BTA Online Resources
Mathematical Reasoning: 35 questions, 40 minutes
Mathematical Reasoning gives a Year 6 student 35 questions in 40 minutes, which is a little over a minute each. It is the component families prepare for most, because it looks the most like schoolwork, and it is also the one where that resemblance misleads them.
This is one of the four components of the selective school test.
Why strong maths students still find it hard
The arithmetic in this component is almost always within reach of a capable Year 6 student. The difficulty is somewhere else: working out what the question is asking before any calculating can start.
A typical question describes a situation in words and expects the student to turn it into something computable. That translation step is the test. A child who has been drilled on speed and accuracy has practised the part that was never the constraint, and can still find themselves stuck on a question whose arithmetic they could do in seconds.
This is why a student can be top of their maths class and score modestly here. It is not a gap in their mathematics. It is an unfamiliar task.
The shapes that keep coming back
Most questions are a variation on a handful of underlying shapes. Recognising the shape is most of the work.
Rates and combined work. Two things happening at different speeds, and a question about what happens when they run together or one stops.
Working backwards. The end state is given and the start is asked for. These reward undoing the steps in reverse rather than guessing and checking.
Proportion and scaling. If this many costs this much, what about a different quantity, often with a change of units hidden in the wording.
Missing dimensions. A shape with some measurements given and one that has to be deduced before area or perimeter can be found.
Patterns and rules. A sequence given in a table or a diagram, with a question about a term far enough along that listing them out will not fit in the time.
Number properties. Odd and even, factors, remainders, digits. Usually solved by reasoning about the property rather than by trying numbers.
A worked example
The following is an original question written for this page, not an extract from any real paper.
A tap fills a 60 litre drum in 8 minutes. A second tap fills the same drum in 12 minutes. Both taps run together for 3 minutes, then the first tap is turned off. How long does the second tap take to finish filling the drum?
The instinct is to start calculating immediately. The better move is to name the rates first.
The first tap fills 60 litres in 8 minutes, so 7.5 litres a minute. The second fills 60 in 12 minutes, so 5 litres a minute. Together they put in 12.5 litres a minute, and over 3 minutes that is 37.5 litres.
That leaves 22.5 litres. The second tap alone does 5 litres a minute, so it needs 4.5 minutes.
Every step is arithmetic a Year 6 student can do. The question is not testing whether they can divide 60 by 8; it is testing whether they thought to.
Note also what the question asked for. It asked how long the second tap takes to finish, which is 4.5 minutes, not the total time of 7.5 minutes. A student who works the whole thing out correctly and answers 7.5 gets no mark, and that is a reading error rather than a maths one.
The mistakes that recur
Answering a different question. Total time instead of remaining time, the cost of one instead of the cost of all, the number left instead of the number taken. This is the single largest source of lost marks among strong students.
Computing everything exactly. Some questions can be settled by estimating or by ruling out options. A student who calculates precisely every time will not finish.
Not writing anything down. Multi-step questions held entirely in the head are where able students slip. One line of working per step costs a few seconds and saves the question.
Staying too long. At about a minute a question, two minutes on one hard item costs two easier ones later. Skipping and returning feels wrong to a conscientious student, which is exactly why it needs practising rather than just explaining.
How to practise it
Sit a full paper under the real time limit, in one go, without help. An untimed paper measures what a child knows; a timed one measures what they can produce in an exam, and those are different numbers.
Then mark it properly. For every lost mark, decide which of three things happened: they did not know it, they misread it, or they ran out of time. Only the first is a content gap. The second is a technique problem that practice fixes quickly, and the third is pacing, which is fixed by different work again.
Two or three papers sat a few weeks apart, marked this way, tell you a direction. Eight papers skimmed for a score tell you nothing.
The other components
Reading · Thinking Skills · Writing · All four explained
Independent practice material. Not affiliated with, endorsed by, or sponsored by the NSW Department of Education. All questions are original material written by Better Tuition Academy.
Common questions
Frequently asked questions
- Is Mathematical Reasoning the same as the Year 6 maths syllabus?
- No. It draws on primary content but tests problem solving rather than computation, so most questions look unlike classwork even when the underlying maths is familiar.
- Should we practise mental arithmetic drills?
- They rarely move this mark. Speed of calculation is not usually what is costing marks; interpreting the question is.
- What is a reasonable amount of practice?
- Enough to remove the unfamiliarity and to fix a pacing habit, then stop. If the same kind of question keeps going wrong across several papers, that is a teaching problem rather than a practice one.
- Should a student show working?
- Yes, briefly. One line per step is enough, and it converts a question that would have been lost to a slip into one that is merely slow.
Right Tutor Guarantee
If the first tutor match isn't right and you tell us within your first three lessons, we keep tutoring free until it is.
This is in addition to your rights under the Australian Consumer Law.
Read our FAQsContact Us
Ready to get started, or have a question about tutoring?
Reach our team on 1800 002 085 (free to call) or send us an enquiry through our contact page.