About this unit
Why keep an answer exact when a calculator gives a decimal?
Sections in this unit
Factual
- Why is any base to the power zero equal to one?
- When can two powers be set equal to each other?
- Why does multiplying by the conjugate remove a surd from a denominator?
Conceptual
- Why must a power of one half be a square root?
- Why is the root of a sum not the sum of the roots?
- What makes one form of a number simpler than another when both have the same value?
Debatable
- Is an exact answer always more useful than a decimal one?
- Can an arithmetic sequence mix rational and irrational terms?
Skills
Students should be able to:
- Select and apply an appropriate technique in an unfamiliar situation, where no method is named in the question.
- Generalise from particular cases — state a law in general form having established it on numbers.
- Use correct notation and set out a solution as a sequence of justified steps rather than a jump to an answer.
- Identify and correct one’s own errors from feedback, and choose the next piece of practice accordingly.
How you are assessed
- Cumulative summative test, Criteria A and C
Before you start
Students arrive with:
- Index laws for whole-number powers from Year 9, reviewed from numerical cases in the first lesson rather than assumed.
- Square and cube numbers and their roots, and square factors, needed for simplifying surds.
- Surds met in Year 9 — the pre-assessment establishes what survived, and last year's cohort were reviewing rather than meeting them.
- Reciprocals and equivalent fractions.
- Expanding double brackets and the difference of two squares, from Year 9 and from Unit 1.
- Pythagoras' theorem in two dimensions.
- From Unit 1, arithmetic and geometric sequences, which run through the do-now routines and return carrying surd terms in the last two lessons.