Examples of what pupils should know and be able to do
Recognise that:
- indices are added when multiplying numbers expressed as powers of the
same base number, e.g. 5
× 5
= (5 × 5) × (5 × 5 × 5) = (5 × 5 ×
5 × 5 × 5) = 5
= 5
- indices are subtracted when dividing numbers expressed as powers of
the same base number, e.g. 4
÷ 4
= (4 × 4 × 4 × 4 × 4) ÷ (4 × 4) =
(4 × 4 × 4) = 4
= 4
Probing questions
What the answer to 5 × 5 = ?
Convince me that 3
÷ 3 = 3.
What the answer to 5 + 5? Why don't the same laws apply?
If 2 × 3
= 162, what is the value of n?
If 4
×
4 = 4
and 
,
what are the values of m and n?
What if pupils find this a barrier?
- Investigate questions such as 5 × 5 = ?
- Build on work with powers of ten then extend to other bases.
- Refer back to Step 7.
- Use the ×
key on a calculator to explore the index laws.