NSW Syllabuses

# Mathematics K–10 - Stage 1 - Measurement and Geometry Length

## Length 1

### 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

• MA1-9MG

measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres

### Content

• Students:
• Measure and compare the lengths of pairs of objects using uniform informal units (ACMMG019)
• use uniform informal units to measure lengths and distances by placing the units end-to-end without gaps or overlaps
• select appropriate uniform informal units to measure lengths and distances, eg paper clips instead of pop sticks to measure a pencil, paces instead of pop sticks to measure the length of the playground (Problem Solving)
• measure the lengths of a variety of everyday objects, eg use handspans to measure the length of a table (Problem Solving)
• explain the relationship between the size of a unit and the number of units needed, eg more paper clips than pop sticks will be needed to measure the length of the desk (Communicating, Reasoning)
• record lengths and distances by referring to the number and type of uniform informal unit used
• investigate different informal units of length used in various cultures, including those used in Aboriginal communities (Communicating)
• compare the lengths of two or more objects using appropriate uniform informal units and check by placing the objects side-by-side and aligning the ends
• explain why the length of an object remains constant when units are rearranged, eg 'The book was seven paper clips long. When I moved the paper clips around and measured again, the book was still seven paper clips long' (Communicating, Reasoning)
• estimate linear dimensions and the lengths of curves by referring to the number and type of uniform informal unit used and check by measuring
• discuss strategies used to estimate lengths, eg visualising the repeated unit, using the process 'make, mark and move' (Communicating, Problem Solving)

### Background Information

In Stage 1, measuring the lengths of objects using uniform informal units enables students to develop some key understandings of measurement. These include that:

• units should be repeatedly placed end-to-end without gaps or overlaps
• units must be equal in size
• identical units should be used to compare lengths
• some units are more appropriate for measuring particular objects
• there is a relationship between the size of the chosen unit and the number of units needed.

Using the terms 'make', 'mark' and 'move' assists students in understanding the concept of repeated units. By placing a unit on a flat surface, marking where it ends, moving it along and continuing the process, students see that the unit of measurement is the space between the marks on a measuring device and not the marks themselves.

Recognising that a length may be divided and recombined to form the same length is an important component of conserving length.

It is important that students have had some measurement experiences before being asked to estimate lengths and distances, and that a variety of estimation strategies is taught.

Students will have an informal understanding of measurement prior to school, although this may not align to Western concepts of measurement. In particular, Aboriginal students often have developed a sense of measurement based on their self and their environment.

### Language

Students should be able to communicate using the following language: length, distance, end, end-to-end, side-by-side, gap, overlap, measure, estimate, handspan.

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

When working towards the outcome MA1‑9MG the sub-elements (and levels) of Understanding units of measurement (UuM3-UuM5) 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:

• 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

• MA1-9MG

measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres

### Content

• Students:
• Compare and order several shapes and objects based on length, using appropriate uniform informal units (ACMMG037)
• relate the term 'length' to the longest dimension when referring to an object
• make and use a tape measure calibrated in uniform informal units, eg calibrate a paper strip using footprints as a repeated unit
• use computer software to draw a line and use a simple graphic as a uniform informal unit to measure its length (Communicating)
• compare and order two or more shapes or objects according to their lengths using an appropriate uniform informal unit
• compare the lengths of two or more objects that cannot be moved or aligned (Reasoning)
• record length comparisons informally using drawings, numerals and words, and by referring to the uniform informal unit used
• Recognise and use formal units to measure the lengths of objects
• recognise the need for formal units to measure lengths and distances
• use the metre as a unit to measure lengths and distances to the nearest metre or half-metre
• explain and model, using concrete materials, that a metre-length can be a straight line or a curved line (Communicating, Reasoning)
• record lengths and distances using the abbreviation for metres (m)
• estimate lengths and distances to the nearest metre and check by measuring
• recognise the need for a formal unit smaller than the metre
• recognise that there are 100 centimetres in one metre, ie 100 centimetres = 1 metre
• use the centimetre as a unit to measure lengths to the nearest centimetre, using a device with 1 cm markings, eg use a paper strip of length 10 cm
• record lengths and distances using the abbreviation for centimetres (cm)
• estimate lengths and distances to the nearest centimetre and check by measuring

### Background Information

Students should be given opportunities to apply their understanding of measurement, gained through experiences with the use of uniform informal units, to experiences with the use of the centimetre and metre. They could make a measuring device using uniform informal units before using a ruler, eg using a length of 10 connecting cubes. This would assist students in understanding that the distances between marks on a ruler represent unit lengths and that the marks indicate the endpoints of each unit.

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

Refer also to background information in Length 1.

### Language

Students should be able to communicate using the following language: length, distance, straight line, curved line, metre, centimetre, measure, estimate.

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

When working towards the outcome MA1‑9MG the sub-elements (and levels) of Understanding units of measurement (UuM2-UuM5) and Understanding geometric properties (UGP2) 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.