Boxing On

Purpose

This unit supports students to develop their ideas about capacity using standard units.

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
  • Construct three-dimensional objects using cubic centimetres and state their capacity.
  • Construct a model of one cubic metre.
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.

In this unit students find the capacity of containers using cubic units (cubic centimetres, millilitres, litres and cubic metres), and explore relationships between these measures. By constructing containers of a given volume students strengthen their understanding of standard units.

Opportunities for Adaptation and Differentiation

The learning activities in this unit can be differentiated by varying the scaffolding provided to make the learning opportunities accessible to a range of learners. Students who need additional support with measuring capacity can use the materials described for each session to “fill up” the boxes, then count the number of measures used. Students who need less support will be able to calculate volumes from measured lengths.

This unit can be adapted to suit the experiences of your students. It uses boxes, and describes the use of small boxes from food and household items such as sugar cubes, toothpaste, cocoa, and spices. Use any kind of rectangular box or container that is available, and that students are familiar with. Examples include paper bags, takeaway containers, and small gift boxes. Prior to teaching the unit you may like to source a collection of boxes for students to share. One way to do this would be to ask students to bring boxes from home, or search for suitable boxes around the school.

Required Resource Materials

The resources needed for each session are listed alongside each activity below.

Activity

Session 1: Sugar Boxes

In this session we design boxes to hold 64 sugar cubes.

Resources

  • Multilink cubes
  • Rulers: 30cm and one metre
  1. The Sweet-tooth Company has hired you to design rectangular boxes to hold 64 cubes. Each cube has edges of 2 cm, just like multilink cubes. What sizes of boxes could they have? Sketch rough plans for boxes that can hold 64 sugar cubes, showing the length, width, and height of each box.
  2. How many different boxes could be made? How could this be worked out without having to build each shape with cubes?

Possible boxes include:
2cm x 2cm x 128cm for 64 cubes in a single row
4cm x 2cm x 64cm for 2 rows of 32 cubes
8cm x 4cm x 16cm for 2 layers, each with 4 rows of 8 cubes

Session 2: Toothpaste boxes

In this session we explore the size of commercial boxes and construct a rectangular box (cuboid) of a given size.

Resources

  • Small cardboard boxes from home of different sizes (e.g. toothpaste, cocoa, spice)
  • Place-value blocks
  • Centimetre squared paper
  • Scissors, tape, glue
  • 30cm rulers
  1. How many cubic centimetres (small place-value block cubes) can fit exactly into each box? (There must be no gaps or over-filling.)
    The students may choose to work this out by filling each box with place-value cubes, but is there an easier way?
  2. You are told that a packet can hold 1000 small place value blocks cubes, which is 1000 cubic centimetres, or 1 litre. How big might the packet be? Make the packet from centimetre square paper.

Session 3: Box capacity

In this session we find the capacity of boxes in millilitres and cubic centimetres.

Resources

  • Boxes from session 2
  • Small plastic bags
  • Capacity measures
  1. Use the boxes from session two. Find out how much water, in millilitres, each packet can hold. This can be done in the following way. Push a small plastic bag snugly into the packet (make sure it does not have holes!). Pour water into the bag until the top of the packet is reached. Pull the bag gently out of the packet. Pour the water into a measuring container.
  2. Compare the capacity of each box, in millilitres, with its volume in cubic centimetres. What do you notice? Is there a pattern that is the same for each box?

Session 4: The metre cube

In this session we find the number of place-value blocks that fill a metre cube.

Resources

  • Metre rulers
  • Place value blocks
  • Newspaper
  • Tape, scissors
  1. Using a metre ruler, rolled up newspaper, and tape make the skeleton of a cube with edges of one metre. This is a cubic metre.
  2. How many large place-value block cubes (1000 cm3 or 1 litre) would fill the metre cube?
  3. How many flats, longs and small cubes would fill the cubic metre?

Session 5: Air space

In this session we investigate the capacity of the classroom.

Resources

  • Cubic metres from session four
  1. Use the newspaper cubic metres that you made in session four to help you in this activity.
  2. Your classroom needs a new air-conditioning unit to keep the class warm in winter and cool in summer. It is important to find out how many cubic metres of air space there are in your classroom so that the correct unit can be bought. Work out the air space of your classroom in cubic metres and write a short report to your principal explaining how you worked it out. As extension you might work out the air space of the hall. How many times would your classroom fit into the hall?
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Level Three