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Cambridge Essential Mathematics / HOTmaths Integrated programfor the Australian Curriculum Year 7
1 Aims of the program and suggestions for useCambridge 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: [email protected] 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
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2 How to use the integrated programFrom 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:
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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.
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3 Cambridge Essential Mathematics Year 7 / HOTmaths Integrated Program Key (note that HOTmaths may be abbreviated to Hm)
NUMBER AND ALGEBRA Australian Curriculum strandWidgets (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
A Egyptian & Mayan Subtitle used where more than one HOTmaths lesson links to textbook lesson HOTsheets (worksheets)
1.4 Addition & subtraction algorithms
Grey shading and font indicates a textbook lesson, e.g. 1.4, that employs resources 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 7CHAPTER & 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 systemsA Egyptian & Mayan
Egyptian numbers
WT1 Translate Egyptian
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
B Roman & Greek Arithmetic in Ancient Rome
WT1 Years between dates
WT2 Translate Roman
Lesson: do Roman only, but chapter enrichment refers to the Greek system, which is covered in the HOTmaths lesson and a HOTsheet.
WHOLE NUMBERS: Roman & Greek numerals
1.2 Place value Number reader
Making numbers
WT1 Translate words>nos.
WT2 Write in different forms
Game cards
Exercise 1B enrichment is covered in Whole numbers: Index notation lesson and WT3.
WHOLE NUMBERS: Place value & bases
1.3 Addition & subtractionA Addition
Jump addition
WT1 Add 3-digit numbers
This Hm lesson is used for 1.3A and 1.4A.Partitioning is referred to as ‘splitting’ on HOTmaths.
WHOLE NUMBERS: Adding whole numbers
B Subtraction Jump subtraction
WT1 Subtract using jumps
This Hm lesson is used for 1.3B and 1.4B.The terms ‘decomposition’ and ‘borrow and pay back’ are also referred to.
WHOLE NUMBERS: Subtracting whole numbers
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Essential Maths 7CHAPTER & 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)
1.4 Addition & subtraction algorithms:A Addition
Go to 1.3 Addition & subtraction A Addition
Split-and-add robot
WT2 Add 2-digit numbers
WT2 Add 2-digit numbers uses the compensation method.
WHOLE NUMBERS: Adding whole numbers
B Subtraction Go to 1.3 Addition & subtraction B Subtraction
Subtracting using trading
WT2 Subtract using trading
WT3 Subtract 5-digit nos.
WT2 subtraction uses 4-digit numbers
WHOLE NUMBERS: Subtracting whole numbers
1.5 Multiplication Splitting to multiply
Tricks for multiplying quickly
This Hm lesson is used for 1.5 and 1.6.
WHOLE NUMBERS: Multiplying whole numbers
1.6 Multiplying large numbers
Go to 1.5 Multiplication
Multiplying by 2 digits
WT1 Multiply by thousands
WT2 Multiply by numbersending in zeroes
WHOLE NUMBERS: Multiplying whole numbers
1.7 DivisionA Dividing whole numbers
Recording division
WT1 Divide by numbersending in zeroes
WHOLE NUMBERS: Dividing whole numbers
B Long division methods Long division & remainders
WT1 Use a long division method
WHOLE NUMBERS: Long division methods
1.8 Estimating and rounding Exploring rounding numbers
WT1 Rounding
WT2 Estimate distance
WHOLE NUMBERS: Rounding & estimating
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Essential Maths 7CHAPTER & 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)
1.9 Order of operations Order of operations
WT1 Two operations
WT2 Three operations
WT3 Many operations
Using order of operations
WHOLE NUMBERS: Order of operations
CHAPTER 2: GEOMETRY — MEASUREMENT AND GEOMETRY Geometric reasoning
2.1 Points, lines and angles How to name an angle
WT1 Reflex angles
WT2 Use geometrical language
Matching terms w/ meanings
Naming angles
ANGLES: Points, lines & angles
2.2 Measuring angles: Measuring angles
WT1 Use a protractor / acute angle
WT2 Use a protractor to measure
angles of a triangle
It's all a matter of degrees
UPPER PRIMARY ANGLES: Measuring & drawing angles
2.3 Angles at a point Angle theorems
WT1 Angles about a point
WT2 Using facts about angles
Combining angles
MIDDLE SECONDARYANGLES: Some angle relationships
2.4 Transversal lines and parallel lines Parallel line angles
WT1 Angles in parallel lines
Which angles are equal?
Testing for parallel lines
This Hm lesson is used for 2.4 and 2.5
ANGLES: Angles in parallel lines
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Essential Maths 7CHAPTER & 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)
2.5 Problems with parallel lines
Go to lesson 2.4
WT2 Use a variety of angle properties
ANGLES: Angles in parallel lines
2.6 Circles and constructions Bisecting an angle
Angle bisections
Why does it work?
‘Why does it work?’ explores the construction used to bisect angles and discover why it works.
CONSTRUCTIONS IN GEOMETRYBisecting angles and intervals
2.7 Dynamic Geometry Constructing 60°/120° angles
To a point off a line
To a point on a line
CONSTRUCTIONS IN GEOMETRYConstructing lines & angles
CHAPTER 3: NUMBER PROPERTIES AND PATTERNS — NUMBER AND ALGEBRA Number and place valueLinear and non-linear relationships
3.1 Factors and multiples Factors
Hundred grid
WT1 Multiples of 7
WT2 Create list of factors
WT3 Multiples of 2 & 3
Multiples on hundred grids
HOTsheet ‘Investigate multiples on hundred grids’ look at the patterns multiples make on a 100-square grid.
EXPLORING NUMBERSFactors and multiples
3.2 HCF & LCM:A Highest common factor
Finding the HCF
WT1 HCF of two numbers
WT2 HCF of three numbers
See also HOTsheet ‘Investigating HCFs’ is a factor game.
EXPLORING NUMBERS: Highest common factor
B Lowest common multiple LCM of 10, 25 and 50
WT1 LCM of two numbers
WT2 LCM of three numbers
There is also a widget and HOTsheet to investigate LCM using a 100-square grid.
EXPLORING NUMBERS: Lowest common multiple
3.3 Divisibility Divisibility tests
WT1 Test for divisibility by 4
WT2 Test if no. is multiple of 6
WT3 Product of prime nos.
EXPLORING NUMBERS: Divisibility tests
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Essential Maths 7CHAPTER & 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)
3.4 Prime numbers WT1 Test if 13 is a prime
WT2 Test if 57 is a prime
WT3 Identify prime, composite,
square numbers from their factors
WT4 Using arrays
HOTsheet1 investigates Eratosthenes’ sieve for primes, which is looked at in the Puzzles & Challenges section.
EXPLORING NUMBERS: Prime & composite numbers
3.5 Powers Matching numerals & indices
WT1 Write 81 in index notation
WT2 Write 1260 using bases and
powers of factors
WT4 Evaluate expression containing
powers
Lesson 1.9 Order of operations includes order of operations with indices
WHOLE NUMBERS: Index notation
3.6 Prime decomposition Factor trees for 90
WT1 Write 150 as a factor tree
WT2 Different factor trees for the
same number
WT4 Types of numbers
EXPLORING NUMBERS: Factor trees
3.7 Squares and square roots WT1 Finding square roots
The lesson also contains a widget and walkthrough to find the square root of large numbers using factor trees.
EXPLORING NUMBERS: Square roots
3.8 Number patterns Determine the rule
WT1 Determine the rule governing a
pattern
This Hm lesson is used for 3.8 and 3.10
INTRODUCING ALGEBRANumber patterns & pronumerals
3.9 Spatial patterns WT1 Triangles and matches
WT2 Squares and matches
Toothpick patterns
All of the examples go the additional step of representing the patterns algebraically.
INTRODUCING ALGEBRA: Picture patterns & pronumerals
3.10 Tables and rules Go to lesson 3.8
Julius Squarius
INTRODUCING ALGEBRA: Number patterns & pronumerals
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Essential Maths 7CHAPTER & 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)
3.11 The number plane and graphs Patterns on the number grid
WT1 Ordered pairs
WT2 Write a rule from points on the
number plane
Mix and match
INTRODUCING ALGEBRA: Patterns on the number grid
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
WT2 Fractions of the whole path
WT3 Portions of a group using
fractions
WT4 Fractions on number line
Fractions of an area
Cut-out shapes HOTsheet can be used with Fractions of an area HOTsheet.
FRACTIONS: What is a fraction?
B Fractions of a whole Matching units in fractions
WT1 June as fraction of year
WT2 Compare purchases using
fractions
FRACTIONS: This as a fraction of that
4.2 Equivalence and simplification Comparing fractions
Exploring equivalent fractions
WT1 Complete equivalent
WT2 Fractions in simplest form
WT3 Portions of a diagram
WT4 Portions of a group
Exploring equivalent fractions
Equivalent fraction cards HOTsheet is a set of blank cards which could be used to create sample sets, as suggested in the Let’s start activity.
FRACTIONS: Equivalent fractions
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Essential Maths 7CHAPTER & 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)
4.3 Mixed numbers Mixed vs improper
WT1 Use images to convert
WT2 Rewrite improper>mixed
WT3 Rewrite mixed>improper
Picturing fractions
FRACTIONS: Improper versus mixed
4.4 Ordering fractions Near zero, half or one
Comparing numerators &
denominators
WT1 Comparison symbols
WT2 Selecting fractions
WT3 Comparing results
Lowest common denominator
There is also a HOTsheet to go with the Comparing numerators & denominators widget
FRACTIONS: Comparing & ordering fractions
4.5 Adding fractionsA Proper fractions Adding unlike fractions
WT2 Adding fractions
This Hm lesson is used for 4.5A and 4.6A
FRACTIONS: Adding & subtracting fractions
B Mixed numbers Adding and subtracting mixed
numerals
WT1 Using a mental strategy
This Hm lesson is used for 4.5B and 4.6B
FRACTIONS: Adding & subtracting mixed numerals
4.6 Subtracting fractionsA Proper fractions
Go to lesson 4.5A
WT1 Subtract two fractions
FRACTIONS: Adding & subtracting fractions
B Mixed numbers Go to lesson 4.5B
Adding and subtracting mixed
numerals
WT2 Subtract a mixed numeral
The final subtraction in the widget uses an alternative method to the textbook.
FRACTIONS: Adding & subtracting mixed numerals
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Essential Maths 7CHAPTER & 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)
4.7 Multiplying fractionsA Proper fractions
Whole number × fraction
Multiplying two fractions
WT1 Whole number × fraction
WT2 Fraction × fraction
WT3 Fraction of a length
FRACTIONS: Multiplying fractions
B Mixed numbers Multiplying mixed numerals
WT1 Using a mental strategy
WT2 Two mixed numerals
FRACTIONS: Multiplying mixed numerals
4.8 Dividing fractionsA Simple fractions Comparing multiplying and dividing
fractions
WT1 Divide whole no. by ¼
WT2 Two methods to divide mixed
numeral by a proper fraction
WT3 Share cakes
FRACTIONS: Dividing by simple fractions
B Complex fractions Finding a method
WT1 Divide mixed numeral by whole
number
WT2 Length of a rectangle given its
width and area
Investigating reciprocals
FRACTIONS: Divisions involving fractions
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Essential Maths 7CHAPTER & 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)
4.9 Fractions and percentagesA Fractions to percentages
Changing fractions to percent
WT1 Match fractions to %
WT2 Write 3 groups as % of whole
PERCENTAGES: Writing fractions as percentages
B Percentages to 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
PERCENTAGES: Percentages as fractions
4.10 Percentage of a numberA Percentage of a quantity
WT1 Discount on sale using mental
strategy
WT2 Calculate with different
strategies
The lesson has the additional strategy of converting a percentage to a decimal and using a calculator.
APPLYING PERCENTAGES: Percentage of a quantity
B Profit & loss Profit and loss
WT1 % profit on cost price
WT2 Selling price from % mark-up
WT3 Loss given percentage
Mental magic & manipulation
APPLYING PERCENTAGESProfit & loss
4.11 Expressing a quantity as a proportion
What percentage is it?
WT1 Compare two percentage savings
WT2 One amount as % of another with different units
Lesson 4.1 B Fractions of a whole also relates to this lesson
APPLYING PERCENTAGESOne amount as a percentage of another
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Essential Maths 7CHAPTER & 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 algebraA What is algebra?
Notation for multiplication
Notation for division
WT1 Rewriting multiplication
WT2 Rewrite an expression requiring
indices
Card match-up
The lesson and WT3 touch on substitution.
INTRODUCING ALGEBRA:What is algebra?
B Words into algebra Expressions using pronumerals
WT1 Write expressions for
consecutive even numbers
This Hm lesson is used for 5.1B and 5.7
INTRODUCING ALGEBRA:Words into algebra
C Algebra pictures Writing expressions
WT1 Algebraic expression for
number of baseballs in a picture
INTRODUCING ALGEBRA:Algebra pictures
5.2 Evaluating expressions Substituting one value
Substituting two values
WT1 Substitute integers
WT2 Area of a trapezium
Substituting into expressions
Parts of this lesson involve negative numbers.HOTsheet Substituting into formulas could be used for Lesson 5.7. This Hm lesson is used for 5.2 and 7.6
INTRODUCING ALGEBRA:Substitution
5.3 Equivalent expressions Equivalent expressions
WT1 Cups and counters
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
5.4 Like terms Collecting like terms
WT1 Simplifying expressions
WT2 Checking substitution
Magic puzzles
There are references to negative numbers in the lesson.
INTRODUCING ALGEBRA:Adding & subtracting terms
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Essential Maths 7CHAPTER & 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)
5.5 Multiplying and dividing expressions
Multiplying and dividing terms
WT1 Simplifying expressions
WT2 Simplify expression with
addition and division
Algebra flowcharts
INTRODUCING ALGEBRA:Multiplying & dividing terms
5.6 Expanding brackets Expanding
WT1 Substitute to check
WT2 Using areas to check
MANIPULATING ALGEBRA: Removing grouping symbols
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 valueA Place value
Converting to expanded notation
WT1 Words to numbers
WT2 Place value in subtraction
Decimal place bingo
DECIMALS: What is the point?
B Ordering Numbers between numbers
WT1 Filling the tank
WT2 Dots on the number line
The numbers between
DECIMALS: Ordering decimals
6.2 Rounding decimals Rounding off
WT1 Rounding to 2 dp
DECIMALS: Rounding decimals
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Essential Maths 7CHAPTER & 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)
6.3 Addition and subtraction of decimals:
Adding decimals
Compensation method
WT1 Add using columns
WT2 Subtraction using mental
strategies
Missing numbers
DECIMALS: Adding & subtracting decimals
6.4 Multiplying and dividing by powers of 10
Moving decimal places
WT1 Multiply decimal by 100
WT2 Divide a decimal by 1000
UPPER PRIMARY DECIMALS & PERCENTAGES: Multiplying & dividing decimals by 10, 100, 1000
6.5 Multiplication of decimals How many decimal places?
WT1 Finding the product
Discover the rule about decimal
places
Squaring a half
Includes a review of powers of ten.
DECIMALS: Multiplying and squaring decimals
6.6 Division of decimals: Dividing into a decimal
WT2 Divide a decimal by a decimal
DECIMALS: Strategies for decimal divisions
6.7 Decimals and fractions:A Decimals to fractions
Decimals to fractions
WT1 Fraction in lowest terms
WT2 Mixed numerals
DECIMALS: Changing decimals to fractions
B Fractions to decimals Changing fractions>decimals
Matching fractions & decimals
WT2 Changing to a decimal
Different methods for converting
WT1 & 3 use calculators. DECIMALS: Changing fractions to decimals
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Essential Maths 7CHAPTER & 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)
6.8 Decimals and percentages Changing decimals to percentages
WT1 Matching decimals & %
Matching decimals
PERCENTAGES: Linking percentages & decimals
CHAPTER 7: NEGATIVE NUMBERS — NUMBER AND ALGEBRA Number and place value; Linear and non-linear relationships
7.1 Integers Sorting integers
Graphing inequalities
Number line
WT1 Using the number line
WT2 Greater or less than
Positioning integers
INTEGERS: What are directed numbers?
7.2 Adding and subtracting positive integers
Using the number line
WT1 Evaluating expressions
WT2 Temperature
Integer cards
Integer card games
INTEGERS: Adding & subtracting positive integers
7.3 Adding and subtracting negative integers
Using number patterns & integers
Using embers and ice
Using the number line
WT1 Add negative to negative
WT2 Subtract negative from positive
Exploring adding & subtracting
integers
INTEGERS: Two signs together
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Essential Maths 7CHAPTER & 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)
7.4 Multiplication & divn. of integersA Multiplication
WT2 Determine value of four
products
INTEGERS: Multiplying integers
B Division WT1 Division with integers
Board game: Throne or dungeon
INTEGERS: Dividing integers
7.5 Order of operations Ordering operations with integers
WT1 Evaluate expression with
integers & brackets
Card game: Mixing it up
Enrichment: Powers and negative numbers are also covered in this lesson.
INTEGERS: Mixing the operations
7.6 Substituting integers
Go to Lesson 5.2
Substituting two values
WT1 Substitute integers
WT2 Area of trapezium
Substituting into expressions
ALGEBRA: Substitution
7.7 The number planeA First quadrant
Plotting pictures
Finding coordinates
WT1 Read coordinates and describe
a pattern
THE NUMBER PLANE: The first quadrant
B All four quadrants The four quadrants
WT1 Give coordinates and name
quadrants
WT2 Treasure hunter
THE NUMBER PLANE: All four quadrants
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Essential Maths 7CHAPTER & 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 8: CHANCE AND DATA — STATISTICS & PROBABILITY Chance; Data representation & interpretn. NUMBER & ALGEBRA Linear and non-linear relationships
8.1 Summarising data numerically:A The mean
Moving the mean
WT1 Compare means
WT2 New mean from adding a score
Lesson and HOTsheet 1 address using a calculator to evaluate statistical information.
ANALYSING DATA: Exploring the mean
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
HOTsheet 2 uses Widget 1 to investigate how changing a score effects statistical measures.
ANALYSING DATA: The mode, median & range
8.2 Dot plots and column graphsA Dot plots
WT1 Dot plot for given scores
WT2 Read info from a dot plot
Drawing dot plots
REPRESENTING DATA: Dot plots
B Analysing dot plots Exploring dot plots
WT1 Range, mode, median, mean
from dot plot
WT2 Analyse dot plot
Statistics for dot plots
ANALYSING DATA: Analysing dot plots
C Column graphs Exploring column graphs
WT2 Describe info in a column graph
Exploring column graphs
UPPER PRIMARY DATA: Picture & column graphs
8.3 Line graphs Creating a line graph
WT1 Read info from line graph
Matching graphs to data
Comparing graphs
REPRESENTING DATA: Line, conversion & step graphs
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Essential Maths 7CHAPTER & 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)
8.4 Stem and leaf plotsA Introduction to stem and leaf plots
Creating a stem-and-leaf plot
WT1 Create from unordered data
WT2 Back-to-back stem-and-leaf plot
Reading stem-and-leaf plots
REPRESENTING DATA: Stem-and-leaf plots
B Analysing stem-and-leaf plots WT1 Range & measures of central
tendency
Statistics from stem-and-leaf plots
ANALYSING DATA: Analysing stem-and-leaf plots
8.5 Pie charts and divided bar graphsA Pie charts
Reading sector graphs
Drawing sector graphs
Exploring sector graphs
WT1 Use angles to determine size
WT2 Create a sector graph
Creating sector graphs
REPRESENTING DATA: Using sector graphs
B Divided bar graphs Reading divided bar graphs
Creating divided bar graphs
WT1 Read info from bar graph
WT2 Create divided bar graph
Creating divided bar graphs
Limitations of divided bar graphs
REPRESENTING DATA: Creating divided bar graphs
8.6 Describing chance Probability number line
WT1 Select likely outcomes
WT2 Effect of removing an outcome
CHANCE: The language of chance
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Essential Maths 7CHAPTER & 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)
8.7 Theoretical probabilityA Outcomes
Listing pairs when order matters
Listing pairs when order doesn’t
matter
Working systematically
CHANCE: Listing possible outcomes
B Probability Calculating probability
WT1 Probability of random event
WT2 Use collected data to determine
probability
Designing spinners
The spinner experiment
HOTsheet ‘Designing Spinners’ is an activity similar to the Enrichment question. This lesson also covers 8.8.
CHANCE: Theoretical probability
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
WT2 Use meanings of prefixes
Polygons bent out of shape
Creating a portfolio of 2D images
PLANE SHAPES & TRIANGLES: Plane shapes
9.2 Triangles Triangle properties
WT1 Triangles from folded paper
WT2 Describe triangles using
information provided
Triangle and term match-up
PLANE SHAPES & TRIANGLES: Classifying triangles
9.3 Constructing triangles Constructing triangles
Straw triangles
MIDDLE SECONDARYREASONING IN GEOMETRY: Tests for congruent triangles
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Essential Maths 7CHAPTER & 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)
9.4 Triangle angle sum Angle sum of a triangle
WT1 Use angle sum to determine
unknown angles
Does it all add up?
PLANE SHAPES & TRIANGLES: Angle sum of a triangle
9.5 QuadrilateralsA Trapeziums & kites
Exploring kitesEXPLORING QUADRILATERALS Exploring trapeziums & kites
B Parallelograms & rectangles Exploring parallelograms
Exploring rectangles
EXPLORING QUADRILATERALS Exploring parallelograms & rectangles
C Rhombuses & squares Exploring rhombuses
Exploring squares
EXPLORING QUADRILATERALS Exploring rhombuses & squares
9.6 Quadrilateral angle sum Angle sum of a quadrilateral
WT1 Determine size of angle in a
quadrilateral
WT2 Use angle properties to
determine values of 2 pronumerals
It all adds to 360°
EXPLORING QUADRILATERALS Angle sum of a quadrilateral
9.7 Symmetry: Lines of symmetry
WT1 Determine number of axes of
symmetry
TRANSFORMATION & SYMMETRYReflection & symmetry
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
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Essential Maths 7CHAPTER & 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)
9.8 Reflection and rotation:A Reflection
Reflection
WT1 Simple reflections
WT2 Complex reflections
Reflecting triangles
2D SHAPES: Reflection
B Rotation Order of rotational symmetry
WT1 Movement of clock hands
WT2 Two specified rotations
Flipping and turning
TRANSFORMATION & SYMMETRYRotation & symmetry
9.9 Translation Translation
WT1 Decide whether diagrams
represent translation
TRANSFORMATION & SYMMETRYTranslation
9.10 Drawing solids Drawing tool
Pinboard
3D SHAPES: 3D drawings & projections
9.11 Nets and the Platonic solidsA Nets
Looking at nets
WT1 net for a rectangular prism
3D SHAPESNets
B Classifying Platonic solids Platonic solids
3D SHAPESClassifying solids
CHAPTER 10: EQUATIONS — NUMBER AND ALGEBRA Linear and non-linear relationships
10.1 Introduction to equations Mystery numbers
WT1 Determine mystery number in
subtraction
WT2 Determine missing number in a
balanced number sentence.
WT3 Solve a word problem
Solving mysteries
This elementary lesson introduces equations through missing number sentences
UPPER PRIMARYPATTERNSMystery number sentences
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
Page 23 of 25
Essential Maths 7CHAPTER & 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)
10.2 Solving equations by inspection
Guessing and checking
WT1 Guess, check, improve
WT2 Pronumerals on both sides
This lesson gives students strategies for solving without using formal algebra
EQUATIONS & INEQUALITIES: Guess, check & improve
10.3 Equivalent equations Balancing equations
WT1 Use the idea of a balance beam
WT2 Keep both sides balanced
Looking at the balance
EQUATIONS & INEQUALITIES: Keeping the balance
10.4 Solving equations algebraically
Reversing the operations
Solving equations
WT1 2-step equation (multiplication
& subtraction)
WT2 pronumerals on both sides
Equations crossword
Matching equations & solutions
EQUATIONS & INEQUALITIES: A formal approach
10.5 Equations with fractions Equations with one fraction
WT1 2 terms and a fraction
WT2 3 terms and a fraction
Lesson: Only solve equations with one fraction.
MIDDLE SECONDARYLINEAR EQUATIONS & INEQUALITIES: Equations with fractions
10.6 Equations with brackets Solving equations with brackets
WT1 Solve equations with one set of
grouping symbols
Techniques in solving linear
equations
Lesson: Only solve equations with one set of brackets.
MIDDLE SECONDARYLINEAR EQUATIONS & INEQUALITIES: Equations with brackets
10.7 Formulas and relationships WT1 Convert Celsius to Fahrenheit
WT2 Find the value of one variable in
a formula
EQUATIONS & INEQUALITIES: Equations & formulas
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
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Essential Maths 7CHAPTER & 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)
10.8 Applications The equation converter
WT1 Equation for cost of a scarf.
WT2 Weight of a frog.
Have equation, will solve
EQUATIONS & INEQUALITIES: Equations to solve problems
CHAPTER 11: MEASUREMENT — MEASUREMENT AND GEOMETRY Using units of measurement
11.1 Measurement systems History of measuring length
This Hm lesson is used for 11.1 and 11.2
LENGTH, PERIMETER & AREA: Length
11.2 Using and converting metric lengths
Go to 11.1
Estimating length
WT1 Metres to millimetres
WT3 Limits of a given measurement
Estimating lengths
LENGTH, PERIMETER & AREA: Length
11.3 Perimeter Building perimeters
WT1 Calculate the perimeter
WT2 Length of a rectangle from its
width & perimeter
Toothpick puzzle
LENGTH, PERIMETER & AREA: Perimeter problems
11.4 Areas and rectanglesA Area formulas
Comparing areas & perimeters
WT2 Area of a composite shape
The HOTsheet investigates the perimeter of figures with the same area.
LENGTH, PERIMETER & AREA: Formula for area of a rectangle
B Area units WT1 Convert km2 to m2
WT2 Convert hectares to km2
Perimeter vs. area
The HOTsheets in this lesson investigate how to estimate areas using approximate grids.
LENGTH, PERIMETER & AREA: Converting area units & estimating
11.5 Area of a triangle Investigating areas of triangles
WT1 Calculate area from base and
height
An investigation of area
This Hm lesson is used for 11.5 and 11.7
LENGTH, PERIMETER & AREA: Formula for area of a triangle
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011
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Essential Maths 7CHAPTER & 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)
11.6 Area of a parallelogram Understanding the formula
WT1 Calculate area from base and
height
WT1 Perpendicular height given area
and base
LENGTH, PERIMETER & AREA: Areas of parallelograms
11.7 Area of composite shapes
Go to 11.5
Composite areas and triangles
11.8 Volume of rectangular prisms
Volumes of rectangular prisms
WT1 Volume of two prisms made of
metre cubes
WT2 Use the formula to find the
volume of a rectangular prism
VOLUME & SURFACE AREA: Volume, capacity & prisms
11.9 CapacityA Measuring capacity
Capacity puzzles
Estimating capacity
WT1 No. of glasses filled by 1 litre
WT2 A measured amount of water
UPPER PRIMARYVOLUME & CAPACITY: Measuring capacity
B Litres and cubes Water overflow
WT1 Use difference in water levels to
measure volume
UPPER PRIMARYVOLUME & CAPACITY: Linking litres and cubes
11.10 Mass and temperatureA Measuring and recording mass
Reading scales
Mystery mass
UPPER PRIMARYMASS: Measuring and recording mass
B Converting units of mass Comparing Readings
WT2 Convert kg to g
WT3 Convert g to kg
UPPER PRIMARYMASS: Converting units of mass
Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011