Mathematics Developmental Continuum P-10

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Fractions - Progression Points

Dimension

Level

Progression Point

 

Number

1.0 Standard

... Students form collections of sets of equal size.

1.25
  • Drawing of diagrams to show sharing of up to 20 items

1.5
  • Use of half and quarter as a descriptor; for example a quarter of a cake

1.75
  • Identification of half of a set of objects, including recognition of the need for ½ when sharing an odd numbers of objects

2.0 Standard

... Students describe simple fractions such as one half, one third and one quarter in terms of equal sized parts of a whole object, such as a quarter of a pizza, and subsets such as half of a set of 20 coloured pencils.

2.25
  • Use of fractions with numerators other than one; for example ¾ of a block of chocolate

2.5
  • Development and use of fraction notation and recognition of equivalent fractions such as
    1 / 2 = 4 / 8 , including the ordering of fractions using physical models

3.0 Standard

... Students develop fraction notation and compare simple common fractions such as 3/4 > 2/3 using physical models.

They add and subtract simple common fractions with the assistance of physical models.

3.25
  • Multiplication of fractions by fractions using rectangle area model (grid)

3.5
  • Addition, subtraction and multiplication of fractions and decimals (to one decimal place) using approximations such as whole number estimates and technology to confirm accuracy
  • Representation of simple ratios as percentages, fractions and decimals
  • Ordering of integers (for example, positive and negative temperatures), positive fractions and decimals

3.75
  • Recognition of equivalent rates expressed as percentages, fractions and decimals
  • Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

4.0 Standard

... Students model integers (positive and negative whole numbers and zero), common fractions and decimals.

They place integers, decimals and common fractions on a number line.

They use decimals, ratios and percentages to find equivalent representations of common fractions (for example, 3 / 4 = 9 / 12 = 0.75 = 75% = 3 : 4 = 6 : 8).

They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money.

4.25
  • Knowledge of decimal and percentage equivalents for 1 / 2 , 1 / 4 , 3 / 4 , 1 / 3 , 2 / 3
  • Expression of single digit decimals as fractions in simplest form and conversion between ratio, fraction, decimal and percentage forms
  • Division of fractions using multiplication by the inverse

5.0 Standard

... Students write equivalent fractions for a fraction given in simplest form (for example, 2 / 3 = 4 / 6 = 6 / 9 = … ).

They know the decimal equivalents for the unit fractions 1/2 , 1/3 , 1/4 , 1/5 , 1/8 , 1/9 and find equivalent representations of fractions as decimals, ratios and percentages (for example, a subset: set ratio of 4:9 can be expressed equivalently as 4/9 = 0. 4 ≈ 44.44%).

They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy.