Page 1 of 25
Cambridge Essential Mathematics / HOTmaths Integrated program
for the Australian Curriculum Year 7
1 Aims of the program and suggestions for use
Cambridge HOTmaths teacher and student subscriptions are available to bundle with the
Cambridge Essential Mathematics for the Australian Curriculum textbook series. This program
integrates the content of the two resources, suggesting which HOTmaths topics, lessons, widgets,
walkthroughs and HOTsheets could be used with the textbook topics. It is provided for the use of
teachers and students (and parents).
A Cambridge HOTmaths student account allows students to use the full range of HOTmaths
content in class or at home, and enables the teacher to use the PROGRESS TRACKER (a
learning management system) to monitor students’ work and topic quiz scores. (Parents can also
track their own child’s work). This makes it an ideal homework and revision resource.
A Cambridge HOTmaths teacher account allows HOTmaths to be run on one computer in a
classroom, and is particularly useful when delivered via data projectors and interactive
whiteboards.
Examples of activities which can be done with
student accounts on individual computers at
home or in class:
 Revisit work from earlier terms or years
where requisite prior knowledge is lacking.
 Do a HOTmaths lesson as homework to
prepare for a lesson using the textbook.
 Do a TOPIC QUIZ or a test from the TEST
GENERATOR (new in 2011) as homework
or classwork.
 Do SCORCHER quizzes for homework, or
when other assignments have been finished
early.
 Do a HOTmaths lesson to catch up on
missed work.
 Revise and prepare for tests and exams
using HOTmaths lessons.
 Try the alternative approach of an
interactive WIDGET or WALKTHROUGH
when having difficulty grasping a concept
or learning a skill.
 Use the DICTIONARY to test and reinforce
understanding of mathematical terminology
and use the links provided to see
mathematical terms in use.
 Match work to ability levels.
Suggestions of types of activities to do in class
(which can be accomplished with a teacher
account):
 Revise work from earlier years.
 Display an interactive WIDGET in class to
illustrate a concept.
 After going through a widget, print out
multiple copies of an accompanying
HOTSHEET to work through
 Display a interactive WALKTHROUGH
example for the class to suggest answers for
the embedded questions.
 Use the TEST GENERATOR (new in
2011) to print out a test to do on paper
 Display and discuss the HOTmaths lesson
notes as an alternative to the textbook topic
introduction.
 Set advanced students to work as a group
on higher level HOTmaths activities while
the rest of the class tackles
foundation/standard work.
 Set foundation-level students to work as a
group revisiting previous work (including
previous years) while the rest of the class
tackles other work.
Notes: The HOTmaths lessons contain other resources which teachers may prefer to use instead of
or in addition to those listed in this program. The lessons accessed via the HOTmaths/Essential maths
menu are selected from HOTmaths’ lesson database. The last column in the program shows the
names which the lessons have in HOTmaths’ standard menu.
Please notify any errors in this draft or provide feedback to: rparry@cambridge.org
The exact design and appearance of the menus and lessons may change.
Check periodically for updates to this program at:
www.cambridge.edu.au/hotmaths or www.cambridge.edu.au/go
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 2 of 25
2 How to use the integrated program
From Term 1 2011, the HOTmaths menus will allow you to select Essential Maths and the year
level. You will then be offered a menu based on the structure of the textbook.
1
In the textbook, note the topic/lesson
number of the section you are in
(1.3 in this case).
The HOTmaths icon indicates there
is linked content for the topic.
2
Log on to HOTmaths and choose
Essential Maths and the year level
and the chapter (topic).
3
Choose the lesson number.
Where more than one
HOTmaths lesson links to
a textbook lesson the latter is
divided into parts A, B, C, etc.,
as in the case of 1.3.
4
The matching HOTmaths lesson will open under the textbook headings:
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 3 of 25
Notes
1
Purpose of this document Although it will not be necessary to use this document to
navigate to the right HOTmaths lesson, teachers should still check it for notes on the
widgets, walkthroughs and HOTsheets to use.
2
HOTmaths lessons For the Progress Tracker and other features to work, all widgets,
walkthroughs and HOTsheets have to be accessed from within HOTmaths lessons. In
the Essential Maths program these are the same as HOTmaths’ ‘native’ lessons, as
shown in column 4 of the program. Having been written independently of the textbooks,
they may include some higher or lower level material.
3
Overlap between years HOTmaths’ content is structured on two-year levels whereas
the AC and Essential Maths is structured on single years, so some HOTmaths lessons
are used with both Year 7 and 8 of Essential Maths. In most cases this program suggests
an allocation of different widgets, walkthroughs and HOTsheets in a shared lesson to
each year, but there is also some repetition of resources.
4
HOTmaths questions and tests The questions and tests are based on the complete
HOTmaths lesson. Because not all of the lesson is aligned with Essential Maths, before
doing HOTmaths questions and tests, teachers are advised to check their scope and
levels.
5
Time allocation for the lessons This program is an integration of content rather than
time. The textbook and integrated program together contain more material than can be
covered in a year. HOTmaths lessons have been selected not for what will fit a the time
available, but for the fit of their content with the textbook content. Teachers will still
need to select material to fit the periods and homework time available. It is envisaged
that teachers might use the textbook more for some topics and HOTmaths more for
others, so that students are exposed to a balance of textbook-style and interactive
resources. The large size of the resource also ensures that all abilities and all learning
styles are catered for.
6
Frequent updates HOTmaths is a dynamic resource which is continually updated, and
during 2011 coverage of the AC will be strengthened, and this will be reflected in
updated versions of this program.
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 4 of 25
3 Cambridge Essential Mathematics Year 7 / HOTmaths Integrated Program
Key (note that HOTmaths may be abbreviated to Hm)
NUMBER AND ALGEBRA Australian Curriculum strand
Widgets (interactives)
Number and place value
Substrands
1.1 Number systems
Textbook lesson/topic numbers/titles, also
used in the HOTmaths Essential Maths
menu
Walkthroughs–-interactive
examples–-‘WT’ for short
Subtitle used where more than one
HOTmaths lesson links to textbook lesson
HOTsheets (worksheets)
A Egyptian & Mayan
1.4 Addition & subtraction Grey shading and font indicates a textbook lesson, e.g. 1.4, that employs resources
algorithms
from a HOTmaths unit already linked in the menu to a previous textbook lesson. Users
are directed to the previous lesson to access the resources, 1.3 in this example.
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
CHAPTER 1: WHOLE NUMBERS — NUMBER AND ALGEBRA Number and place value
1.1 Number systems
A Egyptian &
Mayan
Egyptian numbers
WT1 Translate Egyptian
B Roman & Greek
Arithmetic in Ancient Rome
WT1 Years between dates
WT2 Translate Roman
1.2 Place value
Number reader
Making numbers
Lesson: do Egyptian
only, and Mayan
system (Widget 2 and
WT2) as enrichment.
Remind students that
Hindu-Arabic refers to
the modern system.
WHOLE NUMBERS:
Egyptian & Mayan
numerals
Lesson: do Roman
WHOLE NUMBERS:
only, but chapter
Roman & Greek
enrichment refers to the numerals
Greek system, which is
covered in the
HOTmaths lesson and
a HOTsheet.
Exercise 1B enrichment WHOLE NUMBERS:
is covered in Whole
Place value & bases
numbers: Index
notation lesson and
WT3.
WT1 Translate words>nos.
WT2 Write in different forms
Game cards
1.3 Addition &
subtraction
A Addition
Jump addition
WT1 Add 3-digit numbers
B Subtraction
Jump subtraction
WT1 Subtract using jumps
This Hm lesson is used WHOLE NUMBERS:
for 1.3A and 1.4A.
Adding whole numbers
Partitioning is referred
to as ‘splitting’ on
HOTmaths.
This Hm lesson is used WHOLE NUMBERS:
for 1.3B and 1.4B.
Subtracting whole
The terms
numbers
‘decomposition’ and
‘borrow and pay back’
are also referred to.
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 5 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
1.4 Addition &
subtraction
algorithms:
A Addition
Go to 1.3 Addition & subtraction A Addition WT2 Add 2-digit
numbers uses the
compensation method.
Split-and-add robot
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
WHOLE NUMBERS:
Adding whole numbers
WT2 Add 2-digit numbers
B Subtraction
Go to 1.3 Addition & subtraction B
Subtraction
WT2 subtraction uses
4-digit numbers
WHOLE NUMBERS:
Subtracting whole
numbers
Subtracting using trading
WT2 Subtract using trading
WT3 Subtract 5-digit nos.
1.5 Multiplication
Splitting to multiply
This Hm lesson is used WHOLE NUMBERS:
for 1.5 and 1.6.
Multiplying whole
numbers
Tricks for multiplying quickly
1.6 Multiplying large
numbers
Go to 1.5 Multiplication
Multiplying by 2 digits
WHOLE NUMBERS:
Multiplying whole
numbers
WT1 Multiply by thousands
WT2 Multiply by numbers
ending in zeroes
1.7 Division
A Dividing whole
numbers
Recording division
WHOLE NUMBERS:
Dividing whole numbers
WT1 Divide by numbers
ending in zeroes
B Long division
methods
Long division & remainders
WHOLE NUMBERS:
Long division methods
WT1 Use a long division method
1.8 Estimating and
rounding
Exploring rounding numbers
WHOLE NUMBERS:
Rounding & estimating
WT1 Rounding
WT2 Estimate distance
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 6 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
1.9 Order of
operations
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
WHOLE NUMBERS:
Order of operations
Order of operations
WT1 Two operations
WT2 Three operations
WT3 Many operations
Using order of operations
CHAPTER 2: GEOMETRY — MEASUREMENT AND GEOMETRY Geometric reasoning
2.1 Points, lines and
angles
How to name an angle
ANGLES:
Points, lines & angles
WT1 Reflex angles
WT2 Use geometrical language
Matching terms w/ meanings
Naming angles
2.2 Measuring
angles:
Measuring angles
WT1 Use a protractor / acute angle
UPPER PRIMARY
ANGLES:
Measuring & drawing
angles
WT2 Use a protractor to measure
angles of a triangle
It's all a matter of degrees
2.3 Angles at a point
Angle theorems
WT1 Angles about a point
MIDDLE SECONDARY
ANGLES:
Some angle
relationships
WT2 Using facts about angles
Combining angles
2.4 Transversal lines
and parallel lines
Parallel line angles
This Hm lesson is used ANGLES:
for 2.4 and 2.5
Angles in parallel lines
WT1 Angles in parallel lines
Which angles are equal?
Testing for parallel lines
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 7 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
2.5 Problems with
parallel lines
Go to lesson 2.4
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
ANGLES:
Angles in parallel lines
WT2 Use a variety of angle properties
2.6 Circles and
constructions
Bisecting an angle
Angle bisections
‘Why does it work?’
explores the
construction used to
bisect angles and
discover why it works.
CONSTRUCTIONS IN
GEOMETRY
Bisecting angles and
intervals
Why does it work?
2.7 Dynamic
Geometry
CONSTRUCTIONS IN
GEOMETRY
Constructing lines &
angles
Constructing 60°/120° angles
To a point off a line
To a point on a line
CHAPTER 3: NUMBER PROPERTIES AND PATTERNS — NUMBER AND ALGEBRA Number and place value
Linear and non-linear relationships
3.1 Factors and
HOTsheet ‘Investigate EXPLORING
NUMBERS
multiples
multiples on hundred
Factors
grids’ look at the
Factors and multiples
patterns multiples make
Hundred grid
on a 100-square grid.
WT1 Multiples of 7
WT2 Create list of factors
WT3 Multiples of 2 & 3
Multiples on hundred grids
3.2 HCF & LCM:
A Highest
common factor
Finding the HCF
See also HOTsheet
EXPLORING
‘Investigating HCFs’ is a NUMBERS:
factor game.
Highest common factor
WT1 HCF of two numbers
WT2 HCF of three numbers
B Lowest common
multiple
LCM of 10, 25 and 50
WT1 LCM of two numbers
There is also a widget
and HOTsheet to
investigate LCM using a
100-square grid.
EXPLORING
NUMBERS:
Lowest common
multiple
WT2 LCM of three numbers
3.3 Divisibility
Divisibility tests
EXPLORING
NUMBERS:
Divisibility tests
WT1 Test for divisibility by 4
WT2 Test if no. is multiple of 6
WT3 Product of prime nos.
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 8 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
3.4 Prime numbers
WT1 Test if 13 is a prime
WT2 Test if 57 is a prime
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
HOTsheet1 investigates
Eratosthenes’ sieve for
primes, which is looked
at in the Puzzles &
Challenges section.
EXPLORING
NUMBERS:
Prime & composite
numbers
WT3 Identify prime, composite,
square numbers from their factors
WT4 Using arrays
3.5 Powers
Matching numerals & indices
WT1 Write 81 in index notation
Lesson 1.9 Order of
WHOLE NUMBERS:
operations includes
Index notation
order of operations with
indices
WT2 Write 1260 using bases and
powers of factors
WT4 Evaluate expression containing
powers
3.6 Prime
decomposition
EXPLORING
NUMBERS:
Factor trees
Factor trees for 90
WT1 Write 150 as a factor tree
WT2 Different factor trees for the
same number
WT4 Types of numbers
3.7 Squares and
square roots
WT1 Finding square roots
3.8 Number patterns
Determine the rule
WT1 Determine the rule governing a
pattern
3.9 Spatial patterns
WT1 Triangles and matches
WT2 Squares and matches
The lesson also
contains a widget and
walkthrough to find the
square root of large
numbers using factor
trees.
EXPLORING
NUMBERS:
Square roots
This Hm lesson is used INTRODUCING
ALGEBRA
for 3.8 and 3.10
Number patterns &
pronumerals
All of the examples go
the additional step of
representing the
patterns algebraically.
INTRODUCING
ALGEBRA:
Picture patterns &
pronumerals
Toothpick patterns
3.10 Tables and rules
Go to lesson 3.8
Julius Squarius
INTRODUCING
ALGEBRA:
Number patterns &
pronumerals
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 9 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
3.11 The number
plane and graphs
Patterns on the number grid
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
INTRODUCING
ALGEBRA:
Patterns on the number
grid
WT1 Ordered pairs
WT2 Write a rule from points on the
number plane
Mix and match
CHAPTER 4: FRACTIONS — NUMBER AND ALGEBRA Real numbers; Money and financial mathematics
4.1 What are
fractions?
A Introduction
Estimating fractions
WT1 Fractions of pictures
Cut-out shapes
HOTsheet can be used
with Fractions of an
area HOTsheet.
FRACTIONS:
What is a fraction?
WT2 Fractions of the whole path
WT3 Portions of a group using
fractions
WT4 Fractions on number line
Fractions of an area
B Fractions of a
whole
Matching units in fractions
FRACTIONS:
This as a fraction of that
WT1 June as fraction of year
WT2 Compare purchases using
fractions
4.2 Equivalence and
simplification
Comparing fractions
Exploring equivalent fractions
WT1 Complete equivalent
Equivalent fraction
FRACTIONS:
cards HOTsheet is a set Equivalent fractions
of blank cards which
could be used to create
sample sets, as
suggested in the Let’s
start activity.
WT2 Fractions in simplest form
WT3 Portions of a diagram
WT4 Portions of a group
Exploring equivalent fractions
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 10 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
4.3 Mixed numbers
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
FRACTIONS:
Improper versus mixed
Mixed vs improper
WT1 Use images to convert
WT2 Rewrite improper>mixed
WT3 Rewrite mixed>improper
Picturing fractions
4.4 Ordering
fractions
Near zero, half or one
Comparing numerators &
denominators
There is also a
HOTsheet to go with
the Comparing
numerators &
denominators widget
FRACTIONS:
Comparing & ordering
fractions
WT1 Comparison symbols
WT2 Selecting fractions
WT3 Comparing results
Lowest common denominator
4.5 Adding fractions
A Proper fractions
Adding unlike fractions
This Hm lesson is used FRACTIONS:
for 4.5A and 4.6A
Adding & subtracting
fractions
WT2 Adding fractions
B Mixed numbers
Adding and subtracting mixed
numerals
This Hm lesson is used FRACTIONS:
for 4.5B and 4.6B
Adding & subtracting
mixed numerals
WT1 Using a mental strategy
4.6 Subtracting
Go to lesson 4.5A
fractions
A Proper fractions
WT1 Subtract two fractions
B Mixed numbers
Go to lesson 4.5B
Adding and subtracting mixed
numerals
FRACTIONS:
Adding & subtracting
fractions
The final subtraction in
the widget uses an
alternative method to
the textbook.
FRACTIONS:
Adding & subtracting
mixed numerals
WT2 Subtract a mixed numeral
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 11 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
4.7 Multiplying
fractions
A Proper fractions
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Whole number × fraction
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
FRACTIONS:
Multiplying fractions
Multiplying two fractions
WT1 Whole number × fraction
WT2 Fraction × fraction
WT3 Fraction of a length
B Mixed numbers
Multiplying mixed numerals
FRACTIONS:
Multiplying mixed
numerals
WT1 Using a mental strategy
WT2 Two mixed numerals
4.8 Dividing fractions
A Simple fractions
Comparing multiplying and dividing
fractions
FRACTIONS:
Dividing by simple
fractions
WT1 Divide whole no. by ¼
WT2 Two methods to divide mixed
numeral by a proper fraction
WT3 Share cakes
B Complex
fractions
Finding a method
FRACTIONS:
Divisions involving
fractions
WT1 Divide mixed numeral by whole
number
WT2 Length of a rectangle given its
width and area
Investigating reciprocals
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 12 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
4.9 Fractions and
percentages
A Fractions to
percentages
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
PERCENTAGES:
Writing fractions as
percentages
Changing fractions to percent
WT1 Match fractions to %
WT2 Write 3 groups as % of whole
B Percentages to
fractions
PERCENTAGES:
Percentages as
fractions
Writing percentages as fractions
WT1 Percentages as fractions in their
simplest forms
WT2 Convert a fractional percentage
to a simple fraction
Mix and match cards
4.10 Percentage of a
number
A Percentage of a
quantity
WT1 Discount on sale using mental
strategy
WT2 Calculate with different
strategies
B Profit & loss
Profit and loss
The lesson has the
additional strategy of
converting a percentage
to a decimal and using
a calculator.
APPLYING
PERCENTAGES:
Percentage of a
quantity
APPLYING
PERCENTAGES
Profit & loss
WT1 % profit on cost price
WT2 Selling price from % mark-up
WT3 Loss given percentage
Mental magic & manipulation
4.11 Expressing a
quantity as a
proportion
What percentage is it?
WT1 Compare two percentage
savings
Lesson 4.1 B Fractions APPLYING
of a whole also relates PERCENTAGES
to this lesson
One amount as a
percentage of another
WT2 One amount as % of another
with different units
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 13 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
CHAPTER 5: ALGEBRA — NUMBER AND ALGEBRA Patterns and algebra
5.1 Introduction to
algebra
A What is
algebra?
Notation for multiplication
The lesson and WT3
touch on substitution.
INTRODUCING
ALGEBRA:
What is algebra?
Notation for division
WT1 Rewriting multiplication
WT2 Rewrite an expression requiring
indices
Card match-up
B Words into
algebra
Expressions using pronumerals
This Hm lesson is used INTRODUCING
for 5.1B and 5.7
ALGEBRA:
Words into algebra
WT1 Write expressions for
consecutive even numbers
C Algebra
pictures
INTRODUCING
ALGEBRA:
Algebra pictures
Writing expressions
WT1 Algebraic expression for
number of baseballs in a picture
5.2 Evaluating
expressions
Substituting one value
Substituting two values
WT1 Substitute integers
Parts of this lesson
INTRODUCING
involve negative
ALGEBRA:
numbers.
Substitution
HOTsheet Substituting
into formulas could be
used for Lesson 5.7.
This Hm lesson is used
for 5.2 and 7.6
WT2 Area of a trapezium
Substituting into expressions
5.3 Equivalent
expressions
Equivalent expressions
WT1 Cups and counters
5.4 Like terms
Collecting like terms
WT1 Simplifying expressions
This lesson has
examples using
brackets.
The next lesson 5.4
includes Addition &
subtraction squaresaw
HOTsheet which is a
cut-out puzzle on
equivalent expressions
INTRODUCING
ALGEBRA:
Equivalent expressions
There are references to INTRODUCING
negative numbers in the ALGEBRA:
lesson.
Adding & subtracting
terms
WT2 Checking substitution
Magic puzzles
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 14 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
5.5 Multiplying and
dividing
expressions
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Multiplying and dividing terms
WT1 Simplifying expressions
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
INTRODUCING
ALGEBRA:
Multiplying & dividing
terms
WT2 Simplify expression with
addition and division
Algebra flowcharts
5.6 Expanding
brackets
Expanding
WT1 Substitute to check
MANIPULATING
ALGEBRA:
Removing grouping
symbols
WT2 Using areas to check
5.7 Applying algebra Go to Lesson 5.1B
Algebra translator
Go to Lesson 5.2
Substituting into formulas
CHAPTER 6: DECIMALS — NUMBER AND ALGEBRA Real numbers; Money and financial mathematics
6.1 Decimals and
place value
A Place value
Converting to expanded notation
DECIMALS:
What is the point?
WT1 Words to numbers
WT2 Place value in subtraction
Decimal place bingo
B Ordering
Numbers between numbers
DECIMALS:
Ordering decimals
WT1 Filling the tank
WT2 Dots on the number line
The numbers between
6.2 Rounding
decimals
Rounding off
DECIMALS:
Rounding decimals
WT1 Rounding to 2 dp
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 15 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
6.3 Addition and
subtraction of
decimals:
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
DECIMALS:
Adding & subtracting
decimals
Adding decimals
Compensation method
WT1 Add using columns
WT2 Subtraction using mental
strategies
Missing numbers
6.4 Multiplying and
dividing by
powers of 10
UPPER PRIMARY
DECIMALS &
PERCENTAGES:
Multiplying & dividing
decimals by 10, 100,
1000
Moving decimal places
WT1 Multiply decimal by 100
WT2 Divide a decimal by 1000
6.5 Multiplication of
decimals
How many decimal places?
Includes a review of
powers of ten.
DECIMALS:
Multiplying and
squaring decimals
WT1 Finding the product
Discover the rule about decimal
places
Squaring a half
6.6 Division of
decimals:
Dividing into a decimal
DECIMALS:
Strategies for decimal
divisions
WT2 Divide a decimal by a decimal
6.7 Decimals and
fractions:
A Decimals to
fractions
Decimals to fractions
DECIMALS:
Changing decimals to
fractions
WT1 Fraction in lowest terms
WT2 Mixed numerals
B Fractions to
decimals
Changing fractions>decimals
WT1 & 3 use calculators. DECIMALS:
Changing fractions to
decimals
Matching fractions & decimals
WT2 Changing to a decimal
Different methods for converting
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 16 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
6.8 Decimals and
percentages
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Changing decimals to percentages
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
PERCENTAGES:
Linking percentages &
decimals
WT1 Matching decimals & %
Matching decimals
CHAPTER 7: NEGATIVE NUMBERS — NUMBER AND ALGEBRA Number and place value;
Linear and non-linear relationships
7.1 Integers
Sorting integers
INTEGERS:
What are directed
numbers?
Graphing inequalities
Number line
WT1 Using the number line
WT2 Greater or less than
Positioning integers
7.2 Adding and
subtracting
positive integers
Using the number line
INTEGERS:
Adding & subtracting
positive integers
WT1 Evaluating expressions
WT2 Temperature
Integer cards
Integer card games
7.3 Adding and
subtracting
negative integers
Using number patterns & integers
INTEGERS:
Two signs together
Using embers and ice
Using the number line
WT1 Add negative to negative
WT2 Subtract negative from positive
Exploring adding & subtracting
integers
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 17 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
7.4 Multiplication &
divn. of integers
A Multiplication
WT2 Determine value of four
products
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
INTEGERS:
Multiplying integers
B Division
INTEGERS:
Dividing integers
WT1 Division with integers
Board game: Throne or dungeon
7.5 Order of
operations
Ordering operations with integers
WT1 Evaluate expression with
integers & brackets
Enrichment: Powers
and negative numbers
are also covered in this
lesson.
INTEGERS:
Mixing the operations
Card game: Mixing it up
7.6 Substituting
integers
Go to Lesson 5.2
ALGEBRA:
Substitution
Substituting two values
WT1 Substitute integers
WT2 Area of trapezium
Substituting into expressions
7.7 The number
plane
A First quadrant
Plotting pictures
THE NUMBER PLANE:
The first quadrant
Finding coordinates
WT1 Read coordinates and describe
a pattern
B All four
quadrants
The four quadrants
THE NUMBER PLANE:
All four quadrants
WT1 Give coordinates and name
quadrants
WT2 Treasure hunter
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 18 of 25
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
CHAPTER 8: CHANCE AND DATA — STATISTICS & PROBABILITY Chance; Data representation & interpretn.
NUMBER & ALGEBRA Linear and non-linear relationships
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
8.1 Summarising
data numerically:
A The mean
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Moving the mean
WT1 Compare means
Notes
Lesson and HOTsheet
1 address using a
calculator to evaluate
statistical information.
ANALYSING DATA:
Exploring the mean
HOTsheet 2 uses
Widget 1 to investigate
how changing a score
effects statistical
measures.
ANALYSING DATA:
The mode, median &
range
WT2 New mean from adding a score
B Other measures
Changing data
WT1 Range, mode & median
WT2 Complete the sets
Measures of centre & spread
Every score makes a difference
Using dry spaghetti
8.2 Dot plots and
column graphs
A Dot plots
WT1 Dot plot for given scores
REPRESENTING
DATA:
Dot plots
WT2 Read info from a dot plot
Drawing dot plots
B Analysing dot
plots
Exploring dot plots
ANALYSING DATA:
Analysing dot plots
WT1 Range, mode, median, mean
from dot plot
WT2 Analyse dot plot
Statistics for dot plots
C Column graphs
Exploring column graphs
WT2 Describe info in a column graph
UPPER PRIMARY
DATA:
Picture & column
graphs
Exploring column graphs
8.3 Line graphs
Creating a line graph
WT1 Read info from line graph
REPRESENTING
DATA:
Line, conversion & step
graphs
Matching graphs to data
Comparing graphs
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 19 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
8.4 Stem and leaf
plots
A Introduction to
stem and leaf plots
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Creating a stem-and-leaf plot
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
REPRESENTING
DATA:
Stem-and-leaf plots
WT1 Create from unordered data
WT2 Back-to-back stem-and-leaf plot
Reading stem-and-leaf plots
B Analysing stemand-leaf plots
WT1 Range & measures of central
tendency
ANALYSING DATA:
Analysing stem-and-leaf
plots
Statistics from stem-and-leaf plots
8.5 Pie charts and
divided bar
graphs
A Pie charts
Reading sector graphs
REPRESENTING
DATA:
Using sector graphs
Drawing sector graphs
Exploring sector graphs
WT1 Use angles to determine size
WT2 Create a sector graph
Creating sector graphs
B Divided bar
graphs
Reading divided bar graphs
Creating divided bar graphs
REPRESENTING
DATA:
Creating divided bar
graphs
WT1 Read info from bar graph
WT2 Create divided bar graph
Creating divided bar graphs
Limitations of divided bar graphs
8.6 Describing
chance
Probability number line
CHANCE:
The language of chance
WT1 Select likely outcomes
WT2 Effect of removing an outcome
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 20 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
8.7 Theoretical
probability
A Outcomes
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Listing pairs when order matters
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
CHANCE:
Listing possible
outcomes
Listing pairs when order doesn’t
matter
Working systematically
B Probability
Calculating probability
WT1 Probability of random event
HOTsheet ‘Designing
CHANCE:
Spinners’ is an activity Theoretical probability
similar to the
Enrichment question.
This lesson also covers
8.8.
WT2 Use collected data to determine
probability
Designing spinners
The spinner experiment
8.8 Experimental
probability
Done in lesson 8.7B
CHAPTER 9: POLYGONS AND SOLIDS — MEASUREMENT AND GEOMETRY Location and transformation;
Geometric reasoning and Shape
9.1 Polygons
WT1 Identify three shapes
PLANE SHAPES &
TRIANGLES:
Plane shapes
WT2 Use meanings of prefixes
Polygons bent out of shape
Creating a portfolio of 2D images
9.2 Triangles
Triangle properties
PLANE SHAPES &
TRIANGLES:
Classifying triangles
WT1 Triangles from folded paper
WT2 Describe triangles using
information provided
Triangle and term match-up
9.3 Constructing
triangles
Constructing triangles
Straw triangles
MIDDLE SECONDARY
REASONING IN
GEOMETRY:
Tests for congruent
triangles
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 21 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
9.4 Triangle angle
sum
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Angle sum of a triangle
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
PLANE SHAPES &
TRIANGLES:
Angle sum of a triangle
WT1 Use angle sum to determine
unknown angles
Does it all add up?
9.5 Quadrilaterals
A Trapeziums &
kites
B Parallelograms
& rectangles
Exploring kites
Exploring parallelograms
Exploring rectangles
C Rhombuses &
squares
Exploring rhombuses
EXPLORING
QUADRILATERALS
Exploring trapeziums &
kites
EXPLORING
QUADRILATERALS
Exploring
parallelograms &
rectangles
EXPLORING
QUADRILATERALS
Exploring rhombuses &
squares
Exploring squares
9.6 Quadrilateral
angle sum
Angle sum of a quadrilateral
WT1 Determine size of angle in a
quadrilateral
EXPLORING
QUADRILATERALS
Angle sum of a
quadrilateral
WT2 Use angle properties to
determine values of 2 pronumerals
It all adds to 360°
9.7 Symmetry:
Lines of symmetry
TRANSFORMATION &
SYMMETRY
Reflection & symmetry
WT1 Determine number of axes of
symmetry
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 22 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
9.8 Reflection and
rotation:
A Reflection
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Reflection
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
2D SHAPES:
Reflection
WT1 Simple reflections
WT2 Complex reflections
Reflecting triangles
B Rotation
Order of rotational symmetry
TRANSFORMATION &
SYMMETRY
Rotation & symmetry
WT1 Movement of clock hands
WT2 Two specified rotations
Flipping and turning
9.9 Translation
Translation
TRANSFORMATION &
SYMMETRY
Translation
WT1 Decide whether diagrams
represent translation
9.10 Drawing solids
Drawing tool
3D SHAPES:
3D drawings &
projections
Pinboard
9.11 Nets and the
Platonic solids
A Nets
Looking at nets
3D SHAPES
Nets
WT1 net for a rectangular prism
B Classifying
Platonic solids
3D SHAPES
Classifying solids
Platonic solids
CHAPTER 10: EQUATIONS — NUMBER AND ALGEBRA Linear and non-linear relationships
10.1 Introduction to
This elementary lesson UPPER PRIMARY
PATTERNS
equations
introduces equations
Mystery numbers
through missing number Mystery number
sentences
sentences
WT1 Determine mystery number in
subtraction
WT2 Determine missing number in a
balanced number sentence.
WT3 Solve a word problem
Solving mysteries
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 23 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
10.2 Solving
equations by
inspection
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Guessing and checking
WT1 Guess, check, improve
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
This lesson gives
students strategies for
solving without using
formal algebra
EQUATIONS &
INEQUALITIES:
Guess, check &
improve
WT2 Pronumerals on both sides
10.3 Equivalent
equations
EQUATIONS &
INEQUALITIES:
Keeping the balance
Balancing equations
WT1 Use the idea of a balance beam
WT2 Keep both sides balanced
Looking at the balance
10.4 Solving
equations
algebraically
EQUATIONS &
INEQUALITIES:
A formal approach
Reversing the operations
Solving equations
WT1 2-step equation (multiplication
& subtraction)
WT2 pronumerals on both sides
Equations crossword
Matching equations & solutions
10.5 Equations with
fractions
Equations with one fraction
Lesson: Only solve
equations with one
fraction.
MIDDLE SECONDARY
LINEAR EQUATIONS &
INEQUALITIES:
Equations with fractions
Lesson: Only solve
equations with one set
of brackets.
MIDDLE SECONDARY
LINEAR EQUATIONS &
INEQUALITIES:
Equations with brackets
WT1 2 terms and a fraction
WT2 3 terms and a fraction
10.6 Equations with
brackets
Solving equations with brackets
WT1 Solve equations with one set of
grouping symbols
Techniques in solving linear
equations
10.7 Formulas and
relationships
WT1 Convert Celsius to Fahrenheit
EQUATIONS &
INEQUALITIES:
Equations & formulas
WT2 Find the value of one variable in
a formula
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 24 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Notes
10.8 Applications
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
EQUATIONS &
INEQUALITIES:
Equations to solve
problems
The equation converter
WT1 Equation for cost of a scarf.
WT2 Weight of a frog.
Have equation, will solve
CHAPTER 11: MEASUREMENT — MEASUREMENT AND GEOMETRY Using units of measurement
11.1 Measurement
systems
History of measuring length
This Hm lesson is used LENGTH, PERIMETER
for 11.1 and 11.2
& AREA:
Length
11.2 Using and
Go to 11.1
converting metric
lengths
Estimating length
LENGTH, PERIMETER
& AREA:
Length
WT1 Metres to millimetres
WT3 Limits of a given measurement
Estimating lengths
11.3 Perimeter
LENGTH, PERIMETER
& AREA:
Perimeter problems
Building perimeters
WT1 Calculate the perimeter
WT2 Length of a rectangle from its
width & perimeter
Toothpick puzzle
11.4 Areas and
rectangles
A Area formulas
Comparing areas & perimeters
WT2 Area of a composite shape
B Area units
WT1 Convert
km2
to
m2
WT2 Convert hectares to km2
The HOTsheet
investigates the
perimeter of figures with
the same area.
LENGTH, PERIMETER
& AREA:
Formula for area of a
rectangle
The HOTsheets in this
lesson investigate how
to estimate areas using
approximate grids.
LENGTH, PERIMETER
& AREA:
Converting area units &
estimating
Perimeter vs. area
11.5 Area of a triangle
Investigating areas of triangles
WT1 Calculate area from base and
height
This Hm lesson is used LENGTH, PERIMETER
for 11.5 and 11.7
& AREA:
Formula for area of a
triangle
An investigation of area
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 25 of 25
Essential Maths 7
CHAPTER & lesson
(sections in textbook)
11.6 Area of a
parallelogram
HOTmaths widgets, walkthroughs and
HOTsheets suggested for use with
Essential Maths
Understanding the formula
Notes
Equivalent TOPIC &
Lesson in HOTmaths
(Early Secondary
unless stated)
LENGTH, PERIMETER
& AREA:
Areas of parallelograms
WT1 Calculate area from base and
height
WT1 Perpendicular height given area
and base
11.7 Area of
composite
shapes
11.8 Volume of
rectangular
prisms
Go to 11.5
Composite areas and triangles
Volumes of rectangular prisms
WT1 Volume of two prisms made of
metre cubes
VOLUME & SURFACE
AREA:
Volume, capacity &
prisms
WT2 Use the formula to find the
volume of a rectangular prism
11.9 Capacity
A Measuring
capacity
Capacity puzzles
UPPER PRIMARY
VOLUME & CAPACITY:
Measuring capacity
Estimating capacity
WT1 No. of glasses filled by 1 litre
WT2 A measured amount of water
B Litres and
cubes
Water overflow
UPPER PRIMARY
VOLUME & CAPACITY:
Linking litres and cubes
WT1 Use difference in water levels to
measure volume
11.10 Mass and
temperature
A Measuring and
recording mass
B Converting units
of mass
Reading scales
Mystery mass
Comparing Readings
WT2 Convert kg to g
UPPER PRIMARY
MASS:
Measuring and
recording mass
UPPER PRIMARY
MASS:
Converting units of
mass
WT3 Convert g to kg
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011