Generalising with repeated reasoning
Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases
What a learner can do afterwards
- Explain that the interior angle sum of an n-sided polygon is (n−2) × 180° based on the pattern for triangles, quadrilaterals, pentagons
- Predict the 20th term of a linear sequence by identifying and applying the general rule
- Generalise that dividing by n always gives a denominator of n in the fraction, for any whole numbers
The lesson
A pattern that works in a few examples often works for every case. Finding a rule like that is called generalising. You use a letter, like n, to stand for any number, so your rule works even for cases you have not tried.
Maya's sequence is 5, 9, 13, 17, and it goes up by 4 each time. Instead of counting all the way to the 20th term, she writes a rule: multiply the position number by 4, then add 1. For the 20th term: 4 × 20 + 1 = 81. She checks the rule on a term she already knows, term 3: 4 × 3 + 1 = 13. It matches, so the rule works.
Always test a new rule on a case you already know the answer to. If the rule does not match, fix the rule, not the pattern you saw.
Repeated reasoning turns a pattern from a few examples into a rule for any case, then you check the rule against numbers you already know.
Watch it
Where it sits
Learn first
This opens up
Nothing builds on it yet.
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.