Volume and capacity – Bella's building

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Measurement – volume and capacity

  • measures, records, compares and estimates volumes and capacities using uniform informal units MA1-11MG
  • describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM
  • supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM

Content

Measure and compare the capacities of pairs of objects using uniform informal units.

Compare and order several objects based on volume and capacity using appropriate uniform informal units.

Linked syllabus content

Recognise and represent multiplication as repeated addition, groups and arrays MA1-6NA

National Numeracy Learning Progression mapping to the NSW mathematics syllabus

When working towards the outcome MA1-11MG the sub-elements (and levels) of Understanding units of measurement (UuM3-UuM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

Materials

  • interlocking blocks or cubes

Teacher instructions

The purpose of this task is to gauge students’ understanding of initial volume and capacity concepts such as:

  • recognising that models that look different may have the same volume
  • recording the volume of models informally using drawings, numerals and words

Students can complete the task independently, but this activity can be done with a small group with each student building on their own and sharing at the end.  Students are posed with the problem, Bella used 12 blocks to build a building. What might her building look like?

Students are encouraged to build more than one object, so have plenty of blocks available. Make sure that the blocks are of uniform size so that students can compare their structures and see different ways that 12 blocks can be represented.

Teachers or students may take photos and record observations as they are working.

Students are asked to tell the teacher about their building and explain how they built it. This is where you can check what strategies students are using. Prompt students if required so that you can find out their reasoning.

Ask the student what they can tell you about the volume of each building. Do they recognise that buildings of different shapes have the same volume? Do they recognise that the blocks need to be connected with no gaps or overlap? (Interlocking blocks or cubes will work best here).

Student instructions

Bella used 12 blocks to build a building. What might her building look like?

Make some more buildings using 12 blocks.

Take a photo and explain how you built it. What did you notice?

What can you tell me about the volume of the buildings?

Possible areas for further exploration

Ensure that students use exactly 12 blocks and that they are of uniform size and shape so that direct comparisons can be made between buildings.

Do students understand that the blocks need to be close together or connected with no gaps and no overlaps?

Where to next?

Students write their own word problem using a different amount of blocks and ask a friend to solve it.

Students could take the 12 blocks and find a container they fit into, with no gaps or overlap. Discuss types of containers that would fit the blocks? (Rectangular, square, not cylinder shape)

Adapted from ‘Open-ended Maths activities: Using good questions to enhance learning in Mathematics’ (Sullivan and Lilburn, 2004)

Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2012

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