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Page 1 of 34 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 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 Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011

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Page 1: Essential Mathematics for the Australian Curriculum€¦  · Web viewfor the Australian Curriculum Year 7 . 1 Aims of the program and suggestions for use. Cambridge HOTmaths teacher

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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

Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011

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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.

Cambridge University Press Essential Maths / HOTmaths Integrated program Issue: 7 February 2011

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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

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)

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

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)

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

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)

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

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)

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

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)

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

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)

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

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)

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

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)

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

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)

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

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)

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

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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

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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)

10.2 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

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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

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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