Fraction tangram puzzles for the whiteboard

What the fraction tangram does on screen

One shape fills the board, cut into coloured pieces, with the whole it is worth written above it. Tap a piece and its value appears in the middle. Tap it again and the value goes, so you uncover the board in whatever order the talking takes you.

• Six levels. Halves and Quarters, Eighths, Sixteenths, Classic Tangram, Master down to a thirty-second, and Challenge. The first five are the same square cut ever more finely; Challenge is a wider gridded rectangle with awkward triangles in it.
• The whole. The strip of numbers sets what the shape is worth: 64, 128, 256, 512 or 1024, or type your own and press Set. The heading says what it is, and it stays as you move from level to level.
• Show as. Amount, Fraction, Decimal and per cent. Press one and every revealed piece is rewritten at once: 64 becomes a quarter, then 0.25, then 25%, and never moves.
• Grid. Faint lines across the shape so pieces can be counted in squares instead of judged by eye. On by itself on Challenge, available on any level.
• Reveal all and Hide all. Uncovers or clears the board in one press. Changing level clears everything, so each puzzle starts blank.
• Move the pieces. Drag any piece anywhere on the paper. The one you last touched grows a yellow handle: tap it to turn the piece 45 degrees, or drag it to spin. Two quick taps on the piece turn it as well. Whatever a piece does, the fraction it is worth never changes, which is the point.
• Compare. Press it, tap two pieces, and the board reads out the pair: a quarter is greater than an eighth, an eighth equals an eighth. It follows Show as, so you can do it in amounts or in per cent.
• Puzzle, Scatter and Reset. Puzzle lays a grey picture on the board to rebuild, and a piece dropped near its place and roughly the right way round clicks in. Scatter throws the pieces out round the edge, Reset slides them back into the square.
• Print. A two-page PDF: all six puzzles on a sheet with Name and Date, then the same six with the answers on. The wording follows whichever Show as button is lit, so an Amount sheet asks a different question from a Fraction sheet.

How to use it in a lesson

Set the whole before you reveal anything. 256 is the default for a reason: halve it enough times and it is still a whole number at a thirty-second, so nobody has to deal with 12.5.

1. Pick the level and leave it blank. Give the class a moment to look before any number is on it.
2. Point at a piece and ask for a reason. How much is that worth, and how do you know? The reason is the part that matters and the tap only confirms it.
3. Move to a piece that looks nothing like it. On Level 4 the medium triangle, the square and the parallelogram are all an eighth. Reveal those three and leave them up.
4. Ask what is left. Once several pieces are showing, the rest have to make up the difference, which quietly turns the puzzle into subtraction.
5. Flip the representation. Agree it all as an Amount, then press Fraction, then per cent. Nothing has moved, so ask what has actually changed.
6. Break the square up. Press Scatter, then pick a picture from Puzzle and let them rebuild it. The values stay on the pieces while they move, so a cat made of a quarter, a quarter and five smaller pieces is still one whole.
7. Change the whole and do it again, or print the sheet and let them finish the rest on paper.

Ideas by year group

• Year 1. Level 1, Show as Fraction. Which piece is half, and how do you know the two small ones together match the big one?
• Year 2. Level 1, whole 64, Show as Amount. If the square is 64, what is half of it, and half of that?
• Year 3. Level 2, whole 128. Find a quarter and an eighth of 128 without anyone writing a calculation.
• Year 4. Level 3, Show as Fraction then Amount. Sixteenths of 256, and the same pieces read two ways.
• Year 5. Level 4, Show as Fraction then per cent. Three pieces are an eighth and they are different shapes, so what does a fraction actually measure?
• Year 6. Level 6 with the Grid on and the whole at 128. Count the squares in each piece and find which are worth the same.

The misconceptions it helps with

Equal fractions must be the same shape. The one the tangram was made for. On Level 4 a triangle, a square and a parallelogram are all worth an eighth, and revealing them together settles it without you refereeing.

Bigger denominator, bigger piece. Reveal a half and a sixteenth side by side with Show as set to Fraction. Sixteen is the bigger number and the piece is plainly tiny.

A fraction is a shape, not a relationship. Change the whole from 256 to 1024 and every amount changes while every piece stays put. The fractions did not change, the thing they are a fraction of did.

Fractions, decimals and percentages are three topics. Show as changes the writing and nothing else, so a quarter, 0.25 and 25% are one fact seen three ways.

Frequently asked questions