TroveTools

Fraction, Decimal and Percentage Shapes

Fractions · Year 4–Year 6

Fill a shape with pieces that make one whole, written as fractions, decimals, percentages or a mix.

Loading…

About the fraction, decimal and percentage shapes

An empty shape on the board and a tray of pieces under it. Each piece is written as its value, and the class picks the pieces that fill the shape exactly. The shape is one whole, so the pieces have to add up to one, and when it is full the board writes the sum out: 0.4 + 0.3 + 0.3 = 1 whole.

Mixed is the reason it exists. Every piece in the tray is written as a fraction, a decimal or a percentage, so a class filling the ten shape might use 0.2, 20% and 3/5, and has to see that they are two tenths, two tenths and six tenths before they can tell it makes one. Take a piece out of the tray and the next one is written a different way.

The tray holds more pieces than the shape needs and they never run out, so there is more than one answer and the arithmetic is in the choosing. Any set of pieces that adds up to one will fit. Nothing is marked while the class works and there is no running total, because that would be the answer to the question they are working on.

The ten shape is the number shape a class already knows, and its pieces are the number shapes one to ten, so a three is the yellow three with a step in it. The last piece in every tray is the whole as one piece, written 1.0, 100% or 10/10: the shape filled in one go, which is what every other answer has to come to. Tenths there or on a bar model, quarters on a square and a triangle, eighths on a rectangle for decimals to three places, fifths on an L shape, and thirds and sixths for fractions only. A third is 0.333 going on for ever, so three pieces written as 0.33 would add up to 0.99, and the board will not write a sum that is not true.

How to use it on your whiteboard

  1. 1Choose how the pieces are written: Fractions, Decimals, Percentages or Mixed. In Mixed, New labels writes the tray a different way.
  2. 2Open Whole to choose the shape: tenths on the ten shape or a bar model, quarters, eighths, fifths, thirds or sixths.
  3. 3Drag a piece from the tray into the shape. It drops into the nearest place it fits, turned round if it has to be. Or tap a piece in the tray and it goes in for you, packed so the rest still fit.
  4. 4Tap a piece in the shape to turn it, or drag it out of the shape to take it back.
  5. 5When the shape is full, the sum appears underneath. All three writes every piece as a fraction, a decimal and a percentage beside the shape.

Questions

Why can I not choose decimals for thirds?
Because a third does not come out exactly as a decimal. It is 0.333 with the threes going on for ever, so three thirds written as 0.33 add up to 0.99, not 1. Thirds and sixths are fractions only, and every other shape comes out exactly, to three decimal places at most.
Why is there no half piece on the triangle?
Two halves of that triangle would be two diamonds, and the two corners left beside the first one only touch at a point, so the second half could never go in. Any set of pieces in the tray that adds up to one has to fit, so the triangle has quarters and three quarters.
Does it say when the answer is wrong?
No. A piece that does not fit simply will not go in, and the sum appears when the shape is full. Pieces that make more than one whole cannot all fit, so a full shape is always one whole.
Why is 3/5 not written as 6/10?
In Fractions the pieces are written as cells out of the whole, so six pegs on the ten shape is 6/10. In Mixed they are written in their simplest form, 3/5, because seeing that 3/5 is six tenths is the conversion being practised.
Do I need an account?
No. Trove Tools is free with no login, no subscription and no limits.