NSW Syllabuses

# Mathematics K–10 - Stage 3 - Measurement and Geometry Area

## Area 1

### Outcomes

#### A student:

• MA3-1WM

describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

• MA3-10MG

selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

### Content

• Students:
• Choose appropriate units of measurement for area (ACMMG108)
• recognise the need for a formal unit larger than the square metre
• identify situations where square kilometres are used for measuring area, eg a suburb
• recognise and explain the need for a more convenient unit than the square kilometre
• recognise that there are 10 000 square metres in one hectare, ie 10 000 square metres = 1 hectare
• equate one hectare to the area of a square with side lengths of 100 m (Communicating)
• relate the hectare to common large pieces of land, including courts and fields for sports (Reasoning)
• determine the dimensions of different rectangles with an area of one hectare (Problem Solving)
• record areas using the abbreviations for square kilometres (km2) and hectares (ha)
• Calculate the areas of rectangles using familiar metric units (ACMMG109)
• establish the relationship between the lengths, widths and areas of rectangles (including squares)
• explain that the area of a rectangle can be found by multiplying the length by the width (Communicating, Reasoning)
• record, using words, the method for finding the area of any rectangle, eg 'Area of rectangle = length × width'
• calculate areas of rectangles (including squares) in square centimetres and square metres
• recognise that rectangles with the same area may have different dimensions (Reasoning)
• connect factors of a number with the whole-number dimensions of different rectangles with the same area (Reasoning)
• record calculations used to find the areas of rectangles (including squares)
• apply measurement skills to solve problems involving the areas of rectangles (including squares) in everyday situations, eg determine the area of a basketball court
• measure the dimensions of a large rectangular piece of land in metres and calculate its area in hectares, eg the local park

### Background Information

Students should have a clear understanding of the distinction between perimeter and area.

It is important in Stage 3 that students establish a real reference for the square kilometre and the hectare, eg locating an area of one square kilometre or an area of one hectare on a local map.

When students are able to measure efficiently and effectively using formal units, they should be encouraged to apply their knowledge and skills in a variety of contexts.

Students could be encouraged to find more efficient ways of counting when determining area, such as finding how many squares in one row and multiplying this by the number of rows. They should then begin to generalise their methods to calculate the areas of rectangles (including squares) and triangles.

When generalising their methods to calculate areas, students in Stage 3 should use words. Algebraic formulas for areas are not introduced until Stage 4.

### Language

Students should be able to communicate using the following language: area, measure, square centimetre, square metre, square kilometre, hectare, dimensions, length, width.

The abbreviation m2 is read as 'square metre(s)' and not 'metre(s) squared' or 'metre(s) square'.

The abbreviation cm2 is read as 'square centimetre(s)' and not 'centimetre(s) squared' or 'centimetre(s) square'.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑10MG the sub-elements (and levels) of Understanding units of measurement (UuM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.

## Area 2

### Outcomes

#### A student:

• MA3-1WM

describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

• MA3-2WM

selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

• MA3-10MG

selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

### Content

• Students:
• Solve problems involving the comparison of areas using appropriate units (ACMMG137)
• investigate the area of a triangle by comparing the area of a given triangle to the area of the rectangle of the same length and perpendicular height, eg use a copy of the given triangle with the given triangle to form a rectangle
• explain the relationship between the area of a triangle and the area of the rectangle of the same length and perpendicular height (Communicating, Reasoning)
• establish the relationship between the base length, perpendicular height and area of a triangle
• record, using words, the method for finding the area of any triangle, eg
'Area of triangle = $$\frac{1}{2}$$ × base × perpendicular height'
• investigate and compare the areas of rectangles that have the same perimeter, eg compare the areas of all possible rectangles with whole-number dimensions and a perimeter of 20 centimetres
• determine the number of different rectangles that can be formed using whole-number dimensions for a given perimeter (Problem Solving, Reasoning)
• solve a variety of problems involving the areas of rectangles (including squares) and triangles

### Background Information

Refer to background information in Area 1.

### Language

Students should be able to communicate using the following language: area, square centimetre, square metre, dimensions, length, width, base (of triangle), perpendicular height.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑10MG the sub-elements (and levels) of Understanding units of measurement (UuM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.