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VELS Standards & Progression Points Links for MathsWorld 7 chapters (for Mathematics Domain Level 4.0 to 5.0) The following document details how the MathsWorld for VELS series addresses the standards & progression points for Mathematics (Level 4.0–5.0). Chapter 1 Whole Numbers Level Number Standard/Progression point MathsWorld 7 4.0 At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions). They use estimates for computations and apply criteria to determine if estimates are reasonable or not. They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers). * Chapter pre-test Questions 1 – 4 1.1: Place value Exercise 1.1 * Chapter pre-test Questions 9, 10 4.0 4.0 4.5 4.5 Students use ‘equal division by 10’ to simplify division by whole numbers, such as 240 ÷ 40 = 24 ÷ 4 = 6. For estimation in division, they mentally use ‘division fact rounding’. 4.75 Students use efficient mental and/or written methods to multiply or divide by two-digit numbers. 5.0 Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30). Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. 5.0 * Chapter pre-test Questions 5 – 8 1.2: Addition and subtraction Exercise 1.2 Questions 1 – 9 1.3: Multiplication Exercise 1.3 Questions 1 – 6 1.4: Division Exercise 1.4 Questions 1 – 5 1.4: Division Exercise 1.4 Questions 1 – 9 Alternatively see Example 3 (p. 28) 1.6: Estimation Exercise 1.6 Questions 4e, f Example 3c (p. 41) 1.3: Multiplication Example 5 (p. 23) Exercise 1.3 Question 6 1.4: Division Examples 4, 5 (p. 29) Exercise 1.4 Questions 5, 12, 13 1.6: Estimation Examples 2, 3 (p. 40) Exercise 1.6 Questions 2 – 8 1.3: Multiplication Exercise 1.3 Question 7 Structure 4.0 Students establish equivalence relationships between mathematical expressions using properties such as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)). 5.0 Students apply the commutative, associative, and distributive properties in mental and written computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10). They recognise and use inequality symbols. 5.0 Working mathematically 4.0 4.0 At Level 4, students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers). They use calculators and computers to investigate 1.3: Multiplication Examples 2, 3, 4 (pp. 22 – 23) Exercise 1.3 Questions 4, 5 1.5: Order of operations Exercise 1.5 Questions 5, 6, 11, 13 1.3: Multiplication Examples 2, 3, 4 (pp. 22 – 23) Exercise 1.3 Questions 4, 5 1.1: Place value Example 2 (p. 10) Exercise 1.1 Question 4 Analysis task 1: International Standard Book Numbers Analysis task 2: Bar codes Analysis task 1: International VELS curriculum links (by chapter) 2 Level 5.0 Standard/Progression point and implement algorithms (for example, for finding the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform shapes and solids. Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. MathsWorld 7 Standard Book Numbers Analysis task 2: Bar codes Analysis task 1: International Standard Book Numbers Analysis task 2: Bar codes VELS curriculum links (by chapter) 3 Chapter 2 Mathematical thinking Level Number Standard/Progression point MathsWorld 7 4.0 They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money. They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125). 2.2: Developing problem-solving strategies Example problem 3 Try this! p. 64 Students extend their range of personal benchmarks for estimating quantities, such as how far one can drive in an hour or one litre of water weighs 1 kg. Investigation 2 (p. 86) 4.75 They list all subsets of a given set, observing through examples that there are 2n subsets of a set of n elements. 5.0 They list the elements of the set of all subsets (power set) of a given finite set and comprehend the partial-order relationship between these subsets with respect to inclusion (for example, given the set {a, b, c} the corresponding power set is {Ø, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}.) They test the validity of statements formed by the use of the connectives and, or, not, and the quantifiers none, some and all, (for example, ‘some natural numbers can be expressed as the sum of two squares’). They apply these to the specification of sets defined in terms of one or two attributes, and to searches in data-bases. 2.1: Mathematising: representing a problem Example problem 3 (p. 57) See note in MathsWorld 7 Teacher Edition, p. 57 2.1: Mathematising: representing a problem Example problem 3 (p. 57) See note in MathsWorld 7 Teacher Edition 5.0 Measurement, Chance and Data 4.5 2.4 Mathematical reasoning Example investigation 1 (p. 79) Structure 5.0 5.0 Working mathematically 4.0 4.0 4.0 Students develop and test conjectures. They understand that a few successful examples are not sufficient proof and recognise that a single counter-example is sufficient to invalidate a conjecture. For example, in: number (all numbers can be shown as a rectangular array) computations (multiplication leads to a larger number) number patterns ( the next number in the sequence 2, 4, 6 … must be 8) shape properties (all parallelograms are rectangles) chance (a six is harder to roll on die than a one). Students use the mathematical structure of problems 2.3: Developing strategies to think about my thinking Problem set 2.3 Question 8 2.3: Developing strategies to think about my thinking Problem set 2.3 Question 8 2.4: Mathematical reasoning: conjecturing Example Investigation 1 Try this! pp. 80, 81 Example Investigation 2 Try this! p. 85 Investigation 1 2.4: Mathematical reasoning: conjecturing Example Investigation 2 2.1: Representing a problem VELS curriculum links (by chapter) 4 Level Standard/Progression point to choose strategies for solutions. 4.0 They explain their reasoning and procedures and interpret solutions. They create new problems based on familiar problem structures. 4.0 4.0 Students engage in investigations mathematical modelling. 4.25 Students develop generalisations inductively, from examples such as angle sums in triangles. 5.0 They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context. involving MathsWorld 7 Example problems 1 – 3 Practice problems 1 – 3 Problem set 2.1 2.2: Developing problem-solving strategies Example problems 1 – 6 Practice problems 1 – 4 Problem set 2.2 Investigation 2 p. 86 2.4: Mathematical reasoning: conjecturing Example Investigation 2 Try this! p. 85 2.4: Mathematical reasoning: conjecturing Example investigations 1, 2 Investigations 1, 2 2.4: Mathematical reasoning: Conjecturing Example investigation 2 Try this! p. 85 Investigation 2 (p. 86) VELS curriculum links (by chapter) 5 Chapter 3 Lines and angles Level Space Standard/Progression point MathsWorld 7 4.25 Students use a wide range of geometric language correctly when describing or constructing shapes and solids. 4.5 Students apply properties of angles and lines in two dimensions, such as calculate angles of an isosceles right-angle triangle or finding all the angles of a symmetric trapezium from one angle. 3.1: Lines, rays and segments Try this! (p. 93) Exercise 3.1 Questions 1, 2, 3 Analysis task 1: Catching the sun's heat Analysis task 2: Boom angles Analysis task 3: A parking problem 3.3 Vertically opposite, complementary and supplementary angles Examples 1, 2, 3 (pp. 113 – 114) Exercise 3.3: Questions 1 – 15 Measurement, Chance and Data 4.0 They measure angles in degrees. 4.25 They estimate and measure angles 0° to 360° Working mathematically 4.0 4.0 4.0 4.75 5.0 At Level 4, students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers). They understand that a few successful examples are not sufficient proof and recognise that a single counter-example is sufficient to invalidate a conjecture. Students engage in investigations involving mathematical modelling. They link known facts together logically, such as parallelograms have rotational symmetry, therefore they have equal opposite angles. Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. * Chapter pre-test Questions 9, 10 3.2: Angles Examples 2, 3 (p. 388) Exercise 3.2 Questions 1, 2, 6, 7, 9, 12 Analysis task 1: Catching the sun's heat Analysis task 2: Boom angles Analysis task 3: A parking problem Chapter pre-test Questions 5, 9, 10 3.2: Angles Examples 2, 3 (pp. 102, 103) Exercise 3.2 Questions 1, 2, 6, 7, 9, 11, 12 Analysis task 1: Catching the sun's heat Analysis task 2: Boom angles Analysis task 3: A parking problem 3.1: Lines, rays and segments Try this! p. 95 Analysis task 3: A parking problem 3.3 Vertically opposite, complementary and supplementary angles Try this! p. 112 3.2: Angles Exercise 3.2 Question 8 VELS curriculum links (by chapter) 6 Chapter 4 Number patterns Level Number Standard/Progression point MathsWorld 7 4.0 They create sets of number multiples to find the lowest common multiple of the numbers. 4.0 Students identify square, prime and composite numbers. 4.0 They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers. 4.0 They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers). They recognise and calculate simple powers of whole numbers (for example, 24 = 16). * Chapter pre-test Questions 1 – 3 4.1: Multiples Examples 2, 3 (pp. 134 – 135) Exercise 4.1 Questions 3, 5 Analysis task 3: Fleadles * Chapter pre-test Questions 9, 10 4.5: Prime numbers Try this! (pp. 152 – 153) Exercise 4.5 Questions 1 – 15 * Chapter pre-test Questions 6 - 8 4.2: Factors Exercise 4.2 Questions 1 – 5 4.6: Finding prime factors Exercise 4.6 Questions 1 – 6 * Chapter pre-test Questions 4, 5 4.0 4.25 4.25 Students determine prime factors and use them to express any whole number as a product of powers of primes and to find its composite factors. They use knowledge of perfect squares to determine exact square roots. 4.75 They estimate and use a calculator to find squares, cubes, square and cube roots of any numbers. 5.0 At Level 5, students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes (for example, 36 000 = 25 × 32 × 53). They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125). 5.0 5.0 They evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9). 4.4: Square numbers, square roots and powers Exercise 4.4 Questions 1, 3 - 7 4.6: Finding prime factors Examples 1 – 5 (pp. 157 – 161) Exercise 4.6 Questions 1 – 7 4.4: Square numbers, square roots and powers Exercise 4.4 Question 2 4.4: Square numbers, square roots and powers Example 3 (p. 148) Exercise 4.4 Questions 2, 7, 8, 12 Using your calculator p. 149 Questions 1, 2, 7 – 9, 12, 13 4.6: Finding prime factors Examples 1 – 5 (pp. 157 – 161) Exercise 4.6 4.6: Finding prime factors Examples 4, 5 (pp. 160 – 161) Exercise 4.6 Questions 5, 6 4.3: Square numbers, square roots and powers Example 1 (p. 147) Examples 7, 8 (p. 150) Exercise 4.3 Questions 7, 8, 9, 12 Structure 4.25 5.0 They extend linear number patterns and give a general formula using symbols and/or words such as 3, 7, 11 start with 3 and add 4 to get the next term. They test the validity of statements formed by the use of the connectives and, or, not, and the quantifiers none, some and all, (for example, ‘some 4.7: Investigating number sequences Exercise 4.7 Question 5 4.1: Multiples Common multiples p. 133 Example 2 (p. 134) VELS curriculum links (by chapter) 7 Level Working mathematically 4.0 4.25 Standard/Progression point natural numbers can be expressed as the sum of two squares’). MathsWorld 7 Exercise 4.1 Question 5 4.2: Factors Common factors p. 139 Example 2 (p. 140) Exercise 4.2 Question 3 They use calculators and computers to investigate and implement algorithms (for example, for finding the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform shapes and solids. Students develop generalisations inductively, from examples such as angle sums in triangles. 4.5: Prime numbers Exercise 4.5 Questions 7 – 9, 13 4.7: Looking at number sequences Exercise 4.7 Question 2 Analysis task 2: How many candles single step rules 4.25 They find patterns and relationships by looking at examples and recording the outcomes systematically. 4.25 Students extend mathematical arguments, such as finding angle sum of a pentagon by extending the argument that angle sum of quadrilateral is 360° because it can be split into two triangles. They explain mathematical relationships by extending patterns. 4.25 5.0 Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. 4.7: Investigating number sequences Exercise 4.7 Questions 6, 7 Analysis task 1: Adding odd integers Analysis task 2: How many candles? Warm-up: Pascal's Triangle Try This! p. 131 4.7: Looking at number sequences Exercise 4.7 Questions 1 – 8 Analysis task 1: Adding odd integers Analysis task 2: How many candles Analysis task 2: How many candles? part h (p. 170) 4.7: Looking at number sequences Exercise 4.7 Analysis task 1: Adding odd integers Analysis task 2: How many candles 4.7: Looking at number sequences Exercise 4.7 Question 2 Analysis task 2: How many candles VELS curriculum links (by chapter) 8 Chapter 5 Algebra: expressions and relationships Level Structure Standard/Progression point MathsWorld 7 4.0 Students construct and use rules for sequences based on the previous term, recursion (for example, the next term is three times the last term plus two), and by formula (for example, a term is three times its position in the sequence plus two). Students establish equivalence relationships between mathematical expressions using properties such as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)). They determine the independent variable and specify the allowable values for both variables when describing a function relating two variables. 5.8: Using rules to solve problems Example 1 (p. 215) Exercise 5.8 Questions 1 – 8 4.0 4.25 4.25 4.25 Students interpret an algebraic letter as a number and not an object or abbreviation. They express relationships algebraically, such as there are n biscuits in a packet therefore there are 2 x n biscuits in two packets. 4.25 They observe generality in a number pattern and express it verbally or algebraically, such as square numbers 1, 4, 9, 16, 25 generalises to n x n . 4.25 They extend linear number patterns and give a general formula using symbols and/or words such as 3, 7, 11 start with 3 and add 4 to get the next term. They recognise equivalence between simple equivalent expressions, such as a + a + a = 3 x a = 3a. 4.25 Working mathematically 4.25 5.0 They identify relevant variables (independent and dependent) in real situations. They substitute numbers for variables (for example, in equations, inequalities, identities and formulas). 5.2: Combining expressions Examples 1 – 3 (pp. 184 – 185) Exercise 5.2 Questions 1 – 9 5.3: Using rules to make tables Try this! p. 187 Example 1 (p. 188) (Independent and dependent are represented as Input and Output numbers in MathsWorld 7, with formal introduction of the concept of independent and dependent variables in MathsWorld 8. 5.8: Using rules to solve problems Example 1 (p. 215) Exercise 5.8 Questions 1 – 8 5.1: Introduction to variables Examples 1, 2, 3 (pp. 178 – 179) 5.1: Introducing variables Examples 2, 3 (pp. 180 – 181) Exercise 5.1 Questions 1 – 12 5.2: Combining expressions Try this! p. 183 5.8: Using rules to solve problems Example 1 (pp. 215 – 216) Exercise 5.8 Questions 1 – 9 Analysis task 1: Tom and Tori's towers Analysis task 2: Shape animals 5.4: Finding single step rules Exercise 5.4 Questions 1, 2, 4, 5, 5.1: Introduction to variables Example 3 (p. 181) 5.2: Combining expressions Try this! p. 183 Examples 1, 2 (pp. 183 – 184) Exercise 5.2 Questions 1 – 9 5.8: Using rules to solve problems Example 1 (p. 215) Exercise 5.8 5.1: Introduction to variables Examples 1 – 3 (pp. 179 – 181) Exercise 5.1 Questions 1 – 12 5.2: Combining expressions Example 2 (p. 184) Exercise 5.2 Questions 1 – 12 5.3: Using rules to make tables VELS curriculum links (by chapter) 9 Level Standard/Progression point 5.0 Students develop simple mathematical models for real situations (for example, using constant rates of change for linear models). 5.0 They develop generalisations by abstracting the features from situations and expressing these in words and symbols. 5.0 Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. MathsWorld 7 Exercise 5.3 Questions 1 – 15 5.4: Finding single-step rules Exercise 5.4 Questions 4, 7 5.6: Substituting several input numbers into rules and expressions Try this! p. 205 Examples 1, 2 (pp. 206) Exercise 5.6 Questions 1 – 9 5.8: Using rules to solve problems Example 1 (pp. 215 – 216) Exercise 5.8 Questions 1 – 8 5.8: Using rules to solve problems Example 1 (pp. 215 – 216) Exercise 5.8 Questions 1 – 8 Analysis task 3: Phone cards 5.8: Using rules to solve problems Example 1 (pp. 215 – 216) Exercise 5.8 Questions 1 – 9 5.3: Using rules to make tables Exercise 5.3 Questions 8, 9, 10 5.4: Finding single step rules Exercise 5.4 Question 8 VELS curriculum links (by chapter) 10 Chapter 6 Fractions Level Number Standard/Progression point MathsWorld 7 4.0 They model integers (positive and negative whole numbers and zero), common fractions and decimals. 4.0 They place integers, decimals and common fractions on a number line. Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, ¾ = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money. * Chapter pre-test Questions 1, 2 Warm-up p. 229 6.1: What is a fraction? Exercise 6.1 Questions 1 – 6, 13 6.1: What is a fraction? Exercise 6.1 Question 7 6.1: What is a fraction? Exercise 6.1 Questions 9 – 16 4.0 4.0 4.0 They create sets of number multiples to find the lowest common multiple of the numbers. 4.25 They describe ratio as a comparison of either subset to subset (part to part) or subset to set (part to whole), using simple whole number ratios. 5.0 They write equivalent fractions for a fraction given in simplest form (for example, 2/3 = 4/6 = 6/9 = … ). They evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9). 5.0 5.0 They calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √(9/16) = ¾). 5.0 They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy. 5.0 Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. * Chapter pre-test Questions 8 – 10 6.4: Adding and subtracting proper fractions Exercise 6.4 Questions 1 – 3 6.5: Adding and subtracting mixed number fractions Exercise 6.5 Questions 1 – 2 6.6: Multiplying fractions Exercise 6.6 Questions 1, 5 6.3: Common denominators and comparing fractions Example 2 (p. 245) – see Reasoning column) Analysis task 1: Lotus flowers This analysis task provides an introduction to the concept of ratio as subset: subset fractions and subset: whole fractions 6.1: What is a fraction? Examples 1, 2 Exercise 6.1 Questions 8 – 13 6.8: Squares and square roots of fractions Examples 1 (p. 264) Exercise 6.8 Questions 1, 2 6.8: Squares and square roots of fractions Examples 1, 2 (p. 264) Exercise 6.8 Questions 1 – 6 6.7 Dividing fractions Try this! (p. 261) Examples 1, 2 (p. 262) Exercise 6.7 * Chapter pre-test Questions 8 – 10 6.4: Adding and subtracting proper fractions Exercise 6.4 Questions 1 – 3 6.5: Adding and subtracting mixed number fractions Exercise 6.5 Questions 1 – 2 6.6: Multiplying fractions Exercise 6.6 Questions 1, 5 Structure 4.0 They use Venn diagrams and Karnaugh maps to test the validity of statements using the words none, 6.3: Common denominators and comparing fractions VELS curriculum links (by chapter) 11 Level 5.0 Working mathematically 4.25 Standard/Progression point some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even numbers’). They recognise and use inequality symbols. MathsWorld 7 Try this! p. 244 They find patterns and relationships by looking at examples and recording the outcomes systematically. Analysis task 2: Mixed number multiplication patterns Analysis task 3: Equivalent fractions from graphs 6.3: Common denominators and comparing fractions Example 1 (p. 245) Exercise 6.3 Question3 VELS curriculum links (by chapter) 12 Chapter 7 Polygons Level Space Standard/Progression point MathsWorld 7 4.0 At Level 4, students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater than 90°), and surfaces. 4.0 They develop and follow instructions to draw shapes and nets of solids using simple scale. 4.0 They identify congruent shapes and solids when appropriately aligned. 4.25 Students use a wide range of geometric language correctly when describing or constructing shapes and solids. 4.5 Students apply properties of angles and lines in two dimensions, such as calculate angles of an isosceles right-angle triangle or finding all the angles of a symmetric trapezium from one angle. 4.5 They identify congruent shapes and objects, using mental rotation or reflection. Students apply properties of angles, lines and congruence in two dimensions, such as explaining why shapes will not tessellate if no combination of angles adds to 360o. At Level 5, students construct two-dimensional and simple three-dimensional shapes according to specifications of length, angle and adjacency. * Chapter pre-test Questions 1 – 10 7.1: Triangles Types of triangles (p. 283) Exercise 7.1 Questions 2, 8 7.2: Quadrilaterals Exercise 7.2 Questions 1 – 5 7.3: Polygons Exercise 7.3 Question 1 7.1: Triangles Examples 5, 6 (pp. 284 – 285) Try this! p. 284 Exercise 7.1 Questions 3 – 6 7.2: Quadrilaterals Exercise 7.2 Questions 14, 16 7.3: Polygons Exercise 7.3 Questions 13, 14 7.1: Triangles Congruent triangles p. 281 Analysis task 1: Tangram 7.1: Triangles Exercise 7.1 Questions 1, 2, 8, 13 7.2: Quadrilaterals Try this! p. 293 Exercise 7.2 Questions 7, 8, 11 7.3: Polygons Exercise 7.3 Questions 1, 4, 5, 7, 11, 12, 13 7.1 Triangles Examples 3, 4 (p. 282) Exercise 7.1 Questions 10, 12 – 14 7.2: Quadrilaterals Example 2 (p. 296) Exercise 7.2 Questions 5, 8, 12, 13, 15 7.3: Polygons Analysis task 2: Drawing polygons in MicroWorlds Analysis task 3: Polygon seats Analysis task 1: Tangram 4.5 5.0 5.0 They describe and apply the angle properties of regular and irregular polygons, in particular, triangles and quadrilaterals. Section 7.3 Polygons Try this! p. 301 Exercise 7.3 Question 8 7.1: Triangles Example 2 (p. 282) Exercise 7.1 Questions 3, 6, 9, 11 7.2 Quadrilaterals Exercise 7.2 Questions 6, 9, 10 7.3: Other polygons Exercise 7.3: Question 14 Analysis task 2: Drawing polygons in MicroWorlds 7.1: Triangles Examples 3, 4, 6 7.2: Quadrilaterals Example 1 (p. 291), example 2 (p. VELS curriculum links (by chapter) 13 Level Standard/Progression point MathsWorld 7 297) Exercise 7.2 Questions 5, 8 Exercise 7.3 Questions 2, 3, 6, 7 7.3: Polygons Examples 1 – 3 Exercise 7.3 Questions 2, 3, 6, 7 5.0 They recognise congruence of shapes and solids. 7.1: Triangles Exercise 7.1 Question 8 7.2: Quadrilaterals Exercise 7.2 Questions 2 – 4 They test the validity of statements formed by the use of the connectives and, or, not, and the quantifiers none, some and all, (for example, ‘some natural numbers can be expressed as the sum of two squares’). 7.2: Quadrilaterals Try this! pp. 292 – 293 Exercise 7.2: Question 11 At Level 4, students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers). Students develop generalisations inductively, from examples such as angle sums in triangles. 7.2: Quadrilaterals Try this! p. 289 Exercise 7.2 Question 7 Analysis task 3: Polygon seats Structure 5.0 Working mathematically 4.0 4.25 4.5 4.5 5.0 5.0 Students extend mathematical arguments, such as finding angle sum of a pentagon by extending the argument that angle sum of quadrilateral is 360° because it can be split into two triangles. Students use computer drawing tools, such as MS Word, Geometer’s Sketchpad, MicroWorlds and Cabri Geometry, to explore geometric situations. At Level 5, students formulate conjectures and follow simple mathematical deductions (for example, if the side length of a cube is doubled, then the surface area increases by a factor of four, and the volume increases by a factor of eight). Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. 7.1: Triangles Angles of a triangle Try this! p. 281 7.2: Quadrilaterals Angles of a quadrilateral Try this! p. 290 7.3: Polygons Example 1 (p. 303) Exercise 7.3 Questions 2, 5, 6 7.1: Triangles Exercise 7.1 Question 9 7.2: Quadrilaterals Exploring parallelograms with MicroWorlds Exercise 7.2 Questions 9, 10 Analysis task 2: Drawing polygons in MicroWorlds 7.3: Polygons Sum of the angles of polygons pp. 302 – 304 7.1: Triangles Exercise 7.1 Question 9 7.2: Quadrilaterals Exploring parallelograms with MicroWorlds Exercise 7.2 Questions 9,10 Analysis task 2: Drawing polygons in MicroWorlds VELS curriculum links (by chapter) 14 Chapter 8 Decimals Level Number Standard/Progression point MathsWorld 7 4.0 At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions). They place integers, decimals and common fractions on a number line. Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, ¾ = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money. * Chapter pre-test Question 4 8.1: Place value Exercise 8.1 8.1: Place value Exercise 8.1 Questions 5, 6 * Chapter pre-test Question 5 8.13: Percentages, decimals and fractions Exercise 8.13 Questions 1 – 6 * Chapter pre-test Question 7, 8 8.5: Multiplication and division by powers of 10 Exercise 8.5 Questions 1 – 6 8.6: Adding and subtracting decimals Try this! p. 344 Exercise 8.6 Questions 1 a – d, 3 a – c, 5, 6 8.7: Multiplication by a whole number Exercise 8.7 Questions 1, 2, 8, 10 * Chapter pre-test Question 6 8.8: Multiplication of a decimal by a decimal Students should be encouraged to check their answers as demonstrated in Examples 1 – 3 (pp. 352 – 353) * Chapter pre-test Questions 9, 10 8:5: Multiplication and division by powers of 10 Exercise 8.5 Questions 1 - 9 8.2: Comparing decimals Exercise 8.2 Questions 3c, d 8:5: Multiplication and division by powers of 10 Number slides (p. 336) Exercise 8.5 Questions 1 - 9 8.12: Dividing a decimal by a decimal Try this! p. 363 See also Practice and Enrichment Worksheet 2, Question 14 (P & E Workbook, pp. 76 – 77) 8.10: Dividing by a whole number Examples 1 – 3 (pp. 358 – 359) Exercise 8.10 8:12: Dividing a decimal by a decimal Examples 1, 2 (pp. 363 – 364) Students should be encouraged to apply this type of checking to all calculations, including when using a calculator. 8.10: Dividing by a whole number Examples 1 – 3 (pp. 358 – 359) Exercise 8.10 Questions 1 – 8 8.13: Percentages, decimals and 4.0 4.0 4.0 4.0 They use estimates for computations and apply criteria to determine if estimates are reasonable or not. 4.25 Students multiply by powers of 10, link division by powers of 10 to multiplication by decimals and use these in estimation. 4.25 They know that the position of the digit zero affects the size of numbers, such as 00.070 = 0.07. 4.25 They explain dividing by a number between one and zero, such as dividing by 0.1 is finding out how many tenths. 4.25 Students use mental estimation to check the result of calculator computations. 4.25 They use written and/or mental methods to divide decimals by single digit whole numbers, interpreting the remainder. Students convert between fraction, decimal and 4.25 VELS curriculum links (by chapter) 15 Level Standard/Progression point percentage forms, and use them to calculate and estimate, such as estimate 63% of 300 by finding two thirds. 4.5 They divide by powers of 10, and multiplication by powers of 10, in mental estimation, such as 30 ÷ 0.01 is the same as 30 x 100 = 3000. 4.5 They estimate the square roots of whole numbers using nearby perfect squares. Students use equal multiplication by 10 to divide by decimals, such as 0.24 ÷ 0.04 = 24 ÷ 4 = 6. 4.75 4.75 They use a range of strategies for estimating multiplication and division calculations with decimals, fractions and integers. 4.75 They convert between decimals, ratios, fractions and percentages, such as compare 3 out of 4 to 5 out of 7. They know the decimal equivalents for the unit fractions ½, 1/3, ¼, 1/5, 1/8, 1/9 and find equivalent representations of fractions as decimals, ratios and percentages (for example, a subset: set ratio of 4:9 can be expressed equivalently as 4/9 = 0.4 ≈ 44.44%). 5.0 5.0 5.0 5.0 Students use knowledge of perfect squares when calculating and estimating squares and square roots of numbers (for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30). They calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √(9/16) = ¾). Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. MathsWorld 7 fractions Examples 1, 2 (p. 367) Exercise 8.13 Questions 1 – 9 Analysis task 1: Dad goes shopping 8.5: Multiplication and division by powers of 10 Examples 1, 2 (pp. 340, 341) Exercise 8.5 Questions 1 – 11 Analysis task 3: Approximate square roots 8.12: Dividing a decimal by a decimal Example 1 (p. 363), Example 2 (p. 364) Exercise 8.12 Questions 1, 2 8.7: Multiplication by a whole number Examples 1 – 3 Exercise 8.7 Question 7 8.12: Dividing a decimal by a decimal See check in Example 1, p. 363; example 2, p. 364 8.13: Percentages, decimals and fractions Exercise 8.13 8.11: Recurring decimals and changing fractions to decimals Example 1 (p. 361) Exercise 8.11 Questions 1, 5 8.13: Percentages, decimals and fractions Examples 1, 2 (p. 367) Exercise 8.13 Analysis task 3: Approximate square roots 8.9: Squares and square roots of decimals Examples 1, 2 (p. 356) Exercise 8.9 Questions 1 – 9 * Chapter pre-test Question 7, 8 8.5: Multiplication and division by powers of ten Exercise 8.5 Questions 1 – 6 8.6: Adding and subtracting decimals Exercise 8.6 Questions 1 a – d, 3 a – c, 5, 6 8.7: Multiplication by a whole number Exercise 8.7 Questions 1, 2, 8, 10 Structure 5.0 They recognise and use inequality symbols. 8.2: Comparing decimals Example 1 (p. 325) Exercise 8.2 Question 2 VELS curriculum links (by chapter) 16 Chapter 9 Units: length, mass and time Level Measurement, chance and data 4.0 Standard/Progression point MathsWorld 7 At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity time and temperature. 4.0 They convert between metric units of length, capacity and time (for example, L–mL, sec–min). 4.5 Students extend their range of personal benchmarks for estimating quantities, such as how far one can drive in an hour or one litre of water weighs 1 kg. They calculate with time, including using bus timetables to determine duration of a trip. * Chapter pre-test Questions 1 – 7 9.1: Units Try this! p. 380 Exercise 9.1 * Chapter pre-test Questions 3, 6 9.2: Length Try this! p.388 Examples 1, 2 (p. 388) Exercise 9.2 Questions 1, 2 9.4: Time calculations Examples 1 – 6 (p. 399 – 401) Exercise 9.4 Questions 1 – 15 9.3: Mass Exercise 9.3 Question 3 4.5 4.75 Students convert between a wide range of metric units. 4.75 They can calculate with time using a calculator. 5.0 At Level 5, students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. Working mathematically 5.0 Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. 9.5 Time and travel Example 1 Exercise 9.5 Questions 1 - 15 Analysis task 1: Coach to Warrnambool 9.3: Mass Try this! p. 392 Example 1 (p. 393) Exercise 9.3 Questions 3, 5 – 8, 11, 14, 15 9.4: Time calculations Example 2 (p. 399) Exercise 9.4 Questions 13, 15 All sections and analysis tasks Analysis task 3: Celsius and Fahrenheit temperatures VELS curriculum links (by chapter) 17 Chapter 10 Take a chance! Level Measurement, Chance and Data 4.0 Standard/Progression point MathsWorld 7 Students describe and calculate probabilities using words, and fractions and decimals between 0 and 1. 4.0 They calculate probabilities for chance outcomes (for example, using spinners) and use the symmetry properties of equally likely outcomes. They simulate chance events (for example, the chance that a family has three girls in a row) and understand that experimental estimates of probabilities converge to the theoretical probability in the long run. * Chapter pre-test Questions 4 – 6 10.1: The language of chance Try this! p. 425 Example 1 Exercise 10.1 10.2: Predicting probability Example 1 Exercise 10.2 Questions 1, 2, 3 10.3: Theoretical versus long run probability Try this! p. 440 Example 1 (p. 441) Try this! p. 442 Exercise 10.3 Questions 4, 5 10.1: The language of chance Examples 2, 3 (p. 430) Example 6 (p. 434) Exercise 10.2 Questions 1, 2, 4, 13 10.3: Theoretical versus long-run probability Example 10.3 Questions 1 - 6 10.2: Predicting probability Exercise 10.2 Question 11 10.3: Theoretical versus long-run probability Exercise 10.3 Question 3 10.3: Theoretical versus long-run probability Try this! p. 442 Exercise 10.3 Questions 1 – 3 10.3: Theoretical versus long-run probability Exercise 10.3 Questions 1 – 7 10.2: Predicting probability Examples 1 – 4 (pp. 428 – 432) Exercise 10.2 Questions 1 – 10 10.2: Predicting probability Example 5 (pp. 432 – 433) Exercise 10.2 Questions 13 – 15 4.0 4.25 Students systematically list outcomes for a multiple event experiment such as getting at least one tail if a coin is tossed three times. 4.25 They can identify empirical probability as long-run relative frequency including random number generator to simulate rolling two dice. 4.25 They design simulations for simple chance events, such as designing a spinner to simulate a probability of two out of five. 5.0 Students use appropriate technology to generate random numbers in the conduct of simple simulations. 5.0 Students identify empirical probability as long-run relative frequency. 5.0 They calculate theoretical probabilities by dividing the number of possible successful outcomes by the total number of possible outcomes. They use tree diagrams to investigate the probability of outcomes in simple multiple event trials. 5.0 Working mathematically 4.0 4.0 They understand that a few successful examples are not sufficient proof and recognise that a single counter-example is sufficient to invalidate a conjecture. For example, in: number (all numbers can be shown as a rectangular array) computations (multiplication leads to a larger number) number patterns ( the next number in the sequence 2, 4, 6 … must be 8) shape properties (all parallelograms are rectangles) chance (a six is harder to roll on die than a one). They use calculators and computers to investigate and implement algorithms (for example, for finding 10.3: Theoretical versus long run probability Exercise 10.3 Question 7 10.3: Theoretical versus long run probability VELS curriculum links (by chapter) 18 Level 4.5 5.0 Standard/Progression point the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform shapes and solids. They independently plan and carry out an investigation with several components and report the results clearly using mathematical language. Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. MathsWorld 7 Try this! p. 442 Exercise 10.3 Questions 1 – 3 10.3: Theoretical versus long run probability Exercise 10.3 Question 3 10.3: Theoretical versus long-run probability Simulation Try this! p. 442 Exercise 10.3 Questions 1 – 3 VELS curriculum links (by chapter) 19 Chapter 11 Solving equations Level Structure Standard/Progression point MathsWorld 7 4.0 They use words and symbols to form simple equations. 4.0 They solve equations by trial and error. 4.0 Students recognise that addition and subtraction, and multiplication and division are inverse operations. 4.5 They solve linear equations using tables of values and a series of inverse operations, including backtracking, such as 3m – 14 = 20, 2(3m – 14) + 8 = 48). They solve simple equations (for example, 5x+ 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations. Chapter pre-test Questions 5, 6 Warm-up Try this! p. 457 11.2: Solving equations: Arithmetic strategies Exercise 11.2 Questions 10 – 15 11.2: Solving equations: Arithmetic strategies Examples 1, 2 (pp. 462 – 463) Exercise 11.2 Questions 1 – 18 11.3: Solving equations: flow charts Try this! p. 467, 468 Examples 1, 2 (pp. 470 – 471) Exercise 11.3 11.3: Solving equations: flowcharts Examples 1, 2 (pp. 469 – 470) Exercise 11.3 Questions 1 – 19 5.0 Working mathematically 5.0 5.0 Students develop simple mathematical models for real situations (for example, using constant rates of change for linear models). Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. 11.5: Solving equations: Doing the same to both sides Examples 1 – 9 (pp. 484 – 488) Exercise 11.5 Questions 1 – 15 Analysis task 1: Carly's jeans Analysis task 3: Travelling overseas 11.2: Solving equations: arithmetic strategies Exercise 11.2 Question 9 VELS curriculum links (by chapter) 20 Chapter 12 Perimeter, area and volume Level Number Standard/Progression point MathsWorld 7 5.0 They use approximations to π in related measurement calculations (for example, π × 52 = 25π = 78.54 correct to two decimal places). They use technology for arithmetic computations involving several operations on rational numbers of any size. 12.2: Circumference of a circle Examples 1 – 3 (pp. 519 – 520) Exercise 12.2 At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity time and temperature. * Chapter pre-test Questions 1 – 10 12.1: Perimeter Try this! p. 509 Examples 1, 2 (pp. 510, 511) Exercise 12.1 Question 1 12.3: Area: Rectangles Examples 1 – 6 pp. 524, 525 Exercise 12.3 Questions 1 – 4 12.5: Volume Try this! p. 540 Examples 1, 2 (p. 543) Exercise 12.5 Questions 1 – 4 12.2: Circumference of a circle Try this! p. 518 12.5: Volume Exercise 12.5 Question 5 12.6: Capacity Exercise 12.6 Questions 2, 6, 8, 12 12.1: Perimeter Try this! p. 509 Include further school-based activities 12.1: Perimeter Try this! (p. 510) Examples 2, 3 (p. 511) 12.2: Circumference of a circle Examples 5, 6 (pp. 526) Exercise 12.3 Questions 3, 4 12.4: Area: Parallelograms and triangles Examples 1 – 3 (pp. 533 – 5) Exercise 12.4 Questions 12.3: Area: rectangles Example 7 (p. 527) Exercise 12.3 Questions 11, 13, 14 12.4: Area: Parallelograms and triangles Exercise 12.4 Questions 6 – 15 12.6: Capacity Exercise 12.6 Question 1 5.0 Measurement, Chance and Data 4.0 4.0 They measure as accurately as needed for the purpose of the activity. 4.0 They convert between metric units of length, capacity and time (for example, L–mL, sec–min). Students estimate length, perimeter, area of rectangles and time providing suitable lower and upper bounds for estimates. 4.25 4.25 They use measurement formulas for perimeter and area of a rectangle and use correct units. 4.5 They use measurement formulas for the area and perimeter of triangles and parallelograms. 4.5 They calculate areas of simple composite shapes, such as the floor area of a house. 4.5 Students extend their range of personal benchmarks for estimating quantities, such as how far one can drive in an hour or one litre of water weighs 1 kg. They explain the links between metric units such as mL and cm3, 1 litre of water and 1 kg. 4.75 4.75 Students convert between a wide range of metric units. Most questions in all exercises 12.6: Capacity Example 1 Exercise 12.6 Questions 3 – 5, 7, 9 – 11, 13, 15 12.3: Area: Rectangles Area units (p. 524) VELS curriculum links (by chapter) 21 Level Standard/Progression point 4.75 They use measurement formulas for the area and circumference of circles and composite shapes. 4.75 They explain the links between the area of a rectangle with areas of triangles, parallelograms and trapezia, including demonstrating how the area of a given non-right-angle triangle is half the area of a rectangle with same base and height. At Level 5, students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. They interpret and use measurement formulas for the area and perimeter of circles, triangles and parallelograms and simple composite shapes. 5.0 5.0 5.0 They calculate the surface area and volume of prisms and cylinders. MathsWorld 7 Exercise 12.3 Question 1 12.2: Circumference of a circle Try this! p. 518 Examples 1 – 3 (pp. 519 – 520) Exercise 12.2 12.4: Area: Parallelograms and triangles Area of parallelograms (p. 533) Area of triangles (p. 534) Exercise 12.4 Questions 2, 3, 4 All sections and analysis tasks 12.1: Perimeter 12.2: Circumference of a circle 12.3: Area: Rectangles 12.4: Area: Parallelograms and triangles Analysis task 1: Paint calculator Analysis task 2: Paint calculator Analysis task 3: Paper sizes 12.5: Volume 12.6: Capacity Structure 5.0 Working mathematically 4.25 5.0 5.0 Students use inverses to rearrange simple mensuration formulas, and to find equivalent algebraic expressions (for example, if P = 2L + 2W, then W = P/2 − L. If A = πr2 then r = √A/π). 12.2: Circumference of a circle Example 2 Exercise 12.2 Question 15 They find patterns and relationships by looking at examples and recording the outcomes systematically. At Level 5, students formulate conjectures and follow simple mathematical deductions (for example, if the side length of a cube is doubled, then the surface area increases by a factor of four, and the volume increases by a factor of eight). Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. Analysis task 3: Paper sizes 12.3: Area: rectangles Exercise 12.3 Question 7 12.5: Volume Exercise 12.4 Question 9 12.2: Circumference of a circle Try this! p. 518 12.3: Area: Rectangles Exercise 12.3 Question 6 12.4: Area: Parallelograms and triangles Cabri HTML: Area of a parallelogram; Area of a triangle VELS curriculum links (by chapter) 22 Chapter 13 Maps, coordinates and directions Level Space Standard/Progression point MathsWorld 7 4.0 They develop and follow instructions to draw shapes and nets of solids using simple scale. Students use the ideas of size, scale, and direction to describe relative location and objects in maps. 13.1: Scale drawings Exercise 13.1 Questions 10, 11, 13 * Chapter pre-test Questions 1, 4 13.1: Scale drawings Example 1 (p. 564) Exercise 13.1 Questions 1 – 4 13.3: Locating direction Examples 1 – 4 (pp. 584 – 585) Try this! p. 582 * Chapter pre-test Questions 5 – 7 13.3: Locating direction Analysis task 1: Tower Hill Analysis task 2: Cycling on French Island 13.2: Locating position Try this! (pp. 573 – 574) Examples 1, 2 Exercise 13.2 Questions 3 – 11 13.2: Locating position Highlight box p. 574 Try this! pp. 572, 573 Exercise 13.2 Questions 1 – 11 13.3: Locating position Try this! p. 573 Try this! p. 574 Example 1 (p. 575) Exercise 13.3 Questions 3 – 10 Analysis task 2: Coordinate tracks 13.1: Scale drawings Examples 1 – 5 (pp. 564 – 565) Exercise 13.1 Questions 1 – 13 4.0 4.0 They use compass directions, coordinates, scale and distance, and conventional symbols to describe routes between places shown on maps. 4.25 Students identify points in the first quadrant of the plane using co-ordinates. 4.25 They distinguish between a coordinate naming a point and a map reference such as D12 naming a region. 4.25 Students accurately identify points in any quadrant of the plane or on a map by interpolating between labelled coordinates. 4.25 They use scales on maps and plans, whether presented graphically or as comparison of units such as 1cm = 1km, or as a ratio such as 1:100000, to accurately convert between map measurements and real distances. Students use coordinates to identify position in the plane. 5.0 5.0 They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. 13.2: Locating position Exercise 13.2 Questions 3 – 15 Analysis task 3: Coordinate tracks 13.3: Locating direction Examples 1 – 4 Exercise 13.3 Questions 1 – 12 Analysis task 1: Tower Hill Analysis task 2: Cycling on French Island Structure 4.5 Working mathematically 4.5 4.5 Students use functions such as when sharing a 60 cm strap of liquorice among friends, the length of liquorice each gets is 60 cm divided by number of friends, L = 60/n described in words or symbols to create a table of values and plot points to make a graph. 13.2: Locating position Example 3 (pp. 576 - 577) Exercise 13.2 Questions 14, 15 They explain mathematical relationships by extending patterns. They identify situations with constant rate of change and represent with a linear graph, such as 13.2: Locating position Exercise 13.2 Questions 14, 15 13.2: Locating position Example 3 (pp. 576 – 577) VELS curriculum links (by chapter) 23 Level 5.0 5.0 Standard/Progression point taxi fares. Students develop simple mathematical models for real situations (for example, using constant rates of change for linear models). Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. MathsWorld 7 Exercise 13.2 Questions 14, 15 13.2: Locating position Example 3 (p. 576) Exercise 13.2 Questions 14, 15 13.1: Scale drawings Exercise 13.1 Question 13 VELS curriculum links (by chapter) 24 Chapter 14 Making sense of data Level Measurement, chance and data 4.0 Standard/Progression point MathsWorld 7 Students recognise and give consideration to different data types in forming questionnaires and sampling. 4.0 They distinguish between categorical and numerical data and classify numerical data as discrete (from counting) or continuous (from measurement). They present data in appropriate displays (for example, a pie chart for eye colour data and a histogram for grouped data of student heights). 14.1: Types of data Try this! p. 601 Exercise 14.1 Question 4 Analysis task 3: The class survey 14.1: Types of data Examples 1, 2 (pp. 602, 603) Exercise 14.1 Questions 1 – 3 * Chapter pre-test Question 4 14.3: Displaying and interpreting data in graphs Example 2 (p. 613) Exercise 14.3 Questions 1, 3 * Chapter pre-test Questions 3, 5, 6 14.4: Summarising data: Measures of centre Examples 1, 2, 3 (pp. 623 – 625) Exercise 14.4 Questions 1 – 10 14.2: Collecting and recording data Example 2 (p. 606) Exercise 14.2 Questions 3, 4, 5 14.5: Summarising data: visually Examples 1, 2, 3 (pp. 629 – 634) Exercise 14.5 Questions 1 – 12 14.4: Summarising data Examples 1 – 4 (pp. 623 – 625) Exercise 14.4 Questions 1 – 10 4.0 4.0 They calculate and interpret measures of centrality (mean, median, and mode) and data spread (range). 4.25 Students organise and tabulate univariate data, including grouped and ungrouped, continuous and discrete. Students represent uni-variate data in appropriate graphical forms such as stem and leaf plots, bar charts and histograms. They calculate mean, median, mode and range for ungrouped data and make simple inferences. 4.5 4.5 Working mathematically 4.25 5.0 Students use a spreadsheet as a database, to sort and categorise data and generate statistical graphs. Students use technology such as graphic calculators, spreadsheets, dynamic geometry software and computer algebra systems for a range of mathematical purposes including numerical computation, graphing, investigation of patterns and relations for algebraic expressions, and the production of geometric drawings. Warm-up: The First Fleet database 14.3: Displaying and interpreting data in graphs Exercise 14.3 Questions 3, 11 Analysis task 1: Which were the best AFL teams in 2005 Chapter Warm-up Try this! p. 600 14.5: Summarising data: visually Exercise 14.5 Question 1, 6, 7 Analysis task 1: Which were the best AFL teams in 2005? VELS curriculum links (by chapter) 25