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Fractions

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Two dice, one die displaying 1/4 and the other 5. One set of 5 cubes in one colour, three sets of 5 cubes in another colour to make a total of 20.

Example: One quarter of my collection is 5 so altogether I have __

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Diagrammatic explanation of the problem posed with calculations and written responses.

Student work sample

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The equal division of 17 biscuits to 3 puppies, each receiving 5 2/3.

Screen grab from L2808 Divide it up: puppies.
Source: © Education Services Australia Ltd, 2011

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three times four equals twelve, twelve divided by three equals four, one third of twelve equals four

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three times four equals twelve, twelve divided by three equals four, one third of twelve equals four

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Three groups of four counters, each group a different colour.

Using 12 counters to model division.

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A total of twelve counters arranged in a 3 by 4 array next to a 3 by 4 blank grid.

An array of 12 and a grid of 12.

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Three groups of four counters, each group a different colour. The thirteenth counter is divided into three equal parts.

Using 13 counters to model division.

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Three circular 'pancakes' made of modelling dough, each divided into four equal parts.

'Pancakes' divided into quarters.

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Two circles divided into halves and one circle into quarters surrounded by four stick figures. A colour code shows that each will receive one half and one quarter.

A student’s sharing diagram.

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Nine circles each divided into quarters with each quarter numbered. Written explanation of sharing.

A student’s sharing diagram.

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Three groups of four stick figures, each group with three pancakes which are subdivided to represent the equal division.

Another sharing diagram.

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Each loaf is cut into three equal pieces and the six pieces arranged as three groups of two.

Two loaves shared evenly between three people.

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Four horizontal strips of paper of equal length. First strip marked as one whole, the next folded in two and marked as halves, the next into quarters and the last into eighths.

A fraction wall.

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Cards marked with equivalent fractions.

Pairs of equivalent fractions.

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Game board showing one completely coloured fraction wall and one partially coloured fraction wall, and a completed record of the rolls and the colourings made.

A completed game.

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Number line marked with sixths below the line and thirds above the line to show equivalence.

Visualising equivalent fractions.

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Selection of grid transparencies with one pair overlaid and equivalent fractions recorded.

Use of overlay templates.

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Sample of a 4 by 3 grid with four parts shaded. The equivalent fractions 4/12 and 1/3 are recorded.

Screen grab from L134 Dynamic fractions.
Source: © Education Services Australia Ltd, 2011 

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Rectangle divided into thirds horizontally. Top layer divided into halves vertically, second into thirds, last into sixths.

A fraction wall.

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Two equally sized squares, first divided into halves vertically, second into thirds horizontally, then combined to show sixths.

Combining grids.

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Three circles, one divided into halves, one into quarters, one into eighths.

Subdividing with related denominators.

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Number line between 0 and 1,divided into eighths, showing ‘jumps’ from 0 to 4/8 then a further 3/8 to 7/8.

Student work sample showing addition of fractions with related denominators.

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The addition of 1/6 and 5/6 to reach the target of 1, shown with fraction bars and a number line.

A screen grab from L2804 Fraction fiddle: hit the apple.
Source: © Education Services Australia Ltd, 2011 

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Examples of addition and subtraction of fractions with related denominators using grids and number lines

Student work sample.

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