Extending Table Patterns
Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences
What a learner can do afterwards
- Notice that all multiples of 4 are even and use this to check answers
- Derive 8 × 7 from 8 × 5 + 8 × 2 by spotting the pattern
- Describe a rule for a growing pattern (e.g. 'add 50 each time') and use it to predict the next terms
1 · Read
You can use a fact you know to find a new fact. Multiples of 4 are even: 4, 8, 12, 16. A number pattern has a steady jump, such as 10, 20, 30 or 3, 6, 9. Say the jump, then use it again. To find a new product, split one factor into parts you know and add the smaller products.
To find 8 × 7, split 7 into 5 + 2. You know 8 × 5 = 40 and 8 × 2 = 16. Add them together: 40 + 16 = 56. So 8 × 7 = 56.
Here is a quick check: every multiple of 4 is even. If a × 4 answer is odd, go back and try again.
Break a new fact into facts you know and add them. For a pattern, find what is added each time, then predict what comes next.
The rewritten readings were written for this dataset. Retained academy readings are credited per item. x1-x9 are original P17 authoring with null license; publisher terms for retained corpus records were not independently verified.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.