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Heinemann VELS 7–10 Progression Points Textbooks and Worksheets Audit
|VELS Standard or |Descriptors for Standard or Progression Point |Heinemann Maths Zone VELS Edition 7–10 Textbook and Worksheet references |
|Progression Point | | |
|Number |
|Nu3.0 |At Level 3, students use place value (as the idea that ‘ten of these is one of those’) to determine the | MZ7 VELS Textbook: |
| |size and order of whole numbers to tens of thousands, and decimals to hundredths. They round numbers up |Ex 1.1 Q 1–10 |
| |and down to the nearest unit, ten, hundred, or thousand. They develop fraction notation and compare |Ch 1 Laugh Zone |
| |simple common fractions such as 3/4 > 2/3 using physical models. They skip count forwards and backwards,|Ex 1.5 Q 1 |
| |from various starting points using multiples of 2, 3, 4, 5, 10 and 100. |Ch 1 Maths in Action Q 1, 2 |
| |They estimate the results of computations and recognise whether these are likely to be over-estimates or|Ch 3 Investigation p. 100 Q 1–5 |
| |under-estimates. They compute with numbers up to 30 using all four operations. They provide automatic |MZ7 VELS Worksheets with explanations and questions: |
| |recall of multiplication facts up to 10 × 10. |R1.2; R1.3; R1.4; R1.5; R1.6; R1.7; R1.8; R1.9; R1.13; |
| |They devise and use written methods for: |R1.14; R2.4; R2.6; R2.7; R2.8; R3.1; R3.2; R4.1; R4.2; |
| |whole number problems of addition and subtraction involving numbers up to 999 |R4.3; R4.4; R4.5; R4.8 |
| |multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten |C1.3; C1.4 |
| |(for example, 5 × 100, 5 × 70) |MZ7 VELS Worksheets with questions only: |
| |division by a single-digit divisor (based on inverse relations in multiplication tables). |R1.1; R2.1; R2.2; R6.2; R6.3; R10.1 |
| |They devise and use algorithms for the addition and subtraction of numbers to two decimal places, |C1.1; C1.5 |
| |including situations involving money. They add and subtract simple common fractions with the assistance |MZ8 VELS Worksheets with explanations and questions: |
| |of physical models. |R1.2; R1.11; R1.19; R2.12; R3.1; R3.7; R5.7; R6.2 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R1.17 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R3.12 |
|Nu3.25(1 |Use of large number multiples of ten to approximate common quantities; for example, 100 000 people in a | MZ7 VELS Textbook: |
| |major sports venue |Ex 1.5 Q 5 |
| | |Ch 1 Investigation p. 28 Q 1–4 |
|Nu3.25(2 |Representation of square numbers using a power of 2; for example, 9 = 32 | MZ7 VELS Textbook: |
| | |Ex 2.6 Q 1, 3 |
|Nu3.25(3 |Use of ratios to describe relative sizes | MZ8 VELS Textbook: |
| | |Ex 5.1 Q 1–4 |
|Nu3.25(4 |Appropriate selection and use of mental and written algorithms to add, subtract, multiply and divide (by| MZ7 VELS Worksheets with explanations and questions: |
| |single digits) natural numbers |R4.6; R4.7 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.3; R1.4; R1.5; R1.6; R1.7 |
|Nu3.25(5 |Multiplication of fractions by fractions through the use of the rectangle area model (grid) | |
|Nu3.25(6 |Use of brackets to determine order of operations | MZ7 VELS Textbook: |
| | |Ex 1.6 Q 5 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R1.15; R9.3 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.9 |
|Nu3.5(1 |Listing of objects and their size, where size varies from thousandths to thousands of a unit | MZ7 VELS Textbook: |
| | |Ex 4.1 Q 1–14 |
| | |Ch 4 Problem solving p. 138 Q (a), (b) |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R3.3 |
| | |C4.1; C4.2 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.1; R1.10; R1.12; R4.9 |
|Nu3.5(2 |Addition, subtraction and multiplication of fractions and decimals (to one decimal place) using | MZ7 VELS Textbook: |
| |approximations such as whole number estimates and technology to confirm accuracy |Ex 3.1 Q 1–13 |
| | |Ch 3 Investigation p. 100 Q 6–8 |
| | |Ex 3.3 Q 1–4 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R1.18; R3.4 |
| | |C3.1; C3.2; C3.3; C3.4; C4.5 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R5.2; R5.4; R5.5 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R10.1; R10.2; R10.3 |
|Nu3.5(3 |Representation of simple ratios as percentages, fractions and decimals | MZ8 VELS Textbook: |
| | |Ex 5.6 Q 1, 2 |
|Nu3.5(4 |Identification of calculation errors resulting in unreasonable results | MZ7 VELS Textbook: |
| | |Ex 1.7 Q 7 |
|Nu3.5(5 |Ordering of integers (for example, positive and negative temperatures), positive fractions and decimals | MZ7 VELS Textbook: |
| | |Ex 3.2 Q 1–7 |
| | |Ex 4.2 Q 1–13 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R10.3 |
| | |MZ8 VELS Textbook: |
| | |Ex 1.1 Q 1–8 |
| | |Ch 1 Investigation p. 5 Q 1–5 |
| | |Ex 1.2 Q 1–12 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C1.1; C1.2; C1.3 |
|Nu3.75(1 |Multiplication by increasing and decreasing by a factor of two; for example, | |
| |24 × 16 | |
| |= 48 × 8 | |
| |= 96 × 4 | |
| |= 192 × 2 | |
| |= 384 × 1 | |
| |= 384 | |
|Nu3.75(2 |Recognition of equivalent rates expressed as percentages, fractions and decimals | MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 5 |
| | |Ex 5.1 Q 1–9 |
|Nu3.75(3 |Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication | MZ7 VELS Textbook: |
| |by fractions or decimals) |Ex 3.5 Q 1 |
|Nu3.75(4 |Use of inverse relationship between multiplication and division to validate calculations | MZ7 VELS Textbook: |
| | |Ex 3.6 Q 1 |
|Nu3.75(5 |Creation of sets of multiples of numbers and their representation in index form; for example, 3, 9, 27 | MZ7 VELS Textbook: |
| |written as 31, 32, 33 respectively |Ch 2 VELS Design Task Q 4–7 |
| | |Ex 2.8 Q 11 |
|Nu4.0 |At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers | MZ7 VELS Textbook: |
| |(to millions). They model integers (positive and negative whole numbers and zero), common fractions and |VELS Assignment 1 Q 4 |
| |decimals. They place integers, decimals and common fractions on a number line. They create sets of |VELS Assignment 4 Q 1, 2, 4 |
| |number multiples to find the lowest common multiple of the numbers. They interpret numbers and their |Ex 1.2 Q 1–20 |
| |factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be|Ch 1 Investigation p. 15 Q (a)–(c) |
| |found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4). |Ex 1.3 Q 1–6 |
| |Students identify square, prime and composite numbers. They create factor sets (for example, using |Ch 1 VELS Design Task Q 1–8 |
| |factor trees) and identify the highest common factor of two or more numbers. They recognise and |Ex 1.4 Q 1–6 |
| |calculate simple powers of whole numbers (for example, 24 = 16). |Ex 1.6 Q 1–9 |
| |Students use decimals, ratios and percentages to find equivalent representations of common fractions |Ch 1 Problem solving p. 32 |
| |(for example, 3/4 = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). They explain and use mental and written |Ch 1 Investigation p. 33 Q (a)–(h) |
| |algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole|Ex 1.7 Q 1–7 |
| |numbers). They add, subtract, and multiply fractions and decimals (to two decimal places) and apply |Ex 2.1 Q 1–15 |
| |these operations in practical contexts, including the use of money. They use estimates for computations |Ch 2 Problem solving p. 58 Q 1, 2 |
| |and apply criteria to determine whether or not estimates are reasonable. |Ex 2.3 Q 1–8 |
| | |Ch 2 Investigation p. 62 Q 1–3 |
| | |Ex 2.4 Q 1–14 |
| | |Ch 2 Problem solving p. 64 |
| | |Ch 2 Investigation p. 65 Q 1, 2 |
| | |Ex 2.5 Q 1 |
| | |Ch 2 Maths in Action Q 1–6 |
| | |Ex 2.6 Q 1, 3, 8(a), 9, 10, 14 |
| | |Ch 2 VELS Design Task Q 4, 8 |
| | |Ch 2 Laugh Zone |
| | |Ex 3.2 Q 8–14 |
| | |Ch 3 Problem solving p. 104 Q 1, 2 |
| | |Ex 3.3 Q 5–9 |
| | |Ch 3 VELS Design Task Q 1–5 |
| | |Ch 3 Maths in Action Q 2–5 |
| | |Ex 3.5 Q 1, 4, 6–8, 10 |
| | |Ch 3 Problem solving p. 115 |
| | |Ch 3 Investigation p. 118 Q 1–5 |
| | |Ch 3 Laugh Zone |
| | |Ex 3.7 Q 1(a)–(c) |
| | |Ex 3.8 Q 1–3, 5, 6, 11–14 |
| | |Ex 4.3 Q 1–12 |
| | |Ex 4.5 Q 1–11 |
| | |Ex 4.6 Q 1–15 |
| | |Ch 4 Problem solving p. 153 Q 1 |
| | |Ch 4 Laugh Zone |
| | |Ex 4.7 Q 1– 4 |
| | |Ex 4.8 Q 1–15 |
| | |Ex 4.9 Q 1–12 |
| | |Ch 4 VELS Design Task Q 1, 5 |
| | |Ex 4.10 Q 1–17 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R1.11; R1.17; R2.3; R2.5; R2.9; R2.11; R3.5; R5.1; |
| | |R10.2; R10.5 |
| | |C2.1; C2.2; C2.3; C2.4; C2.5; C3.5; C3.6; C3.8; C3.9; |
| | |C4.7 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C1.2; C1.7; C2.7; C4.6 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 1 Q 2–7 |
| | |Ch 2 Maths in Action Q 1, 4 |
| | |Ex 3.1 Q 1–9 |
| | |Ex 5.2 Q 1–16 |
| | |Ch 5 Investigation p. 197 Q 1 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.14; R1.16; R1.18; R2.1; R2.2; R2.5; R2.6; R2.8; |
| | |R2.11; R2.15; R3.3; R3.4; R3.5; R3.6; R3.8; R3.9; R3.11; |
| | |R3.14; R4.2; R4.8; R5.3; R6.3; R10.6 |
| | |C5.1 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R2.9 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 1 Q 2, 3, 4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.4; R2.1; R3.2; R3.3; R4.5; R4.8; R4.9 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.4; R3.7; R3.8; R6.1; R10.1; R10.2 |
| | |C10.7 |
| | |VCE Worksheets: |
| | |ZGM R8.1 |
| | |ZM1&2 R5.1; R5.2 |
|Nu4.25(1 |Identification of square numbers up to, and including, 100 | MZ7 VELS Textbook: |
| | |Ex 2.6 Q 4 |
| | |Ch 2 VELS Design Task Q 4, 8 |
| | |Ch 2 Laugh Zone |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C2.8; C2.9 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C2.9 |
| | |VCE Worksheets: |
| | |ZGM R1.1 |
|Nu4.25(2 |Knowledge of decimal and percentage equivalents for | MZ7 VELS Textbook: |
| |1/2, 1/4, 3/4, 1/3, 2/3 |Ch 4 Investigation p. 168 Q 1 |
|Nu4.25(3 |Expression of single-digit decimals as fractions in simplest form and conversion between ratio, | MZ7 VELS Textbook: |
| |fraction, decimal and percentage forms |Ex 4.4 Q 1–10 |
| | |Ch 4 Investigation p. 168 Q 2–8 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R1.16 |
| | |C4.3; C4.4 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 5 |
| | |VELS Assignment 4 Q 1–4 |
| | |Ex 2.1 Q 1, 2, 8 |
| | |Ex 2.3 Q 1, 4, 6 |
| | |Ex 3.2 Q 1–15 |
| | |Ex 3.3 Q 1–7 |
| | |Ex 3.4 Q 1–11 |
| | |Ex 3.5 Q 1–6 |
| | |Ch 3 Laugh Zone |
| | |Ch 5 Problem solving p. 211 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R2.3; R2.4; R3.2 |
| | |C2.1; C2.2; C2.3; C3.1; C3.2; C3.3; C3.4 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C3.5 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.1 Q 3, 4, 13 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.1; R1.2; R1.8; R1.14; R2.9; R5.5; R10.4; R10.5 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C8.8; C8.9; C8.10; C8.11 |
| | |VCE Worksheets: |
| | |ZGM R1.1; R1.4; R4.5; R13.1 |
| | |ZFM R9.3 |
|Nu4.25(4 |Use of index notation to represent repeated multiplication | MZ7 VELS Textbook: |
| | |Ex 2.8 Q 1–7, 11 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C2.9 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C2.11 |
| | |MZ8 VELS Textbook: |
| | |Ex 2.7 Q 1, 2, 4–6 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R4.6 |
|Nu4.25(5 |Division of fractions using multiplication by the inverse | MZ7 VELS Textbook: |
| | |Ex 3.6 Q 1–4, 7, 9, 11 |
| | |Ch 3 Laugh Zone |
| | |Ex 3.7 Q 1(d)–(f) |
| | |Ex 3.8 Q 7 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C3.10; C3.11 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 1 Q 2–7 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.9 |
|Nu4.5(1 |Representation of collections of objects in base 2 notation | MZ7 VELS Textbook: |
| | |Ex 2.7 Q 1–8 |
|Nu4.5(2 |Location of the square roots from √(1) to √(100) by their approximate position on the real number line | MZ7 VELS Textbook: |
| | |Ex 2.6 Q 6, 11 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.3 |
|Nu4.5(3 |Construction of factor trees for the expression of numbers in terms of powers of prime factors | MZ7 VELS Textbook: |
| | |Ex 2.5 Q 2–8 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C2.6 |
| | |MZ8 VELS Textbook: |
| | |Ex 2.7 Q 9 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R3.12 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R2.7; R4.5 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.3 Q 5 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R1.11 |
|Nu4.5(4 |Use of calculations involving operations with mixed numbers | MZ7 VELS Textbook: |
| | |Ex 3.4 Q 1–8 |
| | |Ex 3.5 Q 2, 3, 5, 9 |
| | |Ex 3.6 Q 5, 6, 8, 10 |
| | |Ch 3 Laugh Zone |
| | |Ex 3.7 Q 1(g)–(l), 2–7 |
| | |Ex 3.8 Q 4, 8–10 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C3.7; C3.12 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.5 Q 1–6, 13–15, 17 |
| | |Ch 1 Maths in Action Q 1–3 |
| | |Ch 1 VELS Design Task Q 1–3 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.15 |
| | |VCE Worksheets: |
| | |ZGM R12.4 |
|Nu4.5(5 |Knowledge of the first several digits of decimal approximations to pi, π | MZ8 VELS Textbook: |
| | |Ch 6 Investigation p. 238 |
|Nu4.75(1 |Addition, multiplication and division of integers | MZ7 VELS Textbook: |
| | |Ex 4.11 Q 1–12 |
| | |Ex 4.12 Q 1–12 |
| | |Ch 4 Maths in Action Q 2–4 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C4.8 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C4.9 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 1 Q 2–7 |
| | |Ex 1.3 Q 1–10 |
| | |Ex 1.5 Q 1–10 |
| | |Ch 1 VELS Design Task Q 1–8 |
| | |Ch 1 Problem solving p. 20 |
| | |Ex 1.6 Q 1–10 |
| | |Ex 1.7 Q 1–11 |
| | |Ex 1.8 Q 1–13 |
| | |Ch 1 Laugh Zone |
| | |Ch 1 Maths in Action Q 1–4 |
| | |Ex 2.1 Q 3–7, 9 |
| | |Ch 2 Investigation p. 44 Q 1–8 |
| | |Ex 2.3 Q 5, 7–20 |
| | |Ch 2 Maths in Action Q 2, 3 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C1.4; C1.6; C1.8; C1.10; C1.11 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C1.9; C1.12 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.1 Q 1, 2, 5, 6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R2.8; R3.8; R4.8 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R1.12 |
|Nu4.75(2 |Representation of subtraction of integers through the use of a physical model, and of integer | MZ8 VELS Textbook: |
| |subtraction as an equivalent integer addition, and as the difference between integers |Ex 1.3 Q 11 |
| | |Ex 1.4 Q 1–12 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C1.5; C1.7 |
|Nu4.75(3 |Calculation of squares and cubes of rational numbers | MZ7 VELS Textbook: |
| | |Ex 2.6 Q 2, 5, 15 |
| | |Ch 2 Laugh Zone |
|Nu4.75(4 |Mental computation of square roots of rational numbers associated with known perfect squares; for | MZ8 VELS Textbook: |
| |example, |Ex 2.4 Q 1 |
| |√(0.64) = 0.8 because | |
| |82 = 64; √(6.4) is not related to 8 | |
|Nu4.75(5 |Use of technology to confirm the results of operations with squares and square roots | MZ7 VELS Worksheets with explanations and questions: |
| | |C2.10 |
| | |MZ8 VELS Textbook: |
| | |Ex 1.8 Q 12 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C2.10 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R3.4 |
|Nu5.0 |At Level 5, students identify complete factor sets for natural numbers and express these natural numbers| MZ7 VELS Textbook: |
| |as products of powers of primes (for example, 36 000 = 25 × 32 × 53). |Ex 1.5 Q 2–4, 6–14 |
| |They write equivalent fractions for a fraction given in simplest form (for example, 2/3 = 4/6 = 6/9 = … |Ch 1 Investigation p. 40 Q 1 |
| |). They know the decimal equivalents for the unit fractions 1/2, 1/3, 1/4, 1/5, 1/8, 1/9 and find |Ex 2.6 Q 7, 8(b), 12, 13 |
| |equivalent representations of fractions as decimals, ratios and percentages (for example, a subset : set|Ex 2.7 Q 1–9 |
| |ratio of 4:9 can be expressed equivalently as 4/9 = 0.4 ≈ 44.44%). They write the reciprocal of any |Ch 2 Computer investigation p. 76 Q 1–6 |
| |fraction and calculate the decimal equivalent to a given degree of accuracy. |Ex 2.8 Q 8–10, 12 |
| |Students use knowledge of perfect squares when calculating and estimating squares and square roots of |MZ8 VELS Textbook: |
| |numbers (for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30). They evaluate natural |VELS Assignment 1 Q 2–7 |
| |numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9). They |VELS Assignment 4 Q 3, 4 |
| |know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125). They calculate squares and |VELS Assignment 5 Q 2, 6, 7 |
| |square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √9/16 = 3/4). |Ch 1 Investigation p. 32 |
| |They calculate cubes and cube roots of perfect cubes (for example, 3√64 = 4). Using technology they find|Ex 2.2 Q 1–8 |
| |square and cube roots of rational numbers to a specified degree of accuracy (for example, 3√200 = 5.848 |Ex 2.4 Q 2–7 |
| |to three decimal places). |Ex 2.5 Q 1–11 |
| |Students express natural numbers base 10 in binary form, (for example, 4210 = 1010102), and add and |Ch 2 VELS Design Task Q 1–6 |
| |multiply natural numbers in binary form (for example, 1012 + 112 = 10002 and 1012 × 112 = 11112). |Ch 2 Laugh Zone |
| |Students understand ratio as both set : set comparison (for example, number of boys : number of girls) |Ex 2.6 Q 1–11 |
| |and subset : set comparison (for example, number of girls : number of students), and find integer |Ex 2.7 Q 3, 7, 8, 10–13 |
| |proportions of these, including percentages (for example, the ratio number of girls : the number of boys|Ch 2 Investigation p. 73 Q 1–3 |
| |is 2 : 3 = 4 : 6 = 40% : 60%). |Ex 3.6 Q 1–24 |
| |Students use a range of strategies for approximating the results of computations, such as front-end |Ex 3.7 Q 1–10 |
| |estimation and rounding (for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30). |Ex 3.8 Q 1–20 |
| |Students use efficient mental and/or written methods for arithmetic computation involving rational |Ex 3.9 Q 1–11 |
| |numbers, including division of integers by two-digit divisors. They use approximations to π in related |Ch 3 Problem solving p. 113 |
| |measurement calculations (for example, π × 52 = 25π = 78.54 correct to two decimal places). |Ex 3.11 Q 1–4 |
| |They use technology for arithmetic computations involving several operations on rational numbers of any |MZ8 VELS Worksheets with explanations and questions: |
| |size. |R4.7 |
| | |C2.4; C2.8; C3.6 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C2.5; C2.6; C2.7; C3.7 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 2 Q 2, 4 |
| | |Ex 1.1 Q 7–9 |
| | |Ch 3 Maths in Action Q 2, 3 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R3.5 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R2.10 |
| | |MZ10 VELS Textbook: |
| | |Ex 1.1 Q 1–9 |
| | |Ch 1 VELS Design Task Q 1–7 |
| | |Ch 1 Maths in Action Q 1–4 |
| | |Ex 2.1 Q 5, 6, 8–12 |
| | |Ch 2 Graphics calculator investigation p. 87 Q 1 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.1; R1.16; R2.3; R2.7; R4.1 |
| | |C2.1; C10.9 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R2.2 |
| | |C1.2 |
| | |VCE Worksheets: |
| | |ZGM R3.3; R12.7 |
| | |ZM1&2 R2.2 |
| | |ZFM R7.3; R7.6; R9.4 |
| | |ZM3&4 R3.1; R3.2 |
|Nu5.25(1 |Relationships between real, rational, irrational, integer and natural numbers on a Venn diagram | MZ10 VELS Textbook: |
| | |Ex 2.1 Q 1 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.2; R1.3 |
|Nu5.25(2 |Determination of lowest common multiple through investigation of prime factors | MZ7 VELS Textbook: |
| | |Ex 2.5 Q 6 |
|Nu5.25(3 |Solution of problems involving ratio and proportion | MZ8 VELS Textbook: |
| | |Ex 5.3 Q 1–15 |
| | |Ch 5 Investigation p. 196 Q 1, 2 |
| | |Ex 5.4 Q 1–5 |
| | |Ch 5 Laugh Zone |
| | |Ex 5.6 Q 1–19 |
| | |Ex 5.7 Q 1–14 |
| | |Ex 5.8 Q 1–16 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C5.2; C5.3; C5.8 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C5.4 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.1 Q 10–12, 14–17 |
| | |Ex 1.2 Q 1–6, 11–15, 19 |
| | |Ch 1 Problem solving p. 30 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.5; R1.6; R1.7 |
| | |MZ10 VELS Textbook: |
| | |Ch 1 Problem solving p. 11 Q 1, 2 |
|Nu5.25(4 |Representation and recognition of large and small numbers in scientific notation | MZ10 VELS Textbook: |
| | |Ex 2.13 Q 1–11 |
| | |Ch 2 Maths in Action Q 1, 2 |
|Nu5.25(5 |Calculation and use of percentage change in practical situations; for example, discounts | MZ8 VELS Textbook: |
| | |Ex 3.10 Q 1–15 |
| | |Ch 3 Maths@Work |
| | |Ex 3.11 Q 5–20 |
| | |Ch 3 Investigation p. 122 Q 1, 2 |
| | |Ch 3 VELS Design Task Q 1, 2, 5–7 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 1 Q 6 |
| | |Ex 1.2 Q 19 |
| | |Ex 1.5 Q 7–12, 16, 18, 19 |
| | |Ch 1 VELS Design Task Q 4–7 |
| | |Ex 1.6 Q 1–10 |
| | |Ex 1.7 Q 1–28 |
| | |Ch 1 Laugh Zone |
| | |Ex 1.8 Q 1–6 |
| | |Ex 1.9 Q 1–9 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C1.1; C1.2; C1.3; C1.9 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C1.10 |
| | |MZ10 VELS Textbook: |
| | |Ex 1.2 Q 1–19 |
| | |Ch 1 Graphics calculator investigation p. 19 Q 1, 3 |
| | |Ex 1.3 Q 1–11 |
| | |Ch 1 Investigation p. 26 Q 1–3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.2; R1.3; R3.10 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R1.6 |
| | |C1.1; C1.3; C1.4; C1.5 |
|Nu5.5(1 |Simplification of surds; for example, √(12) = 2√(3) | MZ10 VELS Textbook: |
| | |Ex 2.1 Q 1, 4, 7 |
| | |Ex 2.2 Q 1–8 |
| | |Ex 2.3 Q 1–7 |
| | |Ex 2.4 Q 1–10 |
| | |Ch 2 CAS investigation p. 63 Q 1, 2 |
| | |Ch 2 Problem solving p. 74 Q 1, 2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.6 |
| | |C2.2; C2.3; C2.4 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C2.5; C2.6 |
| | |VCE Worksheets: |
| | |ZM1&2 R2.4 |
|Nu5.5(2 |Calculation of the whole given the size of a percentage; for example, if a 20% discount is $7, what was | MZ8 VELS Textbook: |
| |the original value? |Ch 3 Investigation p. 122 Q 1, 2 |
| | |Ch 3 VELS Design Task Q 3, 4, 8 |
| | |MZ9 VELS Textbook: |
| | |Ex 1.2 Q 7–10, 16–18 |
| | |Ch 1 Graphics calculator investigation p. 45 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.9 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R1.4 |
|Nu5.5(3 |Solution of proportion problems using real numbers | MZ8 VELS Textbook: |
| | |Ex 5.4 Q 6–20 |
| | |Ch 5 VELS Design Task Q 3, 5–7 |
| | |Ex 5.5 Q 1–13 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C5.5; C5.6 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C5.7 |
| | |MZ10 VELS Textbook: |
| | |Ch 1 Maths in Action Q 4 |
| | |Ch 1 Investigation p. 26 Q 1–3 |
| | |Ch 2 VELS Design Task Q 1 |
|Nu5.5(4 |Calculation of approximate values for φ, the golden ratio, using measurement, definition, and successive| MZ8 VELS Textbook: |
| |ratios of the Fibonacci sequence |Ch 5 Maths in Action Q 1–11 |
|Nu5.5(5 |Computation involving natural numbers, integers, finite decimals and surds without the aid of | MZ10 VELS Textbook: |
| |technology, giving exact answers as applicable |Ex 2.2 Q 1–8 |
| | |Ex 2.3 Q 1–7 |
| | |Ex 2.4 Q 1–10 |
| | |Ex 2.5 Q 1–10 |
| | |Ex 2.6 Q 1–10 |
|Nu5.5(6 |Calculation of the remainder after division by using multiplication (Euclid’s method) | |
|Nu5.75(1 |Division and multiplication of numbers in index form, including application to scientific notation | MZ9 VELS Textbook: |
| | |Ex 1.3 Q 1–4, 6–11 |
| | |Ex 1.4 Q 1–11 |
| | |Ch 6 Maths in Action Q 3, 4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C1.4; C1.5; C1.6; C1.7; C1.8 |
| | |MZ10 VELS Textbook: |
| | |Ex 2.7 Q 1–8 |
| | |Ex 2.8 Q 1–5 |
| | |Ex 2.9 Q 1–7 |
| | |Ex 2.10 Q 1–7 |
| | |Ch 2 Problem solving p. 74 Q 3, 4 |
| | |Ex 2.12 Q 1–7 |
| | |Ex 2.13 Q 1, 2, 4–7 |
| | |Ch 2 Graphics calculator investigation p. 87 Q 2, 3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R2.5 |
| | |C2.9; C2.11 |
| | |VCE Worksheets: |
| | |ZFM R4.4 |
| | |ZM3&4 R2.1 |
|Nu5.75(2 |Knowledge of the equivalence of (1/10)3 and 10−3 | MZ10 VELS Textbook: |
| | |Ex 2.11 Q 2 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C2.10 |
|Nu5.75(3 |Application of scientific notation and recalled approximations to squares and square roots to | MZ10 VELS Textbook: |
| |approximate values for expressions |Ex 2.13 Q 3, 8–11 |
|Nu5.75(4 |Rationalisation of expressions where division by a square root is involved; for example, √(5)/√(3) = | MZ10 VELS Textbook: |
| |√(15)/3 |Ex 2.6 Q 1–3, 5, 8 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C2.7 |
|Nu6.0 |At Level 6, students comprehend the set of real numbers containing natural, integer, rational and | MZ9 VELS Textbook: |
| |irrational numbers. They represent rational numbers in both fractional and decimal (terminating and |Ch 1 Investigation p. 16 Q 1–5 |
| |infinite recurring) forms (for example, 14/25 = 0.56, 0.47 = 47/99). They comprehend that irrational |MZ10 VELS Textbook: |
| |numbers have an infinite non-terminating decimal form. They specify decimal rational approximations for |Ex 2.11 Q 1–8 |
| |square roots of primes, rational numbers that are not perfect squares, the golden ratio φ, and simple |Ch 2 VELS design Task Q 8, 9 |
| |fractions of π correct to a required decimal place accuracy. |Ex 2.13 Q 3, 8–11 |
| |Students use the Euclidean division algorithm to find the greatest common divisor (highest common |Ch 2 Graphics calculator investigation p. 87 Q 4, 5; |
| |factor) of two natural numbers (for example, the greatest common divisor of 1071 and 1029 is 21 |Extension |
| |as 1071 = 1029 × 1 + 42, 1029 = 42 × 24 + 21 and 42 = 21 × 2 + 0). |Ch 2 Maths in Action Q 1, 2 |
| |Students carry out arithmetic computations involving natural numbers, integers and finite decimals using|VCE Worksheets: |
| |mental and/or written algorithms (one- or two-digit divisors in the case of division). They perform |ZM1&2 R2.5 |
| |computations involving very large or very small numbers in scientific notation (for example, 0.0045 × | |
| |0.000028 = 4.5 × 10−3 × 2.8 × 10−5 = 1.26 × 10−7). | |
| |They carry out exact arithmetic computations involving fractions and irrational numbers such as square | |
| |roots (for example, √18 = 3√2, √(3/2) = √6/2) and multiples and fractions of π (for example π + π/4 = | |
| |5π/4). They use appropriate estimates to evaluate the reasonableness of the results of calculations | |
| |involving rational and irrational numbers, and the decimal approximations for them. They carry out | |
| |computations to a required accuracy in terms of decimal places and/or significant figures. | |
|Nu6.25(1 |Representation of various rational and irrational real numbers by their infinite decimal expansion, as a| |
| |limiting value of a sequence of rational numbers, or by location on a geometric number-line model; for | |
| |example, the compass and straight edge constructible numbers | |
|Nu6.25(2 |Knowledge of the relation ≤ as a total (linear) order on the set of real numbers (the continuum) and use| |
| |of |x| = √(x²) to specify the magnitude of a real number | |
|Nu6.25(3 |Efficient and reliable use of written algorithms for all four arithmetic operations with integers, | MZ10 VELS Textbook: |
| |rational numbers (decimal and fractional) and exact form irrational numbers |Ex 2.5 Q 1–10 |
| | |Ex 2.6 Q 4, 6, 7, 9, 10 |
| | |Ch 2 CAS investigation p. 63 Q 3, 4 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C2.8 |
| | |VCE Worksheets: |
| | |ZM1&2 R4.5 |
|Nu6.5(1 |Recognition that rational numbers are a dense subset of real numbers and that real numbers are complete | |
|Nu6.5(2 |Use of closed and open intervals to specify an interval (or union of intervals) over which a given | VCE Worksheets: |
| |inequality is true |ZM3&4 R1.5 |
|Nu6.5(3 |Use of real number properties to reformulate computations involving several operations so that they can | |
| |be carried out more efficiently using a suitable combination of mental, written or technology-assisted | |
| |methods | |
|Nu6.75(1 |Use of concepts and operations of other number systems, such as modulo (clock) arithmetic, matrices or | VCE Worksheets: |
| |Gaussian integers |ZGM R4.2 |
| | |ZFM R8.3; R8.4; R9.1 |
|Nu6.75(2 |Knowledge of the properties that formally define the set of real numbers with the operations of + and × | |
| |and the relation < as an ordered number field, and their application to proving simple number properties| |
| |or order results about real numbers; for example, −a × −b = ab; if 0 < a < b then a² < b² | |
|Nu6.75(3 |Efficient and reliable use of number facts and techniques to carry out mental computation where a | |
| |written algorithm or technology might otherwise be used; for example, 492 = 2500 − 100 + 1 | |
|Space |
|Sp3.0 |At Level 3, students recognise and describe the directions of lines as vertical, horizontal or diagonal.| MZ7 VELS Worksheets with explanations and questions: |
| |They recognise angles are the result of rotation of lines with a common end-point. They recognise and |R6.5 |
| |describe polygons. They recognise and name common three-dimensional shapes such as spheres, prisms and | |
| |pyramids. They identify edges, vertices and faces. They use two-dimensional nets, cross-sections and | |
| |simple projections to represent simple three-dimensional shapes. They follow instructions to produce | |
| |simple tessellations (for example, with triangles, rectangles, hexagons) and puzzles such as tangrams. | |
| |They locate and identify places on maps and diagrams. They give travel directions and describe positions| |
| |using simple compass directions (for example, N for North) and grid references on a street directory. | |
|Sp3.25(1 |Recognition of angles between lines, particularly when lines are parallel or perpendicular | MZ7 VELS Textbook: |
| | |Ex 7.5 Q 1 |
| | |MZ8 VELS Textbook: |
| | |Ex 9.2 Q 1–13 |
|Sp3.25(2 |Use of scaled grids to draw similar figures (enlarged or reduced) | MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 1, 4 |
|Sp3.25(3 |Use of a graphical scale to determine actual size and distance from a map | MZ8 VELS Textbook: |
| | |VELS Assignment 4 Q 8 |
|Sp3.25(4 |Interpretation of maps of their own immediate environment using various scales; for example, school | MZ7 VELS Textbook: |
| |ground, suburb, state, country |Ch 6 Maths@Work Q 1–8 |
|Sp3.25(5 |Description of a path by a set of coordinates | MZ7 VELS Textbook: |
| | |Ex 6.8 Q 4–10 |
|Sp3.5(1 |Classification and sorting of two-dimensional shapes using the properties of lines (curvature, | MZ7 VELS Textbook: |
| |orientation and length) and angles (less than, equal to, or greater than, 90°) |Ch 9 Investigation p. 409 Q 1–9 |
|Sp3.5(2 |Construction or selection of possible objects given a plan (bird’s eye view) or an elevation (side view)| MZ8 VELS Textbook: |
| | |Ex 9.5 Q 1, 2 |
|Sp3.5(3 |Construction of transformed shapes and patterns by stamping, folding and rotating | MZ7 VELS Textbook: |
| | |Ex 9.6 Q 1, 4, 5 |
|Sp3.5(4 |Representation of relationships within a family (people or animals) through use of a tree diagram | |
| |(network) | |
|Sp3.75(1 |Construction of a copy of a shape, given details about side lengths and angles | MZ7 VELS Textbook: |
| | |Ex 9.7 Q 4 |
|Sp3.75(2 |Use of two-dimensional isometric drawings of three-dimensional objects, noting how shapes are not always| MZ7 VELS Textbook: |
| |preserved; for example, squares become parallelograms |Ch 9 Maths in Action Q 1–3 |
|Sp3.75(3 |Knowledge that the sum of angles at a point on a straight line is 180° | MZ7 VELS Textbook: |
| | |Ex 7.5 Q 3(b), (c), 4, 5 |
|Sp3.75(4 |Use of a compass and compass directions to describe orientation in the school ground | |
|Sp4.0 |At Level 4, students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and | MZ7 VELS Textbook: |
| |cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater |Ch 6 Investigation p. 287 Rook’s tours Q 1–3; Bishop’s |
| |than, 90°), and surfaces. They create two-dimensional representations of three-dimensional shapes and |tours Q 1–3; Queen’s tours Q 1–3 |
| |objects found in the surrounding environment. They develop and follow instructions to draw shapes and |Ch 6 Maths@Work Q 3, 6 |
| |nets of solids using a simple scale. They describe the features of shapes and solids that remain the |Ch 7 Maths in Action Q 1–5 |
| |same (for example, angles) or change (for example, surface area) when a shape is enlarged or reduced. |Ex 7.4 Q 1–7 |
| |They apply a range of transformations to shapes and create tessellations using tools (for example, |Ch 7 VELS Design Task Q 1–7 |
| |computer software). |Ch 7 Investigation p. 332 Q 1–4 |
| |Students use the ideas of size, scale, and direction to describe relative location and objects in maps. |Ex 9.1 Q 1, 2 |
| |They use compass directions, coordinates, scale and distance, and conventional symbols to describe |MZ7 VELS Worksheets with explanations and questions: |
| |routes between places shown on maps. Students use network diagrams to show relationships and |R2.12 |
| |connectedness such as a family tree and the shortest path between towns on a map. |C9.1 |
| | |MZ8 VELS Textbook: |
| | |Ex 9.3 Q 1–6 |
| | |Ch 9 Investigation p. 412 Q 3, 5–10 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C9.3 |
|Sp4.25(1 |Construction of a plan, elevations and cross-sections for a three-dimensional object | MZ8 VELS Textbook: |
| | |Ex 9.5 Q 1–6 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 2 Q 1, 3 |
|Sp4.25(2 |Knowledge of how features (for example, an angle) change, or not, when a shape undergoes a | MZ7 VELS Textbook: |
| |transformation (for example, a rotation) |Ex 9.6 Q 1–8 |
| | |Ch 9 Computer investigation p. 432 Q 1–5 |
|Sp4.25(3 |Classification of polygons with reference to a definition or a key property | MZ7 VELS Textbook: |
| | |Ex 9.1 Q 3–11 |
| | |Ex 9.3 Q 1–7 |
| | |Ch 9 Problem solving p. 418 Q 1–4 |
| | |Ex 9.5 Q 1–5 |
| | |Ch 9 Investigation p. 427 Q 1 , 2 |
| | |Ch 9 VELS Design Task Q 1–8 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C9.3; C9.6; C9.9 |
| | |MZ8 VELS Textbook: |
| | |Ex 9.4 Q 1–6 |
| | |MZ9 VELS Textbook: |
| | |Ex 5.1 Q 1–6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R2.4; R3.1; R4.7; R5.2 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C8.3 |
| | |VCE Worksheets: |
| | |ZGM R10.3 |
|Sp4.25(4 |Construction of parallel and perpendicular lines | MZ7 VELS Worksheets with questions only: |
| | |C9.2 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R9.1 |
|Sp4.25(5 |Use of a map reference to locate a point or region on a map | MZ7 VELS Textbook: |
| | |Ex 6.7 Q 1–6 |
| | |Ch 6 Maths@Work Q 1, 2, 4–8 |
|Sp4.25(6 |Use of networks to display relationships between people and pathways between objects | MZ8 VELS Textbook: |
| | |Ex 9.7 Q 4 |
|Sp4.5(1 |Identification of congruent shapes | MZ8 VELS Textbook: |
| | |Ex 8.10 Q 1–4 |
| | |Ch 8 Computer investigation p. 412 Q 1 |
|Sp4.5(2 |Tessellation of suitable irregular shapes | MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 6, 7 |
| | |MZ9 VELS Textbook: |
| | |Ex 8.6 Q 1–9 |
| | |Ch 8 Investigation p. 394 Q 1–4 |
|Sp4.5(3 |Use of angle facts for a triangle | MZ7 VELS Textbook: |
| | |Ch 9 Investigation p. 411 Q 1–4 |
| | |Ex 9.2 Q 1–8 |
| | |Ch 9 Laugh Zone |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C9.4 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C9.5 |
| | |MZ9 VELS Textbook: |
| | |Ex 8.2 Q 1–8 |
| | |Ex 8.3 Q 1–7 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R5.4 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C8.1; C8.2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.13; R6.4 |
|Sp4.5(4 |Use of conventional symbols and contours to describe a route marked on a map | MZ8 VELS Textbook: |
| | |VELS Assignment 4 Q 7–9 |
|Sp4.5(5 |Representation of pathways between objects as part of a network | MZ8 VELS Textbook: |
| | |Ex 9.7 Q 5 |
| | |Ch 9 Investigation p. 428 Q 1–3 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C9.5 |
|Sp4.75(1 |Knowledge of methods for creating the illusion of depth in a two-dimensional image, and description of | MZ7 VELS Textbook: |
| |the related process in geometrical terms |Ch 9 Maths in Action Q 1–3 |
| | |MZ8 VELS Textbook: |
| | |Ex 9.5 Q 1, 2 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C9.4 |
|Sp4.75(2 |Production and analysis of images based on projection from a point (one point perspective) and a line | MZ7 VELS Textbook: |
| | |Ch 9 Maths in Action Q 1–3 |
|Sp4.75(3 |Calculation of size of objects using a numerical map scale | MZ7 VELS Textbook: |
| | |VELS Assignment 2 Q 2 |
|Sp4.75(4 |Use of bearings and distances to plot a route on a map | MZ10 VELS Textbook: |
| | |Ex 6.9 Q 1, 6 |
|Sp4.75(5 |Equivalence of components of a three-dimensional object and its net; for example, vertices and nodes, | MZ8 VELS Textbook: |
| |arcs and edges, faces and regions |Ex 9.6 Q 1–3 |
| | |Ex 9.7 Q 1–3, 6–9 |
|Sp5.0 |At Level 5, students construct two-dimensional and simple three-dimensional shapes according to | MZ7 VELS Textbook: |
| |specifications of length, angle and adjacency. They use the properties of parallel lines and |Ch 9 Investigation p. 409 Q 1–9 |
| |transversals of these lines to calculate angles that are supplementary, corresponding, allied |Ex 9.4 Q 1–8 |
| |(co-interior) and alternate. They describe and apply the angle properties of regular and irregular |Ch 9 Laugh Zone |
| |polygons, in particular, triangles and quadrilaterals. They use two-dimensional nets to construct a |Ch 9 Investigation p. 428 Q 3–9 |
| |simple three-dimensional object such as a prism or a platonic solid. They recognise congruence of shapes|Ex 9.7 Q 1–8 |
| |and solids. They relate similarity to enlargement from a common fixed point. They use single-point |MZ7 VELS Worksheets with explanations and questions: |
| |perspective to make a two-dimensional representation of a simple three-dimensional object. They make |C9.7; C9.10 |
| |tessellations from simple shapes. |MZ7 VELS Worksheets with questions only: |
| |Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, |C9.8 |
| |scales and bearings to specify location and direction on plans and maps. They use network diagrams to |MZ8 VELS Textbook: |
| |specify relationships. They consider the connectedness of a network, such as the ability to travel |Ex 9.1 Q 1–6 |
| |through a set of roads between towns. |Ex 9.2 Q 1–13 |
| | |Ch 9 Laugh Zone |
| | |Ch 9 Computer investigation p. 406 Q 6, 7 |
| | |Ex 9.6 Q 4–7 |
| | |Ch 9 Problem solving p. 427 |
| | |Ex 9.8 Q 1–9 |
| | |Ex 9.9 Q 1–6 |
| | |Ch 9 Maths@Work |
| | |Ch 9 VELS Design Task Q 1–6 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C9.1 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C9.2 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 4 Q 3, 4 |
| | |Ch 3 Maths in Action Q 3 |
| | |Ex 5.1 Q 7 |
| | |Ch 5 Maths@Work Q 1 |
| | |Ex 8.1 Q 1–4 |
| | |Ch 8 Investigation p. 375 Q 1–4 |
| | |Ch 8 Problem solving p. 376 |
| | |Ch 8 Computer investigation p. 384 Q 1, 2 |
| | |Ex 8.4 Q 1–10 |
| | |Ex 8.5 Q 1–8 |
| | |Ch 8 Investigation p. 390 Q 1, 2 |
| | |Ch 8 Laugh Zone |
| | |Ex 8.7 Q 1–6 |
| | |Ex 8.8 Q 1–7 |
| | |Ch 8 Maths@Work Q 1, 2 |
| | |Ex 8.9 Q 1–5 |
| | |Ex 8.11 Q 1–8 |
| | |Ch 8 Computer investigation p. 412 Q 2–5 |
| | |Ch 8 VELS Design Task Q 1–6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R8.2 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R8.4; R8.5 |
| | |C8.4; C8.5; C8.7; C8.9; C8.10; C8.11 |
| | |MZ10 VELS Textbook: |
| | |Ch 8 Problem solving p. 426 Q 1, 2 |
| | |Ch 8 Computer investigation p. 426 Q 1–6 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R8.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R2.14 |
| | |VCE Worksheets: |
| | |ZGM R13.2; R13.3 |
| | |ZM1&2 R8.2 |
| | |ZFM R5.2 |
|Sp5.25(1 |Use of two-dimensional nets and line-segment models to investigate regular, semi-regular and irregular | MZ8 VELS Textbook: |
| |solids |Ex 9.6 Q 1–5 |
|Sp5.25(2 |Application of the angle properties of parallel lines and transversals to other geometrical problems | MZ8 VELS Textbook: |
| | |Ex 9.2 Q 13 |
|Sp5.25(3 |Knowledge of sets of conditions for pairs of triangles to be congruent | MZ9 VELS Textbook: |
| | |Ex 8.10 Q 1–4 |
| | |Ch 8 Computer investigation p. 412 Q 1 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C8.6 |
|Sp5.25(4 |Use of Euler’s formula for polyhedra and their nets | MZ10 VELS Textbook: |
| | |Ex 8.5 Q 1–6 |
| | |VCE Worksheets: |
| | |ZFM R8.1 |
|Sp5.5(1 |Recognition of the features of circles (centre, radius, diameter, chord, arc, semi-circle, | MZ10 VELS Textbook: |
| |circumference, segment, sector and tangent) and the associated angle relationships |Ex 8.1 Q 1–11 |
| | |Ex 8.2 Q 1–10 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C8.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C8.2; C8.3; C8.4 |
|Sp5.5(2 |Investigation of angle properties of circles and tangents | MZ10 VELS Textbook: |
| | |Ex 8.2 Q 1, 8 |
|Sp5.5(3 |Representation of a point on the Earth’s surface in terms of its latitude and longitude | MZ10 VELS Textbook: |
| | |Ch 8 Investigation p. 434 Q 1–3 |
|Sp5.5(4 |Identification of paths and circuits in network diagrams that illustrate connections between objects, | MZ8 VELS Textbook: |
| |locations and events |Ex 9.7 Q 1–9 |
| | |Ex 9.8 Q 1–9 |
| | |Ex 9.9 Q 1–6 |
| | |Ch 9 Maths@Work |
| | |Ch 9 VELS Design Task Q 1–6 |
|Sp5.75(1 |Location of the great circle pathway between two points on a sphere | MZ10 VELS Textbook: |
| | |Ch 8 Investigation p. 434 Q 1–3 |
|Sp5.75(2 |Application of geometrical transformations to graphs | MZ10 VELS Textbook: |
| | |Ex 8.7 Q 1–7 |
|Sp5.75(3 |Knowledge of latitude and longitude in geometrical terms | MZ10 VELS Textbook: |
| | |Ch 8 Investigation p. 434 Q 1–3 |
|Sp6.0 |At Level 6, students represent two- and three-dimensional shapes using lines, curves, polygons and | MZ9 VELS Textbook: |
| |circles. They make representations using perspective, isometric drawings, nets and computer-generated |VELS Assignment 4 Q 3, 4 |
| |images. They recognise and describe boundaries, surfaces and interiors of common plane and |MZ10 VELS Textbook: |
| |three-dimensional shapes, including cylinders, spheres, cones, prisms and polyhedra. They recognise the |Ch 6 Maths in Action Q 1–3 |
| |features of circles (centre, radius, diameter, chord, arc, semi-circle, circumference, segment, sector |Ex 8.5 Q 7–11 |
| |and tangent) and use associated angle properties. |Ex 8.6 Q 1–15 |
| |Students explore the properties of spheres. |Ch 8 Graphics calculator investigation p. 424 Q 1–6 |
| |Students use the conditions for shapes to be congruent or similar. They apply isometric and similarity | |
| |transformations of geometric shapes in the plane. They identify points that are invariant under a given | |
| |transformation (for example, the point (2, 0) is invariant under reflection in the x-axis, so the x-axis| |
| |intercept of the graph of y = 2x − 4 is also invariant under this transformation). They determine the | |
| |effect of changing the scale of one characteristic of two- and three-dimensional shapes (for example, | |
| |side length, area, volume and angle measure) on related characteristics. | |
| |They use latitude and longitude to locate places on the Earth’s surface and measure distances between | |
| |places using great circles. | |
| |Students describe and use the connections between objects/location/events according to defined | |
| |relationships (networks). | |
|Sp6.25(1 |Proof of properties of shapes in plane (Euclidean) geometry, for example, circle and tangent properties | MZ10 VELS Textbook: |
| | |Ch 8 Investigation p. 399 1–5 |
| | |Ch 8 VELS Design Task Q 1–5 |
|Sp6.25(2 |Practical applications of geometry on a sphere, such as methods for determining latitude and longitude, | MZ10 VELS Textbook: |
| |and navigation on the Earth’s surface |Ex 8.4 Q 1–7 |
| | |Ch 8 Investigation p. 434 Q 1–3 |
|Sp6.25(3 |Use of networks and properties to solve practical problems involving paths and circuits, length and | MZ8 VELS Textbook: |
| |coverage |Ex 9.9 Q 6 |
| | |Ch 9 Maths@Work |
| | |Ch 9 VELS Design Task Q 5, 6 |
|Sp6.5(1 |Locus definitions of paths, and their corresponding forms, in various coordinate systems; for example, | MZ10 VELS Textbook: |
| |Cartesian, polar, parametric |Ch 8 Investigation p. 433 Q 1–7 |
| | |Ch 9 CAS investigation p. 472 Q 1–6 |
|Sp6.5(2 |Application of properties of non-Euclidean geometry; for example, projective geometry and the problems | MZ10 VELS Textbook: |
| |of representation in maps, art and engineering, affine transformations and digital images |Ch 8 Maths in Action Q 1–3 |
|Sp6.5(3 |Understanding of dual relationships between faces and edges involving polyhedra | MZ10 VELS Textbook Ex 8.5 Q 11 |
|Sp6.75(1 |Identification and application of self-similarity in spatial constructions; for example, fractal | MZ10 VELS Textbook: |
| |patterns in nature and art |Ch 8 Maths in Action Q 1–3, Research Q 1, 2 |
|Sp6.75(2 |Solution of mathematical puzzles involving topological properties of connectedness; for example, the | |
| |geometry of knots, puzzles where apparently ‘linked’ three-dimensional shapes can be separated | |
|Sp6.75(3 |Invariance of some geometric properties under certain transformations | |
|Measurement, chance and data |
|Me3.0 |At Level 3, students estimate and measure length, area, volume, capacity, mass and time using | MZ7 VELS Textbook: |
| |appropriate instruments. They recognise and use different units of measurement including informal (for |VELS Assignment 5 Q 1–3 |
| |example, paces), formal (for example, centimetres) and standard metric measures (for example, metre) in |MZ7 VELS Worksheets with explanations and questions: |
| |appropriate contexts. They read linear scales (for example, tape measures) and circular scales (for |R7.1 |
| |example, bathroom scales) in measurement contexts. They read digital time displays and analogue clock |MZ7 VELS Worksheets with questions only: |
| |times at five-minute intervals. They interpret timetables and calendars in relation to familiar events. |R5.6 |
| |They compare the likelihood of everyday events (for example, the chances of rain and snow). They | |
| |describe the fairness of events in qualitative terms. They plan and conduct chance experiments (for | |
| |example, using colours on a spinner) and display the results of these experiments. They recognise | |
| |different types of data: non-numerical (categories), separate numbers (discrete), or points on an | |
| |unbroken number line (continuous). They use a column or bar graph to display the results of an | |
| |experiment (for example, the frequencies of possible categories). | |
|Me3.25(1 |Estimation and measurement of perimeter of polygons | MZ7 VELS Textbook: |
| | |Ex 5.1 Q 3–9 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R5.3 |
| | |MZ7 VELS Worksheets with questions only: |
| | |R5.2 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R6.1 |
|Me3.25(2 |Conversion between metric measurements for length; for example, 0.27m = 27cm | MZ7 VELS Textbook: |
| | |Ex 5.2 Q 1–15 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R5.4 |
| | |C5.1 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R4.10; R6.4 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R5.1 |
| | |MZ9 VELS Textbook: |
| | |Ex 2.1 Q 1 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C2.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R4.3 |
|Me3.25(3 |Estimation and measurement of angles in degrees to the nearest 10° | MZ7 VELS Worksheets with explanations and questions: |
| | |R7.2; R7.3 |
|Me3.25(4 |Use of fractions to assign probability values between 0 and 1 to probabilities based on symmetry; for | MZ7 VELS Textbook: |
| |example, Pr(six on a die) = 1/6 |Ex 10.8 Q 1 |
|Me3.25(5 |Identification of mode and range for a set of data | MZ7 VELS Textbook: |
| | |Ex 10.2 Q 1, 2, 4–7 |
|Me3.5(1 |Estimation and measurement of surface area; for example, use of square metres, and area of land; for | MZ7 VELS Worksheets with explanations and questions: |
| |example, use of hectares |R5.3 |
|Me3.5(2 |Awareness of the accuracy of measurement required and the appropriate tools and units | MZ7 VELS Textbook: |
| | |Ex 5.1 Q 1, 2 |
| | |MZ7 VELS Worksheets with questions only: |
| | |R9.2 |
| | |MZ9 VELS Textbook: |
| | |Ex 3.1 Q 2 |
|Me3.5(3 |Subdivision of a circle into two sectors according to a given proportion for arc length | MZ7 VELS Textbook: |
| | |Ex 10.5 Q 1 |
|Me3.5(4 |Design of questionnaires to obtain data from a sample of the population | MZ7 VELS Textbook: |
| | |Ex 10.1 Q 7–10 |
|Me3.5(5 |Sorting of data using technology | MZ7 VELS Textbook: |
| | |Ch 10 Computer investigation p. 465 Q 1–4 |
| | |MZ8 VELS Textbook: |
| | |Ch 10 Computer investigation p. 484 Q 1–6 |
|Me3.75(1 |Conversion between metric units; for example, L to mL, and understanding of the significance of | MZ8 VELS Worksheets with questions only: |
| |thousands and thousandths in the metric system |R5.1 |
| | |MZ9 VELS Textbook: |
| | |Ex 3.1 Q 3 |
| | |VCE Worksheets: |
| | |ZFM R5.1 |
|Me3.75(2 |Simulation of simple random events | MZ8 VELS Textbook: |
| | |Ch 10 Graphics calculator investigation p. 490 |
|Me3.75(3 |Calculation and analysis of the stability of a sequence of long-run frequencies where the number of | MZ7 VELS Textbook: |
| |trials increases, say from 5 to 10 to 20 to 100 |Ch 10 Investigation p. 488 Car colour Q 1, Letter Q 1 |
|Me3.75(4 |Interpretation of pie charts and histograms | MZ7 VELS Textbook: |
| | |Ex 10.5 Q 1, 3 |
| | |Ch 10 Investigation p. 488 Car colour Q 1, 2 |
| | |Ch 10 Laugh Zone |
|Me3.75(5 |Identification of the median for a set of data | MZ7 VELS Textbook: |
| | |Ex 10.2 Q 1–11 |
|Me4.0 |At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, | MZ7 VELS Textbook: |
| |mass, volume, capacity, time and temperature. They measure angles in degrees. They measure as accurately|VELS Assignment 2 Q 1, 3 |
| |as needed for the purpose of the activity. They convert between metric units of length, capacity and |VELS Assignment 4 Q 3 |
| |time (for example, L to mL, sec to min). |VELS Assignment 5 Q 1–3 |
| |Students describe and calculate probabilities using words, and fractions and decimals between 0 and 1. |Ex 5.3 Q 1–16 |
| |They calculate probabilities for chance outcomes (for example, using spinners) and use the symmetry |Ch 5 Problem solving p. 195 |
| |properties of equally likely outcomes. They simulate chance events (for example, the chance that a |Ex 5.4 Q 1–17 |
| |family has three girls in a row) and understand that experimental estimates of probabilities converge to|Ch 5 VELS Design Task Q 1–4 |
| |the theoretical probability in the long run. |Ch 5 Laugh Zone |
| |Students recognise and give consideration to different data types in forming questionnaires and |Ex 5.5 Q 3–9 |
| |sampling. They distinguish between categorical and numerical data and classify numerical data as |Ex 5.6 Q 1 |
| |discrete (from counting) or continuous (from measurement). They present data in appropriate displays |Ex 5.10 Q 1, 4–8 |
| |(for example, a pie chart for eye colour data and a histogram for grouped data of student heights). They|Ex 7.1 Q 1–11 |
| |calculate and interpret measures of centrality (mean, median, and mode) and data spread (range). |Ch 7 Problem solving p. 318 |
| | |Ex 7.2 Q 1–6 |
| | |Ch 7 Investigation p. 322 Q 1–5 |
| | |Ex 7.3 Q 1–7 |
| | |Ch 7 Investigation p. 325 Q 1–4 |
| | |Ch 7 Maths in Action Activity |
| | |Ex 7.4 Q 1–7 |
| | |Ch 7 VELS Design Task Q 1–7 |
| | |Ch 7 Problem solving p. 337 |
| | |Ex 10.1 Q 1–14 |
| | |Ex 10.2 Q 1–11 |
| | |Ch 10 Investigation p. 463 Q 1–4 |
| | |Ex 10.7 Q 1–7 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R2.10; R5.5; R9.1 |
| | |C5.2; C7.1; C7.2; C7.3; C10.1; C10.2; C10.7 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C5.9; C7.4; C10.3 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 2 |
| | |VELS Assignment 5 Q 1–5 |
| | |Ex 6.1 Q 1, 4, 5, 7, 8 |
| | |Ex 6.7 Q 4, 5 |
| | |Ex 10.1 Q 1–9 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R4.11; R9.2; R9.3; R10.1; R10.2; R10.4; R10.5 |
| | |C10.1 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 2 Q 1–3 |
| | |Ex 3.1 Q 4 |
| | |Ch 3 VELS Design Task Q 1 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R8.1; R8.3; R10.6 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 4 Q 2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.14 |
| | |VCE Worksheets: |
| | |ZGM R6.2; R7.2 |
| | |ZFM R1.1; R1.2; R3.3; R3.4 |
|Me4.25(1 |Development and use of formulas for the area and perimeter of triangles and parallelograms | MZ7 VELS Textbook: |
| | |Ex 5.6 Q 2, 3, 6, 7 |
| | |Ex 5.7 Q 1–7 |
| | |Ch 5 Maths@Work Q 3–5 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C5.3; C5.4; C5.5; C5.6 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C5.7 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 3, 4 |
| | |Ex 6.1 Q 2, 3, 6 |
| | |Ex 6.3 Q 1–10 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R2.16; R3.13 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C6.3 |
| | |MZ9 VELS Textbook: |
| | |Ex 2.1 Q 5–8 |
| | |Ch 2 Problem solving p. 70 Q 1–4 |
| | |Ch 2 VELS Design Task Q 2, 4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.17; R1.18; R4.6 |
|Me4.25(2 |Determination of the internal and external angle sums for a polygon and confirmation by measurement | MZ7 VELS Textbook: |
| | |Ex 7.5 Q 1–8 |
| | |Ch 7 Laugh Zone |
| | |Ex 7.6 Q 1–6 |
| | |Ex 7.7 Q 1–6 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C7.5; C7.6; C7.8 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C7.7; C7.9 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R2.14; R6.5; R9.4 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R3.10 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.13; R3.11 |
|Me4.25(3 |Estimation of the likely maximum and minimum error associated with a measurement | MZ9 VELS Textbook: |
| | |Ex 2.2 Q 1, 3, 4 |
|Me4.25(4 |Appropriate use of zero to indicate accuracy of measurement; for example, a piece of timber 2.100 m long| MZ7 VELS Textbook: |
| |is accurate to the nearest mm |Ex 4.3 Q 4, 6, 7, 9, 11, 12 |
|Me4.25(5 |Recognition of the mean value of a set of measurements as the best estimate, and that the range could | MZ8 VELS Textbook: |
| |represent the associated error |Ex 10.5 Q 12–16 |
|Me4.5(1 |Use of appropriate units and measurement of length, perimeter, area, surface area, mass, volume, | MZ7 VELS Textbook: |
| |capacity, angle, time and temperature, in context |VELS Assignment 2 Q 4, 5 |
| | |Ex 5.5 Q 1, 2 |
| | |Ex 5.6 Q 4, 5, 8–24 |
| | |Ch 5 Maths@Work Q 3–5 |
| | |Ex 5.8 Q 1–4 |
| | |Ex 5.10 Q 2, 3, 9–17 |
| | |Ex 5.11 Q 1–9 |
| | |Ex 7.1 Q 12–17 |
| | |Ch 7 Investigation p. 322 Q 5 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 2 Q 3, 4 |
| | |MZ9 VELS Textbook: |
| | |Ex 2.1 Q 9–13 |
| | |Ch 2 Maths in Action Q 1–3, 6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.10; R2.7 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C2.2; C2.5 |
|Me4.5(2 |Calculation of total surface area of prisms, including cylinders, by considering their nets | MZ7 VELS Textbook: |
| | |Ex 5.7 Q 8 |
| | |MZ9 VELS Textbook: |
| | |Ex 2.5 Q 1–11 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C2.4 |
|Me4.5(3 |Contrast between the stability of long-run relative frequency and the variation of observations based on| MZ7 VELS Textbook: |
| |small samples |Ch 10 Investigation p. 499 Q 1, 2 |
|Me4.5(4 |Construction of dot plots, and stem and leaf plots to represent data sets | MZ8 VELS Textbook: |
| | |Ex 10.5 Q 1–3 |
| | |Ch 10 Investigation p. 481 Q 3 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C10.4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R2.6 |
|Me4.75(1 |Understanding of the distinction between error and percentage error | MZ9 VELS Textbook: |
| | |Ex 2.2 Q 2, 9, 10, 14 |
|Me4.75(2 |Use of random numbers to assist in probability simulations and the arithmetic manipulation of random | MZ8 VELS Textbook: |
| |numbers to achieve the desired set of outcomes |Ch 10 Graphics calculator investigation p. 490 |
|Me4.75(3 |Calculation of theoretical probability using ratio of number of ‘successful’ outcomes to total number of| MZ7 VELS Textbook: |
| |outcomes |Ex 10.8 Q 1–6 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C10.8 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C10.9 |
| | |MZ8 VELS Textbook: |
| | |Ex 10.6 Q 1–12 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C10.8 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.20; R10.7 |
| | |MZ10 VELS Textbook: |
| | |Ex 10.1 Q 1–12 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C10.2 |
| | |VCE Worksheets: |
| | |ZM1&2 R5.3; R5.4; R5.5 |
| | |ZM3&4 R8.1 |
|Me4.75(4 |Use of tree diagrams to explore the outcomes from multiple event trials | MZ8 VELS Textbook: |
| | |Ch 10 Investigation p. 489 Q 1, 2 |
| | |VCE Worksheets: |
| | |ZFM R1.4 |
|Me4.75(5 |Display and interpretation of dot plots, and stem and leaf plots, including reference to mean, median | MZ7 VELS Textbook: |
| |and mode as measures of centre |Ch 10 VELS Design Task Q 1–7 |
| | |MZ8 VELS Textbook: |
| | |Ex 10.5 Q 4–19 |
| | |Ch 10 Investigation p. 481 Q 4–6 |
| | |Ch 10 Laugh Zone |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |C10.5 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R7.3 |
|Me5.0 |At Level 5, students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time | MZ7 VELS Textbook: |
| |and temperature using suitable units for these measurements in context. They interpret and use |VELS Assignment 2 Q 5–7 |
| |measurement formulas for the area and perimeter of circles, triangles and parallelograms and simple |VELS Assignment 4 Q 3 |
| |composite shapes. They calculate the surface area and volume of prisms and cylinders. |Ex 5.7 Q 9, 10 |
| |Students estimate the accuracy of measurements and give suitable lower and upper bounds for measurement |Ex 5.8 Q 5–7 |
| |values. They calculate absolute percentage error of estimated values. |Ex 5.9 Q 1–9 |
| |Students use appropriate technology to generate random numbers in the conduct of simple simulations. |Ex 10.3 Q 1–11 |
| |Students identify empirical probability as long-run relative frequency. They calculate theoretical |Ex 10.4 Q 1–12 |
| |probabilities by dividing the number of possible successful outcomes by the total number of possible |Ex 10.5 Q 2, 4–10 |
| |outcomes. They use tree diagrams to investigate the probability of outcomes in simple multiple event |Ex 10.6 Q 1–4 |
| |trials. |Ch 10 Investigation p. 488 Car colour Q 3; Most |
| |Students organise, tabulate and display discrete and continuous data (grouped and ungrouped) using |common letter Q 1–3 |
| |technology for larger data sets. They represent univariate data in appropriate graphical forms including|Ch 10 VELS Design Task Q 8, 9 |
| |dot plots, stem and leaf plots, column graphs, bar charts and histograms. They calculate summary |MZ7 VELS Worksheets with explanations and questions: |
| |statistics for measures of centre (mean, median, mode) and spread (range, and mean absolute difference),|C5.8; C10.4 |
| |and make simple inferences based on this data. |MZ7 VELS Worksheets with questions only: |
| | |C10.5; C10.6 |
| | |MZ8 VELS Textbook: |
| | |VELS Assignment 4 Q 5 |
| | |Ch 6 Investigation p. 238 Q 4, 5 |
| | |Ex 6.2 Q 1–15 |
| | |Ex 6.4 Q 1–8 |
| | |Ex 6.5 Q 1–9 |
| | |Ex 6.6 Q 1–7 |
| | |Ch 6 Laugh Zone |
| | |Ex 6.7 Q 1–3, 6–16 |
| | |Ch 6 VELS Design Task Q 2, 3 |
| | |Ch 6 CAS Investigation p. 275 Q 1–3 |
| | |Ch 6 Maths@Work Q 1, 2 |
| | |Ch 6 Problem solving p. 278 |
| | |Ex 10. 2 Q 1–6 |
| | |Ch 10 VELS Design Task Q 1–7 |
| | |Ex 10.3 Q 1–13 |
| | |Ex 10.4 Q 1–10 |
| | |Ch 10 Investigation p. 489 Q 3, 4 |
| | |Ch 10 Graphics calculator investigation p. 490 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R10.3 |
| | |C6.1; C6.2; C6.4; C6.6; C10.6 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C6.5; C6.7: C10.2; C10.3; C10.7 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 2 Q 2, 3 |
| | |VELS Assignment 3 Q 3, 4, 5 |
| | |Ch 2 Maths in Action Q 4, 5 |
| | |Ex 2.2 Q 1–14 |
| | |Ex 2.3 Q 1–7 |
| | |Ch 2 Problem solving p. 84 |
| | |Ex 2.4 Q 1–10 |
| | |Ch 2 Laugh Zone |
| | |Ch 2 VELS Design Task Q 3, 5, 6 |
| | |Ex 2.6 Q 1–12 |
| | |Ch 2 Graphics calculator investigation p. 100 Q 1–5 |
| | |Ex 7.1 Q 1–7 |
| | |Ex 7.2 Q 1–11 |
| | |Ch 7 Problem solving p. 318 (a)–(c) |
| | |Ch 7 Investigation p. 318 Q 1–4 |
| | |Ex 7.3 Q 1–13 |
| | |Ex 7.5 Q 1–14 |
| | |Ex 7.6 Q 1–12 |
| | |Ex 10.1 Q 1–12 |
| | |Ex 10.2 Q 1–6 |
| | |Ex 10.3 Q 1–17 |
| | |Ch 10 Computer investigation p. 483 Q 5, 6 |
| | |Ch 10 Graphics calculator investigation p. 489 Q 1–9 |
| | |Ch 10 Laugh Zone |
| | |Ch 10 VELS Design Task Q 1–8 |
| | |Ex 10.6 Q 1–4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.21; R2.3; R2.5; R3.10; R7.1; R7.2; R7.4 |
| | |C7.1; C10.1 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C2.3; C2.6; C5.1; C7.2 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 1 Q 1, 2 |
| | |VELS Assignment 2 Q 5, 6 |
| | |Ex 4.1 Q 1, 2, 4, 7–9 |
| | |Ex 4.2 Q 1, 4, 8 |
| | |Ch 4 VELS Design Task Q 1 |
| | |Ch 4 Investigation p. 176 Q 1, 2 |
| | |Ex 4.3 Q 1, 2, 6, 8, 10, 14 |
| | |Ex 4.5 Q 1–9 |
| | |Ex 4.7 Q 1 |
| | |Ch 4 Graphics calculator investigation p. 203 Q 1, 2 |
| | |Ex 8.3 Q 1–7 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.7; R1.15; R1.17; R2.8; R2.13; R3.11; R4.4; R4.5; |
| | |R4.6; R4.7; R7.1; R7.3; R8.3 |
| | |C4.1; C4.3 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R2.15; R7.2 |
| | |C4.2; C4.5; C4.8; C8.4 |
| | |VCE Worksheets: |
| | |ZGM R6.3; R8.3; R8.4 |
| | |ZFM R3.1; R5.3 |
|Me5.25(1 |Conversion between units and between derived units | MZ10 VELS Textbook: |
| | |Ex 4.8 Q 1–5 |
| | |Ex 4.9 Q 1–4 |
|Me5.25(2 |Use of Pythagoras’ Theorem to calculate the length of a hypotenuse | MZ9 VELS Textbook: |
| | |VELS Assignment 4 Q 1 |
| | |Ex 3.1 Q 1–7 |
| | |Ch 3 Investigation p. 120 |
| | |Ex 3.2 Q 1–8 |
| | |Ch 3 Maths in Action Q 1 |
| | |Ex 3.3 Q 1–12 |
| | |Ch 3 Laugh Zone Q 1–6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C3.1; C3.2; C3.3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R2.9; R6.3 |
|Me5.25(3 |Use of symmetry and scale to calculate side lengths in triangles | MZ9 VELS Textbook: |
| | |Ex 8.11 Q 1–8 |
|Me5.25(4 |Representation of compound events involving two categories and the logical connectives and, or and not | MZ9 VELS Textbook: |
| |using lists, grids (lattice diagrams), tree diagrams, Venn diagrams and Karnaugh maps (two-way tables) |Ex 10.4 Q 1–9 |
| |and the calculation of associated probabilities |Ex 10.5 Q 1–10 |
| | |Ch 10 Laugh Zone |
| | |Ch 10 Maths in Action Q 1, 2 |
| | |Ch 10 Problem solving p. 503 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C10.2 |
| | |MZ10 VELS Textbook: |
| | |Ex 10.2 Q 1–10 |
| | |Ex 10.3 Q 1–12 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R10.3; R10.4 |
| | |C10.1; C10.3; C10.4 (Q1); C10.5 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R7.2 |
| | |VCE Worksheets: |
| | |ZM1&2 R5.6; R10.1; R10.2 |
| | |ZFM R9.5 |
|Me5.25(5 |Representation of statistical data using technology | MZ8 VELS Textbook: |
| | |Ex 10.2 Q 7, 8 |
| | |Ch 10 Computer investigation p. 484 Q 1–6 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R10.3 |
| | |MZ9 VELS Textbook: |
| | |Ch 7 Graphics calculator investigation p. 332 Q 1, 4, 5 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 3 Q 2, 4, 6 |
| | |VELS Assignment 4 Q 5, 6 |
|Me5.5(1 |Calculation and application of ratio, proportion and rate of change such as concentration, density and | MZ8 VELS Textbook: |
| |the rate of filling a container |Ex 6.8 Q 1–7 |
| | |MZ10 VELS Textbook: |
| | |Ex 4.1 Q 3, 5, 6, 10 |
| | |Ch 4 Problem solving p. 168 Q 1–3 |
| | |Ex 4.8 Q 1–7 |
| | |Ex 4.9 Q 1–8 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R5.2 |
| | |VCE Worksheets: |
| | |ZGM R5.2 |
|Me5.5(2 |Use of Pythagoras’ Theorem to calculate the length of a side other than a hypotenuse | MZ9 VELS Textbook: |
| | |Ex 3.4 Q 1–10 |
| | |Ch 3 Laugh Zone Q 7–10 |
| | |Ex 3.5 Q 1–16 |
| | |Ch 3 VELS Design Task Q 2–6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C3.4 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C3.5 |
| | |MZ10 VELS Textbook: |
| | |Ch 3 VELS Design Task Q 2–6, 8 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.8; R8.2 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C4.9 |
| | |VCE Worksheets: |
| | |ZGM R8.2 |
|Me5.5(3 |Use of trigonometric ratios to calculate unknown sides in a right-angled triangle | MZ9 VELS Textbook: |
| | |Ex 5.2 Q 1–11 |
| | |Ex 5.3 Q 1–14 |
| | |Ex 5.4 Q 1–13 |
| | |Ch 5 Problem solving p. 217 |
| | |Ch 5 Laugh Zone |
| | |Ch 5 VELS Design Task Q 1, 2 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C5.2; C5.3; C5.4; C5.5 |
| | |MZ10 VELS Textbook: |
| | |Ex 6.1 Q 1–11 |
| | |Ex 6.2 Q 1–6 |
| | |Ex 6.3 Q 1–7 |
| | |Ex 6.5 Q 1–7 |
| | |Ch 6 VELS Design Task Q 1–3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.10; R2.11 |
| | |C6.1; C6.2 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C6.3 |
| | |VCE Worksheets: |
| | |ZGM R9.1; R9.3; R9.4; R10.5 |
| | |ZM1&2 R1.6 |
|Me5.5(4 |Display of data as a box plot including calculation of quartiles and interquartile range and the | MZ9 VELS Textbook: |
| |identification of outliers |Ex 7.4 Q 1–11 |
| | |Ch 7 Graphics calculator investigation p. 332 Q 1, 2, 4 |
| | |Ch 7 VELS Design Task Q 1, 2 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C7.3 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C7.4 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 3 Q 4 |
| | |Ex 7.5 Q 1, 3, 5–8 |
| | |Ch 7 Graphics calculator investigation p. 374 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.12; R7.4 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C7.4 |
|Me5.5(5 |Qualitative judgment of positive or negative correlation and strength of relationship and, if | MZ9 VELS Textbook: |
| |appropriate, application of gradient to find a line of good fit by eye |VELS Assignment 3 Q 6, 7 |
| | |Ex 7.7 Q 1–3 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 1 Q 3, 4 |
| | |VELS Assignment 4 Q 6 |
|Me5.75(1 |Conversion between degrees and radians, and use of radians when calculating arc length and area of | MZ10 VELS Textbook: |
| |sectors |Ch 8 Investigation p. 404 Q 1–5 |
| | |Ex 8.3 Q 8, 9 |
| | |VCE Worksheets: |
| | |ZGM R11.2; R11.3 |
|Me5.75(2 |Use of Pythagoras’ Theorem in three-dimensional applications | MZ10 VELS Textbook: |
| | |Ex 6.11 Q 1, 3–8 |
|Me5.75(3 |Calculation of unknown angle in a right-angled triangle using trigonometric ratios | MZ9 VELS Textbook: |
| | |Ex 5.5 Q 1–9 |
| | |Ch 5 Problem solving p. 222 |
| | |Ch 5 Laugh Zone |
| | |Ch 5 Investigation p. 224 Q 1, 2 |
| | |Ex 5.6 Q 1–10 |
| | |Ch 5 VELS Design Task Q 3–5 |
| | |Ch 5 Maths@Work Q 2 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C5.6 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C5.7 |
| | |MZ10 VELS Textbook: |
| | |Ex 6.6 Q 1–6 |
| | |Ex 6.7 Q 1–8 |
| | |Ex 6.8 Q 1–9 |
| | |Ch 6 Investigation p. 310 Q 1–3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C6.4 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C6.5 |
| | |VCE Worksheets: |
| | |ZGM R9.2 |
| | |ZM3&4 R3.6 |
|Me5.75(4 |Use of surveys as a means of obtaining information about a population, including awareness that sample | MZ10 VELS Textbook: |
| |results will not always provide a reasonable estimate of population parameters |Ex 7.1 Q 1–19 |
| | |Ex 7.6 Q 1 |
|Me5.75(5 |Placement of a line of best fit on a scatter plot using technology and, where appropriate, use of a line| MZ9 VELS Textbook: |
| |of best fit to make predictions |VELS Assignment 3 Q 6, 7 |
| | |Ex 7.7 Q 1(d), 2(c), 4, 5 |
| | |Ch 7 CAS Investigation p. 353 Q 1–3 |
| | |Ch 7 Computer investigation p. 356 Q 5–7 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 4 Q 5 |
| | |VCE Worksheets: |
| | |ZFM R3.5 |
|Me6.0 |At Level 6, students estimate and measure length, area, surface area, mass, volume, capacity and angle. | MZ9 VELS Textbook: |
| |They select and use appropriate units, converting between units as required. They calculate constant |VELS Assignment 3 Q 1, 2, 7 |
| |rates such as the density of substances (that is, mass in relation to volume), concentration of fluids, |MZ10 VELS Textbook: |
| |average speed and pollution levels in the atmosphere. Students decide on acceptable or tolerable levels |VELS Assignment 2 Q 2, 4, 5 |
| |of error in a given situation. They interpret and use mensuration formulas for calculating the |VELS Assignment 3 Q 4, 6 |
| |perimeter, surface area and volume of familiar two- and three-dimensional shapes and simple composites |VELS Assignment 4 Q 6 |
| |of these shapes. Students use Pythagoras Theorem and trigonometric ratios (sine, cosine and tangent) to |Ex 4.2 Q 2, 3, 5–7, 9–12 |
| |obtain lengths of sides, angles and the area of right-angled triangles. |Ch 4 VELS Design Task Q 3 |
| |They use degrees and radians as units of measurement for angles and convert between units of measurement|Ex 4.3 Q 3–5, 9, 11–13 |
| |as appropriate. |Ex 4.4 Q 1–8 |
| |Students estimate probabilities based on data (experiments, surveys, samples, simulations) and assign |Ch 4 Investigation p. 192 Q 1–5 |
| |and justify subjective probabilities in familiar situations. They list event spaces (for combinations of|Ex 4.6 Q 1–8 |
| |up to three events) by lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way tables). |Ex 4.7 Q 2–6 |
| |They calculate probabilities for complementary, mutually exclusive, and compound events (defined using |Ch 4 Graphics calculator investigation p. 203 |
| |and, or and not). They classify events as dependent or independent. |Extension Q 1, 2 |
| |Students comprehend the difference between a population and a sample. They generate data using surveys, |Ch 4 Maths in Action Q 1–3 |
| |experiments and sampling procedures. They calculate summary statistics for centrality (mode, median and |Ex 6.4 Q 1–6 |
| |mean), spread (box plot, interquartile range, outliers) and association (by-eye estimation of the line |Ch 6 Investigation p. 310 Q 4–10 |
| |of best fit from a scatter plot). They distinguish informally between association and causal |Ch 6 Maths in Action Q 1–3 |
| |relationship in bivariate data, and make predictions based on an estimated line of best fit for |Ex 6.9 Q 1–11 |
| |scatter-plot data with strong association between two variables. |Ch 6 Problem solving p. 318 Q 1, 2 |
| | |Ex 6.10 Q 1–9 |
| | |Ex 6.11 Q 1–11 |
| | |Ex 7.2 Q 1–8 |
| | |Ch 7 Investigation p. 351 Q 1–6 |
| | |Ex 7.3 Q 1–8 |
| | |Ch 7 Problem solving p. 364 |
| | |Ex 7.6 Q 2–5 |
| | |Ch 7 Maths in Action Q 1–6 |
| | |Ch 7 VELS Design Task Q 1–5 |
| | |Ch 10 Graphics calculator investigation p. 527 Q 1–5 |
| | |Ex 10.4 Q 1–10 |
| | |Ex 10.5 Q 1–11 |
| | |Ch 10 Problem solving p. 542 Q 1–3 |
| | |Ch 10 Investigation p. 543 Q 1–5 |
| | |Ex 10.6 Q 12, 13 |
| | |Ch 10 VELS Design Task Q 1, 2, 5 |
| | |Ex 10.7 Q 1–10 |
| | |Ch 10 Maths@Work Q 1, 2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C4.4; C4.7; C10.4 (Q2); C10.8; C10.10 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C4.6; C6.6; C7.3; C10.6; C10.11 |
| | |VCE Worksheets: |
| | |ZM1&2 R10.3; R10.4 |
|Me6.25(1 |Derivation of measurement formulas for composite shapes and objects; for example, the surface area of a | MZ10 VELS Textbook: |
| |closed cone |Ch 4 Investigation p. 192 Q 6 |
| | |Ch 4 Maths in Action Q 4, 5 |
| | |Ch 6 Investigation p. 324 Q 1–3 |
|Me6.25(2 |Use of measurement formulas, including cases where more than one type of unit, and/or conversion of | MZ10 VELS Textbook: |
| |units, is involved |Ex 4.6 Q 9, 10 |
| | |VCE Worksheets: |
| | |ZGM R10.2 |
|Me6.25(3 |Use of cumulative frequency distribution to represent and interpret univariate data | MZ10 VELS Textbook: |
| | |Ex 7.4 Q 1–8 |
| | |Ex 7.5 Q 2, 4 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C7.1; C7.2 |
| | |VCE Worksheets: |
| | |ZFM R1.3 |
|Me6.5(1 |Recognition of the effect of rounding and measurement error in numerical computations, for example, | MZ10 VELS Textbook: |
| |where a formula is used |Ch 4 Maths in Action Q 4, 5; Research Q 1 |
|Me6.5(2 |Use of tree diagrams to determine the probability of outcomes for sampling with or without replacement | MZ10 VELS Textbook: |
| | |Ex 10.6 Q 1–11 |
| | |Ch 10 VELS Design Task Q 3, 4 |
| | |VCE Worksheets: |
| | |ZGM R4.6 |
| | |ZM1&2 R10.5; R10.6 |
| | |ZM3&4 R8.3 |
|Me6.5(3 |Identification of random variation and possible hidden variables in analysing association and possible | MZ10 VELS Textbook: |
| |causal relationship in bivariate data |Ch 7 Maths in Action Q 6 |
|Me6.75(1 |Informal use of limiting values to approximate instantaneous rate of change, arc length, area and | MZ10 VELS Textbook: |
| |surface area and volume measures of regular and irregular curves, shapes and objects |Ch 8 Graphics calculator investigation p. 424 Q 1–6; |
| | |Research |
| | |Ch 8 Investigation p. 433 Q 7 |
|Me6.75(2 |Use of conditional probability to distinguish between dependent and independent events | VCE Worksheets: |
| | |ZM3&4 R8.2; R8.4; R8.5; R9.5 |
|Me6.75(3 |Awareness of sampling errors and possible sources of bias | |
|Structure |
|St3.0 |At Level 3, students recognise that the sharing of a collection into equal-sized parts (division) | |
| |frequently leaves a remainder. They investigate sequences of decimal numbers generated using | |
| |multiplication or division by 10. They understand the meaning of the ‘=’ in mathematical statements and | |
| |technology displays (for example, to indicate either the result of a computation or equivalence). They | |
| |use number properties in combination to facilitate computations (for example, 7 + 10 + 13 = 10 + 7 + 13 | |
| |= 10 + 20). They multiply using the distributive property of multiplication over addition (for example, | |
| |13 × 5 = (10 + 3) × 5 = 10 × 5 + 3 × 5). They list all possible outcomes of a simple chance event. They | |
| |use lists, Venn diagrams and grids to show the possible combinations of two attributes. They recognise | |
| |samples as subsets of the population under consideration (for example, pets owned by class members as a | |
| |subset of pets owned by all children). They construct number sentences with missing numbers and solve | |
| |them. | |
|St3.25(1 |Conversion between Venn diagrams and Karnaugh maps as representations of relationships between two sets | |
|St3.25(2 |Recognition and completion of patterns formed by constant addition or subtraction | MZ7 VELS Worksheets with explanations and questions: |
| | |R10.4 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.15 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R2.10 |
|St3.25(3 |Use of add and subtract as inverse operations to solve simple word equations such as ‘I am thinking of a| MZ7 VELS Textbook: |
| |number. If I add 6 I get 18, what number did I start with?’ |Ex 1.2 Q 3 |
|St3.25(4 |Use of trial and error to find a missing number in a number sentence; for example, 4 × ? + 6 = 22 | MZ7 VELS Textbook: |
| | |Ex 8.1 Q 1, 3 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R1.12; R1.15; R6.1 |
| | |C8.1 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.13 |
|St3.25(5 |Use of language to describe change in everyday items or attributes whose value varies over time | MZ7 VELS Worksheets with questions only: |
| | |R8.3 |
|St3.5(1 |Incorporation of tables of information relating pairs of everyday variables | MZ7 VELS Textbook: |
| | |Ex 6.1 Q 5, 6 |
| | |Ex 6.4 Q 1–7 |
|St3.5(2 |Sorting of sequences into certain types (constant addition, constant multiplication, Fibonacci, square, | MZ7 VELS Textbook: |
| |triangular) |Ch 2 Computer investigation p. 76 Q 1–6 |
|St3.5(3 |Use of division and multiplication as inverses; for example, multiplication by 25 can be carried out as | |
| |‘multiplication by 100 followed by division by 4’ | |
|St3.5(4 |Consistent and correct use of conventions for order of operations | MZ7 VELS Worksheets with questions only: |
| | |R6.4; R8.4 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R1.20 |
| | |VCE Worksheets: |
| | |ZGM R1.1 |
|St3.75(1 |Construction of diagrams illustrating the possible relationship between two sets and the truth of | |
| |statements involving the words all, some or none | |
|St3.75(2 |Construction of number patterns and tables of values from an equation or a recurrence relation | MZ7 VELS Textbook: |
| | |Ex 6.1 Q 1, 2, 5, 6 |
| | |Ex 6.2 Q 4 |
|St3.75(3 |Recognition that a given number pattern can be represented by an apparently unrelated equation and | MZ7 VELS Textbook: |
| |recurrence relation; for example, 5, 9, 13 … represented by ‘multiply position in the pattern (first, |Ch 6 CAS investigation p. 279 Q 1–4 |
| |second, third ...) by 4 and add 1’ and ‘start with 5 then repeatedly add 4 to the previous term’ | |
|St3.75(4 |Understanding of zero and its characteristic of not having a multiplicative inverse, and the | |
| |consequences of attempting division by zero | |
|St4.0 |At Level 4, students form and specify sets of numbers, shapes and objects according to given criteria | MZ7 VELS Textbook: |
| |and conditions (for example, 6, 12, 18, 24 are the even numbers less than 30 that are also multiples of |Ex 6.1 Q 1–10 |
| |three). They use Venn diagrams and Karnaugh maps to test the validity of statements using the words |Ex 8.1 Q 2 |
| |none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even |Ex 8.3 Q 1–15 |
| |numbers’). |Ch 8 Problem solving p. 372 |
| |Students construct and use rules for sequences based on the previous term, recursion (for example, the |Ex 8.4 Q 1–12 |
| |next term is three times the last term plus two), and by formula (for example, a term is three times its|MZ7 VELS Worksheets with explanations and questions: |
| |position in the sequence plus two). |R1.10; R8.1; R8.5 |
| |Students establish equivalence relationships between mathematical expressions using properties such as |C6.1; C8.3 |
| |the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)). |MZ7 VELS Worksheets with questions only: |
| |Students identify relationships between variables and describe them with language and words (for |C8.4 |
| |example, how hunger varies with time of the day). |MZ8 VELS Textbook: |
| |Students recognise that addition and subtraction, and multiplication and division are inverse |VELS Assignment 1 Q 6 |
| |operations. They use words and symbols to form simple equations. They solve equations by trial and |Ex 11.3 Q 1 |
| |error. |MZ8 VELS Worksheets with explanations and questions: |
| | |R2.13; R7.1; R7.3; R7.5; R11.2 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.16 |
|St4.25(1 |Use of inverse and identity when subtracting and dividing rational numbers | MZ7 VELS Worksheets with explanations and questions: |
| | |C8.2 |
| | |VCE Worksheets: |
| | |ZGM R2.4 |
|St4.25(2 |Identification of domain and range; independent and dependent variable and their role in graphing | MZ8 VELS Textbook: |
| | |Ex 11.4 Q 1–9 |
| | |VCE Worksheets: |
| | |ZGM R6.1 |
|St4.25(3 |Representation of data by plotting points in the first quadrant and explanation of key features | MZ7 VELS Textbook: |
| | |Ex 6.8 Q 1 10 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C6.7 |
| | |MZ8 VELS Textbook: |
| | |Ex 8.1 Q 1–13 |
| | |Ex 8.2 Q 1–14 |
| | |Ch 8 Maths in Action Q 1, 2 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R8.1; R8.2 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C8.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R3.1 |
|St4.25(4 |Collection and classification of sets of data as either linear or non-linear depending on whether the | MZ8 VELS Textbook: |
| |slope is constant |Ex 8.6 Q 1–10 |
|St4.25(5 |Interpretation of a letter as a symbol for any one of a set of numbers and use in symbolic description | MZ7 VELS Textbook: |
| |of relationships |Ex 6.2 Q 1, 3–7 |
| | |Ex 6.3 Q 1–4, 6, 7 |
| | |Ch 6 Laugh Zone |
| | |Ch 6 Investigation p. 274 Q 3, 4 |
| | |Ex 6.6 Q 1–5 |
| | |Ch 6 CAS Investigation p. 279 Q 1–4 |
| | |Ch 6 VELS Design Task Q 1–3 |
| | |Ex 8.2 Q 1 |
| | |Ex 8.6 Q 1, 2 |
| | |Ch 8 Graphics calculator investigation p. 396 Q 4 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C6.2; C6.3; C6.5 |
| | |MZ7 VELS Worksheets with questions only: |
| | |R8.2 |
| | |MZ8 VELS Textbook: |
| | |Ex 4.2 Q 1–10 |
| | |Ex 4.3 Q 1–10 |
| | |Ex 4.4 Q 1–6 |
| | |Ch 4 Investigation p. 146 Q 1, 2 |
| | |Ex 4.6 Q 1–3 |
| | |Ex 4.7 Q 1–6 |
| | |Ex 4.8 Q 1–6 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R4.1; R4.3; R4.4; R7.4; R11.4 |
| | |C4.1; C4.2; C4.3; C4.4; C4.5; C4.7; C4.8; C4.9; C4.10; |
| | |C4.11 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R3.8; R3.9; R8.3 |
| | |C4.6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R2.11; R2.12; R2.13; R3.13; R4.1; R4.2; R4.10 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R2.2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.3: R3.9 |
| | |MZ10 VELS Worksheets with questions only: R3.1; R3.2 |
| | |VCE Worksheets: |
| | |ZM1&2 R2.3 |
|St4.5(1 |Use of inequality, equality, approximately equal and not equal, including in symbolic expressions | MZ7 VELS Textbook: |
| | |Ex 1.6 Q 5–9 |
| | |Ex 1.8 Q 1–10 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |C1.6 |
| | |MZ8 VELS Textbook: |
| | |Ex 11.5 Q 3, 6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R6.7 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C6.11 |
|St4.5(2 |Translation from verbal description to algebraic representation, and of the structure of algebraic | MZ7 VELS Textbook: |
| |expressions; for example, if $500 is shared between n people, each receives 500/n |Ex 6.2 Q 2 |
| | |Ex 6.3 Q 5, 8–12 |
| | |Ex 6.4 Q 1–7 |
| | |Ex 6.5 Q 1–5 |
| | |Ch 6 Graphics calculator investigation p. 281 Q 1–4, |
| | |Challenge Q 2 |
| | |Ex 8.1 Q 4–13 |
| | |Ex 8.2 Q 2–4, 7, 8, 10, 12 |
| | |MZ8 VELS Textbook: |
| | |Ex 4.1 Q 1–13 |
| | |Ex 4.3 Q 11–14 |
| | |Ex 4.4 Q 7–10 |
| | |Ch 4 Investigation p. 146 Q 3, 4 |
| | |Ex 4.5 Q 1–11 |
| | |Ch 4 VELS Design Task Q 1–6 |
| | |Ch 4 Maths in Action Q 1, 2 |
| | |Ex 4.6 Q 4–9 |
| | |Ex 4.7 Q 7–11 |
| | |Ch 4 Problem solving p. 160 Q 3 |
| | |Ex 4.8 Q 7–10 |
| | |Ex 7.1 Q 1, 4, 6–8 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R4.1; R8.6 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 1 Q 3 |
| | |VCE Worksheets: |
| | |ZFM R9.2 |
|St4.5(3 |Solution of simple linear equations using tables, graphs and inverse operations (backtracking) | MZ7 VELS Textbook: |
| | |Ex 8.2 Q 5, 6, 9, 11 |
| | |Ch 8 Maths@Work Q 1, 2 |
| | |Ex 8.4 Q 13 |
| | |Ex 8.5 Q 1–15 |
| | |Ch 8 VELS Design Task Q 1–7 |
| | |Ch 8 Investigation p. 388 Q 1–5 |
| | |Ex 8.6 Q 3–16 |
| | |Ch 8 Problem solving p. 394 Q 1, 2 |
| | |Ch 8 Laugh Zone |
| | |MZ7 VELS Worksheets with questions only: |
| | |C6.6; C8.5; C8.6 |
| | |MZ8 VELS Textbook: |
| | |Ch 4 Problem solving p. 160 Q 1, 2, 4 |
| | |Ex 7.1 Q 2, 3, 5 |
| | |Ex 7.2 Q 1–11 |
| | |Ch 7 Investigation p. 297 Q 1, 2 |
| | |Ex 7.3 Q 1–6 |
| | |Ex 7.4 Q 1–7 |
| | |Ex 7.5 Q 1–7 |
| | |Ex 7.6 Q 1–8 |
| | |Ch 7 VELS Design Task Q 1–9 |
| | |Ch 7 Problem solving p. 314 |
| | |Ex 7.7 Q 1–6 |
| | |Ex 7.8 Q 1–4 |
| | |Ch 7 Laugh Zone |
| | |Ex 7.9 Q 1–16 |
| | |Ch 7 Investigation p. 326 Q 1–5 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R5.6; R7.2; R8.4; R8.5; R11.5 |
| | |C7.2; C7.3; C7.4; C7.5; C7.7; C7.8 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C7.1; C7.6; C7.9 |
| | |MZ9 VELS Textbook: |
| | |Ex 6.7 Q 1–3, 5–8 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R1.19; R3.6; R3.7; R3.9; R5.1; R6.2; R8.6 |
| | |C6.6; C6.7; C8.8; C8.9; C8.10; C8.11 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R6.4; R6.5 |
| | |MZ10 VELS Textbook: |
| | |Ex 5.1 Q 1–3 |
| | |Ex 5.6 Q 1, 2 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R5.5; R5.6 |
| | |VCE Worksheets: |
| | |ZGM R4.3; R12.1 |
|St4.5(4 |Representation of inequalities as parts of the number line; for example, | MZ9 VELS Textbook: |
| |x < −5 |Ex 6.12 Q 1–9 |
|St4.5(5 |Translation between symbolic rules, patterns and tables for linear functions | MZ7 VELS Textbook: |
| | |Ex 6.2 Q 1–7 |
| | |Ex 6.5 Q 1–6 |
| | |MZ7 VELS Worksheets with questions only: |
| | |C6.4 |
| | |VCE Worksheets: |
| | |ZGM R2.5; R5.3; R5.4; R7.1; R10.1 |
|St4.75(1 |Lists of sets in the power set of a given set and knowledge that the total number of sets equals 2n for | MZ8 VELS Textbook: |
| |n elements in the given set |Ex 11.1 Q 1–11 |
|St4.75(2 |Solution of equations such as x² = 17 as required in measurement situations; for example, using | MZ9 VELS Textbook: |
| |Pythagoras’ Theorem |Ex 3.2 Q 7 |
| | |Ex 3.3 Q 4, 11, 12 |
| | |Ex 3.4 Q 3 |
|St4.75(3 |Graphical representation of simple inequalities such as y ≤ 2x + 4 | MZ8 VELS Worksheets with explanations and questions: |
| | |R11.1 |
| | |MZ10 VELS Textbook: |
| | |Ex 5.7 Q 1–7 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C5.10 |
| | |VCE Worksheets: |
| | |ZM1&2 R1.7 |
|St4.75(4 |Selection of a type of function (linear, exponential, quadratic) to match a set of data | MZ10 VELS Textbook: |
| | |Ex 9.9 Q 1–11 |
|St4.75(5 |Translation between forms (table, graph, rule, recurrence relation) of representation of a function | MZ8 VELS Textbook: |
| | |Ex 8.3 Q 1–12 |
| | |Ex 8.4 Q 1–8 |
| | |Ch 8 Investigation p. 364 Q 1–7 |
| | |Ex 8.5 Q 1–9 |
| | |Ch 8 VELS Design Task Q 1, 2 |
| | |Ch 8 Investigation p. 373 |
| | |Ex 8.6 Q 1–10 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R11.3 |
| | |C8.3; C8.6 |
| | |MZ8 VELS Worksheets with questions only: |
| | |C8.2; C8.4; C8.5; C8.7 |
| | |MZ9 VELS Textbook: |
| | |Ex 6.1 Q 1–8 |
| | |Ex 6.3 Q 1–6 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R6.2; R6.3 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R5.3; R5.4 |
|St5.0 |At Level 5, students identify collections of numbers as subsets of natural numbers, integers, rational | MZ7 VELS Textbook: |
| |numbers and real numbers. They use Venn diagrams and tree diagrams to show the relationships of |Ch 6 Problem solving p. 269 |
| |intersection, union, inclusion (subset) and complement between the sets. They list the elements of the |Ch 6 Investigation p. 274 Q 1, 2, 5 |
| |set of all subsets (power set) of a given finite set and comprehend the partial-order relationship |Ch 6 VELS Design Task Q 4–7 |
| |between these subsets with respect to inclusion (for example, given the set {a, b, c} the corresponding |MZ8 VELS Textbook: |
| |power set is {Ø, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}). |VELS Assignment 3 Q 1–10 |
| |They test the validity of statements formed by the use of the connectives and, or, not, and the |Ex 4.9 Q 1–7 |
| |quantifiers none, some and all, (for example, ‘some natural numbers can be expressed as the sum of two |Ch 4 Laugh Zone |
| |squares’). They apply these to the specification of sets defined in terms of one or two attributes, and |Ch 7 Maths in Action Q 1–4 |
| |to searches in data-bases. |Ex 8.5 Q 10 |
| |Students apply the commutative, associative, and distributive properties in mental and written |Ch 8 VELS Design Task Q 3–7 |
| |computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10). They use |Ex 8.7 Q 1–9 |
| |exponent laws for multiplication and division of power terms (for example 23 × 25 = 28, 20 = 1, 23 ÷ 25 |Ch 8 Laugh Zone |
| |= 2−2, (52)3 = 56 and (3 × 4)2 = 32 × 42). |Ex 8.8 Q 1–7 |
| |Students generalise from perfect square and difference of two square number patterns (for example, 252 =|Ch 8 Investigation p. 388 Q 1, 2 |
| |(20 + 5)2 = 400 + 2 × (100) + 25 = 625. And 35 × 25 = (30 + 5) (30 − 5) = 900 − 25 = 875) |Ex 11.1 Q 1–8 |
| |Students recognise and apply simple geometric transformations of the plane such as translation, |Ex 11.2 Q 1–6 |
| |reflection, rotation and dilation and combinations of the above, including their inverses. |Ch 11 Computer investigation p. 512 Q 6–9 |
| |They identify the identity element and inverse of rational numbers for the operations of addition and |Ch 11 Maths in Action Q 1–5, Research |
| |multiplication (for example, 1/2 + −1/2 = 0 and 2/3 × 3/2 = 1). |Ex 11.3 Q 2–6 |
| |Students use inverses to rearrange simple mensuration formulas, and to find equivalent algebraic |Ex 11.4 Q 1–9 |
| |expressions (for example, if P = 2L + 2W, then W = P/2 − L. If A = πr2 then r = √A/π for r > 0). |Ex 11.5 Q 1–8 |
| |They solve simple equations (for example, 5x + 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables,|Ch 11 VELS Design Task Q 1–7 |
| |graphs and inverse operations. They recognise and use inequality symbols. They solve simple inequalities|Ch 11 Laugh Zone |
| |such as y ≤ 2x + 4 and decide whether or not inequalities such as x2 > 2y are satisfied for specific |MZ8 VELS Worksheets with explanations and questions: |
| |values of x and y. |C4.12; C8.8 |
| |Students identify a function as a one-to-one correspondence or a many-to-one correspondence between two |MZ8 VELS Worksheets with questions only: |
| |sets. They represent a function by a table of values, a graph, and by a rule. They describe and specify |C4.13 |
| |the independent variable of a function and its domain, and the dependent variable and its range. They |MZ9 VELS Textbook: |
| |construct tables of values and graphs for linear functions. They use linear and other functions such as |Ex 6.7 Q 4, 9 |
| |f(x) = 2x − 4, xy = 24, y = 2x and y = x2 − 3 to model various situations. |Ch 6 VELS Design Task Q 1 |
| | |Ex 6.8 Q 1–6 |
| | |Ch 6 Maths in Action Q 2–4 |
| | |Ex 6.9 Q 1–10 |
| | |Ch 6 Laugh Zone |
| | |Ex 6.10 Q 1–12 |
| | |Ch 6 Investigation p. 292 Q 1–3 |
| | |Ex 6.13 Q 1–8 |
| | |Ex 9.1 Q 1 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R4.3; R4.4; R5.3 |
| | |C6.8; C6.9; C6.10 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C6.12 |
| | |MZ10 VELS Textbook: |
| | |Ex 2.7 Q 1–8 |
| | |Ch 2 Problem solving p. 74 Q 3, 4 |
| | |Ex 5.1 Q 4 |
| | |Ex 5.6 Q 3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.11; R3.5 |
| | |C5.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R9.5 |
| | |VCE Worksheets: |
| | |ZGM R2.2; R3.3 |
| | |ZM1&2 R1.1; R2.6; R3.6; R8.1; R10.7 |
| | |ZFM R4.1; R6.4; R6.5; R7.2 |
| | |ZM3&4 R3.3 |
|St5.25(1 |Relationships between two sets using a Venn diagram, tree diagram and Karnaugh map | MZ8 VELS Textbook: |
| | |Ex 11.1 Q 9–11 |
| | |MZ8 VELS Worksheets with explanations and questions: |
| | |R7.6 |
| | |C11.1 |
|St5.25(2 |Factorisation of algebraic expressions by extracting a common factor | MZ8 VELS Textbook: |
| | |Ex 4.10 Q 1–11 |
| | |Ex 4.11 Q 1–10 |
| | |MZ9 VELS Textbook: |
| | |Ex 4.2 Q 1, 3, 5–16 |
| | |Ex 4.5 Q 1–18 |
| | |Ch 4 Laugh Zone |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R2.14; R2.15; R4.11; R6.6 |
| | |C4.1; C4.5; C4.6; C4.7 |
| | |MZ10 VELS Textbook: |
| | |Ex 3.1 Q 1, 2 |
| | |Ex 3.4 Q 1–11 |
| | |Ex 5.1 Q 5–19 |
| | |Ex 5.6 Q 4–10 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R2.4; R3.13 |
| | |C3.2; C5.2 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R2.10 |
| | |C3.1 |
| | |VCE Worksheets: |
| | |ZGM R10.4 |
| | |ZM1&2 R1.2; R1.3; R2.1 |
| | |ZM3&4 R1.1 |
|St5.25(3 |Solution of equations by graphical methods | MZ8 VELS Textbook: |
| | |Ch 8 Investigation p. 388 Q 3–5 |
| | |MZ9 VELS Textbook: |
| | |Ch 6 Graphics calculator investigation p. 299 Q 1, 3–5 |
| | |Ex 9.1 Q 2–9 |
| | |Ex 9.2 Q 1–9 |
| | |Ch 9 Investigation p. 433 Q 1–4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R9.2 |
| | |MZ10 VELS Textbook: |
| | |Ch 1 Graphics calculator investigation p. 19 Q 2, 3 |
|St5.25(4 |Identification of linear, quadratic and exponential functions by table, rule and graph in the first | MZ10 VELS Textbook: |
| |quadrant |VELS Assignment 5 Q 2–7 |
| | |Ch 1 Investigation p. 26 Q 1–3 |
| | |Ch 2 Investigation p. 69 Q 1–3 |
| | |Ch 2 VELS design Task Q 2–6 |
| | |Ch 2 Graphics calculator investigation p. 87 Q 2, 3 |
| | |Ch 5 Investigation p. 231 Q 1–3 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R9.1 |
|St5.25(5 |Knowledge of the quantities represented by the constants m and c in the equation y = mx + c | MZ9 VELS Textbook: |
| | |Ex 6.2 Q 1–10 |
| | |Ch 6 Problem solving p. 254 |
| | |Ch 6 Investigation p. 255 Q 1–3 |
| | |Ch 6 CAS Investigation p. 256 Q 1, 2 |
| | |Ex 6.3 Q 7–11 |
| | |Ch 6 Problem solving p. 262 |
| | |Ex 6.4 Q 1–11 |
| | |Ex 6.5 Q 1–7 |
| | |Ex 6.6 Q 1–7 |
| | |Ch 6 VELS Design Task Q 2–4 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C6.1; C6.2; C6.3; C6.4; C6.5 |
| | |MZ10 VELS Textbook: |
| | |Ex 5.2 Q 1–7 |
| | |Ch 5 Problem solving p. 232 Q 1, 2 |
| | |Ex 5.3 Q 1–13 |
| | |Ex 5.7 Q 1–4 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R2.12; R4.8 |
| | |C5.3; C5.4; C5.5 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C9.8 |
| | |VCE Worksheets: |
| | |ZGM R4.4; R7.3 |
| | |ZM1&2 R4.2; R6.1; R7.3; R7.8; R7.9 |
| | |ZFM R2.1; R2.2; R2.3; R2.4; R6.1; R6.2; R6.3 |
| | |ZM3&4 R1.10; R6.3 |
|St5.5(1 |Expression of the relationship between sets using membership (, complement ′ , intersection ∩, union (, | MZ8 VELS Textbook: |
| |and subset (, for up to two sets |Ex 11.1 Q 1–11 |
| | |MZ10 VELS Textbook: |
| | |Ex 1.4 Q 1–4 |
| | |Ex 10.3 Q 1–7 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.5 |
| | |VCE Worksheets: |
| | |ZM1&2 R5.7 |
|St5.5(2 |Representation of numbers in a geometric sequence (constant multiple, constant percentage change) as an | |
| |exponential function | |
|St5.5(3 |Knowledge of the relationship between geometric and algebraic forms for transformations | MZ9 VELS Textbook: |
| | |Ex 9.3 Q 1–10 |
| | |Ch 9 Problem solving p. 441 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C9.4; C9.5 |
| | |VCE Worksheets: |
| | |ZM1&2 R3.5 |
| | |ZM3&4 R2.3 |
|St5.5(4 |Expansion of products of algebraic factors; for example, | MZ9 VELS Textbook: |
| |(2x + 1)(x − 5) = 2x² − 9x − 5 |Ex 4.3 Q 1–10 |
| | |Ch 4 Investigation p. 165 Q 1, 3 |
| | |Ex 4.4 Q 1–20 |
| | |Ch 4 VELS Design Task Q 4, 7 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R9.3 |
| | |C4.2; C4.3 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C4.4 |
| | |MZ10 VELS Textbook: |
| | |Ex 2.5 Q 1–10 |
| | |Ex 3.1 Q 3–13 |
| | |Ex 3.2 Q 1–9 |
| | |Ch 3 VELS Design Task Q 4–6, 8 |
| | |Ex 3.3 Q 1–10 |
| | |Ch 3 Graphics calculator investigation p. 119 Q 1–3 |
| | |Ex 3.9 Q 1, 8 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.9; R2.6 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R3.12 |
| | |VCE Worksheets: |
| | |ZGM R2.3; R12.5 |
| | |ZM1&2 R6.3; R7.1; R9.4 |
| | |ZM3&4 R7.1 |
|St5.5(5 |Equivalence between algebraic forms; for example, polynomial, factorised and turning point form of | MZ9 VELS Textbook: |
| |quadratics |Ex 9.2 Q 1–9 |
| | |Ex 9.3 Q 1–10 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |C9.3; C9.8 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C9.1; C9.2; C9.9 |
| | |MZ10 VELS Textbook: |
| | |Ch 4 Graphics calculator investigation p. 203 Q 1, 2; |
| | |Extension Q 1, 2 |
| | |Ex 9.3 Q 1–8 |
| | |Ch 9 Graphics calculator investigation p. 463 Q 1–5 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R9.2 |
| | |VCE Worksheets: |
| | |ZM1&2 R8.4 |
| | |ZM3&4 R3.5 |
|St5.5(6 |Use of inverse operations to rearrange formulas to change the subject of a formula | Ex 6.11 Q 1–9 |
| | |MZ10 VELS Textbook: |
| | |Ex 1.2 Q 7–14, 16, 17 |
| | |Ch 1 Graphics calculator investigation p. 19 Extension |
| | |Ex 1.3 Q 2, 6, 8 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R3.10; R8.4 |
| | |VCE Worksheets: |
| | |ZGM R3.2; R14.2 |
| | |ZM1&2 R1.4; R4.1 |
| | |ZM3&4 R4.3 |
|St5.75(1 |Expression of irrational numbers in both exact and approximate form | MZ10 VELS Textbook: |
| | |Ex 2.1 Q 2, 3, 8–12 |
|St5.75(2 |Factorisation of simple quadratic expressions and use of the null factor law for solution of equations | MZ9 VELS Textbook: |
| | |Ex 4.6 Q 1–11 |
| | |Ex 4.7 Q 1–14 |
| | |Ex 4.8 Q 1–12 |
| | |Ex 4.9 Q 1–12 |
| | |Ch 4 Problem solving (a)–(d) |
| | |Ch 4 Laugh Zone |
| | |Ex 9.4 Q 1–11 |
| | |Ex 9.5 Q 1–8 |
| | |Ex 9.7 Q 1–11 |
| | |Ch 9 VELS Design Task Q 1–8 |
| | |Ch 9 Maths@Work Q 1–3 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R9.4; R9.5 |
| | |C4.8; C4.9; C4.10; C4.11; C9.6 |
| | |MZ9 VELS Worksheets with questions only: |
| | |C4.12; C9.7 |
| | |MZ10 VELS Textbook: |
| | |Ex 3.5 Q 1–10 |
| | |Ch 3 Investigation p. 128 Q 1, 2 |
| | |Ex 3.6 Q 1–10 |
| | |Ex 3.7 Q 1, 2 |
| | |Ex 9.1 Q 1–9 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R1.14; R9.3; R9.4 |
| | |C3.3; C3.4 |
| | |VCE Worksheets: |
| | |ZGM R3.5; R3.6 |
| | |ZM1&2 R3.2 |
| | |ZM3&4 R1.6 |
| | |ZM3&4 R1.9 |
|St5.75(3 |Testing of sequences by calculating first difference, second difference or ratio between consecutive | MZ10 VELS Textbook: |
| |terms to determine existence of linear, quadratic and exponential functions |Ex 9.9 Q 1–10 |
|St5.75(4 |Formulation of pairs of simultaneous equations and their graphical solution | MZ10 VELS Textbook: |
| | |Ex 5.5 Q 1 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C5.7 |
|St5.75(5 |Representation of algebraic models for sets of data using technology | MZ10 VELS Textbook: |
| | |Ex 5.4 Q 1–8 |
|St6.0 |At Level 6, students classify and describe the properties of the real number system and the subsets of | MZ9 VELS Textbook: |
| |rational and irrational numbers. They identify subsets of these as discrete or continuous, finite or |Ex 9.6 Q 1–8 |
| |infinite and provide examples of their elements and apply these to functions and relations and the |Ch 9 Graphics calculator investigation p. 454 Q 3–5 |
| |solution of related equations. |Ch 9 Investigation p. 455 Q 1–3 |
| |Students express relations between sets using membership (, complement ′, intersection ∩, union (, and |Ch 9 Laugh Zone |
| |subset (, for up to three sets. They represent a universal set as the disjoint union of intersections of|MZ10 VELS Textbook: |
| |up to three sets and their complements, and illustrate this using a tree diagram, Venn diagram or |VELS Assignment 5 Q 2–7 |
| |Karnaugh map. |Ex 1.4 Q 1–4 |
| |Students form and test mathematical conjectures; for example, ‘What relationship holds between the |Ex 1.5 Q 1, 4–6 |
| |lengths of the three sides of a triangle?’ |Ex 2.8 Q 1–5 |
| |They use irrational numbers such as, π, φ and common surds in calculations in both exact and approximate|Ex 2.9 Q 1–7 |
| |form. |Ex 2.10 Q 1–7 |
| |Students apply the algebraic properties (closure, associative, commutative, identity, inverse and |Ex 2.12 Q 1–7 |
| |distributive) to computation with number, to rearrange formulas, rearrange and simplify algebraic |Ex 2.14 Q 1–8 |
| |expressions involving real variables. They verify the equivalence or otherwise of algebraic expressions |Ch 3 Problem solving p. 114 Q 1–3 |
| |(linear, square, cube, exponent, and reciprocal; |Ex 3.3 Q 11, 12 |
| |(for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 − 12a + 9; (3w)3 = 27w3; (x3y) /xy2 = x2y− |Ex 3.5 Q 11–16 |
| |1; 4/xy = 2/x × 2/y). |Ch 3 Investigation p. 128 Q 3 |
| |Students identify and represent linear, quadratic and exponential functions by table, rule and graph |Ex 3.6 Q 11–15 |
| |(all four quadrants of the Cartesian coordinate system) with consideration of independent and dependent |Ex 3.7 Q 3–12 |
| |variables, domain and range. They distinguish between these types of functions by testing for constant |Ex 3.8 Q 1–13 |
| |first difference, constant second difference or constant ratio between consecutive terms (for example, |Ch 3 Computer investigation p. 144 Q 1–3 |
| |to distinguish between the functions described by the sets of ordered pairs |Ex 3.9 Q 2–23 |
| |{(1, 2), (2, 4), (3, 6), (4, 8) …}; {(1, 2), (2, 4), (3, 8), (4, 14) …}; and {(1, 2), (2, 4), (3, 8), |Ex 5.3 Q 14 |
| |(4, 16) …}). They use and interpret the functions in modelling a range of contexts. |Ch 5 CAS investigation p. 240 Q 1–3 |
| |They recognise and explain the roles of the relevant constants in the relationships f(x) = ax + c, with |Ch 5 Graphics calculator investigation p. 241 |
| |reference to gradient and y-axis intercept, f(x) = a(x + b)2 + c and f(x) = cax. |Ch 5 Maths in Action Q 1, 2 |
| |They solve equations of the form f(x) = k, where k is a real constant (for example, x(x + 5) = 100) and |Ex 5.5 Q 2–20 |
| |simultaneous linear equations in two variables (for example, {2x − 3y = −4 and 5x + 6y = 27} using |Ch 5 VELS Design Task Q 1–6 |
| |algebraic, numerical (systematic guess, check and refine or bisection) and graphical methods. |Ex 9.2 Q 1–10 |
| | |Ch 9 Computer investigation p. 456 Q 1–7 |
| | |Ex 9.3 Q 1–8 |
| | |Ch 9 Graphics calculator investigation p. 463 Q 1–5 |
| | |Ex 9.4 Q 1–8 |
| | |Ex 9.5 Q 1–7 |
| | |Ch 9 Problem solving p. 479 Q 1–3 |
| | |Ex 9.6 Q 1–15 |
| | |Ch 9 Investigation p. 487 Q 1–5 |
| | |Ch 9 Maths in Action Q 1, 2 |
| | |Ex 9.7 Q 1–8 |
| | |Ex 9.8 Q 1–11 |
| | |Ch 9 VELS Design Task Q 1–6 |
| | |Ex 9.9 Q 11 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |C3.5; C5.8; C9.1; C9.2; C9.3; C9.5 |
| | |MZ10 VELS Worksheets with questions only: |
| | |C3.6; C5.9; C9.4; C9.6; C9.7; C9.9 |
| | |VCE Worksheets: |
| | |ZGM R3.4; R11.6; R11.7; R12.3; R12.6; R14.4; R14.5 |
| | |ZM1&2 R1.5; R2.7; R3.3; R3.4; R4.3; R4.5; R6.2; R7.2; R7.4; R7.10; R8.3; R9.1; R9.2; R9.3 |
| | |ZFM R4.3; R4.6; R7.4; R7.5 |
| | |ZM3&4 R1.2; R1.8; R2.2; R2.4; R5.1; R5.5; R7.2; R7.4; |
| | |R8.6 |
|St6.25(1 |Description of linear, reciprocal, quadratic, exponential and logarithmic functions by recursion or | |
| |other functional relation; for example, if f(x) = loga(x), then f(xy) = f(x) + f(y) | |
|St6.25(2 |Knowledge of analytical solution of general equations of the form | |
| |f(x) = k and corresponding numerical solution of particular equations of this form by algorithm, using | |
| |technology as applicable | |
|St6.25(3 |Selection and use of Venn diagrams, Karnaugh maps or tree diagrams to solve logic and/or combinatoric | MZ10 VELS Textbook: |
| |problems |Ex 1.4 Q 4 |
| | |Ex 10.3 Q 5–10 |
|St6.5(1 |Exploration of periodic functions where f(x + k) = f(x) for some non-zero real k; for example, sin(x + | |
| |2π) = sin(x) | |
|St6.5(2 |Solution of simultaneous equations of linear-linear, linear-quadratic, linear-hyperbola types by | VCE Worksheets: |
| |analytical, numerical and graphical methods |ZFM R4.5 |
| | |ZM3&4 R6.8 |
|St6.5(3 |Use of Boolean connectives to conduct searches in relational databases, for example the Internet | MZ8 VELS Textbook: |
| | |Ch 11 Computer investigation p. 512 Q 1–9 |
| | |Ch 11 Maths in Action Q 1–5; Research Q 1, 2 |
|St6.75(1 |Knowledge of the properties that characterise and distinguish mathematical systems; for example, number | |
| |systems (such as integers and rational numbers), matrices, sets and logic, coordinates and vectors | |
|St6.75(2 |Knowledge of how mathematical properties in a given system relate to computation and proof in that | MZ10 VELS Textbook: |
| |system; for example, condition for the existence and nature of solutions to an equation, or a system of |Ex 1.5 Q 1–6 |
| |simultaneous equations | |
|St6.75(3 |Equivalence of Boolean relations using Venn diagrams, Karnaugh maps or truth tables; for example, the de| MZ10 VELS Textbook: |
| |Morgan laws, |Ch 3 Maths in Action Q 1–5 |
| |(A ∩ B)′ = A′ ( B′ and | |
| |(A ( B)′ = A′ ∩ B′ | |
|Working mathematically |
|Wo3.0 |At Level 3, students apply number skills to everyday contexts such as shopping, with appropriate | |
| |rounding to the nearest five cents. They recognise the mathematical structure of problems and use | |
| |appropriate strategies (for example, recognition of sameness, difference and repetition) to find | |
| |solutions. | |
| |Students test the truth of mathematical statements and generalisations. For example, in: | |
| |number (which shapes can be easily used to show fractions) | |
| |computations (whether products will be odd or even, the patterns of remainders from division) | |
| |number patterns (the patterns of digits of multiples, terminating or repeating decimals resulting from | |
| |division) | |
| |shape properties (which shapes have symmetry, which solids can be stacked) | |
| |transformations (the effects of slides, reflections and turns on a shape) | |
| |measurement (the relationship between size and capacity of a container). | |
| |Students use calculators to explore number patterns and check the accuracy of estimations. They use a | |
| |variety of computer software to create diagrams, shapes, tessellations and to organise and present data.| |
|Wo3.25(1 |Consideration of problems with a similar mathematical structure as a problem-solving strategy | |
|Wo3.25(2 |Use of familiar problems to focus on strategies to help in solving an unfamiliar problem | MZ7 VELS Textbook: |
| | |Ch 3 Investigation p. 100 Q 8 |
|Wo3.25(3 |Search for counter-examples in an attempt to disprove a conjecture | MZ7 VELS Textbook: |
| | |Ch 1 Investigation p. 15 |
| | |Ch 1 Investigation p. 40 Q 4 |
| | |Ch 2 Investigation p. 65 |
|Wo3.25(4 |Location of data sources, including use of the World Wide Web | MZ7 VELS Textbook: |
| | |Ch 1 Maths in Action Research |
| | |Ch 2 Maths in Action Research |
| | |Ch 3 Maths in Action Research |
| | |Ch 4 Maths in Action Research |
|Wo3.25(5 |Collection of mathematical data using technology; for example, using data logging | |
|Wo3.5(1 |Application of mathematics to model and solve simple practical problems; for example, the construction | MZ7 VELS Textbook: |
| |of a pair of stilts |Ch 6 Graphics calculator investigation p. 281 Q 1–4; |
| | |Challenge Q 1, 2 |
|Wo3.5(2 |Efficient communication when using mathematical language, symbols and representations | MZ7 VELS Textbook: |
| | |Ex 6.2 Q 1, 3, 6, 7 |
| | |Ex 6.3 Q 8–12 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R6.5 |
| | |MZ7 VELS Worksheets with questions only: |
| | |R6.2; R6.3 |
|Wo3.5(3 |Appreciation of the history of mathematics in development of geometry and number concepts | MZ7 VELS Textbook: |
| | |Ex 1.1 Q 1–10 |
| | |Ch 1 Laugh Zone |
|Wo3.5(4 |Development and testing of conjectures with the aid of a calculator; for example, divisibility tests | MZ7 VELS Textbook: |
| | |Ex 2.2 Q 1–15 |
| | |Ch 2 Investigation p. 65 Q 1, 2 |
|Wo3.5(5 |Incorporation of text, data, images and graphs using technology to report the results of an | MZ7 VELS Textbook: |
| |investigation |Ch 3 Maths in Action Research |
| | |Ch 9 Maths in Action Research |
| | |Ch 10 Maths in Action Research |
|Wo3.75(1 |Knowledge of interpretation of maps, graphs and models | MZ7 VELS Textbook: |
| | |Ch 6 Maths@Work Q 1–8 |
|Wo3.75(2 |Understanding of patterns through the use of systematic strategies such as calculating first differences| MZ7 VELS Textbook: |
| | |Ex 2.1 Q 13–15 |
| | |Ch 2 Problem solving p. 58 Q 1, 2 |
| | |Ch 2 Investigation p. 62 Q 1–3 |
|Wo3.75(3 |Application of a set of questions linked to an area of investigation | MZ7 VELS Textbook: |
| | |Ch 3 Investigation p. 118 Q 1, 2 |
|Wo3.75(4 |Knowledge of appropriate historical information | MZ7 VELS Textbook: |
| | |Ex 1.1 Q 1–10 |
| | |Ch 1 Laugh Zone |
| | |Ex 1.2 Q 16 |
| | |Ch 1 Maths in Action Research |
| | |Ch 3 Maths in Action Q 2–5, Research |
| | |MZ7 VELS Worksheets with questions only: |
| | |C1.1 |
| | |MZ8 VELS Worksheets with questions only: |
| | |R1.17 |
|Wo4.0 |At Level 4, students recognise and investigate the use of mathematics in real situations (for example, | MZ7 VELS Textbook: |
| |determination of test results as a percentage) and historical situations (for example, the emergence of |VELS Assignment 3 Q 1–8 |
| |negative numbers). |Ex 1.2 Q 20 |
| |Students develop and test conjectures. They understand that a few successful examples are not sufficient|Ch 1 Investigation p. 15 Q (a)–(c) |
| |proof and recognise that a single counter-example is sufficient to invalidate a conjecture. For example,|Ch 1 Investigation p. 33 Q (a)–(h) |
| |in: |Ch 1 Maths in Action Q 1, 2 |
| |number (all numbers can be shown as a rectangular array); |Ex 2.1 Q 8, 9, 11 |
| |computations (multiplication leads to a larger number); |Ex 2.2 Q 13–15 |
| |number patterns (the next number in the sequence 2, 4, 6 … must be 8); |Ch 2 Problem solving p. 58 Q 1, 2 |
| |shape properties (all parallelograms are rectangles); |Ex 2.3 Q 8 |
| |chance (a six is harder to roll on die than a one). |Ch 2 Investigation p. 62 Q 1–3 |
| |Students use the mathematical structure of problems to choose strategies for solutions. They explain |Ch 2 Problem solving p. 64 |
| |their reasoning and procedures and interpret solutions. They create new problems based on familiar |Ex 2.5 Q 7, 8 |
| |problem structures. |Ch 2 Maths in Action Q 1–6 |
| |Students engage in investigations involving mathematical modelling. They use calculators and computers |Ch 3 Investigation p. 118 Q 3–5 |
| |to investigate and implement algorithms (for example, for finding the lowest common multiple of two |Ex 3.8 Q 13, 14 |
| |numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in|Ch 4 Problem solving p. 138 Q (a), (b) |
| |a family of four children), and transform shapes and solids. |Ch 4 VELS Design Task Q 1– 6 |
| | |Ch 4 Investigation p. 168 Q 1–8 |
| | |Ch 5 Problem solving p. 195 |
| | |Ex 5.5 Q 5 |
| | |Ch 5 Problem solving p. 208 Q (a)–(c) |
| | |Ch 5 Investigation p. 208 Q 1, 2 |
| | |Ex 6.1 Q 7–10 |
| | |Ex 6.2 Q 6, 7 |
| | |Ex 6.3 Q 8–12 |
| | |Ex 6.4 Q 1–6 |
| | |Ch 6 Problem solving p. 269 |
| | |Ex 6.4 Q 1–5 |
| | |Ch 6 VELS Design Task Q 1, 2 |
| | |Ch 6 Investigation p. 287 Rook’s tours Q 1–3; Bishop’s |
| | |tours Q 1–3; Queen’s tours Q 1–3 |
| | |Ch 6 Maths@Work Q 1–8 |
| | |Ch 7 Problem solving p. 318 |
| | |Ch 7 Investigation p. 322 Q 1–4 |
| | |Ch 7 Investigation p. 325 Q 1 |
| | |Ex 8.1 Q 14 |
| | |Ex 8.2 Q 12 |
| | |Ch 8 Maths@Work Q 1, 2 |
| | |Ex 8.3 Q 15 |
| | |Ch 8 Problem solving p. 372 |
| | |Ch 9 Investigation p. 409 Q 1–9 |
| | |Ch 10 Investigation p. 463 Q 1 – 4 |
| | |Ch 10 Maths in Action Q 1–5 |
| | |Ch 10 Investigation p. 499 Q 1 |
| | |MZ8 VELS Textbook: |
| | |Ch 1 Investigation p. 5 Q 3, 5 |
| | |Ch 1 VELS Design Task Q 1–6 |
| | |Ch 1 Investigation p. 32 |
| | |Ch 2 Investigation p. 44 Q 1–8 |
| | |Ch 2 Maths in Action Q 1–5 |
| | |Ex 3.11 Q 1–20 |
| | |Ch 5 Problem solving p. 211 |
| | |VCE Worksheets: |
| | |ZGM R1.3 |
|Wo4.25(1 |Consideration of evidence to support theorems; for example, in geometry | MZ7 VELS Textbook: |
| | |Ch 1 Investigation p. 15 Q (c) |
| | |Ex 1.3 Q 5, 6 |
| | |Ch 1 VELS Design Task Q 2, 7 |
| | |Ch 3 VELS Design Task Q 6–8 |
| | |Ch 4 Problem solving p. 153 Q 2 |
| | |Ex 5.6 Q 1 |
| | |Ch 7 Investigation p. 325 Q 2–4 |
| | |Ch 7 Maths in Action Q 1–5 |
| | |Ch 7 VELS Design Task Q 1–7 |
| | |Ch 7 Investigation p. 332 Q 1–4 |
| | |Ch 7 Problem solving p. 337 |
| | |Ch 9 Investigation p. 411 Q 1–4 |
| | |Ex 9.2 Q 5–8 |
| | |Ex 9.3 Q 6, 7 |
| | |Ch 9 Investigation p. 428 Q 3–9 |
| | |MZ8 VELS Textbook: |
| | |Ch 6 Investigation p. 238 Q 1–3 |
| | |Ch 6 Investigation p. 262 Q 1–3 |
|Wo4.25(2 |Exploration of the appropriateness of linear models for data | MZ7 VELS Textbook: |
| | |Ch 2 VELS Design Task Q 4 |
| | |Ex 8.4 Q 13 |
| | |Ex 8.6 Q 16 |
| | |Ch 8 Problem solving p. 394 Q 1, 2 |
|Wo4.25(3 |Translation between verbal descriptions and algebraic rules | MZ7 VELS Textbook: |
| | |Ch 1 Investigation p. 28 Q 1 |
| | |Ex 6.4 Q 7 |
| | |Ex 6.5 Q 6 |
| | |Ex 8.5 Q 15 |
| | |Ch 8 VELS Design Task Q 1–7 |
| | |Ch 8 Investigation p. 388 Q 1–5 |
| | |MZ8 VELS Textbook: |
| | |Ch 7 Problem solving p. 301 Q 1–4 |
| | |Ch 7 VELS Design Task Q 2 |
| | |Ch 8 Investigation p. 364 Q 1–7 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R2.1 |
|Wo4.25(4 |Use of technology to extend their own ability to make and test conjectures | MZ7 VELS Textbook: |
| | |Ch 1 Investigation p. 33 Q (a)–(h) |
| | |Ch 1 Investigation p. 40 Q 4 |
| | |Ex 2.6 Q 15 |
| | |Ch 2 Computer investigation p. 76 Q 1–6 |
| | |Ch 6 CAS Investigation p. 279 Q 1–3 |
| | |Ch 6 Graphics calculator investigation p. 281 Q 1 |
| | |Ch 6 VELS Design Task Q 3, 4 |
| | |Ch 8 Computer investigation p. 389 Q 1–6 |
| | |Ch 8 Graphics calculator investigation p. 396 Q 3, 5 |
| | |MZ8 VELS Textbook: |
| | |Ch 1 Investigation p. 32 |
| | |Ch 2 Investigation p. 44 Q 1–8 |
| | |Ex 2.2 Q 8 |
| | |Ch 2 Problem solving |
| | |Ex 2.3 Q 8 |
| | |Ex 2.3 Q 14–20 |
| | |Ch 2 Investigation p. 57 |
| | |Ex 2.5 Q 1–11 |
| | |Ch 2 VELS Design Task Q 1, 3, 5 |
| | |Ch 2 Maths in Action Q 3–5 |
|Wo4.25(5 |Use of spreadsheets to manipulate data and generate graphs | MZ7 VELS Textbook: |
| | |Ch 10 Computer investigation p. 465 Q 1–4 |
|Wo4.5(1 |Application of logic to the creation and use of a database | MZ8 VELS Textbook: |
| | |Ch 11 Computer investigation p. 512 Q 1–9 |
|Wo4.5(2 |Identification of the mathematical information needed to solve a problem or carry out an investigation | MZ7 VELS Textbook: |
| | |Ch 1 VELS Design Task Q 1, 3, 5, 8 |
| | |Ex 1.8 Q 1–10 |
| | |Ch 1 Investigation p. 40 Q 1–4 |
| | |Ex 2.6 Q 14 |
| | |Ch 2 VELS Design Task Q 1–9 |
| | |Ch 3 VELS Design Task Q 6–8 |
| | |Ch 3 Maths in Action Q 5 |
| | |Ch 6 Graphics calculator investigation p. 396 Q 1–6 |
| | |Ch 9 Investigation p. 428 Q 1–9 |
| | |Ch 9 VELS Design Task Q 1–8 |
| | |Ch 10 Maths in Action Q 6, 7 |
| | |Ch 10 Investigation p. 488 Car colour Q 1–3; Most |
| | |common letter Q 1–3 |
| | |Ch 10 VELS Design Task Q 1–9 |
| | |Ch 10 Problem solving p. 501 |
| | |MZ7 VELS Worksheets with explanations and questions: |
| | |R6.1 |
| | |MZ8 VELS Textbook: |
| | |Ch 1 Problem solving p. 12 |
| | |Ch 1 VELS Design Task Q 7, 8 |
| | |Ch 1 Problem solving p. 20 |
| | |Ch 1 Maths in Action Q 1–4 |
| | |Ch 3 Problem solving p. 113 |
| | |Ch 3 Investigation p. 122 Q 1, 2 |
| | |Ch 3 VELS Design Task Q 1–8 |
| | |Ch 4 Investigation p. 146 Q 3, 4 |
| | |Ch 4 VELS Design Task Q 1–3 |
| | |Ch 4 Problem solving p. 160 Q 1–4 |
| | |Ch 5 Investigation p. 197 Q 2 |
| | |Ch 5 VELS Design Task Q 1–4 |
| | |Ch 6 VELS Design Task Q 1–5 |
| | |Ch 6 Problem solving p. 278 |
| | |Ch 7 Investigation p. 297 Q 1, 2 |
| | |Ch 7 Problem solving p. 301 Q 1–4 |
| | |Ch 7 VELS Design Task Q 3–5 |
| | |Ch 7 Problem solving p. 314 |
| | |Ch 8 Investigation p. 364 Q 1–7 |
| | |Ch 8 Investigation p. 373 |
| | |Ch 8 Investigation p. 388 Q 1–5 |
| | |Ch 9 Investigation p. 412 Q 1–10 |
| | |Ch 9 Problem solving p. 427 |
| | |Ch 9 Investigation p. 428 Q 1–3 |
| | |Ch 9 Maths@Work |
| | |Ch 9 VELS Design Task Q 1–6 |
| | |Ch 10 VELS Design Task Q 1–7 |
| | |Ch 10 Maths in Action Q 1–4, Research Q 1–4 |
| | |Ch 11 VELS Design Task Q 1–7 |
| | |MZ9 VELS Textbook: |
| | |Ch 2 Problem solving p. 70 Q 1–4 |
|Wo4.5(3 |Development of deductive proof to reach new conclusions | MZ8 VELS Textbook: |
| | |Ch 6 Investigation p. 238 Q 1–5 |
| | |Ch 6 Investigation p. 262 Q 1–3 |
|Wo4.5(4 |Use of interpolation to make predictions | MZ8 VELS Textbook: |
| | |Ex 8.4 Q 4 (e)–(g), 6 (e)–(g) |
| | |Ch 8 Investigation p. 364 Q 6 |
|Wo4.5(5 |Development of simple geometric and algebraic models for real situations; for example, representation of| MZ7 VELS Textbook: |
| |an animal as a cylinder |Ch 9 Maths in Action Q 1–3 |
|Wo4.75(1 |Communication of the results of a mathematical investigation in an appropriate form | MZ8 VELS Textbook: |
| | |Ch 1 VELS Design Task Q 1, 4 |
| | |Ch 1 Maths in Action Research |
| | |Ch 2 VELS Design Task Q 6 |
| | |Ch 2 Maths in Action Research |
| | |Ch 4 Maths in Action Research |
| | |Ch 6 VELS Design Task Q 4, 5 |
| | |Ch 7 VELS Design Task Q 7, 9 |
| | |Ch 8 Maths in Action Q 1, 2 |
| | |Ch 8 VELS Design Task Q 6, 7 |
| | |Ch 10 Maths in Action Research Q 1–4 |
| | |MZ9 VELS Textbook: |
| | |Ch 1 Maths in Action Research |
|Wo4.75(2 |Creation and manipulation of tables and graphs using technology | MZ8 VELS Textbook: |
| | |Ch 6 CAS Investigation p. 275 Q 1–3 |
|Wo4.75(3 |Numerical and graphical solution of algebraic problems using technology | MZ7 VELS Textbook: |
| | |Ch 6 CAS investigation p. 279 Q 1–4 |
| | |Ch 6 Graphics calculator investigation p. 281 Q 1–4; |
| | |Challenge Q 1, 2 |
| | |Ch 8 Computer investigation p. 389 Q 1–6 |
| | |Ch 10 Computer investigation p. 465 Q 1–4 |
|Wo4.75(4 |Exploration of geometrical propositions using technology | MZ7 VELS Textbook: |
| | |Ch 9 Computer investigation p. 432 Q 1–5 |
| | |MZ8 VELS Textbook: |
| | |Ch 5 Maths in Action Q 1–6, 9–11 |
| | |Ch 9 Computer investigation p. 406 Q 1–7 |
|Wo5.0 |At Level 5, students formulate conjectures and follow simple mathematical deductions (for example, if | MZ7 VELS Textbook: |
| |the side length of a cube is doubled, then the surface area increases by a factor of four, and the |VELS Assignment 3 Q 7, 8 |
| |volume increases by a factor of eight). |VELS Assignment 4 Q 5 |
| |Students use variables in general mathematical statements. They substitute numbers for variables (for |Ex 1.5 Q 13, 14 |
| |example, in equations, inequalities, identities and formulas). |Ch 6 CAS Investigation p. 279 Q 4 |
| |Students explain geometric propositions (for example, by varying the location of key points and/or lines|Ch 6 Graphics calculator investigation p. 281 Q 2–4; |
| |in a construction). |Challenge Q 1 |
| |Students develop simple mathematical models for real situations (for example, using constant rates of |MZ8 VELS Textbook: |
| |change for linear models). They develop generalisations by abstracting the features from situations and |Ch 2 Investigation p. 73 Q 1–3 |
| |expressing these in words and symbols. They predict using interpolation (working with what is already |Ch 5 Maths in Action Q 1–11 |
| |known) and extrapolation (working beyond what is already known). They analyse the reasonableness of |Ch 6 CAS Investigation p. 275 Q 1–3 |
| |points of view, procedures and results, according to given criteria, and identify limitations and/or |Ch 6 Maths@Work Q 1, 2 |
| |constraints in context. |Ch 7 Investigation p. 297 Q 1, 2 |
| |Students use technology such as graphics calculators, spreadsheets, dynamic geometry software and |Ex 7.8 Q 1–4 |
| |computer algebra systems for a range of mathematical purposes including numerical computation, graphing,|Ex 7.9 Q 1–16 |
| |investigation of patterns and relations for algebraic expressions, and the production of geometric |Ch 7 Investigation p. 326 Q 1–5 |
| |drawings. |Ch 8 Maths in Action Q 1, 2 |
| | |Ch 8 VELS Design Task Q 1–7 |
| | |Ch 9 Computer investigation p. 406 Q 1–7 |
| | |Ch 9 Maths@Work |
| | |Ch 9 VELS Design Task Q 1–6 |
| | |Ex 10.2 Q 1–8 |
| | |Ch 10 Investigation p. 481 Q 1–6 |
| | |Ch 10 Computer investigation p. 484 Q 1–6 |
| | |Ch 10 Graphics calculator investigation p. 490 |
| | |Ch 11 Computer investigation p. 512 Q 1–9 |
| | |Ch 11 Maths in Action Q 1–5 |
| | |MZ9 VELS Textbook: |
| | |VELS Assignment 1 Q 3, 4 |
| | |VELS Assignment 3 Q 7 |
| | |Ch 1 Problem solving p. 30 |
| | |Ch 1 Maths in Action Q 1–3 |
| | |Ch 1 VELS Design Task Q 1–7 |
| | |Ch 1 Graphics calculator investigation p. 45 |
| | |Ch 1 Maths in Action Research |
| | |Ch 2 Problem solving p. 84 |
| | |Ch 2 VELS Design Task Q 1–7 |
| | |Ch 2 Graphics calculator investigation p. 100 Q 1–5 |
| | |Ch 3 VELS Design Task Q 1–6 |
| | |Ex 4.1 Q 1–11 |
| | |Ch 4 Maths@Work Q 1, 2 |
| | |Ex 4.2 Q 2, 4 |
| | |Ex 4.2 Q 13–16 |
| | |Ex 4.3 Q 7–10 |
| | |Ex 4.4 Q 19, 20 |
| | |Ch 4 VELS Design Task Q 5 |
| | |Ch 4 Problem solving p. 187 (a)–(d) |
| | |Ch 5 Problem solving p. 217 |
| | |Ch 5 Problem solving p. 222 |
| | |Ch 5 Investigation p. 224 Q 1–3 |
| | |Ch 5 VELS Design Task Q 1–5 |
| | |Ch 6 Problem solving p. 254 |
| | |Ch 6 CAS Investigation p. 256 Q 1, 2 |
| | |Ch 6 Problem solving p. 262 |
| | |Ch 6 VELS Design Task Q 1–6 |
| | |Ch 6 Maths in Action Q 1–4 |
| | |Ch 6 Investigation p. 292 Q 1–3 |
| | |Ch 6 Graphics calculator investigation p. 299 Q 1–5 |
| | |Ch 7 Investigation p. 318 Q 1–4 |
| | |Ch 7 VELS Design Task Q 1–5 |
| | |Ch 8 Investigation p. 375 Q 1–4 |
| | |Ch 8 Problem solving p. 376 |
| | |Ch 8 Computer investigation p. 384 Q 3–8 |
| | |Ch 8 Investigation p. 390 Q 1–3 |
| | |Ch 8 Investigation p. 394 Q 1–4 |
| | |Ch 8 Maths@Work Q 1, 2 |
| | |Ch 8 Computer investigation p. 412 Q 2–5 |
| | |Ch 8 VELS Design Task Q 1–6 |
| | |Ex 9.1 Q 2–9 |
| | |Ch 9 Investigation p. 433 Q 1, 2 |
| | |Ch 9 Problem solving p. 441 |
| | |Ch 9 Graphics calculator investigation p. 454 Q 1–5 |
| | |Ch 9 VELS Design Task Q 1–8 |
| | |Ch 9 Maths@Work Q 1–3 |
| | |Ch 10 Computer investigation p. 483 Q 1–6 |
| | |Ch 10 Graphics calculator investigation p. 489 Q 1–9 |
| | |Ch 10 VELS Design Task Q 1–8 |
| | |Ch 10 Maths in Action Q 1, 2 |
| | |MZ9 VELS Worksheets with explanations and questions: |
| | |R6.1 |
| | |MZ9 VELS Worksheets with questions only: |
| | |R9.1 |
| | |MZ10 VELS Textbook: |
| | |Ch 2 CAS investigation p. 63 Q 1–4 |
| | |Ex 2.11 Q 1–7 |
| | |Ch 2 VELS design Task Q 1–9 |
| | |Ch 2 Graphics calculator investigation p. 87 Q 1–3 |
| | |Ch 2 Maths in Action Q 1, 2 |
| | |Ch 4 Problem solving p. 168 Q 1–3 |
| | |Ch 4 VELS Design Task Q 1–7 |
| | |Ch 4 Investigation p. 176 Q 1, 2 |
| | |Ex 4.3 Q 14 |
| | |MZ10 VELS Worksheets with explanations and questions: |
| | |R5.1 |
| | |MZ10 VELS Worksheets with questions only: |
| | |R4.2 |
| | |VCE Worksheets: |
| | |ZGM R1.5; R2.1; R3.1; R4.1; R5.1; R5.5; R12.2; R12.8; R13.4; R14.1 |
| | |ZM1&2 R3.1 |
| | |ZFM R3.2; R4.2; R7.1; R8.2 |
| | |ZM3&4 R3.4; R4.2 |
|Wo5.25(1 |Development of alternative algebraic models for a set of data and evaluation of their relative merits | MZ10 VELS Textbook: |
| | |Ex 9.9 Q 5–9 |
|Wo5.25(2 |Presentation of algebraic arguments using appropriate mathematical symbols and conventions | MZ9 VELS Textbook: |
| | |Ex 6.10 Q 3–12 |
| | |MZ10 VELS Textbook: |
| | |Ch 1 Problem solving p. 11 Q 1, 2 |
| | |Ch 1 Investigation p. 26 Q 1–3 |
| | |Ch 2 Investigation p. 69 Q 2, 3 |
| | |Ex 2.11 Q 5 |
| | |Ch 2 Problem solving p. 74 Q 1–4 |
| | |Ch 2 Maths in Action Q 1, 2 |
| | |Ch 3 VELS Design Task Q 4–8 |
| | |Ch 3 Investigation p. 128 Q 1, 2 |
|Wo5.25(3 |Evaluation of the appropriateness of the results of their own calculations | MZ9 VELS Textbook: |
| | |Ch 5 Investigation p. 224 Q 3 |
| | |Ch 6 CAS Investigation p. 256 Q 1, 2 |
| | |Ch 6 VELS Design Task Q 5, 6 |
| | |Ch 6 Maths in Action Research |
| | |Ch 7 Graphics calculator investigation p. 332 Q 3, 5, 6 |
| | |Ch 7 VELS Design Task Q 3–5 |
| | |MZ10 VELS Textbook: |
| | |Ch 1 VELS Design Task Q 5–7 |
| | |Ch 1 Maths in Action Q 5 |
| | |Ch 2 Maths in Action Research |
| | |Ch 7 Investigation p. 351 Q 1–6 |
|Wo5.5(1 |Generation of reports from a database by using and, or and not as search tools | MZ8 VELS Textbook: |
| | |Ch 11 Computer investigation p. 512 Q 6–9 |
|Wo5.5(2 |Justification or proof of generalisations made from specific cases | MZ9 VELS Textbook: |
| | |Ch 1 Investigation p. 16 Q 1–4 |
| | |Ex 3.1 Q 2, 4, 6 |
| | |Ch 3 Investigation p. 120 |
| | |Ex 3.2 Q 8 |
| | |Ch 3 Maths in Action Q 1, 2 |
| | |Ch 8 Investigation p. 390 Q 2, 3 |
| | |MZ10 VELS Textbook: |
| | |Ch 3 Problem solving p. 114 Q 1–3 |
| | |Ch 4 Investigation p. 192 Q 6 |
|Wo5.5(3 |Selection and use of technology to explore geometric and algebraic relationships and data trends | MZ9 VELS Textbook: |
| | |Ch 1 Graphics calculator investigation p. 45 |
| | |Ch 2 Graphics calculator investigation p. 100 Q 1, 2, 4, 5 |
| | |Ch 4 Investigation p. 165 Q 2, 4 |
| | |Ch 6 CAS Investigation p. 256 Q 1, 2 |
| | |Ex 6.3 Q 11 |
| | |Ch 6 Graphics calculator investigation p. 299 Q 2–5 |
| | |Ex 7.7 Q 1 – 5 |
| | |Ch 7 CAS Investigation p. 353 Q 1–3 |
| | |Ch 7 Computer investigation p. 356 Q 2–7 |
| | |Ch 8 Computer investigation p. 384 Q 3–8 |
| | |Ch 8 Computer investigation p. 412 Q 1–5 |
| | |Ch 9 Graphics calculator investigation p. 454 Q 4, 5 |
| | |Ch 9 Investigation p. 455 Q 1–3 |
| | |MZ10 VELS Textbook: |
| | |VELS Assignment 3 Q 2, 4, 6 |
| | |Ch 1 Graphics calculator investigation p. 19 Q 1–3 |
| | |Ch 2 CAS investigation p. 63 Q 1–4 |
| | |Ch 2 Graphics calculator investigation p. 87 Q 4, 5 |
| | |Ch 4 Graphics calculator investigation p. 203 Q 1, 2; |
| | |Extension Q 1, 2 |
| | |Ch 7 Maths in Action Q 1–5 |
| | |Ch 8 Graphics calculator investigation p. 424 Q 1–6 |
| | |Ch 9 Computer investigation p. 456 Q 4–7 |
| | |Ch 9 Graphics calculator investigation p. 463 Q 1–3 |
|Wo5.75(1 |Use of an ‘equations editor’ to insert mathematical material in a text document | |
|Wo5.75(2 |Simulation of events using technology | MZ9 VELS Textbook: |
| | |Ch 10 Graphics calculator investigation p. 489 Q 5–9 |
| | |Ex 10.6 Q 1–4 |
| | |MZ10 VELS Textbook: |
| | |Ch 10 Graphics calculator investigation p. 527 Q 1–5 |
|Wo5.75(3 |Representation and manipulation of symbolic expressions using technology | MZ9 VELS Textbook: |
| | |Ch 6 Graphics calculator investigation p. 299 Q 2–5 |
|Wo5.75(4 |Recognition of functionality of technology and its limitations, such as image resolution, | MZ10 VELS Textbook: |
| |discontinuities in graphs and systematic error in computation through rounding |Ch 1 Graphics calculator investigation p. 19 Extension |
| | |Ch 3 Graphics calculator investigation p. 119 Q 1–3 |
|Wo6.0 |At Level 6, students formulate and test conjectures, generalisations and arguments in natural language | MZ9 VELS Textbook: |
| |and symbolic form (for example, ‘if m2 is even, then m is even and if m2 is odd, then m is odd’). They |VELS Assignment 4 Q 1–4 |
| |follow formal mathematical arguments for the truth of propositions (for example, ‘the sum of three |MZ10 VELS Textbook: |
| |consecutive natural numbers is divisible by 3’). |Ch 1 VELS Design Task Q 1–7 |
| |Students choose, use and develop mathematical models and procedures to investigate and solve problems |Ch 1 Maths in Action Q 1–5 |
| |set in a wide range of practical, theoretical and historical contexts (for example, exact and |Ch 1 Graphics calculator investigation p. 19 Q 1–3; |
| |approximate measurement formulas for the volumes of various three-dimensional objects such as truncated |Extension |
| |pyramids). They generalise from one situation to another, and investigate it further by changing the |Ex 1.5 Q 2–6 |
| |initial constraints or other boundary conditions. They judge the reasonableness of their results based |Ex 3.8 Q 11–13 |
| |on the context under consideration. |Ch 3 Maths in Action Q 1–3, 5 |
| |They select and use technology in various combinations to assist in mathematical inquiry, to manipulate |Ch 3 Computer investigation p. 144 Q 2, 3 |
| |and represent data, to analyse functions and carry out symbolic manipulation. They use geometry software|Ch 4 Investigation p. 192 Q 7–9 |
| |or graphics calculators to create geometric objects and transform them, taking into account invariance |Ch 5 Investigation p. 231 Q 1–3 |
| |under transformation. |Ch 5 Problem solving p. 232 Q 1, 2 |
| | |Ch 5 Maths in Action Q 1, 2 |
| | |Ex 5.4 Q 2, 5–8 |
| | |Ch 5 VELS Design Task Q 5, 6 |
| | |Ex 5.7 Q 5–7 |
| | |Ch 6 VELS Design Task Q 1–3 |
| | |Ch 6 Investigation p. 310 Q 1–10 |
| | |Ch 6 Maths in Action Q 1–3 |
| | |Ch 6 Problem solving p. 318 Q 1, 2 |
| | |Ch 6 Investigation p. 324 Q 1–3 |
| | |Ch 7 Graphics calculator investigation p. 374 |
| | |Ch 7 Maths in Action Q 6 |
| | |Ch 8 Investigation p. 399 1–5 |
| | |Ch 8 VELS Design Task Q 1–5 |
| | |Ch 8 Graphics calculator investigation p. 424 Research |
| | |Ch 8 Problem solving p. 426 Q 1, 2 |
| | |Ch 8 Computer investigation p. 426 Q 1–6 |
| | |Ch 8 Investigation p. 433 Q 1–7 |
| | |Ch 8 Investigation p. 434 Q 1–3 |
| | |Ch 8 Maths in Action Q 1–3 |
| | |Ch 9 Computer investigation p. 456 Q 1–7 |
| | |Ch 9 Graphics calculator investigation p. 463 Q 1–5 |
| | |Ch 9 CAS investigation p. 472 Q 1–6 |
| | |Ch 9 Problem solving p. 479 Q 1–3 |
| | |Ch 9 Investigation p. 487 Q 1–5 |
| | |Ch 9 Maths in Action Q 1, 2 |
| | |Ch 9 VELS Design Task Q 1–6 |
| | |Ch 10 Problem solving p. 542 Q 1–3 |
| | |Ch 10 Investigation p. 543 Q 1–5 |
| | |Ch 10 VELS Design Task Q 1–5 |
| | |Ch 10 Maths@Work Q 1, 2 |
| | |VCE Worksheets: |
| | |ZM3&4 R9.3 |
|Wo6.25(1 |Identification of assumptions used to develop a model for a practical situation, and consideration of | MZ10 VELS Textbook: |
| |related constraints and limitations |Ch 1 Graphics calculator investigation p. 19 Extension |
| | |Ch 6 Maths in Action Research |
| | |Ch 8 Graphics calculator investigation p. 424 Q 1–6, |
| | |Research |
| | |Ch 9 Investigation p. 487 Q 1–5 |
| | |Ch 10 Graphics calculator investigation p. 527 Q 1–5 |
|Wo6.25(2 |Efficient and effective use of mathematical concepts, skills and processes, including the effective use | |
| |of technology, to solve a broad range of problems in familiar situations | |
|Wo6.25(3 |Consistent, accurate and appropriate use of mathematical notation, symbols, diagrams and graphs in | |
| |solving problems and in the presentation of mathematical arguments | |
|Wo6.5(1 |Consideration of alternative models for given situations and the application of criteria to select an | MZ10 VELS Textbook: |
| |appropriate model from these alternatives; for example, the best model to use for illustrating the time |Ch 10 VELS Design Task Q 4, 5 |
| |taken for an aspirin tablet to dissolve with respect to water temperature | |
|Wo6.5(2 |Selection and use of mathematical concepts, skills and processes, including the appropriate selection | |
| |and effective use of technology, to solve challenging problems, and consideration of alternative | |
| |approaches in familiar and some unfamiliar situations | |
|Wo6.5(3 |Use of informal mathematical reasoning to establish general results; for example, the formula for the | MZ10 VELS Textbook: |
| |area of a circle by triangle approximation of sectors |Ex 1.5 Q 1–6 |
| | |Ch 8 Graphics calculator investigation p. 424 Q 1–6; |
| | |Research |
| | |Ch 8 Computer investigation p. 426 Q 1–6 |
|Wo6.75(1 |Development or generalisation of an existing model to enhance its applicability in other contexts; for | |
| |example, bounce of a ball over a larger domain where a maximal bounce height occurs | |
|Wo6.75(2 |Development of new approaches or methods, including those that may require the use of technology for | |
| |their solution, to formulate and solve challenging problems in unfamiliar and new situations | |
|Wo6.75(3 |Use of deductive proof techniques; for example, Euler’s proof that there is an infinite number of | MZ10 VELS Textbook: |
| |primes, including indirect proof; for example, the irrationality of log2(5), and mathematical induction;|Ex 1.5 Q 1–6 |
| |for example, the Tower of Hanoi relationship, to establish general results | |
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