The largest section, and the one closest to school maths, but pitched a step sideways. The arithmetic is familiar; what is asked of it is not.
We have written 500 Mathematical Reasoning questions by hand across classes 3 to 8.
One from a class 4 paper and one from class 7, so you can see how the same section grows. Have a go before opening the answer.
What is the value of the digit 7 in the number 4,732?
Answer: 700
Read the places from the right: 2 ones, 3 tens, 7 hundreds and 4 thousands. So the 7 stands for 7 hundreds, which is 700.
Why a child picks 7: 7 on its own is what the digit looks like, but its VALUE depends on its place, and it sits in the hundreds.
Sit the whole paper this came fromThree quarters of a number is 15 more than one third of the same number. What is the number?
Answer: 36
Do not hunt for the number by trial. Take one third away from three quarters FIRST: that leaves five twelfths of the number, and five twelfths of it is 15.
Why a child picks 20: This divides 15 by three quarters. The 15 is the gap BETWEEN the two fractions, not three quarters of the number.
Sit the whole paper this came fromWorth saying out loud the first few times. The order matters more than the speed.
Perimeter or area, factors or multiples, before or after. Half the lost marks in this section are a correct calculation of the wrong thing.
Convert everything to the smallest unit in the question before you start, and convert back at the end. Do not carry two units through the working.
A rough answer takes five seconds and catches a decimal point in the wrong place, which is the single most common arithmetic slip.
If the question says the total is 48, check your answer produces 48. This catches almost every reversed subtraction.
These are not guesses. Each one is a wrong option we deliberately built into real questions, which is why every one of them feels reasonable at the time.
The fix: Underline the actual question. Many questions ask for the difference or the remainder after the thing you just worked out.
The fix: Convert before you calculate, never during. Write the unit next to every number.
The fix: Factors go into it, multiples come out of it. Say which one out loud before starting.
The fix: Use the numbers written on it, never the look of it. Olympiad figures are often deliberately not to scale.
| Class | Mathematical Reasoning | Questions on the paper |
|---|---|---|
| Class 3 | 10 | 35 |
| Class 4 | 10 | 35 |
| Class 5 | 20 | 50 |
| Class 6 | 20 | 50 |
| Class 7 | 20 | 50 |
| Class 8 | 20 | 50 |
Section names and the shape of the paper follow the Science Olympiad Foundation olympiad blueprint. We are not affiliated with them, these questions are our own, and the official pattern is theirs to confirm.
In our papers it is 10 of 35 questions for classes 3 and 4, and 20 of 50 for classes 5 to 8, which makes it the biggest single section in the upper classes.
Rarely in content, often in demand. The topics are ones a child has met, but a question may combine two of them, or ask for the condition under which something is true rather than for a value.
Accuracy, not new topics. Most children lose more marks to unit slips, reversed subtractions and answering the intermediate step than to anything they had not been taught.
A small number, yes, mainly area and perimeter. Beyond that, memorising does less good than being able to check a formula by trying it on a simple case.
One section at a time is how you fix a weakness. A full timed paper is how you find out whether it is fixed.