NSW Syllabuses

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

## Length 1

### Outcomes

#### A student:

• MA3-1WM

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

• MA3-3WM

gives a valid reason for supporting one possible solution over another

• MA3-9MG

selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

• Students:
• Choose appropriate units of measurement for length (ACMMG108)
• recognise the need for a formal unit longer than the metre for measuring distance
• recognise that there are 1000 metres in one kilometre, ie 1000 metres = 1 kilometre
• describe one metre as one thousandth of a kilometre (Communicating)
• measure a kilometre and a half-kilometre
• record distances using the abbreviation for kilometres (km)
• select and use the appropriate unit and measuring device to measure lengths and distances
• describe how a length or distance was estimated and measured (Communicating, Problem Solving)
• question and explain why two students may obtain different measures for the same length, distance or perimeter (Communicating, Reasoning)
• estimate lengths and distances using an appropriate unit and check by measuring
• record lengths and distances using combinations of millimetres, centimetres, metres and kilometres, eg 1 km 200 m
• Calculate the perimeters of rectangles using familiar metric units (ACMMG109)
• use the term 'dimensions' to describe the 'lengths' and 'widths' of rectangles
• measure and calculate the perimeter of a large rectangular section of the school, eg a playground, netball courts
• calculate perimeters of common two-dimensional shapes, including squares, rectangles, triangles and regular polygons with more than four sides (ie regular polygons other than equilateral triangles and squares)
• recognise that rectangles with the same perimeter may have different dimensions (Reasoning)
• explain that the perimeters of two-dimensional shapes can be found by finding the sum of the side lengths (Communicating)
• explain the relationship between the lengths of the sides and the perimeters for regular polygons (including equilateral triangles and squares) (Communicating, Reasoning)
• record calculations used to find the perimeters of two-dimensional shapes

### Background Information

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. Following this, they should be encouraged to generalise their method for calculating the perimeters of squares, rectangles and triangles.

When recording measurements, a space should be left between the number and the abbreviated unit, eg 3 cm, not 3cm.

### Language

Students should be able to communicate using the following language: length, distance, kilometre, metre, centimetre, millimetre, measure, measuring device, ruler, tape measure, trundle wheel, estimate, perimeter, dimensions, width.

'Perimeter' is derived from the Greek words that mean to measure around the outside: peri, meaning 'around', and metron, meaning 'measure'.

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

When working towards the outcome MA3‑9MG the sub-elements (and levels) of Understanding units of measurement (UuM7-UuM8) 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.

## Length 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

• MA3-3WM

gives a valid reason for supporting one possible solution over another

• MA3-9MG

selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

• Students:
• Connect decimal representations to the metric system (ACMMG135)
• recognise the equivalence of whole-number and decimal representations of measurements of length, eg 165 cm is the same as 1.65 m
• interpret decimal notation for lengths and distances, eg 13.5 cm is 13 centimetres and 5 millimetres
• record lengths and distances using decimal notation to three decimal places, eg 2.753 km
• Convert between common metric units of length (ACMMG136)
• convert between metres and kilometres
• convert between millimetres, centimetres and metres to compare lengths and distances
• explain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg 'More metres than kilometres will be needed to measure the same distance, and so to convert from kilometres to metres, I need to multiply' (Communicating, Reasoning)
• Solve problems involving the comparison of lengths using appropriate units (ACMMG137)
• determine the number of different rectangles that can be formed using whole-number dimensions for a given area (Problem Solving, Reasoning)
• solve a variety of problems involving length and perimeter, including problems involving different units of length, eg 'Find the total length of three items measuring 5 mm, 20 cm and 1.2 m'

### Background Information

Refer to background information in Length 1.

### Language

Students should be able to communicate using the following language: length, distance, kilometre, metre, centimetre, millimetre, perimeter, dimensions, width.

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

When working towards the outcome MA3‑9MG the sub-elements (and levels) of Operating with decimals (OwD1) and Understanding units of measurement (UuM7-UuM8) 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.