GCSE Maths: Number — Deep Revision Workbook

Inside GCSE Maths: Number — Deep Revision Workbook

calculate with standard form, apply BIDMAS, find HCF and LCM from prime factorisation, convert and calculate with fractions, decimals and percentages, tackle percentage change, reverse percentages and compound interest, round, estimate, find bounds and simplify indices and surds, then finish with a full exam-style challenge. About 45 minutes.

Learning objectives

• standard form and calculations in 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 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 and simplifying surds.

Activities in this book

1. Section 1 — Standard Form Calculations & BIDMAS

   in standard form a number is A × 10ⁿ with A between 1 and 10. To multiply, multiply the numbers and add the powers; to divide, divide the numbers and subtract the powers. With BIDMAS, deal with brackets and indices before multiplying, dividing, adding or subtracting.

2. Section 2 — Primes, HCF, LCM & Prime Factorisation

   break each number into its prime factors with a factor tree. The HCF is the product of the primes the numbers all share; the LCM is the product of the highest power of every prime that appears. A prime has exactly two factors: 1 and itself.

3. Section 3 — FDP, Percentage Change, Reverse & Compound

   to change a fraction to a decimal, divide the top by the bottom; to change a decimal to a percentage, multiply by 100. For an 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. Section 4 — Rounding, Bounds, Estimation, Indices & Surds

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

5. Section 5 — Extended 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. Move from ordinary numbers to A × 10ⁿ and back, then multiply and divide by adding and subtracting the powers.
• Factor trees first. Model breaking a number into primes before finding an HCF or LCM, including across three numbers.
• The FDP triangle. Move fluently between a fraction, its decimal and its percentage, then layer on percentage change.
• Multipliers for change. Teach ×1.15 for a 15% rise and ÷0.8 to reverse a 20% fall, 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.