Year 4 OC Mathematical Thinking

Large numbers, rounding and estimation for quick checking.

Fluent +, −, ×, ÷ with larger numbers under time pressure.

Evaluating and balancing multi-operation number sentences.

Finding equivalent fractions and ordering fractions.

Decimal notation, money links and comparing decimals.

What one mark is worth, n jumps of a quarter turned into wholes and parts, placing a mixed number on a thirds or fifths line, which mixed number is closest to a whole, and how many jumps cover a distance.

Finding rules, next terms and input-output machines.

Matchstick and tile patterns; predicting later terms.

Breaking a problem into steps and keeping track of the goal.

Starting from the answer and reversing the operations.

Who-owns-what grids, truth-tellers and elimination reasoning.

Which methods balance the scales (find the gap first), "3 pears weigh the same as 5 plums" bag comparisons, made-up money chains converted one link at a time, and picture balances solved by swapping.

Which layer the last brick lands on (remainders), fewest bags under a mass limit (two roundings), two people sharing one job, everyone-plays-everyone tournaments, and steady money-box deposits with one unknown day.

Reasoning problems mixing lengths, perimeters and areas.

Elapsed time, schedules and timetable reading.

Nets, rotations, reflections and views of solids.

Quadrilateral families and "all squares are rectangles" statements, counting right angles in figures made of lines, and what one straight cut does to a shape.

Quarter and half turns chosen from picture options, reflecting on a grid with grid references, turned shapes versus mirror images, and tiles rotated in a wall.

Working out what one gap is worth, then reading thermometers with unlabelled ticks, jugs with unusual scales, map rulers in millimetres against a scale in centimetres, and graphs with a missing scale.

Counting cubes you cannot see, faces hidden by glued joins (2 per join), faces uncovered when a solid is broken apart, rebuilding from loose cubes, and the tallest stack three blocks can make.

Area on a grid with half squares, what doubling every side does to area (× 4) and volume (× 8), matching shaded areas across two squares cut into different pieces, water displaced by sinking blocks, and cut-and-rearrange invariance.

Reading complex graphs and simple averages in test questions.

Chance words as counting words: boxes of discs, "blue or not blue", numbered counters with boundary numbers, spinners with unequal sectors, and changing a bag so two outcomes become equally likely.

Time budgeting, elimination and educated guessing for OC format.

Full-length 35-question, 40-minute Mathematical Reasoning paper in the official format: five options, every strand shuffled, 20 questions with a figure, no calculator.

Second full-length 35-question, 40-minute Mathematical Reasoning paper: different item shapes across every strand, 19 questions with a figure, answers balanced across A–E.

Third full-length 35-question, 40-minute Mathematical Reasoning paper: a leap-year date, a picture balance, a missing-scale graph, cube rebuilding and more, 19 questions with a figure.