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. 'each time we add 5, the ones digit alternates between 0 and 5')
The lesson
Sometimes a new problem is just like one you already know, with one small change. If you notice how the numbers connect, you can use a fact you already know to work out the new one fast.
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, look at what changes every time you move to the next number. Say it in words, like 'each time we add 5'. Then use your rule to guess what comes next.
Spot what changes each time, put the rule into words, and use it to predict the next answer.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.