to stretch their ability to ‘see’ or visualise mathematical patterns. A simple starting point is to colour in (or put counters on) all the squares that meet a certain condition, e.g. multiples of a given number. This is what the teacher in Case Study 3 did.

In the Key Activity you will take away most of the squares (see Resource 3: Partial number squares for some examples) and see if pupils can work out what numbers should go in particular places.

## Case Study 3: Investigating multiplication with number charts

Mrs Kashina, who teaches a Grade 4 class of 41 pupils, gave groups of four pupils a number chart, and 15 small stones. On the board, she wrote down

4, 6, 9, 11

and asked the groups to take one number at a time, and put a seed on all the multiples of that number (e.g. for number 4, multiples are 4, 8, 12, 16). Some of her pupils coloured or shaded in the multiples instead of putting seeds. Then pupils had to write down the patterns they could see, as she showed them with 4, before trying the next number. She asked them to look for any patterns in the answers:

• 4
• 8
• 12
• 16
• 20
• 24
• 28
• 32
• 36
• 40

She asked a different group each time to show their answers and they discussed any patterns on the chart and in their answers.

To see an example of the work Mrs Kashina’s class did, see Resource 4: Mrs Kashina’s multiplication charts.

In a later lesson, Mrs Kashina told a story from a Zambian magazine about a boy who made his own number patterns (see Resource 5: Magic square puzzles). She used a mixture of ciTonga and English. (In this way she built on the pupils’ knowledge of their own language to help them understand the new language.) The pupils became very enthusiastic about number patterns, and Mrs Kashina believed they would enjoy doing similar investigations for multiplication.

## Key Activity: Using a chart of multiplication facts

Building on the previous work, give your pupils an investigation using charts of multiplication facts. Before the lesson, prepare a large chart of number facts for 5, 6, 7, 8 and 9, leaving some squares empty. You are going to ask your pupils to find the missing numbers using their previous knowledge.

Split your pupils into groups of four or five and ask each group to copy your chart.

Ask pupils to discuss together what the missing numbers should be and, if they agree, to fill in their copies and then pin their results on the wall. As they are working, go round the class listening and helping – only where absolutely necessary – by asking questions rather than giving answers.

What facts do you know?

What numbers are missing?

Can you see a pattern in the row? In the column?

Ask a member of each group to explain how they arrived at their answers and have a class discussion to decide the correct solution.

Ask each group to do a neat copy for one multiplication table and mark in the multiples clearly. Display each chart on the classroom wall in order from 2 times to 10 times so they can look at the patterns easily.

Finally, look at the questions in Resource 2 to help you think about how the lesson went.

2. Encouraging pupils to ask questions

Resource 1: 100-square number chart