Click to enlargePercentages, Ratios, Proportions & Probability
Proportional reasoning, the single skill that separates top-set maths from the rest.
- A rules page before every topic, written so a parent can teach from it
- 25 multiple-choice questions per topic, graded from accessible to scholarship level
- Full answer key
- Covers the whole 11+ syllabus across Books 1–6, then applies it in Books 7–12
Want the whole series? The full Maths series is £247, under £21 a book.
How this book is used in our course
Each topic opens with a rules page. A parent reads it with the child, then the child attempts the 25 questions unaided. Mark them, log the score, and work through every wrong answer with the key. Anything under 90% is repeated after a fortnight. The topic is only finished when the cold repeat clears 90%.
Where it sits in the series
- Previous book in the series: Book 2, Fractions, Measures, Money & Time
- Next book in the series: Book 4, Geometry: Shape, Space & Angles
What's inside Maths Mastery 3
Five real pages from the book, so you can see exactly what your child will work from. All 9 sample pages are in the viewer.
Twenty-five topics in four parts: the proportional reasoning that top sets are built on.
Part 1 takes percentages from the hundred grid to reverse percentages, the step most children never reach in school. Part 2 puts them into money: cost price, profit and loss, VAT, discounts and compound interest. Part 3 is ratio and proportion, from writing a ratio to best buys, map scales and gradients. Part 4 is probability, up to tree diagrams and expected outcomes.
Every percentage in the book can be drawn on a hundred grid, so that is where it starts.
Key words, then five grid rules in a box, including the one schools skip: if the grid is not 100 squares, each square is worth 100 ÷ the number of squares. The method teaches counting whole rows first and counting the white squares when most of the grid is shaded. A reference table fixes the fractions a child must know by heart: a fifth is 20%, three quarters is 75%.
The mistake named before the child makes it.
Example 4 is a scholarship question: the border of a 6 by 6 square is 20 squares, not 24, because each corner belongs to two sides. The Common mistake box explains exactly why 24 is wrong. The Exam trap box shows how papers change the grid: two grids side by side make 200%, so a full grid plus 48 squares is 148%, not 74%. Always ask first: how many squares make the whole?
Add, divide, multiply. Then the question scholarship papers turn round.
The three-step method is in a box with its check: the shares must add back to the amount. Then the page does what the exam does and reverses it. Example 2 gives one share and asks for the bill; Example 3 gives the difference, 28 more blue beads than red in the ratio 3 : 7, and asks for the total. A child who has only ever shared £20 in 2 : 3 is stuck on these. A child who has done this page is not.
Every answer, every method, fully worked.
Not just "18 b 36%" but why: "Top 10 + bottom 10 + two sides of 8 (corners already counted) = 36 squares. 40% counts the corners twice." The wrong answer the child was tempted by is named alongside the right one. The instruction at the top is the whole philosophy: follow the method line by line to find where you went wrong, then re-try the question tomorrow.
All 25 topics in the book follow the pattern shown here.
Other Year 4 books in Maths Mastery
Number Relationships & Decimals
Place value, number bonds, factors, multiples and decimals: the ground every later topic stands on.
Fractions, Measures, Money & Time
The four topics that account for most lost marks in Year 4 maths, taught as one connected system.
Geometry: Shape, Space & Angles
Perimeter, area, angles, coordinates and nets, with the diagrams children actually meet in the exam.
Mental Maths Foundations
The Year 4 mental maths book. Speed and accuracy without a pen.