Essential Mathematics for the Australian Curriculum



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 |Suggestions of types of activities to do in class (which can be |

|individual computers at home or in class: |accomplished with a teacher account): |

|Revisit work from earlier terms or years where requisite prior |Revise work from earlier years. |

|knowledge is lacking. |Display an interactive WIDGET in class to illustrate a concept. |

|Do a HOTmaths lesson as homework to prepare for a lesson using the |After going through a widget, print out multiple copies of an |

|textbook. |accompanying HOTsheet to work through |

|Do a TOPIC QUIZ or a test from the TEST GENERATOR (new in 2011) as |Display a interactive WALKTHROUGH example for the class to suggest |

|homework or classwork. |answers for the embedded questions. |

|Do SCORCHER quizzes for homework, or when other assignments have |Use the TEST GENERATOR (new in 2011) to print out a test to do on |

|been finished early. |paper |

|Do a HOTmaths lesson to catch up on missed work. |Display and discuss the HOTmaths lesson notes as an alternative to |

|Revise and prepare for tests and exams using HOTmaths lessons. |the textbook topic introduction. |

|Try the alternative approach of an interactive WIDGET or WALKTHROUGH|Set advanced students to work as a group on higher level HOTmaths |

|when having difficulty grasping a concept or learning a skill. |activities while the rest of the class tackles foundation/standard |

|Use the DICTIONARY to test and reinforce understanding of |work. |

|mathematical terminology and use the links provided to see |Set foundation-level students to work as a group revisiting previous|

|mathematical terms in use. |work (including previous years) while the rest of the class tackles |

|Match work to ability levels. |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@

The exact design and appearance of the menus and lessons may change.

Check periodically for updates to this program at:

cambridge.edu.au/hotmaths or cambridge.edu.au/go

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 |[pic] |

|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|[pic] |

|level | |

|and the chapter (topic). | |

| | |

|3 Choose the lesson number. |[pic] |

|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: |

|[pic] |

| |

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.

3 Cambridge Essential Mathematics Year 7 / HOTmaths Integrated Program

Key (note that HOTmaths may be abbreviated to Hm)

|NUMBER AND ALGEBRA |Australian Curriculum strand |[pic] |Widgets (interactives) |

|Number and place value |Substrands | | |

|1.1 Number systems |Textbook lesson/topic numbers/titles, also used in the |[pic] |Walkthroughs–-interactive |

| |HOTmaths Essential Maths menu | |examples–-‘WT’ for short |

|A Egyptian & Mayan |Subtitle used where more than one HOTmaths lesson links |[pic] |HOTsheets (worksheets) |

| |to textbook lesson | | |

|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 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with Essential Maths | |HOTmaths (Early Secondary unless |

|textbook) | | |stated) |

|CHAPTER 1: WHOLE NUMBERS — NUMBER AND ALGEBRA Number and place value |

|1.1 Number systems |[pic] Egyptian numbers |Lesson: do Egyptian only, and |WHOLE NUMBERS: |

|A Egyptian & Mayan |[pic] WT1 Translate Egyptian |Mayan system (Widget 2 and WT2) |Egyptian & Mayan numerals |

| | |as enrichment. Remind students | |

| | |that Hindu-Arabic refers to the | |

| | |modern system. | |

| B Roman & Greek |[pic] Arithmetic in Ancient Rome |Lesson: do Roman only, but |WHOLE NUMBERS: |

| |[pic] WT1 Years between dates |chapter enrichment refers to the |Roman & Greek numerals |

| |[pic] WT2 Translate Roman |Greek system, which is covered in| |

| | |the HOTmaths lesson and a | |

| | |HOTsheet. | |

|1.2 Place value |[pic] Number reader |Exercise 1B enrichment is covered|WHOLE NUMBERS: |

| |[pic] Making numbers |in Whole numbers: Index notation |Place value & bases |

| |[pic] WT1 Translate words>nos. |lesson and WT3. | |

| |[pic] WT2 Write in different forms | | |

| |[pic] Game cards | | |

|1.3 Addition & subtraction |[pic] Jump addition |This Hm lesson is used for 1.3A |WHOLE NUMBERS: |

|A Addition |[pic] WT1 Add 3-digit numbers |and 1.4A. |Adding whole numbers |

| | |Partitioning is referred to as | |

| | |‘splitting’ on HOTmaths. | |

| B Subtraction |[pic] Jump subtraction |This Hm lesson is used for 1.3B |WHOLE NUMBERS: |

| |[pic] WT1 Subtract using jumps |and 1.4B. |Subtracting whole numbers |

| | |The terms ‘decomposition’ and | |

| | |‘borrow and pay back’ are also | |

| | |referred to. | |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with | |HOTmaths (Early Secondary unless |

|textbook) |Essential Maths | |stated) |

|1.4 Addition & subtraction |Go to 1.3 Addition & subtraction A Addition |WT2 Add 2-digit numbers uses the |WHOLE NUMBERS: |

|algorithms: |[pic] Split-and-add robot |compensation method. |Adding whole numbers |

|A Addition |[pic] WT2 Add 2-digit numbers | | |

| B Subtraction |Go to 1.3 Addition & subtraction B Subtraction |WT2 subtraction uses |WHOLE NUMBERS: |

| |[pic] Subtracting using trading |4-digit numbers |Subtracting whole numbers |

| |[pic] WT2 Subtract using trading | | |

| |[pic] WT3 Subtract 5-digit nos. | | |

|1.5 Multiplication |[pic] Splitting to multiply |This Hm lesson is used for 1.5 |WHOLE NUMBERS: |

| |[pic] Tricks for multiplying quickly |and 1.6. |Multiplying whole numbers |

|1.6 Multiplying large numbers |Go to 1.5 Multiplication | |WHOLE NUMBERS: |

| |[pic] Multiplying by 2 digits | |Multiplying whole numbers |

| |[pic] WT1 Multiply by thousands | | |

| |[pic] WT2 Multiply by numbers | | |

| |ending in zeroes | | |

|1.7 Division |[pic] Recording division | |WHOLE NUMBERS: |

|A Dividing whole numbers |[pic] WT1 Divide by numbers | |Dividing whole numbers |

| |ending in zeroes | | |

| B Long division methods |[pic] Long division & remainders | |WHOLE NUMBERS: |

| |[pic] WT1 Use a long division method | |Long division methods |

|1.8 Estimating and rounding |[pic] Exploring rounding numbers | |WHOLE NUMBERS: |

| |[pic] WT1 Rounding | |Rounding & estimating |

| |[pic] WT2 Estimate distance | | |

|1.9 Order of operations |[pic] Order of operations | |WHOLE NUMBERS: |

| |[pic] WT1 Two operations | |Order of operations |

| |[pic] WT2 Three operations | | |

| |[pic] WT3 Many operations | | |

| |[pic] Using order of operations | | |

|CHAPTER 2: GEOMETRY — MEASUREMENT AND GEOMETRY Geometric reasoning |

|2.1 Points, lines and angles |[pic] How to name an angle | |ANGLES: |

| |[pic] WT1 Reflex angles | |Points, lines & angles |

| |[pic] WT2 Use geometrical language | | |

| |[pic] Matching terms w/ meanings | | |

| |[pic] Naming angles | | |

|2.2 Measuring angles: |[pic] Measuring angles | |UPPER PRIMARY ANGLES: |

| |[pic] WT1 Use a protractor / acute angle | |Measuring & drawing angles |

| |[pic] WT2 Use a protractor to measure angles of a triangle| | |

| |[pic] It's all a matter of degrees | | |

|2.3 Angles at a point |[pic] Angle theorems | |MIDDLE SECONDARY |

| |[pic] WT1 Angles about a point | |ANGLES: |

| |[pic] WT2 Using facts about angles | |Some angle relationships |

| |[pic] Combining angles | | |

|2.4 Transversal lines and |[pic] Parallel line angles |This Hm lesson is used for 2.4 |ANGLES: |

|parallel lines |[pic] WT1 Angles in parallel lines |and 2.5 |Angles in parallel lines |

| |[pic] Which angles are equal? | | |

| |[pic] Testing for parallel lines | | |

|2.5 Problems with parallel lines |Go to lesson 2.4 | |ANGLES: |

| |[pic] WT2 Use a variety of angle properties | |Angles in parallel lines |

|2.6 Circles and constructions |[pic] Bisecting an angle |‘Why does it work?’ explores the |CONSTRUCTIONS IN GEOMETRY |

| |[pic] Angle bisections |construction used to bisect |Bisecting angles and intervals |

| |[pic] Why does it work? |angles and discover why it works.| |

|2.7 Dynamic Geometry |[pic] Constructing 60°/120° angles | |Constructions in geometry |

| |[pic] To a point off a line | |Constructing lines & angles |

| |[pic] 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 multiples |[pic] Factors |HOTsheet ‘Investigate multiples |Exploring numbers |

| |[pic] Hundred grid |on hundred grids’ look at the |Factors and multiples |

| |[pic] WT1 Multiples of 7 |patterns multiples make on a | |

| |[pic] WT2 Create list of factors |100-square grid. | |

| |[pic] WT3 Multiples of 2 & 3 | | |

| |[pic] Multiples on hundred grids | | |

|3.2 HCF & LCM: |[pic] Finding the HCF |See also HOTsheet ‘Investigating |Exploring numbers: |

|A Highest common factor |[pic] WT1 HCF of two numbers |HCFs’ is a factor game. |Highest common factor |

| |[pic] WT2 HCF of three numbers | | |

| B Lowest common multiple |[pic] LCM of 10, 25 and 50 |There is also a widget and |Exploring numbers: |

| |[pic] WT1 LCM of two numbers |HOTsheet to investigate LCM using|Lowest common multiple |

| |[pic] WT2 LCM of three numbers |a 100-square grid. | |

|3.3 Divisibility |[pic] Divisibility tests | |Exploring numbers: |

| |[pic] WT1 Test for divisibility by 4 | |Divisibility tests |

| |[pic] WT2 Test if no. is multiple of 6 | | |

| |[pic] WT3 Product of prime nos. | | |

|3.4 Prime numbers |[pic] WT1 Test if 13 is a prime |HOTsheet1 investigates |Exploring numbers: |

| |[pic] WT2 Test if 57 is a prime |Eratosthenes’ sieve for primes, |Prime & composite numbers |

| |[pic] WT3 Identify prime, composite, square numbers from |which is looked at in the Puzzles| |

| |their factors |& Challenges section. | |

| |[pic] WT4 Using arrays | | |

|3.5 Powers |[pic] Matching numerals & indices |Lesson 1.9 Order of operations |WHOLE NUMBERS: |

| |[pic] WT1 Write 81 in index notation |includes order of operations with|Index notation |

| |[pic] WT2 Write 1260 using bases and powers of factors |indices | |

| |[pic] WT4 Evaluate expression containing powers | | |

|3.6 Prime decomposition |[pic] Factor trees for 90 | |EXPLORING NUMBERS: |

| |[pic] WT1 Write 150 as a factor tree | |Factor trees |

| |[pic] WT2 Different factor trees for the same number | | |

| |[pic] WT4 Types of numbers | | |

|3.7 Squares and square roots |[pic] WT1 Finding square roots |The lesson also contains a widget|Exploring numbers: |

| | |and walkthrough to find the |Square roots |

| | |square root of large numbers | |

| | |using factor trees. | |

|3.8 Number patterns |[pic] Determine the rule |This Hm lesson is used for 3.8 |Introducing algebra |

| |[pic] WT1 Determine the rule governing a pattern |and 3.10 |Number patterns & pronumerals |

|3.9 Spatial patterns |[pic] WT1 Triangles and matches |All of the examples go the |INTRODUCING ALGEBRA: |

| |[pic] WT2 Squares and matches |additional step of representing |Picture patterns & pronumerals |

| |[pic] Toothpick patterns |the patterns algebraically. | |

|3.10 Tables and rules |Go to lesson 3.8 | |INTRODUCING ALGEBRA: |

| |[pic] Julius Squarius | |Number patterns & pronumerals |

|3.11 The number plane and graphs |[pic] Patterns on the number grid | |INTRODUCING ALGEBRA: |

| |[pic] WT1 Ordered pairs | |Patterns on the number grid |

| |[pic] WT2 Write a rule from points on the number plane | | |

| |[pic] Mix and match | | |

|CHAPTER 4: FRACTIONS — NUMBER AND ALGEBRA Real numbers; Money and financial mathematics |

|4.1 What are fractions? |[pic] Estimating fractions |Cut-out shapes HOTsheet can be |FRACTIONS: |

|A Introduction |[pic] WT1 Fractions of pictures |used with Fractions of an area |What is a fraction? |

| |[pic] WT2 Fractions of the whole path |HOTsheet. | |

| |[pic] WT3 Portions of a group using fractions | | |

| |[pic] WT4 Fractions on number line | | |

| |[pic] Fractions of an area | | |

| B Fractions of a whole |[pic] Matching units in fractions | |FRACTIONS: |

| |[pic] WT1 June as fraction of year | |This as a fraction of that |

| |[pic] WT2 Compare purchases using fractions | | |

|4.2 Equivalence and |[pic] Comparing fractions |Equivalent fraction cards |FRACTIONS: |

|simplification |[pic] Exploring equivalent fractions |HOTsheet is a set of blank cards |Equivalent fractions |

| |[pic] WT1 Complete equivalent |which could be used to create | |

| |[pic] WT2 Fractions in simplest form |sample sets, as suggested in the | |

| |[pic] WT3 Portions of a diagram |Let’s start activity. | |

| |[pic] WT4 Portions of a group | | |

| |[pic] Exploring equivalent fractions | | |

|4.3 Mixed numbers |[pic] Mixed vs improper | |FRACTIONS: |

| |[pic] WT1 Use images to convert | |Improper versus mixed |

| |[pic] WT2 Rewrite improper>mixed | | |

| |[pic] WT3 Rewrite mixed>improper | | |

| |[pic] Picturing fractions | | |

|4.4 Ordering fractions |[pic] Near zero, half or one |There is also a HOTsheet to go |FRACTIONS: |

| |[pic] Comparing numerators & denominators |with the Comparing numerators & |Comparing & ordering fractions |

| |[pic] WT1 Comparison symbols |denominators widget | |

| |[pic] WT2 Selecting fractions | | |

| |[pic] WT3 Comparing results | | |

| |[pic] Lowest common denominator | | |

|4.5 Adding fractions |[pic] Adding unlike fractions |This Hm lesson is used for 4.5A |FRACTIONS: |

|A Proper fractions |[pic] WT2 Adding fractions |and 4.6A |Adding & subtracting fractions |

| B Mixed numbers |[pic] Adding and subtracting mixed numerals |This Hm lesson is used for 4.5B |FRACTIONS: |

| |[pic] WT1 Using a mental strategy |and 4.6B |Adding & subtracting mixed |

| | | |numerals |

|4.6 Subtracting fractions |Go to lesson 4.5A | |FRACTIONS: |

|A Proper fractions |[pic] WT1 Subtract two fractions | |Adding & subtracting fractions |

| B Mixed numbers |Go to lesson 4.5B |The final subtraction in the |FRACTIONS: |

| |[pic] Adding and subtracting mixed numerals |widget uses an alternative method|Adding & subtracting mixed |

| |[pic] WT2 Subtract a mixed numeral |to the textbook. |numerals |

|4.7 Multiplying fractions |[pic] Whole number × fraction | |FRACTIONS: |

|A Proper fractions |[pic] Multiplying two fractions | |Multiplying fractions |

| |[pic] WT1 Whole number × fraction | | |

| |[pic] WT2 Fraction × fraction | | |

| |[pic] WT3 Fraction of a length | | |

| B Mixed numbers |[pic] Multiplying mixed numerals | |FRACTIONS: |

| |[pic] WT1 Using a mental strategy | |Multiplying mixed numerals |

| |[pic] WT2 Two mixed numerals | | |

|4.8 Dividing fractions |[pic] Comparing multiplying and dividing fractions | |FRACTIONS: |

|A Simple fractions |[pic] WT1 Divide whole no. by ¼ | |Dividing by simple fractions |

| |[pic] WT2 Two methods to divide mixed numeral by a proper | | |

| |fraction | | |

| |[pic] WT3 Share cakes | | |

| B Complex fractions |[pic] Finding a method | |FRACTIONS: |

| |[pic] WT1 Divide mixed numeral by whole number | |Divisions involving fractions |

| |[pic] WT2 Length of a rectangle given its width and area | | |

| |[pic] Investigating reciprocals | | |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with | |HOTmaths (Early Secondary unless |

|textbook) |Essential Maths | |stated) |

|4.9 Fractions and percentages |[pic] Changing fractions to percent | |PERCENTAGES: |

|A Fractions to percentages |[pic] WT1 Match fractions to % | |Writing fractions as percentages |

| |[pic] WT2 Write 3 groups as % of whole | | |

| B Percentages to fractions |[pic] Writing percentages as fractions | |PERCENTAGES: |

| |[pic] WT1 Percentages as fractions in their simplest forms| |Percentages as fractions |

| |[pic] WT2 Convert a fractional percentage to a simple | | |

| |fraction | | |

| |[pic] Mix and match cards | | |

|4.10 Percentage of a number |[pic] WT1 Discount on sale using mental strategy |The lesson has the additional |APPLYING PERCENTAGES: |

|A Percentage of a quantity |[pic] WT2 Calculate with different strategies |strategy of converting a |Percentage of a quantity |

| | |percentage to a decimal and using| |

| | |a calculator. | |

| B Profit & loss |[pic] Profit and loss | |Applying percentages |

| |[pic] WT1 % profit on cost price | |Profit & loss |

| |[pic] WT2 Selling price from % mark-up | | |

| |[pic] WT3 Loss given percentage | | |

| |[pic] Mental magic & manipulation | | |

|4.11 Expressing a quantity as a |[pic] What percentage is it? |Lesson 4.1 B Fractions of a |Applying percentages |

|proportion |[pic] WT1 Compare two percentage savings |whole also relates to this lesson|One amount as a percentage of |

| |[pic] WT2 One amount as % of another with different units | |another |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with | |HOTmaths (Early Secondary unless |

|textbook) |Essential Maths | |stated) |

|CHAPTER 5: ALGEBRA — NUMBER AND ALGEBRA Patterns and algebra |

|5.1 Introduction to algebra |[pic] Notation for multiplication |The lesson and WT3 touch on |INTRODUCING ALGEBRA: |

|A What is algebra? |[pic] Notation for division |substitution. |What is algebra? |

| |[pic] WT1 Rewriting multiplication | | |

| |[pic] WT2 Rewrite an expression requiring indices | | |

| |[pic] Card match-up | | |

| B Words into algebra |[pic] Expressions using pronumerals |This Hm lesson is used for 5.1B |INTRODUCING ALGEBRA: |

| |[pic] WT1 Write expressions for consecutive even numbers |and 5.7 |Words into algebra |

| C Algebra pictures |[pic] Writing expressions | |INTRODUCING ALGEBRA: |

| |[pic] WT1 Algebraic expression for number of baseballs in | |Algebra pictures |

| |a picture | | |

|5.2 Evaluating expressions |[pic] Substituting one value |Parts of this lesson involve |INTRODUCING ALGEBRA: |

| |[pic] Substituting two values |negative numbers. |Substitution |

| |[pic] WT1 Substitute integers |HOTsheet Substituting into | |

| |[pic] WT2 Area of a trapezium |formulas could be used for Lesson| |

| |[pic] Substituting into expressions |5.7. | |

| | |This Hm lesson is used for 5.2 | |

| | |and 7.6 | |

|5.3 Equivalent expressions |[pic] Equivalent expressions |This lesson has examples using |INTRODUCING ALGEBRA: |

| |[pic] WT1 Cups and counters |brackets. |Equivalent expressions |

| | |The next lesson 5.4 includes | |

| | |Addition & subtraction squaresaw | |

| | |HOTsheet which is a cut-out | |

| | |puzzle on equivalent expressions | |

|5.4 Like terms |[pic] Collecting like terms |There are references to negative |INTRODUCING ALGEBRA: |

| |[pic] WT1 Simplifying expressions |numbers in the lesson. |Adding & subtracting terms |

| |[pic] WT2 Checking substitution | | |

| |[pic] Magic puzzles | | |

|5.5 Multiplying and dividing |[pic] Multiplying and dividing terms | |INTRODUCING ALGEBRA: |

|expressions |[pic] WT1 Simplifying expressions | |Multiplying & dividing terms |

| |[pic] WT2 Simplify expression with addition and division | | |

| |[pic] Algebra flowcharts | | |

|5.6 Expanding brackets |[pic] Expanding | |MANIPULATING ALGEBRA: |

| |[pic] WT1 Substitute to check | |Removing grouping symbols |

| |[pic] WT2 Using areas to check | | |

|5.7 Applying algebra |Go to Lesson 5.1B | | |

| |[pic] Algebra translator | | |

| |Go to Lesson 5.2 | | |

| |[pic] Substituting into formulas | | |

|CHAPTER 6: DECIMALS — NUMBER AND ALGEBRA Real numbers; Money and financial mathematics |

|6.1 Decimals and place value |[pic] Converting to expanded notation | |DECIMALS: |

|A Place value |[pic] WT1 Words to numbers | |What is the point? |

| |[pic] WT2 Place value in subtraction | | |

| |[pic] Decimal place bingo | | |

| B Ordering |[pic] Numbers between numbers | |DECIMALS: |

| |[pic] WT1 Filling the tank | |Ordering decimals |

| |[pic] WT2 Dots on the number line | | |

| |[pic] The numbers between | | |

|6.2 Rounding decimals |[pic] Rounding off | |DECIMALS: |

| |[pic] WT1 Rounding to 2 dp | |Rounding decimals |

|6.3 Addition and subtraction of |[pic] Adding decimals | |DECIMALS: |

|decimals: |[pic] Compensation method | |Adding & subtracting decimals |

| |[pic] WT1 Add using columns | | |

| |[pic] WT2 Subtraction using mental strategies | | |

| |[pic] Missing numbers | | |

|6.4 Multiplying and dividing by |[pic] Moving decimal places | |UPPER PRIMARY DECIMALS & |

|powers of 10 |[pic] WT1 Multiply decimal by 100 | |PERCENTAGES: |

| |[pic] WT2 Divide a decimal by 1000 | |Multiplying & dividing decimals |

| | | |by 10, 100, 1000 |

|6.5 Multiplication of decimals |[pic] How many decimal places? |Includes a review of powers of |DECIMALS: |

| |[pic] WT1 Finding the product |ten. |Multiplying and squaring decimals|

| |[pic] Discover the rule about decimal places | | |

| |[pic] Squaring a half | | |

|6.6 Division of decimals: |[pic] Dividing into a decimal | |DECIMALS: |

| |[pic] WT2 Divide a decimal by a decimal | |Strategies for decimal divisions |

|6.7 Decimals and fractions: |[pic] Decimals to fractions | |DECIMALS: |

|A Decimals to fractions |[pic] WT1 Fraction in lowest terms | |Changing decimals to fractions |

| |[pic] WT2 Mixed numerals | | |

| B Fractions to decimals |[pic] Changing fractions>decimals |WT1 & 3 use calculators. |DECIMALS: |

| |[pic] Matching fractions & decimals | |Changing fractions to decimals |

| |[pic] WT2 Changing to a decimal | | |

| |[pic] Different methods for converting | | |

|6.8 Decimals and percentages |[pic] Changing decimals to percentages | |PERCENTAGES: |

| |[pic] WT1 Matching decimals & % | |Linking percentages & decimals |

| |[pic] Matching decimals | | |

|CHAPTER 7: NEGATIVE NUMBERS — NUMBER AND ALGEBRA Number and place value; |

|Linear and non-linear relationships |

|7.1 Integers |[pic] Sorting integers | |INTEGERS: |

| |[pic] Graphing inequalities | |What are directed numbers? |

| |[pic] Number line | | |

| |[pic] WT1 Using the number line | | |

| |[pic] WT2 Greater or less than | | |

| |[pic] Positioning integers | | |

|7.2 Adding and subtracting |[pic] Using the number line | |INTEGERS: |

|positive integers |[pic] WT1 Evaluating expressions | |Adding & subtracting positive |

| |[pic] WT2 Temperature | |integers |

| |[pic] Integer cards | | |

| |[pic] Integer card games | | |

|7.3 Adding and subtracting |[pic] Using number patterns & integers | |INTEGERS: |

|negative integers |[pic] Using embers and ice | |Two signs together |

| |[pic] Using the number line | | |

| |[pic] WT1 Add negative to negative | | |

| |[pic] WT2 Subtract negative from positive | | |

| |[pic] Exploring adding & subtracting integers | | |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with | |HOTmaths (Early Secondary unless |

|textbook) |Essential Maths | |stated) |

|7.4 Multiplication & divn. of |[pic] WT2 Determine value of four products | |INTEGERS: |

|integers | | |Multiplying integers |

|A Multiplication | | | |

| B Division |[pic] WT1 Division with integers | |INTEGERS: |

| |[pic] Board game: Throne or dungeon | |Dividing integers |

|7.5 Order of operations |[pic] Ordering operations with integers |Enrichment: Powers and negative |INTEGERS: |

| |[pic] WT1 Evaluate expression with integers & brackets |numbers are also covered in this |Mixing the operations |

| |[pic] Card game: Mixing it up |lesson. | |

|7.6 Substituting integers |Go to Lesson 5.2 | |ALGEBRA: |

| |[pic] Substituting two values | |Substitution |

| |[pic] WT1 Substitute integers | | |

| |[pic] WT2 Area of trapezium | | |

| |[pic] Substituting into expressions | | |

|7.7 The number plane |[pic] Plotting pictures | |THE NUMBER PLANE: |

|A First quadrant |[pic] Finding coordinates | |The first quadrant |

| |[pic] WT1 Read coordinates and describe a pattern | | |

| B All four quadrants |[pic] The four quadrants | |THE NUMBER PLANE: |

| |[pic] WT1 Give coordinates and name quadrants | |All four quadrants |

| |[pic] WT2 Treasure hunter | | |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with Essential Maths | |HOTmaths (Early Secondary unless |

|textbook) | | |stated) |

|CHAPTER 8: CHANCE AND DATA — STATISTICS & PROBABILITY Chance; Data representation & interpretn. |

|NUMBER & ALGEBRA Linear and non-linear relationships |

|8.1 Summarising data numerically:|[pic] Moving the mean |Lesson and HOTsheet 1 address |ANALYSING DATA: |

|A The mean |[pic] WT1 Compare means |using a calculator to evaluate |Exploring the mean |

| |[pic] WT2 New mean from adding a score |statistical information. | |

| B Other measures |[pic] Changing data |HOTsheet 2 uses Widget 1 to |ANALYSING DATA: |

| |[pic] WT1 Range, mode & median |investigate how changing a score |The mode, median & range |

| |[pic] WT2 Complete the sets |effects statistical measures. | |

| |[pic] Measures of centre & spread | | |

| |[pic] Every score makes a difference | | |

| |[pic] Using dry spaghetti | | |

|8.2 Dot plots and column graphs |[pic] WT1 Dot plot for given scores | |REPRESENTING DATA: |

|A Dot plots |[pic] WT2 Read info from a dot plot | |Dot plots |

| |[pic] Drawing dot plots | | |

| B Analysing dot plots |[pic] Exploring dot plots | |ANALYSING DATA: |

| |[pic] WT1 Range, mode, median, mean from dot plot | |Analysing dot plots |

| |[pic] WT2 Analyse dot plot | | |

| |[pic] Statistics for dot plots | | |

| C Column graphs |[pic] Exploring column graphs | |UPPER PRIMARY DATA: |

| |[pic] WT2 Describe info in a column graph | |Picture & column graphs |

| |[pic] Exploring column graphs | | |

|8.3 Line graphs |[pic] Creating a line graph | |REPRESENTING DATA: |

| |[pic] WT1 Read info from line graph | |Line, conversion & step graphs |

| |[pic] Matching graphs to data | | |

| |[pic] Comparing graphs | | |

|8.4 Stem and leaf plots |[pic] Creating a stem-and-leaf plot | |REPRESENTING DATA: |

|A Introduction to stem and leaf |[pic] WT1 Create from unordered data | |Stem-and-leaf plots |

|plots |[pic] WT2 Back-to-back stem-and-leaf plot | | |

| |[pic] Reading stem-and-leaf plots | | |

| B Analysing stem-and-leaf plots|[pic] WT1 Range & measures of central tendency | |ANALYSING DATA: |

| |[pic] Statistics from stem-and-leaf plots | |Analysing stem-and-leaf plots |

|8.5 Pie charts and divided bar |[pic] Reading sector graphs | |REPRESENTING DATA: |

|graphs |[pic] Drawing sector graphs | |Using sector graphs |

|A Pie charts |[pic] Exploring sector graphs | | |

| |[pic] WT1 Use angles to determine size | | |

| |[pic] WT2 Create a sector graph | | |

| |[pic] Creating sector graphs | | |

| B Divided bar graphs |[pic] Reading divided bar graphs | |REPRESENTING DATA: |

| |[pic] Creating divided bar graphs | |Creating divided bar graphs |

| |[pic] WT1 Read info from bar graph | | |

| |[pic] WT2 Create divided bar graph | | |

| |[pic] Creating divided bar graphs | | |

| |[pic] Limitations of divided bar graphs | | |

|8.6 Describing chance |[pic] Probability number line | |CHANCE: |

| |[pic] WT1 Select likely outcomes | |The language of chance |

| |[pic] WT2 Effect of removing an outcome | | |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with Essential Maths | |HOTmaths (Early Secondary unless |

|textbook) | | |stated) |

|8.7 Theoretical probability |[pic] Listing pairs when order matters | |CHANCE: |

|A Outcomes |[pic] Listing pairs when order doesn’t matter | |Listing possible outcomes |

| |[pic] Working systematically | | |

| B Probability |[pic] Calculating probability |HOTsheet ‘Designing Spinners’ is |CHANCE: |

| |[pic] WT1 Probability of random event |an activity similar to the |Theoretical probability |

| |[pic] WT2 Use collected data to determine probability |Enrichment question. This lesson | |

| |[pic] Designing spinners |also covers 8.8. | |

| |[pic] 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 |[pic] WT1 Identify three shapes | |PLANE SHAPES & TRIANGLES: |

| |[pic] WT2 Use meanings of prefixes | |Plane shapes |

| |[pic] Polygons bent out of shape | | |

| |[pic] Creating a portfolio of 2D images | | |

|9.2 Triangles |[pic] Triangle properties | |PLANE SHAPES & TRIANGLES: |

| |[pic] WT1 Triangles from folded paper | |Classifying triangles |

| |[pic] WT2 Describe triangles using information provided | | |

| |[pic] Triangle and term match-up | | |

|9.3 Constructing triangles |[pic] Constructing triangles | |MIDDLE SECONDARY |

| |[pic] Straw triangles | |REASONING IN GEOMETRY: |

| | | |Tests for congruent triangles |

|9.4 Triangle angle sum |[pic] Angle sum of a triangle | |PLANE SHAPES & TRIANGLES: |

| |[pic] WT1 Use angle sum to determine unknown angles | |Angle sum of a triangle |

| |[pic] Does it all add up? | | |

|9.5 Quadrilaterals |[pic] Exploring kites | |EXPLORING QUADRILATERALS |

|A Trapeziums & kites | | |Exploring trapeziums & kites |

| B Parallelograms & rectangles |[pic] Exploring parallelograms | |EXPLORING QUADRILATERALS |

| |[pic] Exploring rectangles | |Exploring parallelograms & |

| | | |rectangles |

| C Rhombuses & squares |[pic] Exploring rhombuses | |EXPLORING QUADRILATERALS |

| |[pic] Exploring squares | |Exploring rhombuses & squares |

|9.6 Quadrilateral angle sum |[pic] Angle sum of a quadrilateral | |EXPLORING QUADRILATERALS |

| |[pic] WT1 Determine size of angle in a quadrilateral | |Angle sum of a quadrilateral |

| |[pic] WT2 Use angle properties to determine values of 2 | | |

| |pronumerals | | |

| |[pic] It all adds to 360° | | |

|9.7 Symmetry: |[pic] Lines of symmetry | |transformation & symmetry |

| |[pic] WT1 Determine number of axes of symmetry | |Reflection & symmetry |

|Essential Maths 7 |HOTmaths widgets, walkthroughs and HOTsheets suggested for|Notes |Equivalent TOPIC & Lesson in |

|CHAPTER & lesson (sections in |use with Essential Maths | |HOTmaths (Early Secondary unless |

|textbook) | | |stated) |

|9.8 Reflection and rotation: |[pic] Reflection | |2D SHAPES: |

|A Reflection |[pic] WT1 Simple reflections | |Reflection |

| |[pic] WT2 Complex reflections | | |

| |[pic] Reflecting triangles | | |

| B Rotation |[pic] Order of rotational symmetry | |transformation & symmetry |

| |[pic] WT1 Movement of clock hands | |Rotation & symmetry |

| |[pic] WT2 Two specified rotations | | |

| |[pic] Flipping and turning | | |

|9.9 Translation |[pic] Translation | |transformation & symmetry |

| |[pic] WT1 Decide whether diagrams represent translation | |Translation |

|9.10 Drawing solids |[pic] Drawing tool | |3D SHAPES: |

| |[pic] Pinboard | |3D drawings & projections |

|9.11 Nets and the Platonic solids|[pic] Looking at nets | |3D shapes |

|A Nets |[pic] WT1 net for a rectangular prism | |Nets |

| B Classifying Platonic solids |[pic] Platonic solids | |3D shapes |

| | | |Classifying solids |

|CHAPTER 10: EQUATIONS — NUMBER AND ALGEBRA Linear and non-linear relationships |

|10.1 Introduction to equations |[pic] Mystery numbers |This elementary lesson introduces|UPPER PRIMARY |

| |[pic] WT1 Determine mystery number in subtraction |equations through missing number |Patterns |

| |[pic] WT2 Determine missing number in a balanced number |sentences |Mystery number sentences |

| |sentence. | | |

| |[pic] WT3 Solve a word problem | | |

| |[pic] Solving mysteries | | |

|10.2 Solving equations by |[pic] Guessing and checking |This lesson gives students |EQUATIONS & INEQUALITIES: |

|inspection |[pic] WT1 Guess, check, improve |strategies for solving without |Guess, check & improve |

| |[pic] WT2 Pronumerals on both sides |using formal algebra | |

|10.3 Equivalent equations |[pic] Balancing equations | |EQUATIONS & INEQUALITIES: |

| |[pic] WT1 Use the idea of a balance beam | |Keeping the balance |

| |[pic] WT2 Keep both sides balanced | | |

| |[pic] Looking at the balance | | |

|10.4 Solving equations |[pic] Reversing the operations | |EQUATIONS & INEQUALITIES: |

|algebraically |[pic] Solving equations | |A formal approach |

| |[pic] WT1 2-step equation (multiplication & subtraction) | | |

| |[pic] WT2 pronumerals on both sides | | |

| |[pic] Equations crossword | | |

| |[pic] Matching equations & solutions | | |

|10.5 Equations with fractions |[pic] Equations with one fraction |Lesson: Only solve equations with|MIDDLE SECONDARY |

| |[pic] WT1 2 terms and a fraction |one fraction. |LINEAR EQUATIONS & INEQUALITIES: |

| |[pic] WT2 3 terms and a fraction | |Equations with fractions |

|10.6 Equations with brackets |[pic] Solving equations with brackets |Lesson: Only solve equations with|MIDDLE SECONDARY |

| |[pic] WT1 Solve equations with one set of grouping symbols|one set of brackets. |LINEAR EQUATIONS & INEQUALITIES: |

| |[pic] Techniques in solving linear equations | |Equations with brackets |

|10.7 Formulas and relationships |[pic] WT1 Convert Celsius to Fahrenheit | |EQUATIONS & INEQUALITIES: |

| |[pic] WT2 Find the value of one variable in a formula | |Equations & formulas |

|10.8 Applications |[pic] The equation converter | |EQUATIONS & INEQUALITIES: |

| |[pic] WT1 Equation for cost of a scarf. | |Equations to solve problems |

| |[pic] WT2 Weight of a frog. | | |

| |[pic] Have equation, will solve | | |

|CHAPTER 11: MEASUREMENT — MEASUREMENT AND GEOMETRY Using units of measurement |

|11.1 Measurement systems |[pic] History of measuring length |This Hm lesson is used for 11.1 |LENGTH, PERIMETER & AREA: |

| | |and 11.2 |Length |

|11.2 Using and converting metric |Go to 11.1 | |LENGTH, PERIMETER & AREA: |

|lengths |[pic] Estimating length | |Length |

| |[pic] WT1 Metres to millimetres | | |

| |[pic] WT3 Limits of a given measurement | | |

| |[pic] Estimating lengths | | |

|11.3 Perimeter |[pic] Building perimeters | |LENGTH, PERIMETER & AREA: |

| |[pic] WT1 Calculate the perimeter | |Perimeter problems |

| |[pic] WT2 Length of a rectangle from its width & perimeter| | |

| |[pic] Toothpick puzzle | | |

|11.4 Areas and rectangles |[pic] Comparing areas & perimeters |The HOTsheet investigates the |LENGTH, PERIMETER & AREA: |

|A Area formulas |[pic] WT2 Area of a composite shape |perimeter of figures with the |Formula for area of a rectangle |

| | |same area. | |

| B Area units |[pic] WT1 Convert km2 to m2 |The HOTsheets in this lesson |LENGTH, PERIMETER & AREA: |

| |[pic] WT2 Convert hectares to km2 |investigate how to estimate areas|Converting area units & |

| |[pic] Perimeter vs. area |using approximate grids. |estimating |

|11.5 Area of a triangle |[pic] Investigating areas of triangles |This Hm lesson is used for 11.5 |LENGTH, PERIMETER & AREA: |

| |[pic] WT1 Calculate area from base and height |and 11.7 |Formula for area of a triangle |

| |[pic] An investigation of area | | |

|11.6 Area of a parallelogram |[pic] Understanding the formula | |LENGTH, PERIMETER & AREA: |

| |[pic] WT1 Calculate area from base and height | |Areas of parallelograms |

| |[pic] WT1 Perpendicular height given area and base | | |

|11.7 Area of composite shapes |Go to 11.5 | | |

| |[pic] Composite areas and triangles | | |

|11.8 Volume of rectangular prisms|[pic] Volumes of rectangular prisms | |VOLUME & SURFACE AREA: |

| |[pic] WT1 Volume of two prisms made of metre cubes | |Volume, capacity & prisms |

| |[pic] WT2 Use the formula to find the volume of a | | |

| |rectangular prism | | |

|11.9 Capacity |[pic] Capacity puzzles | |UPPER PRIMARY |

|A Measuring capacity |[pic] Estimating capacity | |VOLUME & CAPACITY: |

| |[pic] WT1 No. of glasses filled by 1 litre | |Measuring capacity |

| |[pic] WT2 A measured amount of water | | |

| B Litres and cubes |[pic] Water overflow | |UPPER PRIMARY |

| |[pic] WT1 Use difference in water levels to measure volume| |VOLUME & CAPACITY: |

| | | |Linking litres and cubes |

|11.10 Mass and temperature |[pic] Reading scales | |UPPER PRIMARY |

|A Measuring and recording mass |[pic] Mystery mass | |MASS: |

| | | |Measuring and recording mass |

| B Converting units of mass |[pic] Comparing Readings | |UPPER PRIMARY |

| |[pic] WT2 Convert kg to g | |MASS: |

| |[pic] WT3 Convert g to kg | |Converting units of mass |

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