Maths K–6
Stage 3A
Stage 3A – Unit 53
Number
Multiplication and Division
Entry 7: Written Multiplication
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3A 43834
Centre for Learning Innovation
Number: 43834
Title: Using Maths Tracks Stage 3A Unit 53
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 p 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
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:
Desktop Publishing:
Averil Griffith
Sally Watts, Rae Lister
Barbara Gurney, 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 3A – Unit 53
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
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:
•
multiplying three-digit and four-digit numbers by one-digit numbers using mental or
written strategies.
Prior knowledge
•
•
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.
Language
times, algorithm, factors, product, multiply, multiplication.
What is needed
Activity 3
•
Maths Tracks Student Book Stage 3A, page 45
•
MAB materials
Activity 4
•
Maths Tracks Student Book Stage 3A, page 46
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
1
Teacher notes
Activity 5
•
Guess and check problem-solving poster
Reflection
•
Real Estate section of a newspaper
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
Reflection – for all students
Checking up – for all students
Interactivity
Activity 5: In a satellite lesson students could discuss how they solved the problem.
Did they use the Guess and check strategy?
Did they use any other strategies?
Was there more than one answer?
How did they find the answer?
What made the activity difficult?
Resources
Add any you find suitable:
Websites
Check all websites before recommending them to students.
Go into the pre-made activities. Choose 4th Grade then go to Multiplication and choose
appropriate multiplication activities. Look at multiplication of 2-digit numbers by 1-digit
numbers. <www.mathfactcafe.com/home/>
Add more:
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
2
Teacher notes
Returns
Student sheet 1 – Written Multiplication – Introduction
Student sheet 2 – Written Multiplication – Activity 1
Student sheet 3 – Expanded notation – Activity 2
Student sheet 4 – Problem-solving – Activity 5
Student sheet 5 – Reflection
Checking up sheet
personal tape or recording – Activity 5, Reflection
Supervisor and Student Feedback sheets
the guide (if you wish to ask for it)
Checking up answers
21
1
a
563
x4
2252
b
484
x7
3388
c
833
x6
4998
d
347
x9
3123
a
746
x8
5968
52
11
46
34
2
Check:
700 x 8 + 40 x 8 + 6 x 8
5600 + 320 + 48 = 5968
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
3
Teacher notes
41
b
472
x6
2832
Check:
400 x 6 + 70 x 6 + 2 x 6
2400 + 420 + 12 = 2832
13
c
839
x4
3356
Check:
800 x 4 + 30 x 4 + 9 x 4
3200 + 120 + 36 = 3356
53
d
385
x7
2695
Check:
3
300 x 7 + 80 x 7 + 5 x 7
2100 + 560 + 35 = 2695
Check that the number story problem matches the algorithm and the way the
student has checked their answer.
a
750
b
1120
c
2190
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3A – Unit 53
Number: Multiplication and Division
Entry 7: Written Multiplication
Circle the numbers of the activities the student completed.
1
2
3
4
5
The student:
Indicator
multiplied three-digit and fourdigit numbers by
one-digit numbers using
mental or written strategies
(NS3.3)
•
selected an appropriate
strategy for the solution of a
multiplication problem
(WMS3.2)
•
gave a valid reason for a
solution to a multiplication
problem
(WMS3.4)
Comment
1, 2, 3, 4,
5
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
4, 5
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
•
Activity
5
5
Teacher notes
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
6
Teacher notes
Maths K–6
Stage 3A – Unit 53
Number
Multiplication and Division
Entry 7: Written Multiplication
Supervisor notes
and
Student and supervisor guide
P/M 3A 43834
Centre for Learning Innovation
Number: 43834
Title: Using Maths Tracks Stage 3A Unit 53
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 p 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
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:
Desktop Publishing:
Averil Griffith
Sally Watts, Rae Lister
Barbara Gurney, 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 3A – Unit 53
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
Preparation
Words you need to know.
Your student’s teacher may have selected the appropriate activities from 1 to 5 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
Activity 5 - can provide extra challenge
Reflection and Checking up – for all students.
Using Maths Tracks, Stage 3A, Unit 53
© 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
Estimate the answer first:
300 x 6 = 1800
Use expanded notation to find the answer:
200 x 6 + 90 x 6 + 5 x 6
1200 + 540 + 30
1770
Now use the written form (formal algorithm) to show 295 x 6:
53
295
x6
1770
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
2
Supervisor notes
Introduction – Student sheet 1
Algorithm
Estimation
18 x 5
20 x 5 = 100
= 10 x 5 + 8 x 5
= 50 + 40
= 90
75 x 8
80 x 8 = 640
= 70 x 8 + 5 x 8
= 560 + 40
= 600
54 x 7
50 x 7 = 350
= 50 x 7 + 4 x 7
= 350 + 28
= 378
98 x 6
100 x 6 = 600
= 90 x 6 + 8 x 6
= 540 + 48
= 588
484 x 2
500 x 2 = 1000
= 400 x 2 + 80 x 2 + 4 x 2
= 800 + 160 + 8
= 968
325 x 3
300 x 3 = 900
= 300 x 3 + 20 x 3 + 5 x 3
= 900 + 60 + 15
= 975
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
Expanded notation
(mental)
3
Formal
algorithm
(written)
4
18
x5
90
4
75
x8
600
2
54
x7
378
4
98
x6
588
1
484
x2
968
1
325
x3
975
Supervisor notes
Activity 1 – Student sheet 2
Algorithm
Estimation
57 x 6
60 x 6 = 360
= 50 x 6 + 7 x 6
= 300 + 42
= 342
63 x 5
60 x 5 = 300
= 60 x 5 + 3 x 5
= 300 + 15
= 315
346 x 2
350 x 2 = 700
= 300 x 2 + 40 x 2 +
6x2
= 600 + 80 + 12
= 692
346
x2
692
117 x 5
120 x 5 = 600
= 100 x 5 + 10 x 5 +
7x5
= 500 + 50 + 35
= 585
117
x5
585
833 x 3
800 x 3 = 2400
= 800 x 3 + 30 x 3 +
3x3
= 2400 + 90 + 9
= 2499
1325 x 3
1300 x 3 = 3900
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
Expanded notation
(mental)
= 1000 x 3 + 300 x
3 + 20 x 3 + 5 x 3
= 3000 + 900 +
60 + 15
= 3975
4
Formal
algorithm
(written)
4
57
x6
342
1
63
x5
315
1
3
833
x3
2499
1
1325
x3
3975
Supervisor notes
Activity 2 – Student sheet 3
Problem
H
Plus
T
Plus
Ones
Equals
57 x 5
50 x 5 = 250
+
7 x 5 = 35
285
81 x 3
80 x 3 = 240
+
1x3=3
243
38 x 9
30 x 9 = 270
+
8 x 9 = 72
342
48 x 3
40 x 3 = 120
+
8 x 3 = 24
144
58 x 9
50 x 9 = 450
+
8 x 9 = 72
522
293 x 3
200 x 3 = 600
+
90 x 3 = 270
+
3x3=9
879
369 x 7
300 x 7 = 2100
+
60 x 7 = 420
+
9 x 7 = 63
2583
419 x 4
400 x 4 = 1600
+
10 x 4 = 40
+
9 x 4 = 36
1676
501 x 7
500 x 7 = 3500
+
1x7=7
3507
Activity 4
2 1
142
x7
$994
Activity 5 – Student sheet 4
2
2
9403
x7
65821
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
5
Supervisor notes
Using Maths Tracks, Stage 3A, Unit 53
© 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
Activity
•
multiply three-digit and four-digit
numbers by one-digit numbers
using mental or written strategies
(NS3.3)
1, 2, 3, 4, 5
•
select an appropriate strategy for
the solution of a multiplication
problem
(WMS3.2)
4, 5
•
give a valid reason for a solution to
a multiplication problem
(WMS3.4)
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
with
difficulty
(Tick along line)
with
independently
help
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Did your student:
5
7
Supervisor notes
Feedback
Student
Help your student
to give feedback
on their learning
for completed
activities.
In this unit I learnt how to _________________________________________________
______________________________________________________________________.
The extend and multiply strategy is when you __________________________________
______________________________________________________________________.
Written multiplication is often referred to as a _________________________________
______________________________________________________________________.
Expanded notation in multiplication is when ___________________________________
______________________________________________________________________.
Using Maths Tracks, Stage 3A, Unit 53
© 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 3A – Unit 53
Multiplication and Division: Addition and Subtraction
Entry 7: Written Multiplication
2
Write the algorithm that matches each expanded notation statement.
Then solve the problem.
a
500 × 4 + 60 × 4 + 3 × 4 =
b
400 × 7 + 80 × 7 + 4 × 7 =
c
800 × 6 + 30 × 6 + 3 × 6 =
d
300 × 9 + 40 × 9 + 7 × 9 =
Rewrite each multiplication problem using the formal written algorithm,
then solve it. Use expanded notation to check each answer.
a
746 x 8 =
Check:
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
9
Supervisor notes
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
1
b
472 x 6
Check:
c
839 x 4
Check:
d
385 x 7
Check:
Create a story problem for each algorithm below.
Solve the problem and show how you check the answer.
Algorithm
Problem
Check
125
x6
280
x4
365
x6
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
10
Supervisor notes
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
3
Stage 3A – Unit 53
Student and supervisor guide
Unit contents
About this unit ....................................................................................... ii
What you’ll do ................................................................................... ii
What you need ................................................................................ iii
Preparation ........................................................................................ 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 ................................................................................................. 10
Activity 5 ................................................................................................. 12
Reflection ................................................................................................ 13
Checking up .......................................................................................... 14
Student sheets ................................................................................... 15
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
i
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
revise the vertical format for multiplication by aligning the digits in
columns for hundreds, tens and ones
•
expand the number and multiply
•
calculate using a formal algorithm
•
revise rounding to assist estimation
Activity 1
•
calculate a formal algorithm on a place-value chart
•
calculate multiplication of two- and three-digit numbers by a single
digit using extend and multiply strategy (long multiplication)
Activity 2
•
answer algorithms using expanded notation
Activity 3
•
revise expanded notation of three-digit numbers
•
review multiplying the ones, tens and hundreds
•
show how you exchanged when multiplying 3-digit numbers by a
single digit in a formal algorithm
•
use extend and multiply strategy to calculate algorithms
•
round to estimate the answers to problems and then calculate
using a formal algorithm
Activity 4
•
revise underlining important data to find which process can be
used to solve a problem
•
use a formal algorithm to solve problems and then check using
estimation
•
use extend and multiply to check answers to formal algorithms
•
find missing numbers in formal algorithms
•
use extend and multiply strategy to solve problems and check
answers using estimation
Activity 5
•
use the Guess and check problem-solving poster to solve a
multiplication problem
√
√
Reflection
•
calculate the rent for two rental properties from 1 month to 12
months
•
compare the rent prices, calculating the difference over 12 months
Checking up
•
use expanded notation to solve the problem
•
use the formal algorithm to solve a multiplication problem and
check using expanded noation
•
create a story problem for given algorithms
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
ii
Student and supervisor guide
What you need
Activity 3
•
Maths Tracks Student Book Stage 3A, page 45
•
MAB materials
Activity 4
•
Maths Tracks Student Book Stage 3A, page 46
Activity 5
•
Guess and check problem-solving poster
Reflection
•
Real Estate section of a newspaper.
Preparation
For the Reflection activity your student needs the real estate section of a
newspaper. The teacher may provide a copy of the real estate section if
you are unable to purchase one.
Words you need to know
times
algorithm
factors
product
multiply
multiplication
expanded notation
extend
estimate
TARNELLA
PARANELL
0761 947 231
0374 753 469
MONTVIEW
NORTHALL
0534 975 396
0514 754 906
Icons
TARNELLA
Record this for the teacher.
Return this to the teacher.
0761 947 231
EAST PARKVILLE
0552 875-428
Use the page in the Maths Tracks Student Book.
Page x
Use a computer for this activity.
Using Maths Tracks, Stage 3A, Unit 53
© 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.
Returns
Student sheet 1 – Written Multiplication – Introduction
Student sheet 2 – Written Multiplication – Activity 1
Student sheet 3 – Expanded notation – Activity 2
Student sheet 4 – Problem-solving – Activity 5
Student sheet 5 – Reflection
Checking up sheet
personal tape or recording – Activity 5, Reflection
Supervisor and Student Feedback sheets
this guide (if your teacher asks for it)
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
iv
Student and supervisor guide
Introduction
In this unit you will learn how to multiply
two-digit, three-digit, and four-digit numbers
by one-digit numbers using mental and written
strategies.
Written strategies are often called formal
algorithms and they are usually written in a
vertical format.
323
x4
Using the formal algorithm method:
•
To answer this using the formal algorithm you
need to multiply 3 ones x 4, which equals 12
ones, place the 2 ones in the ones column and
exchange the ten.
Now multiply 4 x 2 tens which equals 8 tens
plus one ten equals 9 tens. Place the 9 in the
tens column.
Now multiply the 3 hundreds x 4, which equals
12 hundreds. Place 2 in the hundreds column
and the 1 in the thousands column.
1
323
x4
1292
•
•
You can use MAB
materials to show this
algorithm.
1
2
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
9
2
1
Student and supervisor guide
When we use a place-value chart it can help
us to understand what is happening in the
algorithm:
Th
1
H
T
O
3
2
x
3
4
2
9
2
1
A mental strategy for multiplying larger numbers
is the expanded notation method.
Always estimate an
answer first as this will
tell you if your calculation
is correct.
To answer the same algorithm mentally you
need to expand the hundreds, then tens and
then the ones.
323 x 4
= 300 x 4 + 20 x 4 + 3 x 4
= 1200 + 80 + 12
= 1292
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
2
Student and supervisor guide
Look at 295 x 6 =
Estimate the answer first and write it below.
Show below how you use the expanded notation
method to find the answer.
Now write the formal algorithm to show
Refer to the answer guide
in the Supervisor notes.
295 x 6 =
Let’s have a go at multiplying a four-digit
number by a one-digit number!
We’ll use estimation, the expanded notation
method as well as the formal algorithm.
2145 x 7 =
Using estimation: 2100 x 7 = 14 700
(if you rounded to the nearest thousand it would
be 14 000)
Using the expanded notation method:
2145 x 7 = 2000 x 7 + 100 x 7 + 40 x 7
+ 5 x 7 = 14 000 + 700 + 280 + 35
= 15 015
Extended form:
2145
x7
35
280
700
14000
15015
The extended form
is usually used when
multiplying numbers by 2
or more digits.
(7 x 5 ones)
(7 x 4 tens)
(7 x 1 hundred)
(7 x 2 thousand)
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
3
Student and supervisor guide
Using the place-value chart and formal algorithm
you can see more clearly the exchanging:
T Th
Th
1
1
H
T
3
3
O
2
1
4
x
5
7
5
0
1
5
Using the formal written algorithm:
•
Multiply the ones first, 5 ones x 7 = 35.
Place the 5 ones in ones column and exchange
the 3 tens above the 4 into the tens column.
Multiply the tens, 4 tens x 7 = 28 tens, add the
3 tens equals 31 tens. Place the 1 in the tens
column and exchange the 30 tens
(3 hundreds) above the 1 in the hundreds
column.
Multiply the hundreds, 1 hundred x 7 = 7
hundreds, add the 3 hundreds which equals 10
hundreds (1 thousand).
Place the 0 in the hundreds column and
exchange the 1 thousand above the 2 in
thousands column.
Multiply the thousands, 2 thousand x 7 = 14
thousand, add the 1 thousand which equals 15
thousand. Place the 5 in the thousands column
and 1 in the Ten thousands column.
The answer is 15 015.
1 3 3
2145
x
7
15015
•
•
When using the formal
algorithm multiply the
ones first, then tens,
then hundreds and so
on.
•
•
Find Student sheet 1 and find the answers to the
algorithms using estimation, expanded notation
and the formal algorithm.
Refer to the answer guide in
the Supervisor notes.
Feedback:
lots of
help
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
4
some
help
no
help
Student and supervisor guide
Activity 1
Written Multiplication
Often placing an algorithm on a place-value
chart helps us to understand what is happening
when we multiply using a formal algorithm.
Look at 46 x 3 on the place-value chart.
H
T
1
1
O
4
x
6
3
3
8
The formal algorithm looks like this:
1
46
x3
138
•
Multiply the ones first, 3 x 6 ones = 18 ones.
Place the 8 in the ones column and exchange
the ten above the 4 in the tens column.
Multiply the tens,
3 x 4 tens = 12 tens, plus 1 tens equals,
13 tens. Place the 3 in the tens column and the
1 in the hundreds column.
The answer is 138.
•
•
You can also work out a written multiplication
algorithm using the extend and multiply method.
Estimate: 50 x 3 = 150
Extended form:
46
40
6
=
+
x3
x3
x3
120
18 = 138
Extended multiplication
is usually used when
multiplying numbers by 2
or more digits.
It can be set out like this.
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
5
Student and supervisor guide
Find Student sheet 2 and answer the algorithms
using estimation, extend and multiply and the
formal written algorithm.
Refer to the answer guide
in the Supervisor notes.
You can use the extend
and multiply form to solve
a multiplication algorithm.
Feedback:
lots of
help
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
6
some
help
Student and supervisor guide
no
help
Activity 2
Expanded Notation
Expanded notation is used when we multiply the
tens and ones.
The idea behind this strategy is to break up
numbers into other groups that are easier to
multiply.
It is an excellent way to do multiplication
mentally.
For example, let’s look at 57 multiplied by 5.
You can break up the difficult looking number
57 into its tens and ones: 50 and 7.
You can then work out 50 times 5, and 7
times 5.
Emphasise to your student
that the formal algorithm
is a written strategy for
solving multiplication and
the expanded notation
method will help them solve
a multiplication problem
mentally.
I know 5 x 5 is 25 so 50 times 5 is 250.
7 x 5 is 35.
I would then add 250 and 35 together to get
my answer: 285
It can also look like this:
57 x 5 = 50 x 5 + 7 x 5
= 250 + 35 = 285
= 85
Find Student sheet 3 and answer the algorithms
using expanded notation.
Refer to the answer guide in
the Supervisor notes.
142 x 7 = 100 x 7 + 40 x
7+2x7
= 700 + 280 + 14
= 994
Feedback:
lots of
help
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
7
some
help
Student and supervisor guide
no
help
Activity 3
We use expanded notation to answer algorithms
mentally. It is also a good way of checking if a
formal algorithm is correct.
Encourage your student
to use this method when
solving multiplication
problems mentally.
Look at the example 352 x 4
300 x 4 + 50 x 4 + 2 x 4
1200
+ 200
+ 8
=
1408
Now let’s look at solving the three–digit problem
using a formal written algorithm.
2
352
x4
1408
•
•
•
Multiply the ones first, 4 x 2 ones = 8 ones.
Multiply the tens,
4 x 5 tens = 20 tens. Place the 0 in the tens
column and exchange the 2 into the hundreds
column.
Multiply the hundreds, 4 x 3 hundreds = 12
hundreds, plus 2 hundreds equals 14 hundreds.
Place the 4 in the hundreds column and the 1 in
the thousands column.
You can use MAB materials to show this
algorithm:
14 hundreds
0 tens
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
8 ones
8
Student and supervisor guide
Find page 45 in the Maths Tracks Student Book.
Page 45
1
Draw the MAB materials to show how
you traded. You may need to do this on
a separate piece of paper. Solve each
problem using the formal algorithm method.
2
Use the example to help you extend the
numbers and multiply.
3
Use rounding to estimate the answers then
solve using the formal algorithm method.
4
You will need to extend the numbers to
help solve the problems. Do this in the box
below as there is not enough working out
space. Then write your answers in the table
in the Maths Tracks Student Book.
Check your student’s
algorithms when they use
MAB materials.
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 3A, Unit 53
© NSW DET 2006
9
some
help
no
help
Student and supervisor guide
Activity 4
Underlining important information in
multiplication problems.
Underline the information that you think is
important in the following problem:
Christmas tree light sets cost $142 each.
I bought 7 sets. How much did I pay?
Check that your student
underlines $142 each, 7
sets and How much.
Now work out the answer using a formal
algorithm:
Refer to the answer guide
in the Supervisor notes.
Find page 46 in the Maths Tracks Student Book.
Page 46
1
Solve the problems using the formal
algorithm method and then use estimation
to check your answer.
2
Extend the numbers and multiply.
Look at Task 2 on page 45 in the Maths
Tracks Student Book if you are not sure how
set out the extend and multiply method.
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
10
Student and supervisor guide
3
You can use estimation to help you guess
and check the answers to the missing
numbers. The algorithms in the book aren’t
lined up in place-value columns.
4
Choose a multiplication method to answer
the questions. Don’t forget to underline the
important information first.
Your student may choose
the formal algorithm, the
extend and multiply or the
expanded notation method.
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 3A, Unit 53
© NSW DET 2006
11
some
help
no
help
Student and supervisor guide
Activity 5
Problem-solving
Find the Guess and check problem-solving
poster and Student sheet 4 and solve the
number problem.
?
?
Record your answers to the following questions
for your teacher.
•
•
•
Did you use the ‘Guess and check’ strategy?
If not what strategy did you use?
How did you find the answer?
What did you find that was difficult?
Stop recording now.
?
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
?
12
?
Refer to the answer guide
in the Supervisor notes.
Student and supervisor guide
Reflection
Calculating rental prices
This activity shows you a practical way of using
maths in real-life situations.
NORTHALL
0596 539 687
Find Student sheet 5.
Find the real estate section from a newspaper
or the copy of a newspaper provided by your
teacher.
Find ‘Rental Properties’, cut out two properties
and paste onto the table on Student sheet 6.
Most rents are per week so you will have to
multiply the amount by four to get the monthly
rent.
Write that rent amount beside one month for
both properties.
Continue calculating the rent on the table.
PARANELL
0374 753 469
Your student should
find two properties with
different rents.
NORTHALL
0534 975 396
MONTVIEW
Compare rent prices, calculating the difference
over 12 months.
0514 754 906
Record your answers to the following questions
for your teacher.
•
•
•
•
•
•
What was the difference in rent prices over
12 months?
Which rental property was cheaper over 12
months?
How much money would you save renting
the cheaper property?
Why would a person need to know this sort
of information?
Did you need to write the formal written
algorithm or were you able to use expanded
notation to complete the task mentally?
What other strategy did you use?
Stop the recording now.
TARNELLA
0761 947 231
EAST PARKVILLE
0552 875-428
WEST PARKVILLE
0918 975- 239
Feedback:
lots of
help
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
13
some
help
no
help
Student and supervisor guide
Checking up
Record this for your teacher.
Stop the recording now.
Complete the Checking up sheet and, with help,
fill in the feedback sheet.
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.
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
14
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.
Student and supervisor guide
Student's name:
Written Multiplication
Introduction
Estimate, use expanded notation and then the formal algorithm to
answer the following algorithms:
Algorithm
Estimation
18 x 5
Expanded notation
method (mental)
10 x 5 + 8 x 5
= 50 + 40
= 90
Formal
algorithm
(written)
4
18
x5
90
75 x 8
54 x 7
98 x 6
484 x 2
325 x 3
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
15
Student sheet 1
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
16
Student sheet 1
Student's name:
Written Multiplication
Algorithm
Estimation
57 x 6
360
Activity 1
Expanded notation
method (mental)
50 x 6 + 7 x 6
= 300 + 42
= 342
Formal
algorithm
(written)
4
57
x6
342
63 x 5
346 x 2
117 x 5
833 x 3
1325 x 3
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
17
Student sheet 2
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
18
Student sheet 2
Student's name:
Expanded notation
Problem
H
Plus
57 x 5
Activity 2
T
Plus
Ones
Equals
50 x 5 = 250
+
7 x 5 = 35
285
81 x 3
38 x 9
48 x 3
58 x 9
293 x 3
369 x 7
419 x 4
501 x 7
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
19
Student sheet 3
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
20
Student sheet 3
Student's name:
Problem-solving
Activity 5
Use the digits 0-9 to fill in the boxes to make the calculation correct.
All ten numbers are used only once.
Handy hints:
1
Don’t give up!
9
x
5
2
3
4
5
6
7
7
2
Use Guess and check strategy.
You can’t have 0 in the ones place of the multiplicand (the number
being multiplied) as you would get a zero in the product also.
You can’t have 1 in the ones place of the multiplicand as you would
get a repeat of the number 7.
Do not try to work it out with a calculator, as the exchange of
numbers is important.
Write the numbers 0-9 above the problem and cross them off as you
use them.
You may need to try several times so use scrap paper for working
out.
Return to Activity 5 to record for the teacher.
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
21
Student sheet 4
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
22
Student sheet 4
Student's name:
Reflection
Real estate rental tables
Property 1
(Paste here)
Rent
amount
Property 2
(Paste here)
1 month
1 month
2 months
2 months
3 months
3 months
4 months
4 months
5 months
5 months
6 months
6 months
7 months
7 months
8 months
8 months
9 months
9 months
10 months
10 months
11 months
11 months
12 months
12 months
Rent amount
Calculate the difference in rent prices over 12 months:
Check:
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
23
Student sheet 5
Using Maths Tracks, Stage 3A, Unit 53
© NSW DET 2006
24
Student sheet 5
Centre for Learning Innovation
NSW Department of Education and Training
51 Wentworth Road
Strathfield NSW 2135