# Boxing On

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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 the measurement strand of the New Zealand Curriculum, the terms volume and capacity are used interchangeably.

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. Ways to differentiate include:

• allowing students to explore the equipment independently prior to beginning the task
• using the materials described for each session to “fill up” the boxes, then count the number of measures used
• buddying students to support each other and scaffold their learning in a tuakana/teina relationship
• providing contexts that students can relate to
• encouraging students who need less support 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. This could be linked to learning in the technology area (e.g. design a container for a new chocolate bar). 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. These activities could be taken outside and related to places around the school. For example Activity 4. Students’ ideas and explanations can be recorded digitally to be able to share with their family and whānau. Also consider making links with the expertise of community members (e.g. builders) who may be able to talk to your class about the importance of cubic metres and capacity in their work.

Te Reo Māori vocabulary terms such as kītanga (capacity), ritamano (millilitres), rita (litre), mita pūtoru (cubic metre), and mitarau pūtoru (cubic centimetre) could be introduced in this unit and used throughout other mathematical learning.

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

• 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. Consider sketching a design as a class, and then giving students opportunities to draw their own.
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, small woven harakeke (flax) containers)
• 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. The task in this session could be introduced as the teacher modelling to the whole class. Then, students could work in pairs or small groups to estimate and measure the capacity of the different containers. Students could record their estimates and measurements on mini whiteboards or in a table.

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. Estimate the capacity of the container. Pour the water into a measuring container to measure the capacity.
Compare the estimates and measurements - consider why they are different or similar
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. This task could be completed as a whole class introduction to the size of a metre cube. To reinforce learning, students could estimate how many metre cubes might fit in different classrooms or spaces around the school.

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 is 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 an extension activity you might work out the air space of the hall. How many times would your classroom fit into the hall?