Expected level of development
Australian Curriculum Mathematics V9: AC9M2M01
Numeracy Progression: Understanding units of measurement: P3
Students extend their understanding of uniform informal units to measure and compare lengths, mass and capacities.
Provide opportunities for students to:
- select the appropriate size of an informal unit to measure and compare attributes
- choose and use appropriate uniform informal units to measure length without gaps or overlaps (e.g. use the same sized paper clips to measure the length of a book)
- use multiple uniform informal units to measure the mass of objects (e.g. a balance scale and a number of same-sized marbles to compare mass)
- use multiple uniform informal units to measure the capacity of objects (e.g. a number of cups of water or cups of sand to measure capacity.
Use a variety of teaching strategies to facilitate learning.
- Provide access to a range of physical materials to use as uniform informal units (e.g. Multilink cubes, marbles, paperclips, matchsticks and popsticks) and provide hands-on opportunities to measure and compare items.
- Encourage visualising as a strategy for estimating length and capacity using uniform informal units. Probe student thinking to draw out mathematical reasoning when estimating and making measurements.
- Provide explicit explanations to support their learning, such as how to use tiling (using many copies of a unit to measure without gaps or overlaps) and iteration (using one copy of an informal unit to measure by repeatedly moving it along) to measure the length or area of a shape.
Teaching and learning summary:
- Estimate, compare and measure lengths using informal units.
- Estimate, compare and measure capacities using informal units.
- Estimate, compare and measure mass using informal units.
- Compare length, mass and capacities of objects using informal units and everyday language.
- Apply measurement skills and knowledge to familiar and unfamiliar problems.
- Look for opportunities to explicitly teach the key ideas of measuring.
- choose appropriate uniform informal units to measure and compare length, mass or capacity
- measure and describe length, mass or capacity of two or more objects in order to then make comparisons.
Some students may:
- inaccurately measure by having gaps or overlapping units when tiling or by not tracking carefully when iterating. Provide feedback and discuss the need for accuracy.
- not yet understand that using smaller units will produce a larger total measure than using larger units, and that using larger units will produce a smaller total measure than using smaller units. Provide opportunities to use small and large units and make explicit the impact of using each on the overall measurement.
- not yet understand that capacity is the property of a container and describes how much a container can hold. When measuring capacity, ask how much the container holds. Discuss the appropriate types of informal units that could be used such as cups of sand or water, or cubes for a rectangular object.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
- We are learning how to measure length using informal units.
Why are we learning about this?
- We often need to measure things to work out which is longer.
What to do
- Find three things to measure.
- Choose an informal unit such as your hand span, paperclip or pencil to measure the length of your three items.
- Measure each item using the unit you chose.
- Order the items shortest to longest.
- Draw your ideas to show someone else.
- Compare two of the items. How much longer is one than the other?
- How would you measure something that is curved?
- use an informal unit to measure something
- work out how much longer an object is compared to another
- order objects by length.
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A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
Concrete, Representational, Abstract (CRA)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.Go to resource
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.Go to resource
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.Go to resource
Culturally responsive pedagogies
Culturally responsive pedagogy is a form of teaching that incorporates learners’ cultural background and histories into classroom practice.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
In this estimation activity (p 30) students are presented an image and are invited to think of their own questions before exploring one of the questions posed.Resource details
Which is the longest? Length
In these language-based activities, students explore length and the notion of a unit, using informal units to estimate, measure and compare the length of various objects.Resource details
Counting on Measurement
A sequence of lessons exploring length, volume and area using informal units and a counting-on strategy to keep track of a series of additions.Resource details
Measuring Beads Mass
In this unit, students compare the height and weight of various soft toys directly, and then indirectly, using beads or another uniform informal unit.Resource details
Mass and capacity: an introduction to measuring and comparing
A guide that provides a sequence of steps using hands-on experiences to measure and compare mass, and then to measure and compare capacity.Resource details
A series of five sessions exploring the capacity of cylinders using small objects of the same size (uniform informal units).Resource details
By the end of Year 2, students are using uniform informal units to measure and compare shapes and objects.
Teaching Measurement: Early Stage 1 - Stage 1
Use page 12 of this guide to conduct assessments on measurement topics through individual questioning of a small group of students.Resource details
Refer to the diagnostic task for a guide on how to conduct a one-to-one interview where the student is asked to measure length by choosing an informal unit.Resource details
Pour to Decide
Use this diagnostic task to assess if students know about capacity and comparing containers based on how much they hold.Resource details
Desk through the Doorway
Use this diagnostic task in the style of a one-on-one interview to assess a student's understanding and skills in comparing length.Resource details