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 Okello wanted to do an activity exploring the multiples of 9. He decided that, although his pupils were familiar with square and rectangular numbers, they first needed practice in recognising other simple patterns. They had done similar work in a previous year and so some of this pattern recognition was revision.
He asked them in pairs to fill in the following missing numbers:
- 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 were finished and the answers shared, he asked the class to make up their own patterns and leave a number out. They then swapped their pattern with their partners and filled in the missing numbers.
Next, he asked them to do a pattern using 9.
He started them off and asked them to keep going:
- 0, 9, 18, 27, 36, [ ], [ ], [ ] ….
Mr Okello used pair work often, as it allowed everyone to talk and helped his pupils’ thinking.They were very excited and enjoyed the activity. Mr Okello asked if they could see a pattern. Could they predict the last number and each answer? He was pleased some could.
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?
2. Using games to explore rectangular numbers
