LLL - Number
Factor Trees in Index Form
Students first learn index notation, then use a deterministic factor-tree method: prime numbers stop, the right-hand composite branch keeps reducing. One question appears on each page.
Year 7 number
From repeated multiplication to prime factors.
This lesson makes students say exactly what the base is, exactly how many times it is multiplied, and then apply the same idea to factor trees. The tree method is fixed: smallest prime on the left, remaining number on the right.
Whiteboard examples
The base is the repeated number. The index is how many times it appears.
Teaching
Index form is a shortcut.
When the same number is multiplied by itself, write the repeated number as the base and the number of repeats as the index.
Start with the repeated number.
3 x 3 = 3^2 because the repeated number is 3, and there are 2 threes.
3 x 3 x 3 = 3^3 because there are 3 threes.
3 x 3 x 3 x 3 = 3^4 because there are 4 threes.
When there is more than one repeated number, keep each repeated number as its own base: 2 x 2 x 4 x 4 = 2^2 x 4^2.
Later questions combine three bases, such as 2 x 2 x 3 x 3 x 4 x 4 = 2^2 x 3^2 x 4^2.
Then use the same idea with factor trees.
After a factor tree, list the prime factors. Then count matching primes and write them in index form.
A factor tree is deterministic when we use this class rule: put the smallest prime factor on the left. Prime numbers cannot be reduced further, so that branch stops. The right-hand side is reduced again until it is also prime.
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6
The six twos matter: five twos would only make 32.
- Split the number into smallest prime factor x remaining factor.
- Stop the prime branch because it cannot be reduced further.
- Keep reducing the right-hand branch while it is composite.
- Write the prime factors across the bottom, then count repeats for index form.
Summary
Index form journal
Progress is saved in this browser and, during a live class session, sent to the teacher dashboard.