# Stage 4 - measurement -surface area and volume

## Strategy

Students can:

• convert between millilitres and litres and between litres and kilolitres
• use formulas for calculating volumes of prisms and cylinders
• recognise the relationship between the capacity of liquids and the volume of solids

## Activities to support the strategy

### Activity 1 – kilolitres

1. Introduce the litre as the basic unit for measuring capacity in the metric system.

• 1000 millilitres (mL) = 1 litre (1 L)
• 1000 litres (L) = 1 kilolitre (1 kL)

Students discuss liquids that are usually measured in:

• millilitres e.g. medicine, cans of drink
• litres e.g. cartons of milk, bottles of juice
• kilolitres e.g. water usage bill, pools

2. Students reach the capacity of:

• Sydney Harbour
• Warragamba Dam
• the nearest swimming pool
• the local water supply for the closest town or city
• irrigation water used in NSW in 2008
• a large rainwater tank
• a petrol tanker
• the hot water system at home
• the local dam, river, creek or stream

and the amount of water:

• used in an average household in one month
• listed on the last water bill.

The amount in kilolitres for each is reported back to the class.

3. Discuss the process to convert between millilitres and litres and between litres and kilolitres.

The teacher models the process by working through examples, e.g.

4. Students solve a variety of problems which involve converting between millilitres and litres and between litres and kilolitres.

View/print (PDF 57.61KB)

5. Students match equivalent measurements in this table.

68 kilolitres 5.17 kilolitres 0.276 L 20 300 L 276 L
20.3 kL 97 L 2.3 kilolitres 68 000 litres 2.05 kL
361 litres 2 050 L 68.8 kL 0.000 276 kL 68 800 L
2300 litres 0.276 kL 0.361 kilolitres 0.097 kL 5 170 litres

View/print (PDF 51.78KB)

Cut the table into cards. Students shuffle the cards and turn over. Play concentration with the cards.

Activity 2 – Volume and capacity of solids

1. Students use the Interactive online activity to count the number of centicubes used to build different prisms. Students can then check their answers using Interactive.

2. The teacher uses Interactive to demonstrate using the formula for calculating volumes of prisms.

3. Students use formulas for calculating volumes of prisms and cylinders.

View/print (PDF 757.95KB)

4. Introduce the relationship between the capacity of liquids and the volume of solids.

• A container with a volume of 1 cubic centimetre can hold 1 millilitre of liquid.
• A container with a volume of 1000 cubic centimetre can hold 1 litre of liquid.
• A container with a volume of 1 cubic metre can hold 1 kilolitre of liquid.

Students work in pairs to determine the capacity of a variety of rectangular prisms.

• Ask: How many millilitres would each of these containers hold?

5. The teacher reviews the conversions with the class and students complete these statements:

• 1 cubic centimetre is the same as (how many) cubic millimetres?
• 1 litre is the same as (how many) millilitres?
• 1 litre is also the same as (how many) cubic centimetres
• 1 cubic metre is the same as (how many) litres
• 1 cubic metre is also the same as (how many) kilolitres.

## Resources

### Australian curriculum

ACMMG195: Choose appropriate units of measurement; for area and volume and convert from one; unit to another

### NSW syllabus

MA4-13MG: Uses formulas to calculate the areas of quadrilaterals and circles and converts between units of area MA4-14MG: Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume.
The text passage is an educational resource that outlines strategies and activities for teaching students about measurement, specifically focusing on surface area, volume, and capacity. It includes a series of activities and questions that involve converting units and calculating volumes.
multiple_questions

the passage contains multiple questions and problems that students are expected to solve, such as converting between different units of measurement and calculating the volume of various prisms and cylinders. however, the answers to these questions are not provided within the text.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Stage 4 - measurement -surface area and volume

## Strategy

Students can:

• convert between millilitres and litres and between litres and kilolitres
• use formulas for calculating volumes of prisms and cylinders
• recognise the relationship between the capacity of liquids and the volume of solids

## Activities to support the strategy

### Activity 1 – kilolitres

1. Introduce the litre as the basic unit for measuring capacity in the metric system.

• 1000 millilitres (mL) = 1 litre (1 L)
• 1000 litres (L) = 1 kilolitre (1 kL)

Students discuss liquids that are usually measured in:

• millilitres e.g. medicine, cans of drink
• litres e.g. cartons of milk, bottles of juice
• kilolitres e.g. water usage bill, pools

2. Students reach the capacity of:

• Sydney Harbour
• Warragamba Dam
• the nearest swimming pool
• the local water supply for the closest town or city
• irrigation water used in NSW in 2008
• a large rainwater tank
• a petrol tanker
• the hot water system at home
• the local dam, river, creek or stream

and the amount of water:

• used in an average household in one month
• listed on the last water bill.

The amount in kilolitres for each is reported back to the class.

3. Discuss the process to convert between millilitres and litres and between litres and kilolitres.

The teacher models the process by working through examples, e.g.

4. Students solve a variety of problems which involve converting between millilitres and litres and between litres and kilolitres.

View/print (PDF 57.61KB)

5. Students match equivalent measurements in this table.

68 kilolitres 5.17 kilolitres 0.276 L 20 300 L 276 L
20.3 kL 97 L 2.3 kilolitres 68 000 litres 2.05 kL
361 litres 2 050 L 68.8 kL 0.000 276 kL 68 800 L
2300 litres 0.276 kL 0.361 kilolitres 0.097 kL 5 170 litres

View/print (PDF 51.78KB)

Cut the table into cards. Students shuffle the cards and turn over. Play concentration with the cards.

Activity 2 – Volume and capacity of solids

1. Students use the Interactive online activity to count the number of centicubes used to build different prisms. Students can then check their answers using Interactive.

2. The teacher uses Interactive to demonstrate using the formula for calculating volumes of prisms.

3. Students use formulas for calculating volumes of prisms and cylinders.

View/print (PDF 757.95KB)

4. Introduce the relationship between the capacity of liquids and the volume of solids.

• A container with a volume of 1 cubic centimetre can hold 1 millilitre of liquid.
• A container with a volume of 1000 cubic centimetre can hold 1 litre of liquid.
• A container with a volume of 1 cubic metre can hold 1 kilolitre of liquid.

Students work in pairs to determine the capacity of a variety of rectangular prisms.

• Ask: How many millilitres would each of these containers hold?

5. The teacher reviews the conversions with the class and students complete these statements:

• 1 cubic centimetre is the same as (how many) cubic millimetres?
• 1 litre is the same as (how many) millilitres?
• 1 litre is also the same as (how many) cubic centimetres
• 1 cubic metre is the same as (how many) litres
• 1 cubic metre is also the same as (how many) kilolitres.

## Resources

### Australian curriculum

ACMMG195: Choose appropriate units of measurement; for area and volume and convert from one; unit to another

### NSW syllabus

MA4-13MG: Uses formulas to calculate the areas of quadrilaterals and circles and converts between units of area MA4-14MG: Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume.
user
The text passage is an educational resource that outlines strategies and activities for teaching students about measurement, specifically focusing on surface area, volume, and capacity. It includes a series of activities and questions that involve converting units and calculating volumes.

TYPE: MULTIPLE_QUESTIONS

The passage contains multiple questions and problems that students are expected to solve, such as converting between different units of measurement and calculating the volume of various prisms and cylinders. However, the answers to these questions are not provided within the text.