Mathematical Reasoning: what the paper asks, and what we teach for it
The Department publishes this section's counts, its timings, how many options a question carries and the rules a child sits it under. Here is that structure, one real question from the app, and the fourteen lessons that cover it.
What this section is
Mathematical Reasoning is the one section with the same shape at both ages: 35 questions in 40 minutes, whether it's sat in Year 4 for Opportunity Class or in Year 6 for Selective High School.
It also gives five options a question, where Thinking Skills gives four, and calculators are not allowed, nor are dictionaries. Nothing is deducted for a wrong answer, so a guess is never worse than a blank: the practice papers tell a child so in their own instructions. The test is sat on a computer supplied by the department, and paper is provided for working out. The counts, timings and option counts above are the Department's, published on its practice-test pages for the Opportunity Class and Selective High School tests, where those practice papers are also free to download, and what happens on the day is on its placement test page.
What we teach for it
Fourteen lessons, each built around one real thing the section asks a child to do. Eleven are filed under Maths, and three more, The Day Ribbon, Calendar Cracker and The Tuckshop, are filed under Real Life because that is how a child finds them, but they are maths wearing an everyday name and count toward this section just the same.
- The Number Fete: biggest equal shares, and when two things line up.
- Mystery Shapes: finding an unknown from two clues, using shapes rather than letters.
- Fraction Kitchen: equivalence, simplifying, comparing, and fractions of an amount.
- Pattern Detective: finding the rule, then jumping straight to the 100th term.
- Measure Up: reading scales and jugs, including ones that don't start at zero.
- Fence & Field: the walk around versus the ground covered, on composite shapes.
- Flat Pack: which nets really fold into a cube, and which only look like they should.
- Data & Chance: reading a chart carefully, and the "which statements are correct" format.
- The Place Value Vault: what each digit is really worth, and rounding as "which is it nearer".
- Ways to Count: counting without listing everything, and the overlap trap.
- Maps & Mirrors: grid references, compass directions, and shapes that slide, flip and turn.
- The Day Ribbon: elapsed time as hops along the day.
- Calendar Cracker: days in each month, weekday arithmetic, and counting days between dates.
- The Tuckshop: totals and change, unit price, and which pack is the better buy.
Star Chart, the times-tables game, is not listed here. It's a fluency drill, not exam practice, so in the app it lives on its own Games shelf rather than under Maths.
A question, quoted whole
One question from Ways to Count, exactly as a child sees it in the app, hint and explanation included. Five options, because this section uses five.
In a competition, 6 teams each play every other team once. How many games are played altogether?
- A15 games
- B21 games
- C30 games
- D36 games
- E60 games
Hint: Count the games from one team's point of view first. Then ask how many teams a single game belongs to.
Why A. 6 × 5 = 30 counts every game twice, once for each team, so halve it: 15 games. Counting down works too: the first team has 5 opponents, the next has 4 games still unplayed, and so on down to 1, and 5 + 4 + 3 + 2 + 1 is 15 again.
6 × 5 is a fact a child already knows cold. The work in this one is noticing that counting each team's games separately counts every match twice, once from each side, which is exactly what halving corrects for.
What else is in there
Clocks, calendars and money get their own lessons rather than being folded into general arithmetic practice. The Day Ribbon, Calendar Cracker and The Tuckshop each isolate one everyday skill, elapsed time, dates and weekdays, and change and best buy, because each has its own traps that a child needs to meet on its own ground before mixing it back in with everything else.
Try a lesson
All fourteen are in the app now, free, offline, with no account.