11 plus 2D Shapes & Properties questions

What a 2D Shapes & Properties question looks like

2D Shapes & Properties is the part of 11 plus maths that asks your child to name a flat shape and say what is true about it. A question gives a shape’s name or a list of clues about one, then five options. It never asks for the shape to be measured, moved, turned or plotted on a grid: perimeter, area, position and movement are their own questions.

The shapes are the ones a Year 5 child has met already: triangle, square, rectangle, rhombus, parallelogram, trapezium, kite, pentagon, hexagon and octagon. The properties are the ones you can count or check by looking: sides, corners (papers often call a corner a vertex), pairs of parallel sides, right angles, equal sides and lines of symmetry.

Some questions name a shape and ask for a number, some give the clues and ask for the name, and some list five statements and ask which is NOT true. About a quarter put a drawing on the screen or a table of properties to match, but most are pure text and need no more than a rough sketch in the margin.

Example one: four equal sides and exactly two lines of symmetry

A shape has 4 equal sides and exactly 2 lines of symmetry. What is the name of this shape? The options are parallelogram, rectangle, trapezium, square and rhombus.

Take the first clue and see which shapes survive. Four equal sides rules out the rectangle, whose long sides are longer than its short ones, and the trapezium and parallelogram with it. That leaves the square and the rhombus. A square folds onto itself four ways: across the middle, down the middle, and along each diagonal. A rhombus is a squashed square and folds only along its two diagonals. The answer is rhombus.

Square tempts twice: it passes the first clue, and it is what children picture the moment they hear four equal sides. The word doing the work is exactly. Four lines of symmetry is not two.

Example two: pairs of parallel sides in a regular hexagon

How many pairs of parallel sides does a regular hexagon have? The options are 2, 6, 0, 3 and 1.

Regular means all six sides are the same length and all six corners are the same, so it is the tile shape, the one a bee builds with. Sketch it, then start at any side and look straight across. One side sits directly opposite, running in exactly the same direction, so the two are parallel. That is one pair. Move round to the next side, then the one after. Three pairs, and all six sides are used up. The answer is 3.

The option that catches most children is 6. It is the number of sides: it counts every side that has a partner instead of counting the partnerships. Option 1 catches a child who draws the hexagon with a flat top, spots the top and bottom pair and stops there.

Example three: is Priya right about squares?

Priya says: “All squares are rectangles, but not all rectangles are squares.” Is she correct? The right option is “Yes, a square meets all the requirements of a rectangle.”

Answer the two halves separately. Is every square a rectangle? Write down what a rectangle needs: four sides, four right angles, opposite sides equal. Four sides, yes. Four right angles, yes. Opposite sides equal, yes, since all four are. The first half is true. Is every rectangle a square? A square also needs all four sides the same length, and most rectangles are longer than they are wide, so no. Priya is right.

The tempting wrong option is “Yes, but only if the rectangle has equal sides.” It sounds careful, but it adds a condition that is not needed: a square is a rectangle, full stop.

How to answer it

1. Underline the filtering words first: exactly, all, NOT, at least, only. They decide the answer more often than the shape names do.
2. Turn the question into a checklist, one line per clue, and test every option against every line. Never stop at the first clue: two options usually pass it.
3. Sketch the shape if you cannot see it in your head. A rough drawing is enough to count sides, fold lines and square corners.
4. Lean on the rules for regular shapes. A regular shape has as many lines of symmetry as it has sides, so a regular octagon has eight. With an even number of sides each side has a partner opposite it, giving half as many pairs of parallel sides; with an odd number, like a regular pentagon, none of the sides are parallel.
5. Read the answer back against every clue before moving on. It takes seconds and it catches the near-miss options.

Common mistakes

• Counting sides when the question asked for pairs. A regular hexagon has six parallel sides but three pairs of them, and 6 is sitting right there in the options.
• Stopping after the first clue. Four equal sides points at the square, and it gets picked before the child reads that the shape has exactly two lines of symmetry.
• Losing fold lines, or looking the wrong way for them. A square is often answered as two, from the fold across and the fold down, with both diagonals forgotten. A capital A folds down the middle but not from top to bottom, so it has no horizontal line of symmetry.
• Reading straight past NOT. Asked which statement about a rhombus is not true, a child picks “it has 4 equal sides” because it is true and it looks right.
• Treating shape families as separate boxes. Believing a square cannot also be a rectangle, or that a rhombus is not a parallelogram. The families sit inside each other.

How to practise 11 plus 2D Shapes & Properties questions

Most of this is vocabulary, and vocabulary responds to short, frequent practice. A child who can say without pausing that a trapezium has exactly one pair of parallel sides, and that a parallelogram has no lines of symmetry at all, will answer half of these in seconds and buy time elsewhere in the paper. Say the properties out loud, draw the shapes, and fold the drawings to find the lines of symmetry. Then work on the questions that carry two clues, where the marks go. 11+ Daily has a 2D Shapes & Properties project that mixes the naming, counting, NOT true and shape-family questions together, and it sits alongside the rest of 11 plus maths practice so a child keeps meeting them across the eleven plus year. Every question is original to 11+ Daily, nothing is a past paper, and the bank is re-checked in rounds. For how much time to give it, we have written about how much 11 plus practice a child needs each day.

Questions parents ask