Using Maths Tracks: Displacement strategy

Maths K–6
Stage 3B
Stage 3B – Unit 28
Measurement
Volume and Capacity
Entry 2: Displacement Strategy
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3B 43873
Centre for Learning Innovation
Number: 43873
Title: Using Maths Tracks Stage 3B Unit 28
This publication is copyright New South Wales Department of Education and Training (DET), however it may contain
material from other sources which is not owned by DET. We would like to acknowledge the following people and
organisations whose material has been used:
Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002
Teacher notes pp 1,
5, 6, Supervisor
notes p 3
Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and
Jennifer Vincent.
Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and Jennifer
Vincent.
The copyright in the Maths Tracks material is vested in the publisher, Reed International Books
Australia Pty Ltd, trading as Harcourt Education Australia. Maths Tracks for NSW has been
published under the Rigby imprint and the series covers seven stages from Early Stage 1 to
Stage 3B. Each stage has a Teacher’s Resource Book, Student Book and Homework Book.
For professional development and support, view online at www.rigby.com.au/pd/event.asp
Supervisor notes p
5, Student sheet 2b
p 21
COMMONWEALTH OF AUSTRALIA
Copyright Regulations 1969
WARNING
This material has been reproduced and communicated to you on behalf of the
New South Wales Department of Education and Training
(Centre for Learning Innovation)
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under the Act.
Any further reproduction or communication of this material by you may be the
subject of copyright protection under the Act.
CLI Project Team acknowledgement:
Writer:
Editors:
Illustrators/Photographers:
Desktop Publishing:
Jillian James
Alan Barnes, Nicholas Perkins
Tom Brown, David Stanley
Esta Tserpes
All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.
Published by
Centre for Learning Innovation (CLI)
51 Wentworth Rd
Strathfield NSW 2135
________________________________________________________________________________________________
Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or
transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without
the written authority of the Centre for Learning Innovation (CLI).
© State of New South Wales, Department of Education and Training 2006.
Stage 3B – Unit 28
These Teacher notes support ‘Using Maths Tracks’. The teacher should detach them
before sending the Supervisor notes and the Student and supervisor guide to the
supervisor and student. They contain:
•
•
•
•
•
•
•
•
•
•
Student outcomes
Prior knowledge
Language
What is needed
Preparation
Interactivity
Resources (including websites)
Returns
Checking up answers
Assessment record
Student outcomes
Outcomes from the Mathematics K–6 Syllabus, © Board of Studies NSW 2002
Measurement
MS3.3
Volume and Capacity
Selects and uses the appropriate unit to estimate and measure volume
and capacity, including the volume of rectangular prisms
Working Mathematically
WMS3.2
Applying Strategies
Selects and applies appropriate problem-solving strategies, including
technological applications, in undertaking investigations
WMS3.5
Reflecting
Links mathematical ideas and makes connections with, and generalisations
about, existing knowledge and understanding in relation to Stage 3 content
Students will learn about:
•
demonstrating that a cube of side 10 cm will displace 1 L of water
•
demonstrating by using a medicine cup that a cube with 1 cm sides will displace 1
mL of water
•
equating 1 cubic centimetre to 1 millilitre and 1000 cubic centimetres to 1 litre
•
recording volume and capacity using decimal notation to 3 decimal places; for
example, 1.275 mL.
Prior knowledge
•
•
•
constructing rectangular prisms using cubic centimetre blocks and counting to
determine volume
estimating then measuring the capacity of rectangular containers by packing with
cubic centimetre blocks
selecting the appropriate unit to measure volume and capacity.
Language
displacement, cubic centimetres, millilitres, litres, capacity, volume, rectangular prisms
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
1
Teacher notes
What is needed
Introduction
•
bucket, or other water container such as a watering can, marked in litres
•
measuring jug
•
medicine glass
•
one MAB maxi, one MAB long and five MAB minis
Activity 1
•
four empty milk cartons cut down to heights of 1cm, 2cm, 3cm and 4cm
respectively
•
MAB minis
•
measuring jug
Activity 3
•
Maths Tracks Student Book Stage 3B, page 128
Activity 4
•
Maths Tracks Student Book Stage 3B, page 129
•
pot, large enough to hold one MAB maxi
•
measuring jug
•
baking tray, or other wide flat container
•
one MAB maxi
Activity 5
•
Maths Tracks Student Book Stage 3B, page 130
Activity 6
•
websites and books with information about Archimedes
Reflection
•
set of interlocking cubes such as centicubes
•
measuring jug
•
baking tray
Checking up
•
one MAB maxi, one MAB mini
•
measuring jug
•
medicine glass
•
baking tray
Maths Tracks Homework Book Stage 3B, page 35 (if you are using it)
Preparation
Select the activities you think suitable for the student by ticking the boxes beside the
activity numbers in the Student and supervisor guide.
Introduction (explicit teaching) – for all students
Activity 1 (beginning) – can provide extra support
Activity 2 (additional assistance) – can provide extra support
Activity 3 (consolidating) – for all students
Activity 4 (establishing) – for all students
Activity 5 (problem solving) – can provide extra challenge
Activity 6 (extension) – can provide extra challenge
Reflection – for all students
Checking up – for all students
Activity 6: Students will require printed information and websites about Archimedes.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
2
Teacher notes
Interactivity
Introduction: Students could create a mind map during a satellite lesson, linking
the displacement strategy to other parts of the Maths syllabus and other KLAs such as
Science.
Activity 5: During a teleconference, students could discuss the strategies they used to
solve the problems and check their solutions. Via email or telephone, they could help
each other find ways to overcome difficulties.
Activity 6: In a satellite lesson, students could discuss ways Archimedes’ principle is
used today.
Resources
Mr Archimedes Bath by Pamela Allen, Angus & Robertson, 1991.
Though this is a picture book for young children, Stage 3 students could enjoy reading it
as part of a reflection on their learning in this unit.
Add any others you find suitable.
Websites [Accessed 27 February, 2006]
Check all websites before recommending them to students.
Activity 6: These websites give information about Archimedes.
Grandpa Pencil looks at Measuring Things
<http://www.grandpapencil.com/science/archimed.htm>
The Golden Crown, Rorres, C., 1995
<http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html>
Ask a Scientist, Water displacement, USA Department of Energy
<http://www.newton.dep.anl.gov/askasci/phy99/phy99x34.htm>
Add any others you find suitable.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
3
Teacher notes
Returns
Student sheet 1 – Volume and capacity of milk cartons – Activity 1
Student sheet 3 –The Archimedes Principle – Activity 6
Student sheet 4 – Shape, volume and water displacement – Reflection
Checking up sheet
personal tape or recording – Introduction, Activities 5, 6, Reflection and
Checking up
Supervisor and Student Feedback sheets
the guide (if you ask for it)
Checking up answers
Recording
There are two displacement strategies to find the capacity of an object.
In the first strategy, the water levels are compared before and after the object is placed
in the water.
In the second, the container is filled to the brim. The overflow of water is measured after
the object is placed in the water.
Checking up sheet
The supervisor will provide feedback on the practical part of the assessment task.
The student should show in diagrams how they demonstrated that a 10 cm cube
displaces 1L of water and a 1 cm cube displaces 1 mL of water.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3B – Unit 28
Measurement: Volume and Capacity
Entry 2: Displacement Strategy
Circle the numbers of the activities the student was asked to complete.
1
2
3
4
5
6
The student:
Activity
Comment
•
demonstrates that a cube of
side 10cm will displace 1L of
water
(MS3.3)
Introduction,
3, 4,
Checking up
•
demonstrates by using a
medicine cup, that a cube of
side 1cm will displace 1mL of
water
(MS3.3)
Introduction,
3, Checking
up
•
records volume and capacity
using decimal notation to three
decimal places
(MS3.3)
•
recognises that an object that
Introduction,
displaces 300mL of water has a
3, 4, 5,
volume of 300 cubic centimetres Reflection,
(WMS3.5)
Checking up
•
selects the appropriate unit to
measure volume and capacity
(MS3.3)
•
calculates the volume of
rectangular prisms
(MS3.3)
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
3, 4, 5
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Indicator
Introduction,
1, 3, 4, 5,
Reflection,
Checking up
4, 5,
Reflection
5
Teacher notes
Indicator
Activity
Comment
uses problem-solving strategies 5, Reflection,
including those based on
Checking up
selecting and organising key
information in a systematic way
(WMS3.2)
•
uses correct mathematical
language to explain
mathematical situations
(WMS3.3)
Introduction,
5, 6,
Reflection,
Checking up
•
explains and gives reasons why
particular results were obtained
(WMS3.4)
5, 6,
Checking up
•
corrects answers and explains
where his/her thinking or
execution was incorrect
(WMS3.4)
5
•
explains some ways that maths
is used, or has been used, to
represent, describe and explain
our world
(WMS3.5)
6
•
explains that objects with
the same volume may have
different shapes
(WMS3.3)
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
•
Reflection
6
Teacher notes
Maths K–6
Stage 3B – Unit 28
Measurement
Volume and Capacity
Entry 2: Displacement Strategy
Supervisor notes
and
Student and supervisor guide
P/M 3B 43873
Centre for Learning Innovation
Number: 43873
Title: Using Maths Tracks Stage 3B Unit 28
This publication is copyright New South Wales Department of Education and Training (DET), however it may contain
material from other sources which is not owned by DET. We would like to acknowledge the following people and
organisations whose material has been used:
Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002
Teacher notes pp 1,
5, 6, Supervisor
notes p 3
Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and
Jennifer Vincent.
Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and Jennifer
Vincent.
The copyright in the Maths Tracks material is vested in the publisher, Reed International Books
Australia Pty Ltd, trading as Harcourt Education Australia. Maths Tracks for NSW has been
published under the Rigby imprint and the series covers seven stages from Early Stage 1 to
Stage 3B. Each stage has a Teacher’s Resource Book, Student Book and Homework Book.
For professional development and support, view online at www.rigby.com.au/pd/event.asp
Supervisor notes p
5, Student sheet 2b
p 21
COMMONWEALTH OF AUSTRALIA
Copyright Regulations 1969
WARNING
This material has been reproduced and communicated to you on behalf of the
New South Wales Department of Education and Training
(Centre for Learning Innovation)
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under the Act.
Any further reproduction or communication of this material by you may be the
subject of copyright protection under the Act.
CLI Project Team acknowledgement:
Writer:
Editors:
Illustrators/Photographers:
Desktop Publishing:
Jillian James
Alan Barnes, Nicholas Perkins
Tom Brown, David Stanley
Esta Tserpes
All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.
Published by
Centre for Learning Innovation (CLI)
51 Wentworth Rd
Strathfield NSW 2135
________________________________________________________________________________________________
Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or
transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without
the written authority of the Centre for Learning Innovation (CLI).
© State of New South Wales, Department of Education and Training 2006.
Stage 3B – Unit 28
These Supervisor notes support the Student and supervisor guide for ‘Using Maths
Tracks’. The supervisor should detach them before giving the guide to the student.
They contain information on:
•
•
•
•
•
How to use this unit
Support and extension
Answer guide
Feedback
Checking up
How to use this unit
Read
•
•
•
with your student:
What you’ll do
What you need
Words you need to know
Your student’s teacher may have selected the appropriate activities from 1 to 6 by ticking
them in the list of What you’ll do. See also Support and extension.
The boxes on the right-hand side of the pages in the Student and supervisor guide
contain information and suggestions to help you support your student.
There is also space for you to make notes about how your student managed. You can use
your notes to help you fill in the Feedback sheet at the end of the unit.
An icon
shows when to refer to the Maths Tracks Student Book pages.
page x
After completing the unit, ask your student to complete the Checking up sheet
independently and return it to the teacher. Complete the supervisor side of
the Feedback sheet. Discuss the student side of the Feedback sheet and help
your student complete it.
Support and extension
The activities following the Introduction are at different levels. Your student’s teacher
may have selected the activities for your student. If activities have not been selected in
the guide, choose activities as below:
Introduction – for all students
Activities 1 and 2 – can provide extra support
Activities 3 and 4 – for all students
Activities 5 and 6 – can provide extra challenge
Reflection and Checking up – for all students
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
1
Supervisor notes
Answer guide
This guide helps you give your student feedback on questions and tasks in the unit or in
the Maths Tracks Student Book, especially where answers will vary.
Activity 1 – Student sheet 1
Based on a milk carton 7 cm x 7 cm, your student should get the following results:
1 cm carton: volume = 49 cm3 or 49 mL
capacity = 49 cm3 or 49 mL
2 cm carton: volume = 98 cm3 or 98 mL
capacity = 98 cm3 or 98 mL
3 cm carton: volume = 147 cm3 or 147 mL
capacity = 147 cm3 or 147 mL
4 cm carton: volume = 196 cm3 or 196 mL
capacity = 196 cm3 or 196 mL
Activity 5 – Maths Tracks Student Book Stage 3B, page 130
3
4
Possible answers (other dimensions are also acceptable, so long as they equal the
total volume of the displaced water)
a
17.5 L – 9.5 L = 8 L = 8000 mL = 8000 cm3 = 20 cm x 20 cm x 20 cm
b
39 mL – 15mL = 24 mL = 24 cm3 = 4 cm x 3 cm x 2 cm
c
2.25 L – 1.25L = 1 L = 1000 mL = 1000 cm3 = 10 cm x 10 cm x 10 cm
d
13.67 L – 10.67 L = 3 L = 3000 mL = 3000 cm3 = 15 cm x 20 cm x 10 cm
Total capacity of tank = 25 cm x 50 cm x 25 cm = 31 250 cm3
31 250 cm3 is equivalent to 31 250 mL or 31.250 L
At the rate of 1 fish per litre, 31.25 litres will support 31 fish,
so Justina should buy 31 fish.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
2
Supervisor notes
Feedback
Supervisor
The feedback you provide will help teachers assess your student’s progress and plan
future learning experiences. Please mark the scale and comment on the activities that
your student completed.
Student’s name
Date
Activity
•
understand that the volume of a
prism is equal to its capacity
(MS3.3, WMS3.3)
Introduction
•
find the capacity of a prism by
measuring how much water it
displaces
(MS3.3)
Introduction,
1, 4,
Checking up
•
calculate the volume by finding the
volume of one layer and multiplying
the answer by the number of layers
(WMS3.2)
5
•
use a displacement strategy to
measure the volume of a cube
accurately by doing things such as
placing the jug on a level surface,
having their eye at water level when
reading the scale on the jug and not
spilling any water
(WMS3.3)
1, 4,
Checking up
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
3
with
difficulty
(Tick along line)
with
independently
help
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Did your student:
Supervisor notes
Feedback
Student
Help your student
to give feedback
on their learning
for completed
activities.
My favourite activity for this unit was ________________________________________
because _______________________________________________________________.
I had to work hard at _____________________________________________________
______________________________________________________________________.
When I want to measure the capacity of something, I ___________________________
______________________________________________________________________.
I check my work by ______________________________________________________
______________________________________________________________________.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
4
Supervisor notes
Student’s name:
Checking up
Using Maths Tracks, Stage 3B – Unit 28
Measurement: Volume and Capacity
Entry 2: Displacement Strategy
Conduct an activity which shows how a:
•
10 cm cube will displace 1 litre (1L) of water
•
1 cm cube will displace 1 millilitre (1mL) of water.
Make sure your student
completes this work
independently for return
to the teacher.
Provide feedback to the
teacher on the way your
student measured the
volume of the cubes.
Check that the student
places the jug on a level
surface and brings their
eye level to the water
level when reading the
scale.
10 cm cube
1 cm cube
Diagram of jug of water without the cube
Diagram of jug of water with the cube
Diagram of jug of water with the cube
Diagram of jug of water without the cube
Procedure for finding volume of cube:
Procedure for finding volume of cube:
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
5
Supervisor notes
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
Write the procedures for the experiments and show how you calculated the results.
Make sure you label all diagrams.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
6
Supervisor notes
Stage 3B – Unit 28
Student and supervisor guide
Unit contents
About this unit
ii
What you’ll do ................................................................................ ii
What you need .............................................................................. iii
Words you need to know .......................................................... iii
Icons .................................................................................................. iv
Using this guide ............................................................................ iv
Returns ............................................................................................. iv
Introduction
....................................................................................
..........................................................................................
1
Activity 1
.................................................................................................
5
Activity 2
.................................................................................................
7
Activity 3
.................................................................................................
8
Activity 4
.................................................................................................
9
Activity 5
..............................................................................................
11
Activity 6
..............................................................................................
12
Reflection
.............................................................................................
14
Checking up
.......................................................................................
Student sheets
................................................................................
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
i
15
17
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
compare the volume and capacity of MAB minis and maxis using
the displacement strategy
Activity 1
•
measure the volume of containers with MAB minis and water
•
state the capacity of containers
•
compare the relationship between volume and capacity
Activity 2
•
play a game where you add volumes to reach 1 litre
Activity 3
•
change millilitres to litres
•
use the volume of prisms to calculate how much water they would
displace
•
calculate the volume of a prism using the displacement strategy
Activity 4
•
measure the overflow of water to find the capacity of a prism
•
read the rise in water level to calculate the capacity of blocks
Activity 5
•
find the capacity of containers by calculating their volume
•
talk to your teacher about how you solved the problem
•
calculate the number of fish that could live in a tank
Activity 6
•
find out about Archimedes and the Archimedes Principle
•
research how his theory is used in industry today
√
√
Reflection
•
compare three prisms with different shapes but the same volume
using the displacement strategy
Checking up
•
ask questions about finding the volume of a cube using the
displacement strategy
•
demonstrate how a MAB maxi will displace one litre of water
•
demonstrate how a MAB mini will displace one millilitre of water
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
ii
Student and supervisor guide
What you need
Introduction
•
bucket, or other water container such as a watering can, marked in
litres
•
measuring jug
•
medicine glass
•
one MAB maxi, one MAB long and five MAB minis
Activity 1
•
four empty milk cartons cut down to heights of 1cm, 2cm, 3cm
and 4cm respectively
•
MAB minis
•
measuring jug
Activity 3
•
Maths Tracks Student Book Stage 3B, page 128
Activity 4
•
Maths Tracks Student Book Stage 3B, page 129
•
pot, large enough to hold one MAB maxi
•
measuring jug
•
baking tray or some other wide, flat container
•
one MAB maxi
Activity 5
•
Maths Tracks Student Book Stage 3B, page 130
Activity 6
•
access to the Internet and books with information about
Archimedes
Reflection
•
centicubes
•
measuring jug
•
baking tray
•
water
Checking up
•
one MAB maxi and one MAB mini
•
measuring jug
•
medicine cup
•
baking tray
Words you need to know
displacement
cubic centimetres
millilitres
litres
capacity
volume
rectangular prisms
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
iii
Student and supervisor guide
Icons
Record this for the teacher.
Return this to the teacher.
Use the page in the Maths Tracks Student Book.
Page x
Using this guide
The boxes on the right-hand side of pages in the Student and supervisor
guide contain information and suggestions for the supervisor.
After each activity, circle the face that shows how you feel about your
work and talk about it with your supervisor.
Returns
Student sheet 1 – Volume and capacity of milk cartons
– Activity 1
Student sheet 3 – The Archimedes Principle – Activity 6
Student sheet 4 – Shape, volume and water displacement
– Reflection
Checking up sheet
personal tape or recording – Introduction, Activities 5, 6,
Reflection and Checking up
Supervisor and Student Feedback sheets
this guide (if your teacher asks for it)
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
iv
Student and supervisor guide
Introduction
When we measure milk, oil and soft drink in
litres and millilitres, what are we measuring?
We are measuring the volume of the liquid.
How many millilitres are in one litre?
Did you say 1000 millilitres?
To find how many millilitres there are in a
number of litres, you need to multiply the
number of litres by 1000.
How many millilitres in:
•
1.25 L
•
1.5 L
•
3.65 L
•
4.75 L?
[Hint: Move each digit three place value
positions to the left.]
Did your student say:
• 1250mL in 1.25 L
• 1500mL in 1.5 L
• 3650mL in 3.65 L
• 4750mL in 4.75 L?
It may help students to use
the short-cut strategy of
moving the decimal point
three places to the right.
For the next part of this activity you need a
bucket or a container with measurements
marked up the side. If the bucket or container
has no measurements on the side of it, fill it
one litre at a time, marking each new level with
a marking pen (1L, 2L, 3L) till the top of the
bucket is reached. If you cannot see the water
level on the outside, you will need to mark the
levels instead on the inside of the bucket with a
waterproof pen.
Once you have the measurements on your
bucket, pour in two litres of water.
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
1
Student and supervisor guide
Find your MAB maxi.
It has dimensions of 10 cm x 10 cm x 10 cm.
What is its volume?
Did you say it is 1000 cm3?
How far do you think the water will rise in your
bucket when you put the MAB maxi in the
water?
Place the MAB maxi into the water and check
your prediction.
Since the MAB maxi has a volume of 1000 cm3,
you should find that the water in the bucket
rises by 1000 millilitres (or 1 litre).
You could repeat this activity with your other
containers with litres marked on the side.
Your student should see
that in narrower containers
the water will rise higher
than in wider containers.
But the amount doesn’t
change.
The amount of water is
still 1L.
Will the shape of a container change how far the
water rises when a MAB maxi is added?
Did you realise that a cube
with a volume of 1000 cm3 has
the capacity to hold 1000 mL
of water?
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
2
Student and supervisor guide
You have seen the relationship between 1
litre and 1000 cm3. Now let’s explore the
relationship between the millilitre and the cubic
centimetre.
Find your medicine glass and MAB minis.
What is the volume of an MAB mini?
Did you say it is 1 cm3?
Fill the medicine glass with five millilitres of
water.
Place the MAB mini in the water.
How far does the level of water rise?
Does it rise by one millilitre (1 mL)?
Did you realise that 1 cm3
and 1 mL are equivalent?
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
3
Student and supervisor guide
Find your measuring jug.
Fill it with 30 mL of water.
Estimate how far the level of water will rise
when five MAB minis are added.
Check your estimation by adding the MAB minis.
Did you find the water rose by 5 mL?
Estimate how far the level of water will rise
when one MAB long is added.
Check your estimation by adding the MAB long.
Did you find the water rose by 10mL?
Record this talk and your answers to these
questions for your teacher. Use mathematical
words such as capacity, volume, litre, cubic
centimetre, level and equivalent.
Explain what volume and capacity are.
Describe how you showed that an MAB maxi has
the equivalent volume to a litre of water.
Hint: describe how you displaced the water in
the bucket.
How do you make sure your measurement is
accurate when you measure liquid?
Why do you need to measure accurately?
Stop the recording now.
Volume is the amount
of space taken up by an
object or substance.
Capacity is the amount of
something that a container
is capable of holding.
Volume and capacity are
normally measured in
cubic centimetres (cm3) or
mL for small objects and
litres and cubic metres
(m3) for larger objects.
Volume and capacity are
equivalent.
Your student might say
1mL of medicine can help
you, but 5 mL could be
poisonous or make you
worse.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
4
some
help
no
help
Student and supervisor guide
Activity 1
Let’s explore the link between volume and
capacity.
MAB
minis
1 cm
milk carton
2 cm
milk carton
3 cm
milk carton
4 cm
milk carton
Find the milk carton that you cut down to 1
centimetre.
And find your set of MAB minis.
Estimate the volume of your carton: _____ cm3
Check your answer by filling your carton with
MAB minis. (Remember that you can only fill it
to a height of 1 cm.)
The volume of the 1 cm container is _____ cm3
The 1 cm container, when empty, has the
capacity to hold _____ cm3
Empty out the minis and fill the carton with
water.
Then pour the water into a measuring jug to find
the volume of water.
The volume of the 1 cm container is _____ mL.
The 1 cm container, when empty, has the
capacity to hold _____ mL.
The dimensions of the
carton will vary depending
on the type of carton used.
The volume and capacity
of the carton will
vary depending on its
dimensions.
If the carton is 7 cm x
7 cm x 1 cm, it will have a
volume and a capacity of
49 mL or 49 cm3.
Did you find the capacity was equivalent to the
volume?
Do you remember that ‘equivalent’
means ‘equal in value’?
Using Maths Tracks, Stage 3B, Unit 28
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Student and supervisor guide
Find the other three cartons that you cut down
and repeat what you did on the previous page
with the other containers.
Find Student sheet 1, Volume and capacity of
milk cartons. Fill in the results of your activities.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
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some
help
no
help
Student and supervisor guide
Activity 2
Play the game ‘Fill it up’ with a partner.
Aim
To fill the container to one litre.
How to play:
Cut out the two gameboards, one for each
player, from Student sheet 2a.
The container on each gameboard has the
capacity to hold 1 litre.
Cut out the game cards from Student sheet 2b.
Each game card represents a different volume of
liquid.
Shuffle the volume cards and place them facedown in a pile between the two players.
Take turns to draw a card from the pile and
decide whether to keep it or place it back on the
bottom of the pile.
If you keep the card, place it on the container on
your gameboard.
Keep a total of the cards you add to your
gameboard.
If you exceed a volume of one litre, you must
return all your cards to the pile and begin again.
The game is over when the cards on one player’s
container total exactly 1 litre.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
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some
help
no
help
Student and supervisor guide
Activity 3
Find page 128 in the Maths Tracks Student Book.
Page 128
Help your student read and
interpret the instructions.
1, 2 and 3 Remember 1 L = 1000 mL
If you have difficulty with this question,
reread the beginning of the Introduction.
4
To find the volume of the prisms, subtract
the volume of liquid in the first container
from the volume of liquid in the container
with the prism.
d Change 1.25 L and 1.75 L into millilitres.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Discuss possible reasons for
different answers and praise
successes.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
8
some
help
no
help
Student and supervisor guide
Activity 4
The displacement strategy is an important way
mathematicians and scientists work out the
volume of an object.
When an MAB mini (1 cm3) is placed in water,
the water level rises 0.001 L (or 1 mL).
When an MAB maxi (1000 cm3) is placed in
water, the water level rises 1000 mL (or 1 L).
Let’s look at another way to use the
displacement strategy to measure capacity.
Sit a pot in a baking tray.
Fill the pot with water right to the brim.
Be careful not to spill even a drop.
Now place the MAB maxi in your pot and let the
water overflow into the tray.
Remove the pot and use a measuring jug to
measure the water that spilled into the baking
tray.
You should collect one litre of water from the
tray.
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Student and supervisor guide
Find page 129 in the Maths Tracks Student Book.
Page 129
Help your student read and
interpret the instructions.
1&3 To find the volume of one layer of a prism,
multiply the length by the width or breadth.
To find the total volume, multiply the
volume of one layer by the number of layers
or the height.
2
Remember the volume of a solid (measured
in cm3 and m3) is equivalent to the volume of
the liquid it displaces (measured in millilitres
and litres).
1000 cm3 = 1000 mL =1 L
4
Remember, the amount of water that
overflowed is equivalent to the volume of
the blocks.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Discuss possible reasons
for different answers and
praise successes.
Remember, the volume
of a solid is equivalent
to the volume of the
liquid it displaces.
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Student and supervisor guide
Activity 5
Find page 130 in the Maths Tracks Student Book.
Page 130
1
Calculate the capacity of each container in
cm3.
Convert that to mL and then write the
answer in litres. (Your answer will be in
decimals.)
2
Notice that this problem is using the
displacement strategy described at the
beginning of Activity 4.
Water equal to the total volume of blocks
spills out of the tub when the blocks are
added.
When the blocks are taken out, the water
level will drop an amount equal to their
volume.
3
Find the volume of each block, before you
calculate its dimensions.
4
First, calculate the capacity of the tank in
cm3.
Then convert that into mL, then into litres.
Then work out how many fish the tank could
support. [Remember, 1000 mL = 1 L.]
Help your student read and
interpret the instructions.
Refer to the Answer guide
in the Supervisor notes for
3 and 4.
For Task 4, BLM 11 has not
been supplied.
Let your student use
various methods to find the
solution.
To check your solution, work backwards
through the problem. If you multiplied, then
divide. If you added, then subtract.
Record the following for your teacher. Use
mathematical language such as volume, capacity,
multiply and equal.
Describe how you solved the problem in Task 4.
How did you check your solution?
What difficulties did you have and how did you
overcome them?
Feedback:
Stop recording now.
lots of
help
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some
help
no
help
Student and supervisor guide
Activity 6
It is said that Archimedes discovered an
important mathematical theory while sitting in
his bath.
Graphic: Archimedes sitting in his bath as
the water spills out of it.
Find out information about:
•
Archimedes and his life
•
the Archimedes Principle of water
displacement
•
the importance of his theory in measuring
capacity and volume
•
the industries where the Archimedes
Principle is used.
Make sure your information comes from at least
three different sources.
You can find articles on the World Wide Web,
encyclopedias or books about Ancient Greece.
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Shipbuilding, for instance,
uses his principle in the
design of boats.
Student and supervisor guide
Find Student sheet 3, The Archimedes Principle.
On your sheet:
•
make notes by writing key words
•
write a couple of sentences about each part
of the task
•
write down the authors and books, or
websites, where you found the information.
Record this talk for your teacher. Use
mathematical words such as displacement,
volume and capacity.
Give a talk about Archimedes and the
Archimedes Principle.
Explain why his theory of water displacement is
so important today.
Stop recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
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13
some
help
no
help
Student and supervisor guide
Reflection
Make three differently-shaped prisms, each
using the same number of interlocking cubes.
Find the volume of these prisms by putting them
in water.
On Student sheet 4, Shape, volume and water
displacement, find a way of showing what you
discovered in the above activity.
Hints:
•
draw diagrams with such mathematical
labels as volume, capacity, water
displacement, litres, millilitres and cubic
centimetres
•
write simple instructions with diagrams
•
divide your page into three sections, one
section for each prism
•
explain what the activity showed.
This activity demonstrates
that the amount of water
displaced is determined by
volume and capacity, not
shape.
Your student can choose
which displacement
strategy they use.
Method 1 is to measure the
rise in water level.
Method 2 is to measure the
amount of water that spills
over into another container.
If the prisms float,
encourage your student to
find a solution.
For example, to make the
prism sink, your student
needs to find something
which sinks.
If that means adding a
weight to the prism, then
the volume of the weight
will need to be calculated
and subtracted from the
total amount of water
displaced by the prism and
weight together.
Record the following for your teacher.
Use mathematical words such as volume,
capacity, water displacement, litres, millilitres
and cubic centimetres.
Describe how you organised the activity and the
information.
Why did you organise the information that way?
What can you say about the amount of water
displaced by each prism?
Stop the recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
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some
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Student and supervisor guide
Checking up
Record the following for your teacher. Use
mathematical words such as volume, capacity,
displacement of water, litres, millilitres and cubic
centimetres.
Explain how the water displacement strategy
works.
Stop the recording now.
Complete the Checking up sheet without any
help from your Supervisor.
After you have finished the Checking up sheet,
fill in the student side of the Feedback sheet.
You may need to look back at the smiley faces
you circled to remind yourself how you felt about
each activity.
The Checking up sheet and
Feedback sheet are near
the back of the Supervisor
notes for this unit.
Make sure your student
works on this assessment
task independently, with
your assistance to read and
interpret the instructions.
Return the Checking
up sheet to the teacher
unmarked.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
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some
help
no
help
Student and supervisor guide
Using Maths Tracks, Stage 3B, Unit 28
© NSW DET 2006
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Student and supervisor guide
Name:
Volume and capacity of milk cartons
Using Maths Tracks, Stage 3B, Unit 28
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Activity 1
Student sheet 1
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Student sheet 1
Gameboard 1
Gameboard 2
Activity 2
Fill it up
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Student sheet 2a
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Student sheet 2a
Activity 2
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
Game cards
Using Maths Tracks, Stage 3B, Unit 28
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Student sheet 2b
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Student sheet 2b
Name:
The Archimedes Principle
Activity 6
Write down key words for each part.
Write a couple of sentences, using your own words.
Websites and books used:
Archimedes and his life
The Archimedes Principle of
water displacement
Notes (key words)
Notes (key words)
Sentences
Sentences
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Student sheet 3
The importance of his theory in
measuring capacity and volume
The industries where the
Archimedes Principle is used
Notes (key words)
Notes (key words)
Sentences
Sentences
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Student sheet 3
Name:
Shape, volume and water displacement
Reflection
Organise the information and results from your activity clearly on
these pages.
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Student sheet 4
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© NSW DET 2006
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Student sheet 4
Centre for Learning Innovation
NSW Department of Education and Training
51 Wentworth Road
Strathfield NSW 2135