MathsWorld 8 Teacher edition - Macmillan Publishers · Web viewe.g., Exercise 12.2 Level VELS Standard/PP MathsWorld 7 MathsWorld 8 Space 4.0 (Standard) At Level 4, students classify

VELS Standards & Progression Points

(for Mathematics Domain Level 4.0 to 5.0)

The following document details how the MathsWorld for VELS series addresses the standards & progression points for Mathematics (Level 4.0–5.0). We trust that you will find this resource valuable for your planning purposes.

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MathsWorld for VELS

MathsWorld for VELS Standards/PP links (Level 4.0-5.0)

Level VELS Standard/PP MathsWorld 7 MathsWorld 8

Number 4.0 (Standard)

At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions).

Chapter 1: Whole numbers* Chapter pre-test Q. 1 – 4 1.1: Place valueExercise 1.1Chapter 8: Decimals* Chapter pre-test Q. 48.1: Place valueExercise 8.1

They model integers (positive and negative whole numbers and zero), common fractions and decimals.

Chapter 6: Fractions* Chapter pre-test Q. 1, 2Warm-up p. 2296.1: What is a fraction?Exercise 6.1 Q. 1 – 6, 13

Chapter 1: Integers* Chapter pre-test Q. 2, 4, 5, 6, 8Warm-up: Protons and antiprotons

They place integers, decimals and common fractions on a number line.

Chapter 6: Fractions6.1: What is a fraction?Exercise 6.1 Q. 7Chapter 8: Decimals8.1: Place valueExercise 8.1 Q. 5, 6

Chapter 1: Integers* Chapter pre-test Q. 9, 101.1: Numbers on the other side of zero: negative numbersExercise 1.1: Q. 3, 5, 9

They create sets of number multiples to find the lowest common multiple of the numbers.

Chapter 4: Number patterns* Chapter pre-test Q. 1 – 3 4.1: MultiplesExamples 2, 3 (pp. 134 – 135) Exercise 4.1 Q. 3, 5Analysis task 3: FleadlesChapter 6: Fractions6.3: Common denominators and comparing fractionsExample 2 (p. 245) – see Reasoning column)

Chapter 4: Fractions, decimals and percentages4.1: Common denominators and comparing fractionsExample 1 (p. 158)

They interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4).

See note in MathsWorld 7 Teacher Edition p. 138See also Chapter 12: Perimeter area and volume12.3: Area: RectanglesQ. 6

Students identify square, prime and composite numbers.

Chapter 4: Number patterns* Chapter pre-test Q. 9, 104.5: Prime numbersTry this! (pp. 152 – 153) Exercise 4.5 Q. 1 – 15

MathsWorld 8 Teacher editionCopyright Macmillan Education Australia. Unauthorised copying prohibited.

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Number 4.0 (Standard)(cont.)

They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers.

Chapter 4: Number patterns* Chapter pre-test Q. 6 - 8 4.2: FactorsExercise 4.2 Q. 1 – 54.6: Finding prime factorsExercise 4.6 Q. 1 – 6

They recognise and calculate simple powers of whole numbers (for example, 24 = 16).

Chapter 4: Number patterns4.4: Square numbers, square roots and powersExercise 4.4 Q. 1, 3 - 7

Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, ¾ = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8).

Chapter 6: Fractions6.1: What is a fraction?Exercise 6.1 Q. 9 – 16Chapter 8: Decimals* Chapter pre-test Q. 58.13: Percentages, decimals and fractionsExercise 8.13 Q. 1 – 6

Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 104.9: Interchanging fractions, decimals and percentages

They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

Chapter 1: Whole numbers* Chapter pre-test Q. 5 – 81.2: Addition and subtractionExercise 1.2 Q. 1 – 91.3: MultiplicationExercise 1.3 Q. 1 – 6 1.4: DivisionExercise 1.4 Q. 1 – 5Chapter 4: Number patterns* Chapter pre-test Q. 4, 5


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Number 4.0(Standard)(cont.)

They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money.

Chapter 1: Whole numbers1.3: MultiplicationExercise 1.3 Q. 7Chapter 2: Mathematical thinking2.2: Developing problem-solving strategiesExample problem 3 Try this! p. 64Chapter 6: Fractions* Chapter pre-test Q. 8 – 10 6.4: Adding and subtracting proper fractionsExercise 6.4 Q. 1 – 36.5: Adding and subtracting mixed number fractionsExercise 6.5 Q. 1 – 26.6: Multiplying fractionsExercise 6.6 Q. 1, 5Chapter 8: Decimals* Chapter pre-test Q. 7, 88.5: Multiplication and division by powers of 10Exercise 8.5 Q. 1 – 68.6: Adding and subtracting decimalsTry this! p. 344Exercise 8.6 Q. 1 a – d, 3 a – c, 5, 68.7: Multiplication by a whole numberExercise 8.7 Q. 1, 2, 8, 10

Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 3, 4, 7, 84.2: Multiplying and dividing fractionsExamples 1 – 4 (pp. 161 – 163)Exercise 4.24.3: Adding and subtracting mixed numbersExamples 1, 2 (pp. 166, 167)Exercise 4.3

They use estimates for computations and apply criteria to determine if estimates are reasonable or not.

Chapter 1: Whole numbers* Chapter pre-test Q. 9, 10Chapter 8: Decimals* Chapter pre-test Q. 68.8: Multiplication of a decimal by a decimalStudents should be encouraged to check their answers as demonstrated in Examples 1 – 3 (pp. 352 – 353)

Chapter 4: Fractions, decimals and percentages4.6 Operations with decimalsStudents should be encouraged to check their answers as demonstrated in Examples 3 – 5 (pp. 178 – 179)


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Number 4.25

Students multiply by powers of 10, link division by powers of 10 to multiplication by decimals and use these in estimation.

Chapter 8: Decimals* Chapter pre-test Q. 9, 108:5: Multiplication and division by powers of 10Exercise 8.5 Q. 1 - 9

They know that the position of the digit zero affects the size of numbers, such as 00.070 = 0.07.

Chapter 8: Decimals8.2: Comparing decimalsExercise 8.2 Q. 3c, d8:5: Multiplication and division by powers of 10Number slides (p. 336)Exercise 8.5 Q. 1 - 9

Chapter 4: Fractions, decimals and percentages4.5: Place value, comparing decimals and rounding Examples 1, 2 (pp. 172, 173)4.6: Operations with decimalsExample 1b (p. 177): writing a zero after 35.9 does not alter the size of the number. Similarly in Example 6 (p. 179)

They explain dividing by a number between one and zero, such as dividing by 0.1 is finding out how many tenths.

Chapter 8: Decimals8.12: Dividing a decimal by a decimalTry this! p. 363See also Practice and Enrichment Worksheet 2, Q. 14 (P & E Workbook, pp. 76 – 77)

Students determine prime factors and use them to express any whole number as a product of powers of primes and to find its composite factors.

Chapter 4: Number patterns4.6: Finding prime factorsExamples 1 – 5 (pp. 157 – 161)Exercise 4.6 Q. 1 – 7

Chapter 8: Indices8.1: Numbers in index formExamples 4, 5 (p. 391)

Students use mental estimation to check the result of calculator computations.

Chapter 8: Decimals8.10: Dividing by a whole numberExamples 1 – 3 (pp. 358 – 359)Exercise 8.108:12: Dividing a decimal by a decimal Examples 1, 2 (pp. 363 – 364)Students should be encouraged to apply this type of checking to all calculations, including when using a calculator.

Chapter 4: Fractions, decimals and percentages4.6 Operations with decimalsStudents should be encouraged to check their answers as demonstrated in Examples 3 – 5 (pp. 178 – 179)


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Number 4.25(cont.)

They use written and/or mental methods to divide decimals by single digit whole numbers, interpreting the remainder.

Chapter 8: Decimals8.10: Dividing by a whole numberExamples 1 – 3 (pp. 358 – 359) Exercise 8.10 Q. 1 – 8

Chapter 4: Fractions, decimals and percentages4.6 Operations with decimalsExercise 4.6 Q. 6

They use knowledge of perfect squares to determine exact square roots.

Chapter 4: Number patterns4.4: Square numbers, square roots and powers Exercise 4.4 Q. 2

Chapter 1: IntegersExercise 1.7 Q. 4 – 8 Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 5c, d

Students convert between fraction, decimal and percentage forms, and use them to calculate and estimate, such as estimate 63% of 300 by finding two thirds.

Chapter 8: Decimals8.13: Percentages, decimals and fractionsExamples 1, 2 (p. 367)Exercise 8.13 Q. 1 – 9Analysis task 1: Dad goes shopping

Chapter 4: Fractions, decimals and percentages4.10: Finding a given percentage of a quantityExercise 4.10 Q. 1 - 3

They describe ratio as a comparison of either subset to subset (part to part) or subset to set (part to whole), using simple whole number ratios.

Chapter 6: FractionsThis analysis task provides an introduction to the concept of ratio as subset: subset fractions and subset: whole fractionsAnalysis task 1: Lotus flowers

Chapter 10: Ratios and rates10.1: RatioExercise 10.1 Q. 1 – 3, 8 – 10

They find equivalent ratios. Chapter 10: Ratios and rates10.1: RatioExercise 10.1 Q. 5

Number 4.5 Students use ‘equal division by 10’ to simplify division by whole numbers, such as 240 ÷ 40 = 24 ÷ 4 = 6.

Chapter 1: Whole numbers1.4: DivisionExercise 1.4 Q. 1 – 9Alternatively see Example 3 page 28

For estimation in division, they mentally use ‘division fact rounding’.

Chapter 1: Whole numbers1.6: EstimationExercise 1.6 Q. 4e, fExample 3c page 41

They divide by powers of 10, and multiplication by powers of 10, in mental estimation, such as 30 ÷ 0.01 is the same as 30 x 100 = 3000.

Chapter 8: Decimals8.5: Multiplication and division by powers of 10Examples 1, 2 (pp. 340, 341)Exercise 8.5 Q. 1 – 11

Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 8a – d 4.6: Operations with decimalsExample 5 (p. 179)


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Number 4.5(cont.)

Students use a model to subtract one integer, positive or negative, from another and show its equivalence to adding the opposite (additive inverse).

Chapter 1: IntegersWarm-up: Protons and antiprotons1.1: Numbers on the other side of zero: negative numbersTry this! Temperature (p. 5)1.3: Adding and subtracting integersTry this!: Flexitime (p. 14)1.4:More addition and subtraction of integersTry this! Ships and sharks (p. 19)

They estimate the square roots of whole numbers using nearby perfect squares.

Chapter 8: DecimalsAnalysis task 3: Approximate square roots

Chapter 1: IntegersAnalysis task 2: Integers as rational numbers

Students describe ratio as a comparison of either subset to subset or subset to set, where the scale factor is greater than 1 such as 2 : 5 = 1 : 2.5.

Chapter 10: Ratios and ratesExample 4 (p. 492)Exercise 10.1 Q. 7, 10, 13, 14Exercise 10.3 Q. 11

Number 4.75

Students use equal multiplication by 10 to divide by decimals, such as 0.24 ÷ 0.04 = 24 ÷ 4 = 6.

Chapter 8: Decimals8.12: Dividing a decimal by a decimalExample 1 (p. 363), Example 2 (p. 364)Exercise 8.12 Q. 1, 2

Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 8i4.6: Operations with decimalsExample 5 (p. 179)

They use a range of strategies for estimating multiplication and division calculations with decimals, fractions and integers.

Chapter 8: Decimals8.7: Multiplication by a whole numberExamples 1 – 3Exercise 8.7 Q. 78.12: Dividing a decimal by a decimalSee check in Example 1, p. 363; example 2, p. 364

Chapter 4: Fractions, decimals and percentages4.6: Operations with decimalsStudents should be encouraged to check their calculations as inExamples 1 – 5 (pp. 177 – 179)

Students use efficient mental and/or written methods to multiply or divide by two-digit numbers.

Chapter 1: Whole numbers1.3: MultiplicationExample 5 (p. 23)Exercise 1.3 Q. 61.4: DivisionExamples 4, 5 (p. 29)Exercise 1.4 Q. 5, 12, 13

Chapter 4: Fractions, decimals and percentages4.6: Operations with decimalsExample 45 (p. 178)


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Number 4.75(cont.)

They estimate and use a calculator to find squares, cubes, square and cube roots of any numbers.

Chapter 4: Number patterns4.4: Square numbers, square roots and powersExample 3 (p. 148)Exercise 4.4 Q. 2, 7, 8, 12Using your calculator p. 149Q. 1, 2, 7 – 9, 12, 13

Chapter 1: Integers1.7: Powers and roots of integersExercise 1.7Analysis task 2: Integers as rational numbers parts a, b

They multiply negative numbers together, and give a reasonable explanation of the result.

Chapter 1: Integers1.5: Multiplying integersTry this! (p. 24)Exercise 1.5Analysis task 1: 1, 2, 3, 4, what numbers are we heading for?

Students describe ratio as a comparison of either subset to subset or subset to set, where the scale factor is less than 1, such as 5 : 2 = 1 : 0.4.

Chapter 10: Ratios and rates10.1: RatioExample 4 (p. 492)Exercise 10.1 Q. 12, 13

They convert between decimals, ratios, fractions and percentages, such as compare 3 out of 4 to 5 out of 7.

Chapter 8: Decimals8.13: Percentages, decimals and fractionsExercise 8.13

Chapter 4: Fractions, decimals and percentages4.8: What is a percentage?Examples 1 – 3Exercise 4.84.9: Interchanging fractions, decimals and percentagesExamples 1 – 3Exercise 4.94.10: Finding a percentage of a given quantityExamples 1 – 5Exercise 4.104.11: Expressing one quantity as a percentage of anotherExamples 1, 2Exercise 4.11

Number 5.0 (Standard)

At Level 5, students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes (for example, 36 000 = 25 × 32 × 53).

Chapter 4: Number patterns4.6: Finding prime factorsExamples 1 – 5 (pp. 157 – 161)Exercise 4.6

Chapter 8: Indices8.1: Numbers in index formExamples 4, 5 (p. 392)Exercise 8.1 Q. 7, 8

They write equivalent fractions for a fraction given in simplest form (for example, 2/3 = 4/6 = 6/9 = … ).

Chapter 6: Fractions6.1: What is a fraction?Examples 1, 2Exercise 6.1 Q. 8 – 13

Chapter 4: Fractions, decimals and percentages4.3: Adding and subtracting mixed numbersExamples 1, 2


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They know the decimal equivalents for the unit fractions ½, 1/3, ¼, 1/5, 1/8, 1/9 and find equivalent representations of fractions as decimals, ratios and percentages (for example, a subset: set ratio of 4:9 can be expressed equivalently as 4/9 = 0.4 ≈ 44.44%).

Chapter 8: Decimals8.11: Recurring decimals and changing fractions to decimalsExample 1 (p. 361)Exercise 8.11 Q. 1, 58.13: Percentages, decimals and fractionsExamples 1, 2 (p. 367)Exercise 8.13

Chapter 4: Fractions, decimals and percentages4.9: Interchanging fractions, decimals and percentagesExamples 1 – 3 (pp. 190 – 191)Exercise 4.9 Q. 110.1 Q. 9

They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy.

Chapter 6: Fractions6.7 Dividing fractionsTry this! (p. 261)Examples 1, 2 (p. 262)Exercise 6.7

Chapter 4: Fractions, decimals and percentages4.2: Multiplying and dividing fractionsExample 3 (p. 163)4.9: Interchanging fractions, decimals and percentagesExercise 4.9Analysis task 1: Pizza fractions

Students use knowledge of perfect squares when calculating and estimating squares and square roots of numbers (for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30).

Chapter 8: DecimalsAnalysis task 3: Approximate square roots

Chapter 1: IntegersAnalysis task 2: Integers as rational numbers (p. 34)

They evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9).

Chapter 4: Number patterns4.3: Square numbers, square roots and powersExample 1 (p. 147)Examples 7, 8 (p. 150)Exercise 4.3 Q. 7, 8, 9, 12Chapter 6: Fractions6.8: Squares and square roots of fractionsExamples 1 (p. 264)Exercise 6.8 Q. 1, 2

Chapter 1: Integers1.7: Powers and roots of integersExample 1 (p. 31)Exercise 1.7 Q. 2, 3, 4, 10, 11, 12, 14, 15Chapter 4: Fractions, decimals and percentages4.4: Squares and square roots of fractionsExample 1 (p. 169)Exercise 4.4 Q. 1, 2, 5 – 9, 11,


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They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125).

Chapter 2: Mathematical thinking2.4 Mathematical reasoningExample investigation 1 (p. 79)Chapter 4: Number patterns4.6: Finding prime factorsExpressing numbers in terms of their prime factors in index form and then writing the complete factor set will familiarise students with powers of 2, 3 and 5.Examples 4, 5 (pp. 160 – 161)Exercise 4.6 Q. 5, 6

Chapter 8: Indices8.1: Numbers in index formExercise 8.1 Q. 11, 12Analysis task 1: Population explosion

They calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √(9/16) = ¾).

Chapter 6: Fractions6.8: Squares and square roots of fractionsExamples 1, 2 (p. 264)Exercise 6.8 Q. 1 – 6 Chapter 8: Decimals8.9: Squares and square roots of decimalsExamples 1, 2 (p. 356)Exercise 8.9 Q. 1 – 9

Chapter 1: Integers1.7: Powers and roots of integersExercise 1.7 Q. 5 – 9Chapter 4: Fractions, decimals and percentages* Chapter pre-test Q. 5, 94.4: Squares and square roots of fractionsExamples 1, 2 (pp. 169 – 170)Exercise 4.4 Q. 1 – 44.7: Squares and square roots of decimalsExamples 1 – 3 (pp. 182 – 183)Exercise 4.7 Q. 1, 2

They calculate cubes and cube roots of perfect cubes (for example, 3√64 = 4).

Chapter 1: Integers1.7: Powers and roots of integersExercise 1.7 Q. 12, 13Chapter 8: Indices8.2: Exploring sums of squares and cubesExercise 8.2 Q. 11

Using technology they find square and cube roots of rational numbers to a specified degree of accuracy (for example, 3√200 = 5.848 to three decimal places).

Chapter 1: IntegersAnalysis task 2: Integers as rational numbers, parts a, b (p. 35)Chapter 8: Indices8.2: Investigating sums of squares and cubesExercise 8.2 Q. 11


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Students express natural numbers base 10 in binary form, (for example, 4210 = 1010102), and add and multiply natural numbers in binary form (for example, 1012 + 112 = 10002 and 1012 × 112 = 11112).

Chapter 8: Indices8.3: Binary numbersExamples 1 – 10Exercise 8.3

Students understand ratio as both set: set comparison (for example, number of boys : number of girls) and subset: set comparison (for example, number of girls : number of students), and find integer proportions of these, including percentages (for example, the ratio number of girls: the number of boys is 2 : 3 = 4 : 6 = 40% : 60%).

Chapter 10: Ratios and rates10.1: RatioExamples 1, 2 (p. 489)Example 3 (p. 491)Exercise 10.1 Q. 1 – 15 10.2: Dividing quantities in given ratiosExamples 1, 2 (p. 497)Exercise 10.2 Q. 1 – 10

Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30).

Chapter 1: Whole numbers1.6: EstimationExamples 2, 3 (p. 40)Exercise 1.6 Q. 2 – 8

Chapter 4: Fractions, decimals and percentages4.6: Operations with decimals See checking in Examples 1 - 6

Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.

Chapter 1: Whole numbers1.3: MultiplicationExercise 1.3 Q. 7Chapter 6: Fractions* Chapter pre-test Q. 8 – 10 6.4: Adding and subtracting proper fractionsExercise 6.4 Q. 1 – 36.5: Adding and subtracting mixed number fractionsExercise 6.5 Q. 1 – 26.6: Multiplying fractionsExercise 6.6 Q. 1, 5Chapter 8: Decimals* Chapter pre-test Q. 7, 88.5: Multiplication and division by powers of tenExercise 8.5 Q. 1 – 68.6: Adding and subtracting decimalsExercise 8.6 Q. 1 a – d, 3 a – c, 5, 68.7: Multiplication by a whole numberExercise 8.7 Q. 1, 2, 8, 10

Chapter 4: Fractions, decimals and percentages4.2: Multiplying and dividing fractionsExamples 1 – 4Exercise 4.24.3 Adding and subtracting mixed numbersExamples 1, 2Exercise 4.34.6: Operations with decimals Examples 1 – 6Exercise 4.6


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They use approximations to π in related measurement calculations (for example, π × 52 = 25π = 78.54 correct to two decimal places).

Chapter 12: Perimeter, area and volume12.2: Circumference of a circleExamples 1 – 3 (pp. 519 – 520) Exercise 12.2

Chapter 11: Length, area and volume* Chapter pre-test Q. 811.1: Measuring and calculating lengthTry This! pp. 555, 556Examples 8 – 10 (pp. 556 – 558)Exercise 11.1 Q. 11 – 19 11.3: Area of a circleExamples 1 – 4 (pp. 578 – 579)Exercise 11.3 Q. 1 – 12 11.5: Surface areaExamples 2, 3 (p. 593)Exercise 11.5 Q. 2, 6, 7, 911.6: VolumeExample 6 (p. 602)Exercise 11.6 Q. 8, 9, 10c,d, 11, 12a, b, 13, 14, 15

They use technology for arithmetic computations involving several operations on rational numbers of any size.

e.g.Chapter 12: Perimeter, area and volumeMost Q. in all exercises

e.g.Chapter 4: Fractions, decimals and percentages4.6: Operations with decimalsExercise 4.6 Q. 13 – 20 Chapter 11: Length, area and volumeMost Q. in all exercisesChapter 12: Investigating datae.g., Exercise 12.2


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Space 4.0 (Standard)

At Level 4, students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater than 90°), and surfaces.

Chapter 7: Polygons* Chapter pre-test Q. 1 – 10 7.1: TrianglesTypes of triangles (p. 283)Exercise 7.1 Q. 2, 87.2: QuadrilateralsExercise 7.2 Q. 1 – 57.3: PolygonsExercise 7.3 Q. 1

Chapter 7: Polyhedra and networks* Chapter pre-test Q. 1, 27.1: Polyhedra and netsExercise 7.1 Q. 4, 7, 10

They create two-dimensional representations of three dimensional shapes and objects found in the surrounding environment.

Chapter 7: Polyhedra and networks7.1: Polyhedra and netsExamples 2, 3 (pp. 346 – 347)Exercise 7.1 Q. 1 – 3 Students can identify and draw three dimensional shapes found at school or at home, e.g., polyhedra – prisms (e.g. chocolate packets, cereal packets, lockers), pyramids (e.g., some roof designs) – cylinders (posts, drink cans), spheres (soccer ball)

They develop and follow instructions to draw shapes and nets of solids using simple scale.

Chapter 7: Polygons7.1: TrianglesExamples 5, 6 (pp. 284 – 285)Try this! p. 284Exercise 7.1 Q. 3 – 6 7.2: QuadrilateralsExercise 7.2 Q. 14, 167.3: PolygonsExercise 7.3 Q. 13, 14Chapter 13: Maps, coordinates and directions13.1: Scale drawingsExercise 13.1 Q. 10, 11, 13

Chapter 7: Polyhedra and networks* Chapter pre-test Q. 5, 87.1: Polyhedra and netsExercise 7.1 Q. 8, 9

They describe the features of shapes and solids that remain the same (for example, angles) or change (for example, surface area) when a shape is enlarged or reduced.

Chapter 6: Transformations and tessellations6.2: Congruency and similarityExercise 6.2 Q. 1 – 10

They apply a range of transformations to shapes and create tessellations using tools (for example, computer software).

Chapter 6: Transformations and tessellations6.3: TessellationsExercise 6.3 Q. 1, 4, 8


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Space 4.0 (Standard)(cont.)

Students use the ideas of size, scale, and direction to describe relative location and objects in maps.

Chapter 13: Maps, coordinates and directions* Chapter pre-test Q. 1, 413.1: Scale drawingsExample 1 (p. 564)Exercise 13.1 Q. 1 – 413.3: Locating directionExamples 1 – 4 (pp. 584 – 585) Try this! p. 582

They use compass directions, coordinates, scale and distance, and conventional symbols to describe routes between places shown on maps.

Chapter 13: Maps, coordinates and directions* Chapter pre-test Q. 5 – 7 13.3: Locating directionAnalysis task 1: Tower HillAnalysis task 2: Cycling on French Island

Students use network diagrams to show relationships and connectedness such as a family tree and the shortest path between towns on a map.

Chapter 1: Whole numbers1.2: Addition and subtractionExercise 1.2 Q.15

Chapter 7: Polyhedra and networksChapter pre-test Q. 107.3: Networks Exercise 7.3 Q. 1 – 13

Space 4.25 Students use a wide range of geometric language correctly when describing or constructing shapes and solids.

Chapter 3: Lines and angles3.1: Lines, rays and segmentsTry this! (p. 93)Exercise 3.1 Q. 1, 2, 3Analysis task 1: Catching the sun's heatAnalysis task 2: Boom anglesAnalysis task 3: A parking problem

Chapter 6: Transformations and tessellations6.2: Congruency and similarityExamples 1, 2, 4, 5, 6, 7Chapter 7: Polyhedra and networks7.1: Polyhedra and netsExercise 7.1 Q. 4, 7

They identify congruent shapes and solids when appropriately aligned.

Chapter 7: Polygons7.1: TrianglesCongruent triangles p. 281Analysis task 1: Tangram

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesExamples 10, 11, 12Exercise 3.2 Q. 11

Students identify points in the first quadrant of the plane using co-ordinates.

Chapter 13: Maps, coordinates and directions13.2: Locating positionTry this! (pp. 573 – 574)Examples 1, 2Exercise 13.2 Q. 3 – 11


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Space 4.25(cont.)

They distinguish between a coordinate naming a point and a map reference such as D12 naming a region.

Chapter 13: Maps, coordinates and directions13.2: Locating positionHighlight box p. 574Try this! pp. 572, 573Exercise 13.2 Q. 1 – 11

Space 4.5 Students apply properties of angles and lines in two dimensions, such as calculate angles of an isosceles right-angle triangle or finding all the angles of a symmetric trapezium from one angle.

Chapter 7: Polygons7.1 TrianglesExamples 3, 4 (p. 282)Exercise 7.1 Q. 10, 12 – 147.2: QuadrilateralsExample 2 (p. 296)Exercise 7.2 Q.5,8,12,13,157.3: PolygonsAnalysis task 2: Drawing polygons in MicroWorldsAnalysis task 3: Polygon seats

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesExamples 3, 4, 5 (pp. 108 – 9)Exercise 3.2 Q. 4, 5, 6

They visualise a polyhedron from its net and vice versa.

Chapter 7: Polyhedra and networks* Chapter pre-test Q. 47.1: Polyhedra and netsExercise 7.1 Q. 7, 13Analysis task 1: Truncated octahedron

They identify congruent shapes and objects, using mental rotation or reflection.

Chapter 7: PolygonsAnalysis task 1: Tangram

Students use simple fractions and proportional reasoning to interpolate between labelled coordinates in the first quadrant of the plane, or on any scale of positive numbers, such as Melbourne is about three fifths of the way between 35oS and 40oS on this atlas, so it is about 38oS.

Chapter 9: Units of length, mass and time9.1: UnitsExercise 9.1 Q. 1See suggested atlas work in Teacher edition, p. 577

Students apply properties of angles, lines and congruence in two dimensions, such as explaining why shapes will not tessellate if no combination of angles adds to 360o.

Chapter 7: PolygonsSection 7.3 PolygonsTry this! p. 301Exercise 7.3 Q. 8

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesExamples 10 – 12Exercise 3.2 Q. 11Chapter 6: Transformations and tessellations6.3: TessellationsExamples 1, 2 (p. 311)Exercise 6.3 Q. 3, 5, 6, 7


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Space 4.5(cont.)

They understand similarity as preserving shape (angles and proportion) including resizing a photo on a computer.

Chapter 6: Transformations and tessellations6.2: Congruency and similarityEnlarging and reducing: non-isometric transformations p. 294Exercise 6.2 Q. 1 – 14Chapter 10: Ratios and ratesChapter Warm-up (p. 487)

Students accurately identify points in any quadrant of the plane or on a map by interpolating between labelled coordinates.

Chapter 13: Maps, coordinates and directions13.3: Locating positionTry this! p. 573Try this! p. 574Example 1 (p. 575)Exercise 13.3 Q. 3 – 10 Analysis task 2: Coordinate tracks

They use scales on maps and plans, whether presented graphically or as comparison of units such as 1cm = 1km, or as a ratio such as 1:100000, to accurately convert between map measurements and real distances.

Chapter 13: Maps, coordinates and directions13.1: Scale drawingsExamples 1 – 5 (pp. 564 – 565)Exercise 13.1 Q. 1 – 13

Chapter 10:10.3: ProportionExamples 3, 4Exercise 10.3 Q. 5, 6

Space 5.0 (Standard)

At Level 5, students construct two-dimensional and simple three-dimensional shapes according to specifications of length, angle and adjacency.

Chapter 7: Polygons7.1: TrianglesExample 2 (p. 282)Exercise 7.1 Q. 3, 6, 9, 117.2 QuadrilateralsExercise 7.2 Q. 6, 9, 107.3: Other polygonsExercise 7.3: Q. 14Analysis task 2: Drawing polygons in MicroWorlds

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesExamples 6 – 9Exercise 3.2 Q. 8 – 10Analysis task 2: Constructing drag-resistant shapesAnalysis task 3: Drawing star polygons in MicroWorlds

They use the properties of parallel lines and transversals of these lines to calculate angles that are supplementary, corresponding, allied (co-interior) and alternate.

Chapter 3: Angles, parallel lines and polygons3.1: Angles and parallel linesExamples 3, 4, 5 (pp. 97 – 98)Exercise 3.1 Q. 5 – 10


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Space 5.0 (Standard) (cont.)

They describe and apply the angle properties of regular and irregular polygons, in particular, triangles and quadrilaterals.

Chapter 7: Polygons7.1: TrianglesExamples 3, 4, 67.2: QuadrilateralsExample 1 (p. 291), example 2 (p. 297)Exercise 7.2 Q. 5, 8Exercise 7.3 Q. 2, 3, 6, 77.3: PolygonsExamples 1 – 3Exercise 7.3 Q. 2, 3, 6, 7

Chapter 3: Polygons3.2: TrianglesTry this p. 104Examples 3, 4, 53.3: QuadrilateralsExamples 1, 2Exercise 3.3 Q. 8, 11, 12, 13, 14, 203.4: Other polygonsExamples 1 – 6Exercise 3.4 Q. 1 – 143.5: Star polygonsExample 1Exercise 3.5 Q. 10, 11

They use two-dimensional nets to construct a simple three-dimensional object such as a prism or a platonic solid.

Chapter 7: Polyhedra and networks7.1: Polyhedra and netsInvestigating polyhedra (p. 344)Analysis task 3: Truncated octahedron

They recognise congruence of shapes and solids.

Chapter 7: Polygons7.1: TrianglesExercise 7.1 Q. 87.2: QuadrilateralsExercise 7.2 Q. 2 – 4

Chapter 3: Polygons3.2: TrianglesExamples 10–12 (pp.113–115)Chapter 6: Transformations and tessellationsAnalysis task 1: Fed. Sq.

They relate similarity to enlargement from a common fixed point.

Chapter 6: Transformations and tessellations6.2: Congruency and similarityAnalysis task 1: Pantographs

They use single-point perspective to make a two-dimensional representation of a simple three-dimensional object.

Chapter 7: Polyhedra and networks7.1: Polyhedra and netsTry this! p. 348Example 4 (p. 349)Exercise 7.1 Q. 1, 2

They make tessellations from simple shapes.

Chapter 6: Transformations and tessellations6.3: TessellationsExercise 6.3 Q. 1, 2, 4Analysis task 2: Fed. Sq.Analysis task 3: RMIT Storey Hall


17



Space 5.0 (Standard)(cont.)

Students use coordinates to identify position in the plane.

Chapter 13: Maps, coordinates and directions13.2: Locating positionExercise 13.2 Q. 3 – 15Analysis task 3: Coordinate tracks

Chapter 6: Transformations and tessellations6.1: Isometric transformationsExamples 2, 3, 4 (pp. 278 – 280)Exercise 6.1 Q. 8, 11, 12Chapter 10: Ratios and rates10.6: Rates of changeExamples 2, 3 (pp. 529, 532)Exercise 10.6 Q. 2 – 9 Analysis task 1: Phone cardsChapter 13: Functions and models13.1: Mapping diagrams and functionsExample 2 (p. 693)Exercise 13.1 Q. 3 – 6

They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps.

Chapter 13: Maps, coordinates and directions13.3: Locating directionExamples 1 – 4Exercise 13.3 Q. 1 – 12 Analysis task 1: Tower HillAnalysis task 2: Cycling on French Island

Chapter 10: Ratios and rates10.5: Gradients and ratesExample 2Try this! p. 521Exercise 10.5 Q. 4 – 9Analysis task 2: Rivergum National ParkAnalysis task 3: Highs, lows and tropical cyclones

They use network diagrams to specify relationships.

Chapter 7: Polyhedra and networks7.3: NetworksExercise 7.3 Q. 1 – 10

They consider the connectedness of a network, such as the ability to travel through a set of roads between towns.

Chapter 7: Polyhedra and networksChapter pre-test Q. 9, 107.3: NetworksExercise 7.3 Q. 10, 11, 12 Analysis task 2: Flight pathsAnalysis task 3: Locating a power station


18



Measurement, chance and data 4.0 (Standard)

At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity time and temperature.

Chapter 9: Units of length, mass and time* Chapter pre-test Q. 1 – 7 9.1: Units Try this! p. 380Exercise 9.1Chapter 12: Perimeter, area and volume* Chapter pre-test Q. 1 – 10 12.1: PerimeterTry this! p. 509Examples 1, 2 (pp. 510, 511)Exercise 12.1 Q. 112.3: Area: RectanglesExamples 1 – 6 pp. 524, 525Exercise 12.3 Q. 1 – 412.5: VolumeTry this! p. 540Examples 1, 2 (p. 543)Exercise 12.5 Q. 1 – 4

Chapter 11: Length, area and volumeAll sections

They measure angles in degrees.

Chapter 3: Lines and angles* Chapter pre-test Q. 9, 103.2: AnglesExamples 2, 3 (p. 388)Exercise 3.2 Q. 1, 2, 6, 7, 9, 12Analysis task 1: Catching the sun's heatAnalysis task 2: Boom anglesAnalysis task 3: A parking problem

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesExamples 7 – 9 pp. 111 – 113Exercise 3.2 Q. 9, 10Further angle work in sections 3.3 – 3.5

They measure as accurately as needed for the purpose of the activity.

Chapter 12: Perimeter, area and volume12.2: Circumference of a circleTry this! p. 51812.5: VolumeExercise 12.5 Q. 5

Chapter 11: Length, area and volume11.6: VolumeExercise 11.6 Q. 6

They convert between metric units of length, capacity and time (for example, L–mL, sec–min).

Chapter 9: Units of length, mass and time* Chapter pre-test Q. 3, 69.2: LengthTry this! p.388Examples 1, 2 (p. 388)Exercise 9.2 Q. 1, 29.4: Time calculationsExamples 1 – 6 (p. 399 – 401)Exercise 9.4 Q. 1 – 15 Chapter 12: Perimeter, area and volume12.6: CapacityExercise 12.6 Q. 2, 6, 8, 12

Chapter 11: Length, area and volumeChapter pre-test Q. 111.1: Measuring and calculating lengthExamples 1, 2 (p. 551)Exercise 11.1 Q. 511.2 Area of polygonsExamples 1, 2 (p. 565)Example 4 (p. 566)Exercise 11.2 Q. 111.6: VolumeExamples 1 – 3 (pp. 599 – 600)Exercise 11.6 Q. 1


19



Measurement, chance and data 4.0 (Standard)(cont.)

Students describe and calculate probabilities using words, and fractions and decimals between 0 and 1.

Chapter 10: Chance* Chapter pre-test Q. 4 – 610.1: The language of chanceTry this! p. 425Example 1Exercise 10.1

They calculate probabilities for chance outcomes (for example, using spinners) and use the symmetry properties of equally likely outcomes.

Chapter 10: Chance10.2: Predicting probabilityExample 1Exercise 10.2 Q. 1, 2, 3

They simulate chance events (for example, the chance that a family has three girls in a row) and understand that experimental estimates of probabilities converge to the theoretical probability in the long run.

Chapter 10: Chance10.3: Theoretical versus long run probabilityTry this! p. 440Example 1 (p. 441)Try this! p. 442Exercise 10.3 Q. 4, 5

Students recognise and give consideration to different data types in forming Q.naires and sampling.

Chapter 14: Making sense of data14.1: Types of dataTry this! p. 601Exercise 14.1 Q. 4Analysis task 3: The class survey

They distinguish between categorical and numerical data and classify numerical data as discrete (from counting) or continuous (from measurement).

Chapter 14: Making sense of data14.1: Types of dataExamples 1, 2 (pp. 602, 603)Exercise 14.1 Q. 1 - 3

Chapter 12: Investigating data12.1: Types of dataExamples 1, 2 (pp. 622, 623)Example 3 (p. 625)Exercise 12.1

They present data in appropriate displays (for example, a pie chart for eye colour data and a histogram for grouped data of student heights).

Chapter 14: Making sense of data* Chapter pre-test Q. 43, 614.3: Displaying and interpreting data in graphsExample 2 (p. 613)Exercise 14.3 Q. 1, 3

They calculate and interpret measures of centrality (mean, median, and mode) and data spread (range).

Chapter 14: Making sense of data* Chapter pre-test Q. 53, 614.4: Summarising data: Measures of centreExamples 1, 2, 3 (pp. 623 – 625)Exercise 14.4 Q. 1 – 10

Chapter 12: Investigating data12.6: Measures of centre and spreadExamples 1 – 4 (pp. 662 – 664)Exercise 12.6 Q. 1 – 7


20



Measurement, chance and data 4.25

Students estimate length, perimeter, area of rectangles and time providing suitable lower and upper bounds for estimates.

Chapter 12: Perimeter, area and volume12.1: PerimeterTry this! p. 509Include further school-based activities

Chapter 11: Length, area and volumeChapter Warm-up Try this!

They estimate and measure angles 0° to 360°

Chapter 3: Lines and anglesChapter pre-test Q. 5, 9, 103.2: AnglesExamples 2, 3 (pp. 102, 103)Exercise 3.2 Q. 1, 2, 6, 7, 9, 11, 12

They use measurement formulas for perimeter and area of a rectangle and use correct units.

Chapter 12: Perimeter, area and volume12.1: PerimeterTry this! (p. 510)Examples 2, 3 (p. 511)12.2: Circumference of a circleExamples 5, 6 (pp. 526)Exercise 12.3 Q. 3, 4

Chapter 11: Length, area and volume11.1: Measuring and calculating lengthExamples 6, 7 (p. 554)Exercise 11.1 Q. 6, 711.2: Area of polygonsExamples 3, 4, 5 (pp. 565 – 566)Exercise 11.2 Q. 2

Students systematically list outcomes for a multiple event experiment such as getting at least one tail if a coin is tossed three times.

Chapter 10: Take a chance!10.1: The language of chanceExamples 2, 3 (p. 430)Example 6 (p. 434)Exercise 10.2 Q. 1, 2, 4, 13

Chapter 9: Exploring chance9.1: ProbabilityExample 1 (pp. 433 – 434)Exercise 9.1 Q. 4

They can identify empirical probability as long-run relative frequency including random number generator to simulate rolling two dice.

Chapter 10: Take a chance!10.3: Theoretical versus long-run probabilityExample 10.3Q. 1 - 6

Chapter 9: Exploring chance9.2: Simulating random processesTry this! p. 441Examples 1, 2 (pp. 442 – 444)Exercise 9.2 Q. 2 – 5

They design simulations for simple chance events, such as designing a spinner to simulate a probability of two out of five.

Chapter 10: Take a chance!10.2: Predicting probabilityExercise 10.2 Q. 1110.3: Theoretical versus long-run probabilityExercise 10.3 Q. 3

Chapter 9: Exploring chance9.1: ProbabilityExercise 9.1 Q. 5

Students organise and tabulate univariate data, including grouped and ungrouped, continuous and discrete.

Chapter 14: making sense of data14.2: Collecting and recording dataExample 2 (p. 606)Exercise 14.2 Q. 3, 4, 5

Chapter 12: Investigating data12.2: Organising data using tablesExample 1 (p. 631)Exercise 12.2 Q. 1 – 8


21




Students extend their range of personal benchmarks for estimating quantities, such as how far one can drive in an hour or one litre of water weighs 1 kg.

Number CrunchMany of the Number Crunch Q. can be used to encourage students to make realistic estimates of quantities. One approach is to have a Number Crunch noticeboard where students can display their estimates and research.Chapter 2: Mathematical thinkingInvestigation 2 (p. 86)Chapter 9: Units of length, mass and time9.3: MassExercise 9.3 Q. 3Chapter 12: Perimeter, area and volume12.6: CapacityExercise 12.6 Q. 1

Number CrunchMany of the Number Crunch Q. can be used to encourage students to make realistic estimates of quantities. One approach is to have a Number Crunch noticeboard where students can display their estimates and research.Chapter 11: Length, area and volumeChapter Warm-up Try this!

They calculate with time, including using bus timetables to determine duration of a trip.

Local timetables should be used where possible.Chapter 9: Units of length, mass and time9.5 Time and travelExample 1Exercise 9.5 Q. 1 - 15 Analysis task 1: Coach to Warrnambool

They use measurement formulas for the area and perimeter of triangles and parallelograms.

Chapter 12: Perimeter, area and volume12.4: Area: Parallelograms and trianglesExamples 1 – 3 (pp. 533 – 5)Exercise 12.4 Q.

Chapter 11: Length, area and volume11.1 Measuring and calculating lengthExercise 11.111.2 Area of polygonsExercise 11.211.3: Area of a circleExercise 11.3

They calculate areas of simple composite shapes, such as the floor area of a house.

Chapter 12: Perimeter, area and volume12.3: Area: rectanglesExample 7 (p. 527)Exercise 12.3 Q. 11, 13, 14Area: Parallelograms and trianglesExercise 12.4 Q. 6 – 15

Chapter 11: Length, area and volume11.4 Composite areasExamples 1, 2, 3 (pp. 584 – 586) Exercise 11.4 Q. 1 – 9

Students use a two way table to display the outcomes for a two-event experiment such as using a 3-by-4 table to show the outcomes when students

Chapter 9: Exploring chance9.4: Two-way tablesExamples 1, 2, 3 (pp. 459 – 465)


22



are randomly allocated a drink (orange, pineapple or apple juice) and a sandwich (salad, cheese, ham or vegemite).

Exercise 9.4 Q. 1 – 11 9.5: Tree diagrams and tablesExample 2 (p. 473)Exercise 9.5 Q. 8, 9


23



Measurement, chance and data 4.5(cont.)

Students represent uni-variate data in appropriate graphical forms such as stem and leaf plots, bar charts and histograms.

Chapter 14: Making sense of data14.5: Summarising data: visuallyExamples 1, 2, 3 (pp. 629 – 634)Exercise 14.5 Q. 1 – 12

Chapter 12: Investigating data12.3: Displaying data using stem plots and dot plotsExamples 1 – 3 (p. 636)Exercise 12.312.4: Pie charts and column graphsExamples 1 – 3Exercise 12.412.5: Line graphs and histogramsExample 1 (p. 654)Exercise 12.5 Q. 3, 4, 5

They calculate mean, median, mode and range for ungrouped data and make simple inferences.

Chapter 14: Making sense of data14.4: Summarising dataExamples 1 – 4 (pp. 623–625)Exercise 14.4 Q. 1 - 10


Students convert between a wide range of metric units.

Chapter 9: Units of length, mass and time9.3: MassTry this! p. 392Example 1 (p. 393)Exercise 9.3 Q. 3, 5 – 8, 11, 14, 15Chapter 12: Perimeter, area and volume12.3: Area: RectanglesArea units (p. 524)Exercise 12.3 Q. 1

Chapter 11: Length, area and volume11.1: Area of polygonsExamples 1, 2 (p. 565)Exercise 11.2 Q. 111.6: VolumeExamples 1, 2 (p. 599)Exercise 11.6Q. 1

They explain the links between metric units such as mL and cm3, 1 litre of water and 1 kg.

Chapter 12: Perimeter, area and volume12.6: CapacityExample 1Exercise 12.6 Q. 3 – 5, 7, 9 – 11, 13, 15

Chapter 11: Length, area and volume11.6: VolumeUnits of capacity p. 599

They can calculate with time using a calculator.

Chapter 9: Units of length, mass and time9.4: Time calculationsExample 2 (p. 399)Exercise 9.4 Q. 13, 15Chapter 12: Perimeter, area and volume12.6: CapacityExercise 12.6 Q. 9, 12

Chapter 10: Ratios and rates10.4: RatesExamples 2, 3 (p. 504)Examples 6, 7, 8 (pp. 507 – 508) Exercise 10.4 Q. 1 – 4, 6, 7Analysis task 1: Phone cards


They explain the links between the area of a rectangle with areas of triangles, parallelograms and trapezia, including demonstrating how

Chapter 12: Perimeter, area and volume12.4: Area: Parallelograms and trianglesArea of parallelograms (p.

Chapter 12: Perimeter, area and volume11.2: Area of polygonsSee pp. 566 – 567, 568 – 569


24



the area of a given non-right-angle triangle is half the area of a rectangle with same base and height.

533)Area of triangles (p. 534)Exercise 12.4 Q. 2, 3, 4


25



They use measurement formulas for the area and circumference of circles and composite shapes.

Chapter 12: Perimeter, area and volume12.2: Circumference of a circleTry this! p. 518Examples 1 – 3 (pp. 519 – 520)Exercise 12.2

Chapter 11: Length, area and volume11.1: Measuring and calculating lengthExamples 8, 9, 10 (pp. 557 – 58)Exercise 11.111.3: Area of a circleExamples 1 – 4 (pp. 578 – 579) Exercise 11.211.4: Composite shapesExamples 1, 2 (pp. 584 – 585)Exercise 11.4

They calculate volumes from estimates of lengths providing suitable lower and upper bounds.

A school treasure hunt activity can incorporate estimating such as estimate the volume of a locker, of the school hall. This could be organised on an inter-class competition basis.

Chapter 11: Length, area and volume11.6: VolumeExercise 11.6 Q. 6See note in MathsWorld 8 Teacher Edition p. 605

They distinguish absolute and percentage error, such as a speed camera is accurate to within 2 km/hr or an underwater pressure meter is accurate to within 0.01%.

Chapter 11: Length, area and volume11.1: Measuring and calculating lengthTry this! p. 550Examples 3 – 5 (pp. 551 – 553)Exercise 11.1 Q. 1 – 4

Students use a tree diagram to calculate theoretical probabilities, such as drawing a tree diagram for the experiment of spinning a red-blue-yellow-green spinner twice and find from the sixteen equally likely outcomes the probability that at least one is blue.

Chapter 9: Exploring chance9.5: Tree diagrams and tablesExample 1 (p. 472)Exercise 9.5 Q. 1 – 6, 11, 12Analysis task 1: Hopping frogs


Students interpret graphical forms and summary statistics in context, including recognising misleading presentations of data or informally identify skewed distributions.

Chapter 12: Investigating data12.5: Line graphs and histogramsTry this! (p. 654)Exercise 12.5 Q. 9

They describe how summary See note in MathsWorld 8


26



statistics for measures of centre and spread are affected by outliers and distribution and make appropriate choices, such as choosing the size when ordering one sized caps to sell at a fair.

Teacher Edition p. 626


27



They organise and tabulate continuous data (grouped and ungrouped) using appropriate technology for larger data sets.

Chapter 12: Investigating data12.5: Line graphs and histogramsExample 1 (pp. 654 – 655)Exercise 12.5 Q. 4, 5

They calculate mean, median and mode for grouped data, such as age to nearest month, and make inferences.

Chapter 12: Investigating data12.6: Measures of centre and spreadTry this! p. 662Examples 1, 2, 3 (pp. 662 – 664)Example 8 (p. 669 – 670) Exercise 12.6 Q. 8, 9, 10

Measurement, chance and data 5.0 (Standard)

At Level 5, students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context.

Chapter 9: Units of length, mass and volumeAll sections and analysis tasksChapter 12: Perimeter, area and volumeAll sections and analysis tasks

Chapter 11: Length, area and volumeAll sections and analysis tasks

They interpret and use measurement formulas for the area and perimeter of circles, triangles and parallelograms and simple composite shapes.

Chapter 12: Perimeter, area and volume12.1: Perimeter12.2: Circumference of a circle12.3: Area: Rectangles12.4: Area: Parallelograms and trianglesAnalysis task 1: Paint calculatorAnalysis task 2: Paint calculatorAnalysis task 3: Paper sizes

Chapter 11: Length, area and volume11.1: Length, area and volume11.2: Area of polygons11.3: Area of a circle11.4: Composite areaAnalysis task 1: Floral clockAnalysis task 3: Snowflake fractal


They calculate the surface area and volume of prisms and cylinders.

Chapter 12: Perimeter, area and volume12.5: Volume12.6: Capacity

Chapter 11: Length, area and volume11.5: Surface areaExamples 1 – 4 (pp. 592 – 595)Exercise 11.5 Q. 3, 411.6: VolumeExamples 5, 6 (pp. 600 – 601)Exercise 11.6 Q. 2 – 16Analysis task 2: Cake boxes

Students estimate the accuracy of measurements and give suitable lower and upper bounds for measurement values.

Chapter 11: Length, area and volume11.1: Measuring and calculating lengthTry this! p. 550


28



Examples 3, 4 (pp. 551 – 553)Exercise 11.1 Q. 1 – 4


29



They calculate absolute percentage error of estimated values.

Chapter 11: Length, area and volume11.1: Measuring and calculating lengthTry this! p. 550Example 4 (p. 552)Exercise 11.1 Q. 3, 4

Students use appropriate technology to generate random numbers in the conduct of simple simulations.

Chapter 10: Take a chance!10.3: Theoretical versus long-run probabilityTry this! p. 442Exercise 10.3 Q. 1 – 3

Chapter 9: Exploring chance9.2: Simulating random processesTry this! p. 441Try this! p. 443Exercise 9.2 Q. 3, 5

Students identify empirical probability as long-run relative frequency.

Chapter 10: Take a chance!10.3: Theoretical versus long-run probabilityExercise 10.3 Q. 1 – 7

Chapter 9: Exploring chance9.2: Simulating random processesTry this! p. 441Try this! p. 443Exercise 9.2 Q. 1 – 5 9.3: Estimating probability using relative frequencyExamples 1, 2, 3 (p. 449 – 453)Exercise 9.3 Q. 1 – 15

They calculate theoretical probabilities by dividing the number of possible successful outcomes by the total number of possible outcomes.

Chapter 10: Take a chance!10.2: Predicting probabilityExamples 1 – 4 (pp. 428 – 432)Exercise 10.2 Q. 1 – 10

Chapter 9: Exploring chance9.1: ProbabilityExample 1 (pp. 433 – 434)Exercise 9.1 Q. 8 – 14


They use tree diagrams to investigate the probability of outcomes in simple multiple event trials.

Chapter 10: Take a chance!10.2: Predicting probabilityExample 5 (pp. 432 – 433)Exercise 10.2 Q. 13 – 15

Chapter 9: Exploring chance9.5 Tree diagrams and tablesExample 1 (p. 471)Exercise 9.5 Q. 1 – 6, 11, 12

Students organise, tabulate and display discrete and continuous data (grouped and ungrouped) using technology for larger data sets.

Chapter 12: Investigating data12.2: Organising data using tables

They represent uni-variate data in appropriate graphical forms including dot plots, stem and leaf plots, column graphs, bar charts and histograms.

Chapter 12: Investigating data12.3: Displaying data using stem plots and dot plots12.4: Pie charts and column graphs12.5: Line graphs and


30



histograms

They calculate summary statistics for measures of centre (mean, median, mode) and spread (range, and mean absolute difference), and make simple inferences based on this data.

Chapter 12: Investigating data12.6: Measures of centre and spreadExample 6 (p. 667)Exercise 12.6


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Structure 4.0 (Standard)

At Level 4, students form and specify sets of numbers, shapes and objects according to given criteria and conditions (for example, 6, 12, 18, 24 are the even numbers less than 30 that are also multiples of three).

They use Venn diagrams and Karnaugh maps to test the validity of statements using the words none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even numbers’).

Chapter 6: Fractions6.3: Common denominators and comparing fractionsTry this! p. 244

Chapter 9: Exploring chance9.4: Two-way tablesExamples 1 – 3 (pp. 459 – 465) Exercise 9.4 Q. 1 – 11

Students construct and use rules for sequences based on the previous term, recursion (for example, the next term is three times the last term plus two), and by formula (for example, a term is three times its position in the sequence plus two).

Chapter 5: Algebra expressions and relationships5.8: Using rules to solve problemsExample 1 (p. 215)Exercise 5.8 Q. 1 – 8

Students establish equivalence relationships between mathematical expressions using properties such as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)).

Chapter 1: Whole numbers1.3: MultiplicationExamples 2, 3, 4 (pp. 22 – 23)Exercise 1.3 Q. 4, 51.5: Order of operationsExercise 1.5 Q. 5, 6, 11, 13Chapter 5: Algebra expressions and relationships5.2: Combining expressionsExamples 1-3 (pp.184-185)Exercise 5.2 Q. 1 – 9

Students identify relationships between variables and describe them with language and words (for example, how hunger varies with time of the day).

Chapter 5: Algebra toolboxAnalysis task 3: Generalising the number laws

Students recognise that addition and subtraction, and multiplication and division are inverse operations.

Chapter 5: Solving equations11.3: Solving equations: flow chartsTry this! p. 467, 468Examples 1, 2 (pp. 470 – 471)Exercise 11.3

Chapter 5: Algebra toolbox5.6: Solving equations: arithmetic strategiesExamples 2, 3 (pp. 242 – 243) Exercise 5.6 Q. 6 – 10


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Structure 4.0 (Standard)(cont.)

They use words and symbols to form simple equations.

Chapter 11: Solving equationsChapter pre-test Q. 5, 6Warm-up Try this! p. 45711.2: Solving equations: Arithmetic strategiesExercise 11.2 Q. 10 – 15

They solve equations by trial and error.

Chapter 11: Solving equations11.2: Solving equations: Arithmetic strategiesExamples 1, 2 (pp. 462 – 463)Exercise 11.2 Q. 1 – 18

Chapter 5: Algebra toolbox5.6 Solving equations: arithmetic strategiesExample 1 (pp. 241 – 242)

Structure 4.25 Students use correct language to describe the relationships between components of a Venn Diagram.

See note in MathsWorld 7 Teacher Edition, p. 133

Students sketch a graph to show relationship and describe key points in words, such as excitement levels during a football game against time.

They determine the independent variable and specify the allowable values for both variables when describing a function relating two variables.

Chapter 5: Algebraic expressions and relationships5.3: Using rules to make tablesTry this! p. 187Example 1 (p. 188)(Independent and dependent are represented as Input and Output numbers in MathsWorld 7, with formal introduction of the concept of independent and dependent variables in MathsWorld 8.5.8: Using rules to solve problemsExample 1 (p. 215)Exercise 5.8 Q. 1 – 8

Chapter 10: Ratios and rates10.6: Rates of changeExample 2 (p. 529)Exercise 10.6 Q. 2 – 9Chapter 13: Functions and modelsAnalysis task 1: How high will it bounce?Analysis task 2: Advertising and sales

Students interpret an algebraic letter as a number and not an object or abbreviation.

Chapter 5: Algebraic expressions and relationships5.1: Introduction to variablesExamples 1, 2, 3 (pp. 178 – 179)


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Structure 4.25(cont.)

They express relationships algebraically, such as there are n biscuits in a packet therefore there are 2 x n biscuits in two packets.

Chapter 5: Algebraic expressions and relationships5.1: Introducing variablesExamples 2, 3 (pp. 180 – 181)Exercise 5.1 Q. 1 – 125.2: Combining expressionsTry this! p. 183

They observe generality in a number pattern and express it verbally or algebraically, such as square numbers 1, 4, 9, 16, 25 generalises to n x n .

Chapter 5: Algebraic expressions and relationships5.8: Using rules to solve problemsExample 1 (pp. 215 – 216)Exercise 5.8 Q. 1 – 9 Analysis task 1: Tom and Tori's towersAnalysis task 2: Shape animals

Chapter 5: Algebra toolboxAnalysis task 2: Odds and evens

They extend linear number patterns and give a general formula using symbols and/or words such as 3, 7, 11 start with 3 and add 4 to get the next term.

Chapter 4: Number patterns4.7: Investigating number sequencesExercise 4.7 Q. 5Chapter 5: Algebra expressions and relationships5.4: Finding single step rulesExercise 5.4 Q. 1, 2, 4, 5,

They recognise equivalence between simple equivalent expressions, such as a + a + a = 3 x a = 3a.

Chapter 5: Algebra expressions and relationships5.1: Introduction to variablesExample 3 (p. 181)5.2: Combining expressionsTry this! p. 183Examples 1, 2 (pp. 183 – 184)Exercise 5.2 Q. 1 – 9

Chapter 5: Algebra toolbox5.1: Algebraic expressionsExamples 1 – 5 (pp. 216 – 219)Exercise 5.1 Q. 1 – 15

Structure 4.5 Students use functions such as when sharing a 60 cm strap of liquorice among friends, the length of liquorice each gets is 60 cm divided by number of friends, L = 60/n described in words or symbols to create a table of values and plot points to make a graph.

Chapter 13: Maps, coordinates and directions13.2: Locating positionExample 3 (pp. 576 - 577)Exercise 13.2 Q. 14, 15


34




Students extend linear number patterns, and describe them in relation to the position number, such as 3, 7, 11, … four times the position number minus 1.


They solve linear equations using tables of values and a series of inverse operations, including backtracking, such as 3m – 14 = 20, 2(3m – 14) + 8 = 48).

Chapter 11: Solving equations11.3: Solving equations: flowchartsExamples 1, 2 (pp. 469 – 470)Exercise 11.3 Q. 1 – 19

Chapter 5: Algebra toolbox5.6: Solving equations: arithmetic strategiesExamples 1 – 3 (pp. 241 – 243)Exercise 5.6 Q. 1 – 10

They solve inequalities showing the solutions on number lines, such as x + 4 > 7.

Chapter 5: Algebra toolbox5.7: Solving with algebraExample 1 (p. 251)Exercise 5.7 Q. 17, 27

They use inverses to rearrange simple formulas, including p = c + m becomes m = p – c, and to find equivalent algebraic expressions.

Chapter 5: Algebra toolbox5.7: Solving with algebraExercise 5.7 Q. 22

They use the distributive law to find and check equivalent expressions, such as 2(m + 5) = 2m + 10.

Chapter 5: Algebra toolbox5.3: Expanding algebraic expressionsTry this! p. 227Examples 1, 2 (p. 228)Exercise 5.3 Q. 1 – 14 5.3: Factorising algebraic expressionsTry this! p. 231Examples 2, 3 (pp. 232 – 233) Exercise 5.3 Q. 3 – 7

Structure 4.75 Students use the terms intersection, union and complement of sets correctly.


See note in MathsWorld 8 Teacher Edition

They list all subsets of a given set, observing through examples that there are 2n subsets of a set of n elements.

Chapter 2: Mathematical thinking2.1: Mathematising: representing a problemExample problem 3 (p. 57) See note in MathsWorld 7 Teacher Edition, p. 57


35




Students use linear and other functions such as f(x) = 2x – 4, xy = 24, y = 2x and y = 4 – x2 to model situations, such as the trajectory when diving into a pool.

Chapter 5: Algebra toolbox5.8: Solving equations: FormulatingTry this! p. 256Chapter 8: IndicesAnalysis task 1: Population explosionChapter 13: Functions and modelsChapter Warm-up Try this! p. 68613.1: Mapping diagrams and functionsExercise 13.1 Q. 13 – 15, 17, 1813.3: Mathematical modelsExample 1 (p. 715)Exercise 13.3 Q. 1 – 10Analysis task 1: How high will it bounce?Analysis task 2: Advertising and salesAnalysis task 3: Fencing a guinea pig enclosure

They create graphs (all four quadrants of the Cartesian coordinate system) and tables of values for linear functions (e.g. f(x) = 0.2x– 4) expressed symbolically and describe how features of the function are reflected in the table or graph.

Chapter 13: Functions and models13.2: Investigating linear functionsExample 1 (pp. 706 – 707)Exercise 13.2 Q. 1 – 10 Exercise 13.1 Q. 13 – 15, 17, 1813.3: Mathematical models

They identify a steady rate of change in terms of the steady slope of a linear graph.

Chapter 10: Ratios & rates10.6: Rates of changeExample 1 (p. 528)

They name situations that might be modelled by a linear function, such as profit as a function of the number of units sold, explaining why by identifying the constant rate of change.

Chapter 13: Functions and models13.2: Investigating linear functions

Students extend number patterns based on square numbers, and generalise the patterns using symbols, such as the next square is found by adding the next odd number (n + 1)2 = n2 + (2n + 1).

Chapter 2: Mathematical thinking2.4: Developing strategies to think about my thinkingProblem set 2.4 Q. 5


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They rearrange simple formulas, such as s = d/t, so t = d/s .

Chapter 5: Algebra toolbox5.7: Solving with algebraExercise 5.7 Q. 23 – 25

Structure 5.0 (Standard)

At Level 5 students identify collections of numbers as subsets of natural numbers, integers, rational numbers and real numbers.


They use Venn diagrams and tree diagrams to show the relationships of intersection, union, inclusion (subset) and complement between the sets.


They list the elements of the set of all subsets (power set) of a given finite set and comprehend the partial-order relationship between these subsets with respect to inclusion (for example, given the set {a, b, c} the corresponding power set is {Ø, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}.)

Chapter 2: Mathematical thinking2.1: Mathematising: representing a problemExample problem 3 (p. 57)See note in MathsWorld 7 Teacher Edition

They test the validity of statements formed by the use of the connectives and, or, not, and the quantifiers none, some and all, (for example, ‘some natural numbers can be expressed as the sum of two squares’).

Chapter 2: Mathematical thinking2.3: Developing strategies to think about my thinkingProblem set 2.3 Q. 8Chapter 4: Number patterns4.1: MultiplesCommon multiples p. 133Example 2 (p. 134)Exercise 4.1 Q. 54.2: FactorsCommon factors p. 139Example 2 (p. 140)Exercise 4.2 Q. 3Chapter 6: Fractions6.3: Common denominators and comparing fractionsTry this! p. 244Chapter 7: Polygons7.2: QuadrilateralsTry this! pp. 292 – 293Exercise 7.2: Q. 11

Chapter 9: Investigating chance9.4: Two-way tablesExample 1, 2, 3 (pp. 459 – 465) Exercise 9.4 Q. 1 – 10


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They apply these to the specification of sets defined in terms of one or two attributes, and to searches in data-bases.

Chapter 2: Mathematical thinking2.3: Developing strategies to think about my thinkingProblem set 2.3 Q. 8

Chapter 9: Investigating chance9.4: Two-way tablesExamples 1 – 3 (pp. 459 – 465) Exercise 9.4 Q. 1 – 10

Students apply the commutative, associative, and distributive properties in mental and written computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10).

Chapter 1: Whole numbers1.3: MultiplicationExamples 2, 3, 4 (pp. 22 – 23)Exercise 1.3Q. 4, 5

They use exponent laws for multiplication and division of power terms (for example 23 × 25 = 28, 20 = 1, 23 ÷ 25 = 2−2, (52)3 = 56 and (3 × 4)2 = 32 × 42).

Chapter 8: Indices8.1: Numbers in index formExamples 6, 7, 8Exercise 8.1 Q. 128.4: Index form with pronumeralsExamples 1 – 5 (pp. 412 – 414) Exercise 8.4 Q. 1 – 12

Students generalise from perfect square and difference of two square number patterns (for example, 252 = (20 + 5)2 = 400 + 2 × (100) + 25 = 625. And 35 × 25 = (30 + 5) (30 - 5) = 900 − 25 = 875)

Chapter 8: Indices8.2: Exploring sums of squares and cubesSee note in MathsWorld 8 Teacher Edition

Students recognise and apply simple geometric transformations of the plane such as translation, reflection, rotation and dilation and combinations of the above, including their inverses.

Chapter 6: Transformations and tessellations6.1: Isometric transformationsExamples 1 – 4 (pp. 277 – 280) Exercise 6.1 Q. 1 – 14 6.2: Congruency and similarityExercise 6.2

They identify the identity element and inverse of rational numbers for the operations of addition and multiplication (for example, ½ + − ½ = 0 and 2/3 × 3/2 = 1).

Chapter 11: Solving equations11.5: Solving equations: Doing the same to both sidesExamples 1 – 9 (pp. 484 – 488) Exercise 11.5 Q. 1 – 15Analysis task 2: Analysing solutions

Chapter 5: Algebra toolbox5.7: Solving with algebraExamples 1 – 6 (pp. 247 – 250)Exercise 5.7 Q. 1 – 20


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Students use inverses to rearrange simple mensuration formulas, and to find equivalent algebraic expressions (for example, if P = 2L + 2W, then W = P/2 − L. If A = πr2 then r = √A/π).

Chapter 12: Perimeter, area and volume12.2: Circumference of a circleExample 2Exercise 12.2 Q. 15

Chapter 5: Algebra toolbox5.7: Solving with algebraExercise 5.7 Q. 23 – 26

They solve simple equations (for example, 5x+ 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations.

Chapter 11: Solving equations11.5: Solving equations: Doing the same to both sidesExamples 1 – 9 (pp. 484 – 488) Exercise 11.5 Q. 1 – 15

Chapter 5: Algebra toolbox5.7: Solving with algebraExamples 1 – 6 (pp. 247 – 250) Try this! p. 246

They recognise and use inequality symbols.

Chapter 1: Whole numbers1.1: Place valueExample 2 (p. 10)Exercise 1.1 Q. 4Chapter 6: fractions6.3: Common denominators and comparing fractionsExample 1 (p. 245)Exercise 6.3 Q.3Chapter 8: Decimals8.2: Comparing decimalsExample 1 (p. 325)Exercise 8.2 Q. 2

Chapter 1: Integers1.2: Comparing and ordering integersExample 1 (p. 11)Exercise 1.2 Q. 4Chapter 5: Algebra toolbox5.7: Solving with algebraExample 7 (p. 251)Exercise 5.7 Q. 17, 27

They solve simple inequalities such as y ≤ 2x+ 4 and decide whether inequalities such as x2

> 2y are satisfied or not for specific values of x and y.

Chapter 5: Algebra toolbox5.7: Solving with algebraExample 1 (p. 251)Exercise 5.7 Q. 17, 27

Students identify a function as a one-to-one correspondence or a many-to-one correspondence between two sets.

Chapter 13: Functions and models13.1: Mapping diagrams and functionsTry this! p. 687Examples 1, 2 (p. 691 – 3)Exercise 13.1 Q. 1, 4, 5, 6, 16

They represent a function by a table of values, a graph, and by a rule.

Chapter 13: Functions and models13.1: Mapping diagrams and functionsExample 2 (p. 693)Exercise 13.1 Q. 5, 6, 11 – 18


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They describe and specify the independent variable of a function and its domain, and the dependent variable and its range.

Chapter 10: Ratios and rates10.6: Rates of changeExample 2 (p. 529)Exercise 10.6 Q. 2 – 6 Chapter 13: Functions and models13.1: Mapping diagrams and functionsMR GLTS in action (p. 692)Example 2 (p. 693)Examples 3, 4, 5 (pp. 695 – 697) Exercise 13.1Analysis task 3: Fencing a guinea pig enclosure

They construct tables of values and graphs for linear functions.

They use linear and other functions such as f(x) = 2x − 4, xy = 24, y = 2x and y = x2 − 3 to model various situations.

Chapter 10: Ratios and rates10.6: Rates of changeExercise 10.6 Q. 2 – 6 Chapter 13: Functions and models13.3: Mathematical modelsExercise 13.3 Q. 1 – 16Analysis task 2: How high will it bounce?Analysis task 3: Fencing a guinea pig enclosure


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Working mathematically4.0 (Standard)

At Level 4, students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers).

Many of the Try! this activities and Analysis Taskse.g., Try this! p. 549Chapter 1: Whole numbersAnalysis task 1: International Standard Book NumbersAnalysis task 2: Bar codesChapter 3: Lines and anglesAnalysis task 1: Catching the sun's heatAnalysis task 2: Boom anglesAnalysis task 3: A parking problem

Many of the Try! this activities and Analysis Taskse.g., Try this! p. 549

Students develop and test conjectures.

Chapter 2: Mathematical thinking2.4: Mathematical reasoning: conjecturingExample Investigation 1Try this! pp. 80, 81Example Investigation 2Try this! p. 85Investigation 1

Chapter 2: Mathematical thinking2.5: Mathematical reasoning: conjecturingExample investigation 1 Try this! pp. 82, 84Practice investigationInvestigation 1: Quotient patterns in 100 gridsInvestigation 2: Kites and boomerangsInvestigation 4: Beprisque number investigationChapter 3: Angles, parallel lines and polygonsAnalysis task 1: Polygon diagonals

They understand that a few successful examples are not sufficient proof and recognise that a single counter-example is sufficient to invalidate a conjecture. For example, in: number (all numbers can be shown as a rectangular array) computations (multiplication leads to a larger number) number patterns ( the next number in the sequence 2, 4, 6 … must be 8) shape properties (all parallelograms are rectangles) chance (a six is harder to roll on die than a one).

Chapter 2: Mathematical thinking2.4: Mathematical reasoning: conjecturingExample Investigation 2Chapter 3: Lines and angles3.1: Lines, rays and segmentsTry this! p. 95Chapter 6: Fractions6.6: Multiplying fractionsExercise 6.6 Q. 15Chapter 8: Decimals8.8: Multiplication of a decimal by a decimalExercise 8.8 Q. 10Chapter 10: Take a chance!10.3: Theoretical versus long run probabilityExercise 10.3 Q. 7

Chapter 3: Angles, parallel lines and polygons3.2: TrianglesTry this! p. 105Example 2 (p. 105)Exercise 3.2 Q. 2


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Working mathematically4.0 (Standard)(cont.)

Students use the mathematical structure of problems to choose strategies for solutions.

Analysis tasks all chaptersChapter 2: Mathematical thinking2.1: Representing a problemExample problems 1 – 3Practice problems 1 – 3Problem set 2.12.2: Developing problem-solving strategiesExample problems 1 – 6Practice problems 1 – 4Problem set 2.2

Analysis tasks all chaptersChapter 2: Mathematical thinking

They explain their reasoning and procedures and interpret solutions.

Analysis tasks all chaptersChapter 2: Mathematical thinkingInvestigation 2 p. 86

Analysis tasks all chaptersChapter 2: Mathematical thinking2.5: Mathematical reasoning: conjecturingExample investigation 1 Try this! pp. 82, 84Practice investigationInvestigation 1: Quotient patterns in 100 gridsInvestigation 2: Kites and boomerangsInvestigation 4: Beprisque number investigation

They create new problems based on familiar problem structures.

Chapter 2: Mathematical thinking2.4: Mathematical reasoning: conjecturingExample Investigation 2Try this! p. 85

Chapter 2: Mathematical thinking2.3: Problem posingExample problems 1 – 3Practice problems 1 – 3

Students engage in investigations involving mathematical modelling.

Chapter 2: Mathematical thinking2.4: Mathematical reasoning: conjecturingExample investigations 1, 2Investigations 1, 2Chapter 3: Lines and anglesAnalysis task 3: A parking problem

They use calculators and computers to investigate and implement algorithms (for example, for finding the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform

Chapter 1: Whole numbersAnalysis task 1: International Standard Book NumbersAnalysis task 2: Bar codesChapter 4: Number patterns4.5: Prime numbersExercise 4.5 Q. 7 – 9, 134.7: Looking at number sequencesExercise 4.7 Q. 2Analysis task 2: How many


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shapes and solids. candlessingle step rulesChapter 10: Take a chance!10.3: Theoretical versus long run probabilityTry this! p. 442Exercise 10.3 Q. 1 – 3


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Working mathematically4.25

Students develop generalisations inductively, from examples such as angle sums in triangles.

Chapter 2: Mathematical thinking2.4: Mathematical reasoning: ConjecturingExample investigation 2Try this! p. 85Chapter 4: Number patterns4.7: Investigating number sequencesExercise 4.7 Q. 6, 7Analysis task 1: Adding odd integersAnalysis task 2: How many candles?Chapter 7: Polygons7.1: TrianglesAngles of a triangleTry this! p. 2817.2: QuadrilateralsAngles of a quadrilateralTry this! p. 290

Chapter 2: Mathematical thinking2.2: Developing problem-solving strategiesProblem set 2.2 Q. 6, 8Chapter 8: Indices8.2: Exploring sums of squares and cubesExercise 8.2 Q. 8

They find patterns and relationships by looking at examples and recording the outcomes systematically.

Chapter 4: Number patternsWarm-up: Pascal's Triangle Try This! p. 1314.7: Looking at number sequencesExercise 4.7 Q. 1 – 8 Analysis task 1: Adding odd integersAnalysis task 2: How many candlesChapter 6: FractionsAnalysis task 2: Mixed number multiplication patternsAnalysis task 3: Equivalent fractions from graphsChapter 12: Perimeter, area and volumeAnalysis task 3: Paper sizes

Chapter 2: Mathematical thinking2.2: Developing problem-solving strategiesTry this!Example problem 2 (p. 52)Practice problem 2 Try this! (p. 53)Example problem 3 Try this! (p. 55)Practice problem 3 Try this! (p. 55)Example problem 4Practice problem 4Example problem 5Example problem 6Practice problem 5Problem set 2.2

They identify relevant variables (independent and dependent) in real situations.

Chapter 5: Algebraic expressions and relationships5.8: Using rules to solve problemsExample 1 (p. 215)Exercise 5.8

Working mathematically4.25(cont.)

Students use a spreadsheet as a database, to sort and categorise data and generate statistical graphs.

Chapter 14: Making sense of dataWarm-up: The First Fleet database14.3: Displaying and interpreting data in graphsExercise 14.3 Q. 3, 11Analysis task 1: Which were the

Chapter 12: Investigating dataAnalysis task2: Be careful on the road!


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best AFL teams in 2005


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Students extend mathematical arguments, such as finding angle sum of a pentagon by extending the argument that angle sum of quadrilateral is 360° because it can be split into two triangles.

Chapter 4: Number patternsAnalysis task 2: How many candles? part h (p. 170)Chapter 7: Polygons7.3: PolygonsExample 1 (p. 303)Exercise 7.3 Q. 2, 5, 6

Chapter 2: Mathematical thinking2.5: Mathematical reasoning: conjecturingPractice investigation 1: Areas of midpoint figures in quadrilateralsChapter 3: Angles, parallel lines and polygons3.2: TrianglesTry this! p. 1043.3: QuadrilateralsExercise 3.3 Q. 20

They explain mathematical relationships by extending patterns.

Chapter 4: Number patterns4.7: Looking at number sequencesExercise 4.7Analysis task 1: Adding odd integersAnalysis task 2: How many candlesChapter 13: Maps, coordinates and directions13.2: Locating positionExercise 13.2 Q. 14, 15

Chapter 3: Angles, parallel lines and polygonsAnalysis task 1: Polygon diagonals

They independently plan and carry out an investigation with several components and report the results clearly using mathematical language.

Chapter 10: Take a chance!10.3: Theoretical versus long run probabilityExercise 10.3 Q. 3

Chapter 3: Angles, parallel lines and polygonsAnalysis task 2:Constructing drag-resistant shapesChapter 9: Exploring chanceAnalysis task 2: At the fairAnalysis task 3: Stick or switch to win a car

They identify situations with constant rate of change and represent with a linear graph, such as taxi fares.

Chapter 13: Maps, coordinates and directions13.2: Locating positionExample 3 (pp. 576 – 577)Exercise 13.2 Q. 14, 15

Chapter 10: Ratios and rates10.6: Rates of changeExamples 1, 2 (pp. 528, 529)Exercise 10.6 Q. 2 – 10 Chapter 13: Functions and models13.3: Mathematical modelsExample 1 (p. 714)Exercise 13.3 Q. 1 – 9

Working mathematically4.5(cont.)

Students use computer drawing tools, such as MS Word, Geometer’s Sketchpad, MicroWorlds and Cabri Geometry, to explore geometric situations.

Chapter 7: Polygons7.1: Triangles Exercise 7.1 Q. 97.2: QuadrilateralsExploring parallelograms with MicroWorldsExercise 7.2 Q. 9, 10Analysis task 2: Drawing polygons in MicroWorlds

Chapter 3: Angles, parallel lines and polygonsAnalysis task 2: Constructing drag-resistant shapesAnalysis task 3: Drawing star polygons in MicroWorldsChapter 6:


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Transformations and tessellations6.1: Isometric transformationsExercise 6.1 Q. 5, 66.2: Congruency and similarityExercise 6.2 Q. 86.3: TessellationsExercise 6.3 Q. 4, 8cAnalysis task 1: Pantographs


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Students organise problem solving using Venn diagrams, tree diagrams and two way tables, for clarifying relationships.

Chapter 9: Exploring chance9.4: Two-way tablesExercise 9.49.5: Tree diagrams and tablesExercise 9.5

They link known facts together logically, such as parallelograms have rotational symmetry, therefore they have equal opposite angles.

Chapter 3: Angles, parallel lines and polygons3.2 TrianglesTry this! p. 104Exercise 3.2 Q. 153.3 QuadrilateralsTry this! p. 121Try this! p. 123Exercise 3.3 Q. 6, 7, 9, 10, 15 – 20Chapter 6: Transformations and tessellations6.2: Congruency and similarityExercise 6.2 Q. 146.3: TessellationsExamples 1,2 (p. 311)

They identify situations with constant rate of change and represent with a linear formula.

Chapter 10: Ratios and rates10.6: Rates of changeExamples 1, 2 (pp. 528, 529)Exercise 10.6 Q. 2 – 10 Chapter 13: Functions and models13.2: Investigating linear functionsTry this! pp. 704 – 706Example 1 (pp. 706 – 707)Exercise 13.2 Q. 1 – 8 13.3: Mathematical modelsExample 1 (p. 714)Exercise 13.3 Q. 1 – 9

Working mathematically5.0 (Standard)

At Level 5, students formulate conjectures and follow simple mathematical deductions (for example, if the side length of a cube is doubled, then the surface area increases by a factor of four, and the volume increases by a factor of eight).

Chapter 7: Polygons7.3: PolygonsSum of the angles of polygons pp. 302 – 304 Chapter 12: Perimeter, area and volume12.3: Area: rectanglesExercise 12.3 Q. 712.5: VolumeExercise 12.4 Q. 9

Chapter 2: Mathematical thinking2.5: Mathematical reasoning: conjecturingExample investigation 1 Try this! pp. 82, 84Practice investigationInvestigation 1: Quotient patterns in 100 gridsInvestigation 2: Kites and boomerangsInvestigation 4: Beprisque number investigation


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Chapter 3: Angles, parallel lines and polygonsAnalysis task 1: Polygon diagonals


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Students use variables in general mathematical statements.

Chapter 8: Indices8.4: Index form with pronumeralsExamples 1 – 5 (pp. 412 – 414) Exercise 8.4 Q. 1 – 12

They substitute numbers for variables (for example, in equations, inequalities, identities and formulas).

Chapter 5: Algebraic expressions and relationships5.1: Introduction to variablesExamples 1 – 3 (pp. 179 – 181)Exercise 5.1 Q. 1 – 12 5.2: Combining expressionsExample 2 (p. 184)Exercise 5.2 Q. 1 – 12 5.3: Using rules to make tablesExercise 5.3 Q. 1 – 155.4: Finding single-step rulesExercise 5.4 Q. 4, 75.6: Substituting several input numbers into rules and expressionsTry this! p. 205Examples 1, 2 (pp. 206)Exercise 5.6 Q. 1 – 9 5.8: Using rules to solve problemsExample 1 (pp. 215 – 216)Exercise 5.8 Q. 1 – 8


Students explain geometric propositions (for example, by varying the location of key points and/or lines in a construction).

Chapter 3: Angles, parallel lines and polygons3.5: Star polygonsExercise 3.5 Q. 8Analysis task 2: Constructing drag-resistant shapesAnalysis task 3: Drawing star polygons in MicroWorlds

Students develop simple mathematical models for real situations (for example, using constant rates of change for linear models).

Chapter 5: Algebraic expressions and relationships5.8: Using rules to solve problemsExample 1 (pp. 215 – 216)Exercise 5.8 Q. 1 – 8 Analysis task 3: Phone cardsChapter 11: Solving equationsAnalysis task 1: Carly's jeansAnalysis task 3: travelling overseasChapter 13: Maps, coordinates and directions13.2: Locating positionExample 3 (p. 576)

Chapter 13: Functions and models13.3: Mathematical modelsExample 1 (p. 714)Exercise 13.3 Q. 1 – 9 Analysis task 1: How high will it bounce?Analysis task 2: Advertising and sales


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Exercise 13.2 Q. 14, 15


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They develop generalisations by abstracting the features from situations and expressing these in words and symbols.

Chapter 5: Algebraic expressions and relationships5.8: Using rules to solve problemsExample 1 (pp. 215 – 216)Exercise 5.8 Q. 1 – 9

Chapter 3: Angles, parallel lines and polygonsAnalysis task 1: Polygon diagonals Analysis task 3: Drawing star polygons in MicroWorldsChapter 8: Indices8.4: Index form with pronumeralsExamples 1–5 (pp. 412–414) Exercise 8.4 Q. 1 – 12 Analysis task 3: Tower of Hanoi

They predict using interpolation (working with what is already known) and extrapolation (working beyond what is already known).

Chapter 8: Decimals8.8: Multiplication of a decimal by a decimalTry this! p. 351

Chapter 3: Angles, parallel lines and polygons3.4: PolygonsExercise 3.4 Q. 8Try this! (p. 123)

They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context.

All Number Crunch Q.Chapter 2: Mathematical thinkingInvestigation 2 (p. 86)

All Number Crunch Q. Chapter 3: Angles, parallel lines and polygons3.3: PolygonsExercise 3.3 Q. 6b, 16b, c, 20b


Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings.

Chapter 1: Whole numbersAnalysis task 1: International Standard Book NumbersAnalysis task 2: Bar codesChapter 3: Lines and angles3.2: AnglesExercise 3.2 Q. 8Chapter 4: Number patterns4.7: Looking at number sequencesExercise 4.7 Q. 2Analysis task 2: How many candlesChapter 5: Algebraic expressions and relationships5.3: Using rules to make tablesExercise 5.3 Q. 8, 9, 105.4: Finding single step rulesExercise 5.4 Q. 8Chapter 6: Fractions6.3: Common denominators and comparing fractionsMicroWorlds Equivalent fractionsChapter 7: Polygons7.1: Triangles Exercise 7.1 Q. 9

Chapter 1: IntegersChapter Warm-up Try this! MicroWorlds HTML: Protons and antiprotons1.4: More addition and subtraction of integersMicroWorlds HTML: Ships and sharks1.5: Multiplying integersMicroWorlds HTML: Train travel multiplicationChapter 3: Angles, parallel lines and polygons3.4: Other polygonsExercise 3.4 Q. 8Analysis task 2: Constructing drag-resistant shapesAnalysis task 3: Drawing star polygons in MicroWorldsChapter 6: Transformations and tessellations6.2: Congruency and similarityExercise 6.2 Q. 8, 9


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7.2: QuadrilateralsExploring parallelograms with MicroWorldsExercise 7.2 Q. 9,10Analysis task 2: Drawing polygons in MicroWorldsChapter 9: Units of length, mass and timeAnalysis task 3: Celsius and Fahrenheit temperaturesChapter 10: Take a chance!10.3: Theoretical versus long-run probabilitySimulation Try this! p. 442Exercise 10.3 Q. 1 – 3 Chapter 11: Solving equations11.2: Solving equations: arithmetic strategiesExercise 11.2 Q. 9Chapter 12: Perimeter, area and volume12.2: Circumference of a circleTry this! p. 51812.3: Area: RectanglesExercise 12.3 Q. 612.4: Area: Parallelograms and trianglesCabri HTML: Area of a parallelogram;Area of a triangleChapter 13: Maps,

coordinates and direction13.1: Scale drawingsExercise 13.1 Q. 13Chapter 14: Making sense of dataChapter Warm-up Try this! p. 60014.5: Summarising data: visuallyExercise 14.5 Q. 1, 6, 7Analysis task 1: Which were the best AFL teams in 2005?

6.3: TessellationsExercise 6.3 Q. 8Chapter 7: polyhedra and networks7.1: polyhedra and netsExercise 7.1 Q. 5, 8, 9Chapter 8: Indices8.2: Exploring sums of squares and cubesExercise 8.2 Q. 8Analysis task 2: Mersenne primesChapter 9: Exploring chance9.2: Simulating chanceTry this! p. 441Exercise 9.2 Q. 1 – 5 Chapter 10: Ratios and rates10.6: Rates of changeExercise 10.6 Q. 2 – 7, 9Analysis task 1: Phone cardsChapter 11: Length, area and volume11.3: Area of a circleExercise 11.3 Q. 311.6: VolumeExercise 11.6 Q. 5Analysis task 2: Cake boxes

Chapter 12: Investigating dataAnalysis task 1: ScrabbleAnalysis task 2: Be careful on the road!Chapter 13: Functions and models13.1: Mapping diagrams and functionsExercise 13.1 Q. 5, 13, 17, 1813.3: Mathematical modelsexercise 13.3 Q. 6, 7, 10Analysis task 1: How high will it bounce?Analysis task 2: Advertising and salesAnalysis task 3: Fencing a guinea pig enclosure


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MathsWorld 8 Teacher edition - Macmillan Publishers · Web viewe.g., Exercise 12.2 Level VELS Standard/PP MathsWorld 7 MathsWorld 8 Space 4.0 (Standard) At Level 4, students classify