Stage 3 Core

Six- and seven-digit numbers, the role of zero, and renaming in thousands and ten thousands.

Rounding to the nearest ten thousand, hundred thousand or million, and finding the difference between two roundings of the same number.

The 3 in 30 060 against the 6 — how many times one digit's value is another's.

Temperatures, depths and debts below zero; ordering and finding differences across zero.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Compensation, bridging and partitioning with four- and five-digit numbers.

Column addition and subtraction across zeros, with a rounded estimate before and a check after.

Money, millions and measurements — lining up the point and trading across it.

Undoing a chain of givings, halvings and spendings from the end to find where it started.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Beyond the 10 × 10 tables: the area model first, then the written algorithm and carrying.

The area model and the two-row algorithm, with an estimate to catch a slipped digit.

Listing factors in pairs, common multiples, and counting multiples of one number that are not multiples of another.

Testing for primes, and the square and triangular patterns as pictures.

Boxes, buses and biscuits — when the remainder means one more, and when it is left over.

Short division by 12, 15, 25 and friends, using known multiples.

The tests for 2, 3, 4, 5, 6, 8, 9 and 10, and why the digit-sum test works.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Brackets, then multiply and divide, then add and subtract; left to right within a level. Not in Stage 2, but assumed by every OC paper.

Writing a situation as 14 × 8 + 5 = 117, and recognising that 12 × 3 = 10 × 3 + 6.

Balancing 9 × □ = 108 and 67 − △ = 32 + 17 by doing the same to both sides.

Stars and hearts, medals and points — using one equation to unlock the other.

One complete row gives the total; each term the sum of the previous three.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Beyond the halving family: renaming both fractions into a shared denominator, and the compare-to-a-half shortcut.

Counting past one whole, and converting between improper fractions and mixed numerals in both directions.

The same fraction on a strip, a 10 × 10 grid and a number line; closest position to a third.

Same denominators, then related ones — renaming one fraction so the pieces match.

Three people eat 4/5, 1 1/5 and 3/5 of four pizzas — how much is left for the fourth, and by how much more.

A half, quarter, fifth and tenth of measures and money, and building up to three-fifths of a wall.

Placing fifths and quarters on one line to judge "less than half" and "more than a quarter" claims.

Eight children and two pies — division as a fraction, and fractions as division.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Thousandths, comparing decimals of different lengths, and rounding to two places. Stage 2 stops at two.

0.1 against 0.08 against 0.0089 — lining up places before comparing digits.

Digits slide, the point stays: 34.2 × 10 and 342 ÷ 100 without a calculator.

One family of names: 1/4 = 0.25 = 25%, and the rest of the 10%, 20%, 50%, 75% table.

Finding 10% first and building the rest from it.

Four colours in a bag whose chances add to 1; one colour twice as likely as another.

15% of $40 from 10% and 5%; the price after a 30% discount.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Inverse operations, and undoing a chain of machines in reverse order to find the starting number.

Patterns that add then double, patterns in decimals and fractions, and finding the rule from three terms.

A rule like "double, then take 4" run forwards to the sixth term and backwards to the first.

Matchsticks and tiles into a table, the rule as words, and the 50th term without drawing it.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Stage 2 measures and compares area; calculating it from side lengths is Stage 3. Built from counting rows of squares.

The kilometre, converting to and from metres, and choosing a sensible unit for a distance.

1500 cm is 15 m; 2.35 km is 2350 m — the ladder of thousands and tens.

L-shapes and steps where the unlabelled sides must add up to the labelled ones.

Split it, or take the hole away from the whole — two routes to the same area.

Cutting a parallelogram into a rectangle, and a triangle as half of one.

A 10 by 6 rectangle and a 4-wide one with the same area — find the other side; perimeter when a rectangle is attached.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Layers of cubes leading to length × width × height, and the link between cubic centimetres and millilitres.

The gram-kilogram-tonne ladder, two-step conversions, and picking the unit that keeps the number sensible.

Jugs marked every 50 mL, kitchen scales marked every 2 kg, pointers halfway between marks.

Keeping track of a bottle and a glass through three moves.

Three boxes weighed two at a time — the total, and each one.

How much a box holds in millilitres from its sides in centimetres.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Counting through to 23:59, converting pm times by adding 12, the midnight and midday special cases, and reading timetables.

From 9:50 pm to 6:30 am, and journeys that take more than a day, counted in hops.

Which film can be seen from start to finish between two pick-up times.

The third Sunday, and what day of the week it is six weeks after a Wednesday.

A 17-hour difference and a 20-hour flight: arriving on Monday morning when you left on Friday.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Measuring angles in degrees, the five angle names including reflex, and finding a reflex angle by subtracting from 360.

180° along a line and 360° around a point; the missing angle by subtraction.

Two crossing lines make two pairs of equal angles — and why.

A shape with one line of symmetry gives its angles in pairs; the one left over comes from 180°.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Sides, angles and parallel pairs; which shape has no parallel sides.

Exactly two lines of symmetry; the largest two-digit number that is symmetrical; the fewest tiles to finish a symmetrical row.

Order of rotational symmetry, and how far a shape has turned after two steps.

Which tile covers a square four times; one grid unit stands for how many centimetres.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Counting on a hexagonal pyramid, and on two solids glued together.

The eleven cube nets; which partial net can be finished with one more square.

Front, side and top views; which cubes you cannot see; how many have exactly two faces painted.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

Across then up; plotting and reading points, and the shape they make.

Reading a grid reference from one labelled cell; distance and direction between two places.

Negative coordinates, and where a point lands after a reflection or a quarter turn.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

When a line beats columns, reading values and shape, timelines as number lines of years, and misleading scales.

Cells that answer two questions at once, row and column totals, finding a missing value two ways, and NOT questions.

One picture for five people; columns on an axis marked in twenties.

Two years on one graph; a quarter of a pie when the total is 600.

Three statements about a rainfall graph — which are correct, and what "more than twice" needs.

When the gridlines go up in twos or fifties and the point sits between them.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

The same chance three ways; certain is 1 and impossible is 0.

Two coins, a spinner and a die — the full list, then the fraction that count.

Which statements about a spinner are correct, given the first spin.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.

$15 for 3 cars, so how many cars for $45; 2 red for every 3 blue.

Fifteen placement-test items on this chapter — five options, two to four steps each, about 17 minutes.