3. Looking for patterns
In this part, we look at another way of seeing patterns in multiplication, which is not based upon shapes and counters, but still looks for patterns in rows and columns. Helping pupils explore patterns through practical activities will develop their deeper thinking.
Imagine two columns, one for ‘tens’ another for ‘units’. If we think, for example, of the 8 times table, the first four numbers are 8, 16, 24, 32.
What happens to the tens and the units as you look down the two columns? You should notice that the tens increase by 1 each time, while the units decrease by 2. Using this observation, what would be the next three numbers? See Resource 3: Tens and units for an example of this exercise.
Such observations and questions can be used to help pupils learn about both multiplication and pattern recognition.
Case Study 3: Recognising patterns in sequences
Mr Lutengano wanted to do an activity exploring number. He wrote the following number sequences on the board, then asked the pupils to help him find the missing number. Pupils had to put their hand up and say what they thought the missing number was, and why.
- 4, 6, 8, [ ] , 12, 14
- 3, 6, [ ] ,12, 15
- 16, 25, [ ] ,49, 64
- 1, 11, 111, [ ] ,11111
- 1, 1, 2, 3, [ ] ,8, 13
When the pupils had finished, he asked them to make up their own patterns and leave a number out. They then swapped their pattern with their partners and tried to fill in the missing numbers.
They were very excited and enjoyed the activity. Mr Inekwe asked if they could see a pattern? Could they predict the last number and each answer? He was pleased some could.
Mr Lutengano used pair work often, as it allowed all pupils to talk and helped their thinking.
Key Activity: Exploring the multiples of 9
You will need Resource 4: Times table
- Stand by the chalkboard and ask pupils to be totally silent. Ask them to watch carefully.
- Write the first five multiples of 9 on the blackboard.
- Pause. Ask them to look at what is happening to the numbers.
- Ask a pupil to complete the pattern to 10 x 9, under the heading ‘tens’ and ‘units’.
- Ask the class to share anything they notice, recording and accepting everything without commenting.
- Carry on, but stop after 13 x 9, skip some and then write 17 x 9 = ? Now, watch carefully while they try to make sense of what is going on. You may have to prompt them to see the pattern in tens and units.
- Finally ask pairs of pupils to investigate other multiples (it is best to start with single digit numbers, 1–9). Can they work out together the pattern for tens and units?