Maths K–6
Stage 3B
Stage 3B – Unit 31
Number
Multiplication and Division
Entry 4: Using Multiples of 10
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3B 43876
Centre for Learning Innovation
Number: 43876
Title: Using Maths Tracks Stage 3B Unit 31
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,
Supervisor notes p 7
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 9, Student sheet 4
p 23
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:
Averil Griffith
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 31
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
Number
NS3.3
Multiplication and Division
Selects and applies appropriate strategies for multiplication and division
Working Mathematically
WMS3.2
Applying Strategies
Selects and applies appropriate problem-solving strategies, including
technological applications, in undertaking investigations
WMS3.4
Reasoning
Gives a valid reason for supporting one possible solution over another
Students will learn about:
•
applying appropriate mental, written or calculator strategies to solve multiplication
and division problems
•
using mental strategies to multiply or divide a number by 100 or a multiple of 10.
Prior knowledge
•
•
Applying appropriate mental, written or calculator strategies to solve multiplication
and division problems
Applying an understanding of place value and the role of zero to read, write and
order numbers of any size.
Language
division, multiplication, divide, multiply, vertical format, place value
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
1
Teacher notes
What is needed
Activity 2
•
Microsoft Word
•
Printer
Activity 3
•
Maths Tracks Student Book Stage 3B, page 40
Activity 4
•
Maths Tracks Student Book Stage 3B, page 41
Activity 5
•
Make a table problem-solving poster
Activity 6
•
die
•
2 counters
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
Interactivity
Reflection: In this activity students are asked to reflect why using a calculator to solve
multiplication problems is not always the quickest method.
In a satellite lesson you could play a game where half the students have to complete ten
multiplication algorithms using a calculator and the other half have to use their mental or
written strategies.
•
•
•
Who was the quickest?
Overall, which is quicker: calculator, or mental or written strategies?
Why do you think this is so?
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
2
Teacher notes
Resources
Add any you find suitable.
Websites
Check all websites before recommending them to students.
Add any you find suitable.
Returns
Student sheets 1a and 1b – Multiplying and dividing by 10s – Activity 1
Student sheet 2 – Multiplication and division patterns – Activity 2
Student sheet 3 – Problem-solving – Activity 5
Checking up sheet
personal tape or recording – Reflection and Checking up
Supervisor and Student Feedback sheets
the guide (if you ask for it)
Checking up answers
From Student and supervisor guide.
•
Look at the number 4800. Provide your teacher with a multiplication fact and a
division fact using 4800.
•
Each fact must contain a multiple of 10.
Teacher will need to check the answer as answers will vary.
From Checking up sheet
1
X
30
40
60
70
80
90
40
1200
1600
2400
2800
3200
3600
400
12 000
16 000
24 000
28 000
32 000
36 000
4000
120 000
160 000
240 000
280 000
320 000
360 000
2
a
b
c
9; 90; 900
13; 13; 13
15; 150; 1500
3
a
b
c
d
350
3500
3500
$1.20 x 5 = 6
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
4
a
b
c
d
90 carriages
$680
40 000 seeds
12 days
3
Teacher notes
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3B – Unit 31
Number: Multiplication and Division
Entry 4: Using Multiplies of 10
Circle the numbers of the activities the student was asked to complete.
1
2
3
4
5
6
The student:
Activity
•
selects and applies mental
strategies to multiply or divide a
number by 100 or a multiple of
10
(NS3.3)
•
selects and applies appropriate
problem-solving strategies,
including technological
application, in undertaking
investigations
(WMS3.2)
4, 5, 6
•
gives a valid reason for
supporting one possible solution
over another
(WMS3.4)
1, 2, 3
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
Comment
1, 2, 3, 4,
5, 6
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Indicator
5
Teacher notes
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
6
Teacher notes
Maths K–6
Stage 3B – Unit 31
Number
Multiplication and Division
Entry 4: Using Multiples of 10
Supervisor notes
and
Student and supervisor guide
P/M 3B 43876
Centre for Learning Innovation
Number: 43876
Title: Using Maths Tracks Stage 3B Unit 31
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,
Supervisor notes p 7
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 9, Student sheet 4
p 23
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:
Averil Griffith
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 31
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 31
© NSW DET 2006
1
Supervisor notes
Answer guide
This guide helps you give your student feedback on questions and tasks in the unit or the
Maths Tracks Student Book, especially where answers will vary.
Introduction
42 x 300 = 12 600
42 x 100 = 4200
4200 x 3 = 12 600
25 x 600 = 15 000
25 x 100 = 2500
2500 x 6 = 15 000
3600 ÷ 400 = 9
3600 ÷ 100 = 36
36 ÷ 4 = 9
81 000 ÷ 300 = 270
81 000 ÷ 100 = 810
810 ÷ 3 = 270
Activity 1 – Student sheets 1a and 1b
H Th
Th
H
T
O
6
0
6
0
0
5
4
0
0
Th
H
T
O
5
0
5
0
0
0
0
0
60 x 90
x 10
x9
Vertical format:
60
x 90
5400
H Th
50 x 60
x 10
x6
3
Vertical format:
50
x 60
3000
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
2
Supervisor notes
H Th
Th
H
T
O
7
0
7
0
0
5
6
0
0
Th
H
T
O
1
5
0
1
5
70 x 80
x 10
x8
Vertical format:
70
x 80
5600
Activity 1 – Student sheet 1b
H Th
150 ÷ 50
÷ 10
÷5
3
H Th
Th
490 ÷ 70
H
T
O
4
9
0
4
9
÷ 10
÷7
7
H Th
Th
720 ÷ 90
÷ 10
÷9
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
H
T
O
7
2
0
7
2
8
3
Supervisor notes
Activity 2
80 x 3
800 x 3
8000 x 3
=
=
=
240
2400
24 000
240 ÷ 3
2400 ÷ 3
24 000 ÷ 3
=
=
=
80
800
8000
63 ÷ 7
630 ÷ 7
6300 ÷ 7
=
=
=
9
90
900
9x7
90 x 7
900 x 7
=
=
=
63
630
6300
7 x 40
7 x 400
7 x 4000
=
=
=
280
2800
28 000
280 ÷ 7
2800 ÷ 7
28 000 ÷ 7
=
=
=
40
400
4000
90 ÷ 30
900 ÷ 30
9000 ÷ 30
=
=
=
3
30
300
30 x 3
30 x 30
30 x 300
=
=
=
90
900
9000
60 x 50
60 x 500
60 x 5000
=
=
=
3000
30 000
300 000
3000 ÷ 60
30 000 ÷ 60
300 000 ÷ 60
=
=
=
50
500
5000
To be marked by supervisor as answers will vary.
To be marked by supervisor as answers will vary.
To be marked by supervisor as answers will vary.
Activity 3
To multiply a whole number by 10, move every number up one place value to the left
and put the zero in the ones column.
To multiply a whole number by 100, move every number up two place value positions to
the left and put the zeros in the ones and tens columns.
To divide a number by 10, every number moves back one place value position to the
right.
To divide a number by 100, every number moves back two place value positions to the
right.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
4
Supervisor notes
Activity 5
Hour
CDs sold
Value of sales
TOTAL
10:00 am
16
16 x 30 =
16 x 10 = 160
160 x 3 = 480
$480
11:00 am
18
18 x 30 =
18 x 10 = 180
180 x 3 = 540
$540
12:00 pm
20
20 x 30 =
20 x 10 = 200
200 x 3 = 600
$600
1:00 pm
22
22 x 30 =
22 x 10 = 220
220 x 3 = 660
$660
2:00 pm
24
24 x 30 =
24 x 10 = 240
240 x 3 = 720
$720
3:00 pm
26
26 x 30 =
26 x 10 = 260
260 x 3 = 780
$780
4:00 pm
28
28 x 30 =
28 x 10 = 280
280 x 3 = 840
$840
5:00 pm
30
30 x 30 =
30 x 10 = 300
300 x 3 = 900
$900
5:30 pm
31
31 x 30 =
31 x 10 = 310
310 x 3 = 930
$930
$6450
The total value of the Hip-hop 2010 CD sales by 5:30 pm was $6450.
Reflection
6 x 7 = 42
6 x 70 = 420
6 x 700 = 4200
420 ÷ 70 = 6
4200 ÷ 700 = 6
50 x 70 = 3500
50 x 700 = 35 000
500 x 700 = 350 000
35 000 ÷ 70 = 500
350 000 ÷ 700 = 500
4 x 60 = 240
40 x 60 = 2400
40 x 600 = 24 000
24 000 ÷ 60 = 400 240 000 ÷ 600 = 400
30 x 8 = 240
30 x 80 = 2400
30 x 800 = 24 000
24 000 ÷ 80 = 300
•
•
24 000 ÷ 800 = 30
Why do you think that using a calculator to solve multiplication problems is
not always the quickest method? It is quicker to use mental and written
strategies than having to put numbers into a calculator.
Give an example of an algorithm that would be easier to solve not using a
calculator. Supervisor to mark as answers will vary.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
5
Supervisor notes
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
6
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
Did your student:
use mental strategies to multiply
or divide a number by 100 or a
multiple of 10
(NS3.3)
•
use appropriate problem-solving
strategies, including making a table,
in undertaking investigations
(WMS3.2)
•
give a valid reason for supporting
one possible solution over another
(WMS3.4)
with
difficulty
(Tick along line)
with
independently
help
1, 2, 3, 4,
5, 6
4, 5, 6
5, 6
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
•
Activity
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
7
Supervisor notes
Feedback
Student
Help your student
to give feedback
on their learning
for completed
activities.
In this unit I learnt about __________________________________________________
______________________________________________________________________.
You can use a place value chart to ___________________________________________
______________________________________________________________________.
Drawing tables helps me to ________________________________________________.
______________________________________________________________________.
Most of the time it is quicker to use strategies to solve multiplication and division
problems than to use a ___________________________________________________
because _______________________________________________________________.
My favourite activity for this unit was ________________________________________
because _______________________________________________________________.
I had to work hard at _____________________________________________________
because _______________________________________________________________.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
8
Supervisor notes
Student's name:
Checking up
Make sure your
student completes
this work
independently
for return to the
teacher.
Using Maths Tracks, Stage 3B – Unit 31
Numbers: Multiplication and Division
Entry 4: Using Multiples of 10
1
Use your knowledge of number patterns to fill in this table.
x
30
40
60
70
80
90
40
400
4000
Use your knowledge of number patterns to help solve these divisions. For example,
32÷ 4 = 8
3
4
a
63 ÷ 7 =
b
39 ÷ 3 =
c
750 ÷ 50 =
320 ÷ 4 = 80
630 ÷ 7 =
390 ÷ 30 =
7500 ÷ 50 =
3200 ÷ 4 = 800
6300 ÷ 7 =
3 900 ÷ 300 =
75 000 ÷ 50 =
One Australian dollar is worth 5 French francs. How many French francs are there
in:
a
$70 AU?
_________________________________________________
b
$700 AU?
_________________________________________________
c
$7000 AU?
_________________________________________________
d
How many French francs would you need to
buy a chocolate bar worth $1.20?
_______________________________
Solve these problems mentally.
a
A train is carrying sheep.
There are 40 sheep to each carriage.
How many carriages would be
needed for 3600 sheep?
_____________________________
b
34 people paid $20 each to attend a
netball game. How much did the
group pay altogether?
_____________________________
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
9
Supervisor notes
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
2
c
There are 5000 seeds in each packet
of lawn seed. How many seeds are
there in 8 packets?
_____________________________
d
Jasmine used 6000 litres of water on
her new lawn each evening.
How many days had she watered
when she had used a total of
72 000 litres?
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
_____________________________
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
10
Supervisor notes
Stage 3B – Unit 31
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 .................................................................................................. iii
Using this guide ............................................................................ iv
Returns ............................................................................................. iv
Introduction
....................................................................................
..........................................................................................
1
Activity 1
.................................................................................................
4
Activity 2
.................................................................................................
5
Activity 3
.................................................................................................
7
Activity 4
.................................................................................................
9
Activity 5
..............................................................................................
10
Activity 6
..............................................................................................
11
Reflection
.............................................................................................
12
Checking up
.......................................................................................
Student sheets
................................................................................
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
i
13
15
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
review the rules for multiplying and dividing by 10 and 100
•
use the vertical format to solve multiplication problems
•
use a place value chart to solve multiplication and division
problems
Activity 1
•
use a place value chart to solve problems involving multiplication
and division by 10
•
use the vertical format to solve multiplication problems
Activity 2
•
use a table in a Word document to help solve multiplication and
division problems
•
choose similar examples to create number patterns of your own
and solve them using the table
Activity 3
•
review the rules for multiplying and dividing by multiples of 10
•
use knowledge of number patterns to solve problems
Activity 4
•
review the rules for multiplying and dividing by multiples of 10 and
100
•
solve problems involving multiplication and division by 10 and 100
Activity 5
•
use the Make a table problem-solving poster to solve a
multiplication and division problem
Activity 6
•
play a game that involves using strategies to solve multiplication
and division problems
√
√
Reflection
•
discuss why using a calculator to solve multiplication problems
involving large numbers is not always the quickest method
•
solve multiplication and division problems
Checking up
•
make up your own multiplication and division facts that contain
multiples of 10
•
use your knowledge of number patterns to answer multiplication
and division problems
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
ii
Student and supervisor guide
What you need
Activity 2
•
Microsoft Word
•
printer, if available
Activity 3
•
Maths Tracks Student Book Stage 3B, page 40
Activity 4
•
Maths Tracks Student Book Stage 3B, page 41
Activity 5
•
‘Make a table’ Problem-solving poster
Activity 6
•
die
•
2 counters
Words you need to know
division
multiplication
divide
multiply
vertical format
place value
Icons
Record this for the teacher
Return this to the teacher
Use the page in the Maths Tracks Student Book
Page x
Use a computer for this activity
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
iii
Student and supervisor guide
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 sheets 1a and 1b – Multiplying and dividing by 10s
– Activity 1
Student sheet 2 – Multiplication and division patterns – Activity 2
Student sheet 3 – Problem solving – Activity 5
Checking up sheet
personal tape or recording – Reflection and Checking up
Supervisor and Student Feedback sheets
this guide (if the teacher asks for it)
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
iv
Student and supervisor guide
Introduction
Reviewing the rules for multiplying
and dividing by 10 and 100
To multiply a whole number by 10 move every
number across one place value position to the
left and put the zero in the ones column.
Take a look at 42 x 60.
This is easier if we look at it as 42 x 10 x 6.
Th
H
T
O
4
2
Think: 42 x 10 = 420
4
2
0
Then: 420 x 6 = 2520
So 42 x 60 = 2520
To multiply a whole number by 100 move every
number across two place value positions to the
left and put zeros in the ones and tens columns.
For example:
16 x 500 =
16 x 100 x 5
Th
H
T
O
1
6
Think: 16 x 100 = 1600
1
6
0
0
1600 x 5 = 8000
So 16 x 500 = 8000
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
1
Student and supervisor guide
Look at 35 x 200 =
35 x 100 x 2
35 x 100 = 3500
3500 x 2 = 7000
Solve these multiplication questions:
42 x 300 =
25 x 600 =
To divide by 10 or 100 requires an understanding
of place value of whole numbers.
To divide a number by 10 every number moves
back one place value position to the right.
320 ÷ 80 =
This is easier if we look at it as 320 ÷ 10 ÷ 8.
Th
H
T
O
3
2
0
Think: 320 ÷ 10 = 32
Digits move one place to the right.
3
2
32 ÷ 8 = 4
So 320 ÷ 80 = 4
Let’s look at 3200 ÷ 80 =
Think: 3200 ÷ 10 ÷ 8 =
3200 ÷ 10 = 320,
320 ÷ 8 = 40
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
2
Student and supervisor guide
Solve these division problems:
4900 ÷ 70 =
3600 ÷ 40 =
To divide a number by 100 every number moves
two place value positions to the right.
7500 ÷ 500 =
Th
H
T
O
7
5
0
0
Think: 7500 ÷ 100 = 75
7
5
Then 75 ÷ 5 = 15
So 7500 ÷ 500 = 15
Now solve these division algorithms:
3600 ÷ 400 =
Refer to the answer guide
in the Supervisor notes.
81 000 ÷ 300 =
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
3
some
help
no
help
Student and supervisor guide
Activity 1
Multiplying and dividing by 10s
On the place value chart you can see the process
of 80 x 40 = ?
H Th
Th
H
T
O
8
0
8
0
0
2
0
0
T
O
8
0
80 x 40
Multiply by 10
3
Multiply by 4
80 x 40 can also be represented in vertical
format:
80
x 40
3200
On the place value chart you can see the
algorithm 80 ÷ 20 = ? Remember that the
digits move one place to the right when you
divide by 10.
H Th
Th
H
80 ÷ 20
Divide by 10
8
Divide by 2
4
Find Student sheets 1a and 1b and complete the
multiplication and division algorithms using the
place value charts and then using the vertical
format.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
4
Refer to the Answer guide in
the Supervisor notes.
Student and supervisor guide
Activity 2
Multiplication and division patterns
Open a Word document and insert an 8 x 6
table.
Type in the numbers shown in the columns
below.
80 x 3
800 x 3
8000 x 3
=
=
=
63 ÷ 7
630 ÷ 7
6300 ÷ 7
240
2400
24 000
240 ÷ 3
2400 ÷ 3
24 000 ÷ 3
=
=
=
=
=
=
9x7
=
=
=
7 x 40
7 x 400
7 x 4000
=
=
=
280 ÷ 7
=
=
=
90 ÷ 30
900 ÷ 30
9000 ÷ 30
=
=
=
30 x 3
=
=
=
60 x 50
60 x 500
60 x 5000
=
=
=
3000 ÷ 60
=
=
=
Then type the answers to the number
patterns in Column 3.
Use column 4 to continue each pattern.
Use multiplication to check division and
division to check multiplication.
Write the answers in column 6.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
5
80
800
8000
Refer to the Answer guide in
the Supervisor notes.
Student and supervisor guide
Tip: On a Macintosh computer, press option to
get the ÷ symbol.
On a PC select Insert, then Symbol and then
click on the ÷ symbol.
Type in 3 similar examples to create number
patterns of your own in rows 6, 7 and 8.
When you have finished, print your
document and paste it onto Student sheet 2 or
email it to your teacher as an attachment.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
6
some
help
no
help
Student and supervisor guide
Activity 3
Multiplying and dividing by multiples
of 10
Fill in the missing words.
To multiply a whole number by 10, move every
number up one place value to the ___________
and put the zero in the _________ column.
To multiply a whole number by 100, move every
number up two place value positions to the
left and put the ______ in the ones and _____
columns.
To divide a number by 10, every number moves
back _______ place value position to the
_______.
To divide a number by 100, every number moves
back _______ place value positions to the
________.
Find page 40 in the Maths Tracks Student Book.
1
Use your knowledge of number patterns to
solve the problems. Don’t forget to multiply
or divide by 10, 100 or 1000 first.
2
Read the question carefully. Treat the
algorithms separately from the doubling or
halving part of the question. For example,
double 40 then add 6 x 60 = 80 + 360 =
440.
3
Fill in the table using your knowledge of
number patterns. You should see a pattern
involving the number of zeros.
Page 40
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
7
Student and supervisor guide
4
Solve the number wheel problems. Don’t
forget to multiply or divide by 10 or 100
first.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
8
some
help
no
help
Student and supervisor guide
Activity 4
Multiplying and dividing by 10 and
100
Find page 41 in the Maths Tracks Student Book.
Page 41
1
Fill in the table. Remember to multiply by
10, 100 or 1000 first.
2
Solve the division problems. Don’t forget to
divide by 10 or 100 first.
3
Read each question carefully. In part b, you
might want to multiply 3600 by 20 and then
by 4, and then add these together, rather
than multiplying by 24.
4
Divide each number by 70. Don’t forget
to divide by 10 first. Use a $ sign in your
answers for Australian dollars.
5
Multiply each amount by 70. Remember to
multiply by 10 first. Make sure you write
your answer in yen not dollars.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
9
some
help
no
help
Student and supervisor guide
Activity 5
Problem solving
Find the ‘Make a Table’ problem-solving poster
and use it to help you solve the following
problem.
A new CD Hip-hop 2010 has just been released.
Bonus Discs opened at 9:00 am. They sold
16 copies of Hip-hop 2010 in the first hour, 18
copies in the second hour and 20 copies in the
third hour.
If the number of copies of Hip-hop 2010 sold in
an hour increased by two every hour, and each
CD cost $30, what was the total value of the
sales when Bonus Discs closed at 5:30 pm?
us
n
o
B
c
Dis
s
0
3
$
Find Student sheet 3 and draw the table you
would use to solve this problem.
Refer to the answer guide in
the Supervisor notes.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
10
some
help
no
help
Student and supervisor guide
Activity 6
Demon Racers
Find Student sheet 4 and play Demon Racers
with your supervisor.
You will need:
•
1 die
•
1 counter each
•
paper and pencils
Aim:
•
To be the first to reach the finish or score
exactly 100 000.
How to play:
•
Both players place their counters on Start.
•
Take turns to roll the die and move the
number of spaces shown.
Then either:
Stay on that space and record the number
of points shown; for example, if you roll 3
and land on ‘2700 x’ keep the 2700 points
or;
Use the number on the die to complete the
number sentence;
2700 x 3 = 8100 points.
•
If you complete the number sentence, you
record the points but move back to Start.
•
Both players keep progressive totals on a
piece of paper.
•
Continue until one player reaches the Finish
by tossing the exact number, or until one
player reaches 100 000 points.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
11
some
help
no
help
Student and supervisor guide
Reflection
Using multiples of 10 and 100
Fill in the following table by solving the
multiplication and division problems.
6x7=
6 x 70 =
6 x 700 =
420 ÷ 70 =
4200 ÷ 700 =
50 x 70 =
50 x 700 =
500 x 700 =
35 000 ÷ 70 =
350 000 ÷ 700 =
4 x 60 =
40 x 60 =
40 x 600 =
24 000 ÷ 60 =
240 000 ÷ 600 =
30 x 8 =
30 x 80 =
30 x 800 =
24 000 ÷ 80 =
24 000 ÷ 800 =
Record your answers to the following questions
for your teacher.
Why do you think that using a calculator to
solve multiplication problems is not always
the quickest method?
Give an example of an algorithm that would
be easier to solve not using a calculator.
Did you find any of the algorithms on the
table hard to solve without a calculator?
Why or why not?
Stop the recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
12
some
help
no
help
Student and supervisor guide
Checking up
Record this for your teacher.
Look at the number 4800. Tell your teacher a
multiplication fact and a division fact using 4800.
Each fact must contain a multiple of 10.
It is expected that your
voice may be heard
prompting and praising your
student.
Show your working out in the box below.
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 you 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 31
© NSW DET 2006
13
some
help
no
help
Student and supervisor guide
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
14
Student and supervisor guide
Name:
Multiplying and dividing by 10s
Activity 1
Use the place value chart and then vertical format to solve these
multiplication problems: 60 x 90, 50 x 60 and 70 x 80.
The first one has been done for you.
H Th
Th
H
T
O
6
0
6
0
0
5
4
0
0
H Th
Th
H
T
O
H Th
Th
H
T
O
60 x 90
x 10
x9
Vertical format:
50 x 60
Vertical format:
70 x 80
Vertical format:
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
15
Student sheet 1a
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
16
Student sheet 1a
Name:
Multiplying and dividing by 10s
Activity 1
Use the place value chart to solve these division problems:
150 ÷ 50,
490 ÷ 70,
720 ÷ 90.
H Th
Th
H
T
O
H Th
Th
H
T
O
H Th
Th
H
T
O
150 ÷ 50
490 ÷ 70
720 ÷ 90
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
17
Student sheet 1b
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
18
Student sheet 1b
Name:
Multiplication and division patterns
Activity 2
Paste your Word document onto this page.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
19
Student sheet 2
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
20
Student sheet 2
Problem solving
Activity 5
Draw your table on this page.
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
21
Student sheet 3
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
22
Student sheet 3
Demon Racers
Activity 6
9000
2500
2700
7000
6200
1500
4800
4200
Using Maths Tracks, Stage 3B, Unit 31
© NSW DET 2006
23
Student sheet 4
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
3600
Using Maths Tracks, Stage 3B, Unit 31
© 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