What's the Connection?

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Purpose

This is a level 3 link measurement activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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.
Student Activity

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Specific Learning Outcomes

explore connections between mass and volume.

Required Resource Materials
classmate

10x10x10 cm solid wooden or plastic cube

bucket, basin, measuring jug, water

kitchen scales with a bowl

various palstic bottles with their labels still on

FIO, Geometry and Measurement Link, What's the Connection? page 14

12 one metre rulers or sticks

sticky tape

Activity

The purpose of this activity is to develop students’ understanding of the relationships between standard units in the metric system by making connections between the measures for mass and volume. Specifically, they should understand that 1 L of water has a mass of 1 kg and occupies the same volume as a cube measuring 10 x 10 x 10 cm.
This is definitely an outside or wet area activity!

Activity

Question 1 is an entirely practical activity and will require some prior organisation. The students need to work in pairs or small groups. It is unlikely that you will be able to collect enough measuring jugs and kitchen scales for an entire class to do this activity simultaneously. For this reason, you may want to have other groups working on one or more of the other measurement-related activities in this book (for example, Secret Scales, Judgment Calls, or Eyeball Estimates).
The students need to carry out the task with a clear understanding that they are looking for the answer to the question posed by part c. With care and fairly accurate measuring equipment (kitchen scales and a graduated jug), they should be able to discover the “handy connection” for themselves.
The following words are relevant and important. List and display them on a chart and encourage your students to use them:

definition.
For a fuller discussion of the words volume and capacity, see the notes for Secret Scales, page 22. Students also need to know these units for volume, mass, and length:

definitions.
In question 2, the idea is to make use of the connection established in question 1. Compared with the mass of the water in them, the mass of the plastic containers is likely to be negligible, and students should be able to predict the total mass with a fair degree of accuracy. The question also makes it clear that volume and capacity have no shape: the amount of water that would fill a 10 cm cube is the same as fills a 1 L drink bottle.
When doing question 3, students need to realise that there are one thousand 10 cm cubes in a cubic metre if they are to use the “handy connection” to work out how much water would fill such a big container and what it would weigh If students need help with this, you could use a 1 000 cm3 cube with the divisions marked and get them to pretend that each of the small cubes is a 10 cm cube. Alternatively, you could draw a diagram like the one shown and ask them to construct a reduced-size version of the solid using multilink cubes. After a short time, they will run out of patience and/or multilink cubes but should be able to visualise the finished solid and the number of cubes that would be needed to make it.

cube.

Extensions

Ask your students whether they think that the connection they have discovered in this activity should be true for liquids other than water.
Strictly speaking, 1 L of water has a mass of 1 kg only if the water is pure, the temperature 4°C, and the pressure 760 mm of mercury. In everyday situations, these factors can be ignored because their effect is minimal.
To help your students see that this connection is not necessarily true for other liquids, ask them to predict what would happen if they put oil and water together in a glass and then get them to find out by pouring a small amount of cooking oil into a glass that is partly filled with water. Ask “If 1 L of water has a mass of 1 kg, how much would you expect the mass of 1 L of oil to be?” (Less than a kilogram – it floats and is therefore lighter than water.) Repeat the experiment with golden syrup, which is heavier than water. Ask “If 1 L of water has a mass of 1 kg, what would you expect the mass of 1 L of golden syrup to be?” (More than a kilogram.)
So, no: the connection is not true for other liquids. But most will weigh quite close to 1 kg, so this is a guide worth remembering.
The “handy” kilogram–litre connection is not a happy accident. All measuring systems have been constructed by humans, and this connection was deliberately made by the people who designed the metric system and set it in place over 200 years ago. You could challenge interested students to find out more; there are a number of very informative sites on the Internet.

There are a number of picture books that explore measurement through  isplacement. These include Mr Archimedes’ Bath (Pamela Allen, Harper Collins, 1998),
Who Sank the Boat? (Pamela Allen, Penguin, Australia, 1990),
and How to Weigh an Elephant (Bob Barner, Bantam Doubleday Dell, 1995).

See also Floating and Sinking (Building Science Concepts, Book 37) and  nderstanding Buoyancy (Building Science Concepts, Book 38).
At the conclusion of this activity, ask:

  • What did you learn today?
  • What was “handy” about the connection?
  • What difficulties did you have? How did you overcome them?

Answers to Activity

1. a. 1 000 mL or 1 L
b. 1 000 g or 1 kg
c. 1 L of water will fill a 1 000 cm3 container and will weigh 1 kg. Or, 1 000 mL of water occupies 1 000 cm3 and weighs 1 000 g.
2. a.–b. Practical task. As examples, the water in a 1.5 L bottle will weigh 1 500 g (1.5 kg) and 250 mL of water will weigh 250 g.
3. Practical task. A cubic metre container filled with water would hold 1 000 L and weigh 1 000 kg (1 tonne).

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Level Three