Making benchmarks: Volume

Purpose

In this unit we will explore the idea of having benchmarks of 1 litre and ½ litre or 500 millilitres, to aid in estimating the volume of given objects.

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Specific Learning Outcomes
  • Use objects of 1 litre volume to estimate the volume of other objects.
  • Understand the need for standard measures of volume.
  • Make sensible estimates about the volume of given objects.
  • Carry out conversions between standard measures of volume (millilitres to litres).
Description of Mathematics

Volume is the measure of space taken up by a three-dimensional object. The space within a container is known as its capacity but as the thickness of many containers is negligible, it has become acceptable to refer to the space inside a container as volume too.

Students need to develop personal measurement benchmarks. A benchmark is an understanding or a “feel” for the size of a measurement unit, which is useful when working with measures in daily life. Often these benchmarks are linked to familiar items such as a one litre milk bottle or a Pyrex jug.

This unit supports students to develop personal benchmarks for a litre and ½ litre, and also strengthens students’ understandings of the relationship between  litres and millilitres.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

  • provide a smaller number of containers for students to work with, and ensure there are clear differences in the volumes of the containers provided
  • have students measure the volume of containers to establish whether they hold more, less, or about the same as 1 litre without the need to estimate first
  • use fractional parts of a litre to describe volume, rather than millilitres e.g. quarter of a litre rather than 250 ml.

This unit is focussed on measuring the volume of containers. Use a range of containers that are familiar to your students to encourage engagement.

Required Resource Materials
  • Waterproof objects of a variety of volumes
  • Various bottles including several that hold 1 litre
Activity

Session 1

For this session you will need plenty of bottles and containers of a range of sizes, including several that hold 1 litre. Fruit juice bottles, shampoo bottles, and yoghurt containers are particularly good containers for this task. You could either ask students to bring bottles and containers to school with them or collect them yourself.

  1. Begin by selecting 5 or 6 containers of various sizes and shapes.
  2. Ask students which one they think has the least space in it.  sk them to explain why they made their choice.
  3. Explain that we are going to order the containers from those the hold the least, to those that hold the most.
  4. Ask for suggestions for how to compare the size of the containers. Ensure that students understand that they are comparing the space inside the containers.
  5. Gather suggested strategies then trial strategies to establish an effective way to order the containers by volume.  The most effective strategy will probably be to pour water from one container to another. If the water that fits in one container does not fit into another then the first must have been larger.
  6. Group students with several containers for each group.  Ask each group to order their containers from those the hold the least, to those that hold the most. Watch to see that your students can organise the ordering of many containers, when the comparisons are two at a time.
  7. Share the techniques and strategies used by each group to order the containers.
  8. Ask 2 groups to pair up to combine their containers on one continuum of least to most volume. Check that they understand that volume is conserved (i.e. that it is the same quantity of water, even though its appearance may change in a different shaped bottle) and that the order of each group’s containers will not change by adding another group’s containers.
  9. An additional challenge can be to anticipate the water level if water is poured from a smaller container into a larger container. Rubber bands can be used to mark the predicted levels. Look for students to discuss strategies for anticipating the levels, such as considering the cross sectional area of the container.

Session 2

The following activities are to provide students with experiences to compare volumes of different objects and to create a benchmark for a container that holds one litre.

  1. Make a 1 litre container available for students to use to give them a ‘feel’ for one litre.
  2. Group students and provide a variety of containers for each group.  Ensure items that hold 1 litre (like a 1 litre measuring jug or a 1 litre container of milk or water) are included as such items will become useful benchmarks. 
  3. Ask each group to draw and label the following buckets on large sheets of paper. 
    "buckets"
  4. Students work together to place the containers in the most appropriate bucket, then check their estimates using a 1 litre container.
  5. Ask students to locate items from around their home that they believe would make good benchmarks for 1 litre and, if possible, bring them to school.

Session 3

In this session students compare their benchmarks for one litre and try to estimate one litre.

  1. Share the containers that have been brought to school as good benchmarks for 1 litre and identify which are closest to 1 litre in volume.
  2. Discuss which of the benchmarks are the most useful. For example, objects which you don’t usually see are not particularly good benchmarks as you will not be familiar with their volume.
  3. Give students a plastic bag and ask them to put one litre of something in it.  You may prefer to do this activity outside in the sand area (using water or sand to make a litre) or you may do it inside and suggest a range of items that could be used to make one litre.
  4. Compare the bags and discuss why they are not all exactly one litre. Compare them to reliable benchmarks.
  5. Introduce millilitres as a unit that is helpful for measuring containers that hold less than a litre.
    • What does milli stand for? 
    • How many millilitres in 1 litre?
    • How many millilitres is 2.5 litres?
    • How many litres in 1500 millilitres?
  6. Take several containers, measure the capacities, and express the measurements using both millilitres and litres, e.g. 750ml = 0.75 L.

Session 4

In this session students work with volume as the amount of space that an object takes up.

  1. Provide a range of familiar objects of different volumes (preferably things that will sink in water). Make sure all items are waterproof.
  2. Ask students which of them has the largest volume.  If there is confusion, explain that volume does not just mean the amount that a container can hold, it also means the amount of space an object takes up.
  3. Show students how they can find the volume by displacement. Place a container full of water inside an empty container or tray.  Submerge the object in the container of water and measure how much water is displaced (overflows) into the empty container. This is equal to the volume of the object – discuss why this is so with the class.  If you can find a copy, read ‘Mr. Archimedes' Bath ’ by Pamela Allen.
  4. Allow students some time to experiment with this concept and to order objects by volume.

Session 5

  1. Bring this unit to a conclusion by asking students to share the benchmarks they are going to use for 1 litre. 
  2. List the various benchmarks on a large sheet of paper to be displayed as a reference. 
  3. Share the various strategies and techniques students have developed to establish near estimates for objects they are asked to estimate the volume of.
  4. Ask students to think about other possible accessible items that could be used as benchmarks to measure items that are less than 1 litre in volume. 
    What is the volume of a can of soft drink? 
    Why might that volume be a good ‘size’?
    What is the volume of your lunchbox?
    Why might that volume be a good ‘size’?
    What would be a good volume for a chillybin?

     
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Level Three