GCSE Maths: Number — Topic Revision Workbook

Inside GCSE Maths: Number — Topic Revision Workbook

work with place value and standard form, use BIDMAS and the four operations, find HCF, LCM and prime factors, convert and calculate with fractions, decimals and percentages, tackle percentage change, reverse percentages and compound interest, then round, estimate, find bounds and simplify indices, roots and surds. About 30 minutes.

Learning objectives

• place value and standard form (A × 10ⁿ) alongside BIDMAS and the four operations;
• recognising factors, multiples and primes, and finding the HCF and LCM through prime factorisation;
• converting between and calculating with fractions, decimals and percentages, including percentage increase and decrease, reverse percentages and compound interest;
• rounding to decimal places and significant figures, estimating and finding bounds of rounded measurements;
• applying the index laws, evaluating roots and simplifying surds.

Activities in this book

1. Task 1 — Place Value, Standard Form & BIDMAS

   in standard form a number is written as A × 10ⁿ where A is between 1 and 10. A large number has a positive power; a small number below 1 has a negative power. With BIDMAS, always work out brackets and indices before multiplying, dividing, adding or subtracting.

2. Task 2 — Factors, Primes, HCF & LCM

   break each number into its prime factors with a factor tree. The HCF is the product of the primes both numbers share; the LCM is the smallest number both divide into. A prime has exactly two factors: 1 and itself.

3. Task 3 — Fractions, Decimals, Percentages & Change

   to change a fraction to a decimal, divide the top by the bottom; to change a decimal to a percentage, multiply by 100. For a percentage increase multiply by 1 + the rate; for a decrease multiply by 1 - the rate. To reverse a percentage, divide by that multiplier. Compound interest multiplies by the same factor each year.

4. Task 4 — Rounding, Estimation, Indices & Surds

   to round, look at the next digit — 5 or more rounds up. The lower bound of a rounded measurement is half a unit below it. When multiplying powers of the same base, add the indices; when raising a power to a power, multiply them. Simplify a surd by taking out the largest square factor.

5. Task 5 — Exam-Style Number Challenge

   multi-step number questions reward clear working. Set out each step, keep exact values until the last line, then round only at the end and check your answer is sensible with an estimate.

Suggestions for teaching

• Standard form both ways. Practise moving from an ordinary number to A × 10ⁿ and back, watching the sign of the power for small numbers.
• Factor trees first. Model breaking a number into primes before finding an HCF or LCM.
• The FDP triangle. Move fluently between a fraction, its decimal and its percentage in either direction, then layer on percentage change.
• Multipliers for change. Teach ×1.2 for a 20% rise and ÷1.2 to reverse it, and repeated multipliers for compound interest.
• Round only at the end. Keep exact or surd form through the working and round or simplify as the final step.