Expected level of development
Australian Curriculum Mathematics V9: AC9M1M02
Numeracy Progression: Understanding units of measurement: P3, Counting processes: P3
At this level, students develop their understanding of uniform informal units to measure the length of objects.
When measuring and comparing length, students use informal units such as paperclips, popsticks or counters that are of an equal size. Discuss more appropriate informal units when measuring distance between two objects, for example, feet placed end to end or uniform steps.
A key understanding is that the unit of measurement used to measure each object must be the same size in order to compare objects. Additional ideas to ensure students grasp this understanding include:
- the conservation principle; that things don’t change in length or capacity just by being moved
- the transitivity principle; that if A is longer than B, and B is longer than C, then A is longer than C
- the iteration principle; that a unit, something of fixed size, can be used over and over again to make a measurement.
Use a variety of teaching strategies to facilitate student learning:
- Provide access to a range of physical materials to use as uniform informal units) and provide hands-on opportunities to measure and compare items.
- Model and encourage the appropriate use of comparative language (e.g. ‘shorter’ and ‘shortest’, ‘longer’ and ‘longest’, ‘taller’ and ‘tallest’). Measure and describe length of two or more objects in order to then make comparisons. (e.g. The paper is 15 paperclips long, the pencil is 5 paperclips long. Therefore, the paper is 10 paperclips longer than the pencil.)
- Encourage visualising as a strategy for estimating length using uniform informal units.
- Probe student thinking to draw out mathematical reasoning when estimating and making measurements. Draw out explanations why the number of units used may be different when comparing length measured with different uniform informal units, for example, paperclip and eraser.
- Explicitly teach and model 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:
- Model how to estimate and measure lengths using informal units.
- Compare length 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.
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.
Learning intention
- We are learning how to compare two objects to see which is longer.
Why are we learning about this?
- We sometimes need to work out which the length of an object.
What to do
1. Find two objects that you can compare and measure.
2. Find an item to use as a unit to help you compare each object. You can use a small item like a paperclip or a larger item like a pencil.
3. Follow these steps:
a. Measure your first object; make sure you place the paperclips, or unit you chose, end to end in a straight line.
b. Count how many units it takes to measure the length of your object.
c. Record your answer.
d. Now take the next object and predict (guess) if this object is longer or shorter than the first object.
e. Count how many units it takes to measure the length of this object. .
f. Record your answer.
g. Which one is longer?
h. Can you work out how much longer it is?
4. Draw a picture of what you found out.
Success criteria
I can:
- use a a unit such as a paperclip to measure the length of an object
- compare two objects to see which one is longer
- work out which object is longer and by how much
- draw and describe what I found out.
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Teaching strategies
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.
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Explicit teaching
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.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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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.
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Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.
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Teaching resources
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.
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Using units of measurement: Foundation – Year 2
Use the activity ‘How many do you need?’ (p 16) to explore the relationship between the size of an informal unit and the quantity required to measure an object.
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Dare to compare
These language-based activities explore the length of familiar objects using uniform informal units.
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Teddy bears and friends
In this unit, students compare the lengths of soft toys directly and then indirectly using multi-link cubes as uniform informal units.
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Using units of measurement: Foundation–Year 2
In the activity ‘Estimate and explain’ (pp 34–35), students estimate measurement through reasoning using informal units such as pegs, counters and Unifix cubes.
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reSolve: Authentic Problems – Target Ball
A sequence of four lessons for developing informal measurement strategies in the context of a sports game.
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Using units of measurement: Foundation–Year 2
Use the activity ‘Tricky comparisons’ (p 37) to explore problems that require an understanding of transitivity; that is, if A is longer than B, and B is longer than C, then A is longer than C.
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Teaching measurement: Early Stage 1 – Stage 1
This teaching guide brings together fundamental measurement ideas about length, area, volume and capacity, and mass.
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Counting on measurement
The unit explores measurement through activities where students make predictions and use non-standard units to answer 'how many' questions.
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About how many paper clips
Students using paper clips a a unit of measure to estimate and measure length.
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Assessment
By the end of Year 1, students are measuring the length of shapes and objects using uniform informal units.
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Snail trails
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.
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Stage 1: measurement – mass
Refer to the three sequenced activities to assess students’ use of a pan balance to compare the mass of two objects.
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Which tin?
Use this diagnostic task in the style of a one-on-one interview to assess a student's knowledge and understanding of an object's properties and their use of comparative language.
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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.
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