Generalising Patterns
Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts
What a learner can do afterwards
- Use a known doubles fact to derive a near-doubles answer (e.g. 6 + 7 = 6 + 6 + 1 = 13)
- Notice that subtracting 10 from any two-digit number always reduces the tens digit by 1
- Describe a rule for a pattern and use it to extend or predict (e.g. 'starting at 5, each time we add 5, the ones digit alternates between 0 and 5')
1 · Read
Sometimes a new problem is a fact you know with one change. If 6 + 6 = 12, then 6 + 7 is one more: 13. Patterns follow steady rules. In 2, 4, 6, 8, add 2 each time. In 3, 6, 9, add 3 each time. Say the rule and use it again. When adding, start at the larger number and count on the smaller part.
Leo knows 6 + 6 = 12. He needs 6 + 7. That is just one more than 6 + 6, so 6 + 7 = 6 + 6 + 1 = 13.
Zara takes 10 away from 34. The ones digit, 4, does not change. The tens digit drops from 3 to 2, so 34 minus 10 is 24. This works for any two-digit number.
To find a rule, check what changes as you move to the next number. Say the rule in words, such as "add 5 each time." Then use it to guess what comes next.
Find what changes each time. Say the rule, then use it to predict the next answer.
Retained academy, math-design and problems records are credited per item. x5, x8 and 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.
18 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.