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NSW Syllabuses

Mathematics K–10 - Stage 1 - Number and Algebra Fractions and Decimals

Fractions and Decimals 1

Outcomes

A student:

  • MA1-1WM

    describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

  • MA1-7NA

    represents and models halves, quarters and eighths

Content

  • Students:
  • Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
  • use concrete materials to model half of a whole object, eg
    The image shows a rectangle that is divided in half by a vertical line.
  • describe two equal parts of a whole object, eg 'I folded my paper into two equal parts and now I have halves' (Communicating) LCCT
  • recognise that halves refer to two equal parts of a whole
  • describe parts of a whole object as 'about a half', 'more than a half' or 'less than a half' L
  • record two equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the fraction notation for half \(\left(\frac{1}{2}\right)\), eg 
    Image shows 2 squares halved - one is divided by a horizontal line; other by a diagonal line. L
  • use concrete materials to model half of a collection, eg 
    Image shows 6 counters in a row and a 2 by 6 tray of seedlings, both halved by a vertical line. SE
  • describe two equal parts of a collection, eg 'I have halves because the two parts have the same number of seedlings' (Communicating) LSECCT
  • record two equal parts of a collection, and the relationship of the parts to the whole, using pictures and fraction notation for half \(\left(\frac{1}{2}\right)\), eg 
    The image shows 2 circles with 5 dots in each. The fraction one-half is written under each circle. L

Background Information

In Stage 1, fractions are used in two different ways: to describe equal parts of a whole, and to describe equal parts of a collection of objects. Fractions refer to the relationship of the equal parts to the whole unit. When using collections to model fractions, it is important that students appreciate the collection as being a 'whole' and the resulting groups as being 'parts of a whole'. It should be noted that the size of the resulting fraction will depend on the size of the original whole or collection of objects.

It is not necessary for students to distinguish between the roles of the numerator and the denominator in Stage 1. They may use the symbol \(\frac{1}{2} \) as an entity to mean 'one-half' or 'a half', and similarly use \(\frac{1}{4} \) to mean 'one-quarter' or 'a quarter'.

Three models of fractions

Continuous model, linear – uses one-directional cuts or folds that compare fractional parts based on length; this model should be introduced first. Cuts or folds may be either vertical or horizontal.

Two rectangles split into 4 equal parts by 3 lines; one rectangle is horizontal, the other vertical.

Continuous model, area – uses multi-directional cuts or folds to compare fractional parts to the whole. This model should be introduced once students have an understanding of the concept of area in Stage 2.

The image shows a square and a circle. Each shape is divided into 4 equal parts.

Discrete model – uses separate items in collections to represent parts of the whole group.

A row of 8 equally spaced counters is divided into 4 groups of 2 by 3 dotted lines.

Language

Students should be able to communicate using the following language: whole, part, equal parts, half, halves, about a half, more than a half, less than a half.

Some students may hear 'whole' in the phrase 'part of a whole' and confuse it with the term 'hole'.

Fractions and Decimals 2

Outcomes

A student:

  • MA1-1WM

    describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

  • MA1-3WM

    supports conclusions by explaining or demonstrating how answers were obtained

  • MA1-7NA

    represents and models halves, quarters and eighths

Content

  • Students:
  • Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
  • use concrete materials to model a half, a quarter or an eighth of a whole object, eg divide a piece of ribbon into quarters
    The image shows a rectangle divided into 4 equal parts by 3 vertical lines.
  • create quarters by halving one-half, eg 'I halved my paper then halved it again and now I have quarters' (Communicating, Problem Solving)
  • describe the equal parts of a whole object, eg 'I folded my paper into eight equal parts and now I have eighths' (Communicating) L
  • discuss why \(\frac{1}{8}\) is less than \(\frac{1}{4}\), eg if a cake is shared among eight people, the slices are smaller than if the cake is shared among four people (Communicating, Reasoning) CCT
  • recognise that fractions refer to equal parts of a whole, eg all four quarters of an object are the same size
  • visualise fractions that are equal parts of a whole, eg 'Imagine where you would cut the rectangle before cutting it' (Problem Solving)
  • recognise when objects and shapes have been shared into halves, quarters or eighths
  • record equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the fraction notation for half \(\left(\frac{1}{2}\right)\), quarter \(\left(\frac{1}{4}\right)\) and eighth \(\left(\frac{1}{8}\right)\), eg
    Rectangle divided into 8 equal parts. The fraction one-eighth is written in each part. 
  • use concrete materials to model a half, a quarter or an eighth of a collection, eg 
    The image shows 4 groups with 3 dots in each group. The word ‘quarters’ is written underneath.
  • describe equal parts of a collection of objects, eg 'I have quarters because the four parts have the same number of counters' (Communicating) LSE
  • recognise when a collection has been shared into halves, quarters or eighths
  • record equal parts of a collection, and the relationship of the parts to the whole, using pictures and the fraction notation for half \(\left(\frac{1}{2}\right)\), quarter \(\left(\frac{1}{4}\right)\) and eighth \(\left(\frac{1}{8}\right)\)
  • use fraction language in a variety of everyday contexts, eg the half-hour, one-quarter of the class

Background Information

Refer to background information in Fractions and Decimals 1.

Language

Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, one-half, one-quarter, one-eighth, halve (verb).

In Stage 1, the term 'three-quarters' may be used to name the remaining parts after one-quarter has been identified.