Heinemann Maths Zone 7 VELS Edition: Teaching and Assessment Program

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Heinemann Maths Zone 7 VELS Edition: Teaching and Assessment Program

This Teaching and Assessment Program (TAP) is presented to assist teachers in planning their school’s courses, and to demonstrate that a program incorporating the Victorian Essential Learning Standards (VELS) may be constructed using the curriculum package of resources published by Heinemann. There are three versions (A, B and C) provided for Years 9 and 10, while the Years 7 and 8 format involves core, background and extension. The TAPs for the other year levels are available on this website. The Heinemann Maths Zone 7 VELS Edition fully integrates VELS Design tasks, graphics calculator and computer material.

Summary

The following table shows the outline of Heinemann Maths Zone 7 VELS Edition TAP.

Unit no.Unit titleLength in weeks

1Whole numbers3

2Number patterns3

3Fractions4

4Decimals4

5Measurement4

6Algebra4

7Angles3

8Equations4

9Shapes3

10Chance and data4

Abbreviations

The following abbreviations have been used in the Year 7 TAP grids:

B = Background

C = Core (note: in the course description the material is core unless otherwise marked)

E = Extension

VELS = Victorian Essential Learning Standards

VELS standard

The appropriate parts of the standards are included. The VELS correlation grid and the audit appear both on this website and at the front of the Heinemann Maths Zone 7 VELS Edition.

Heinemann references

MZ7 refers to the textbook Heinemann Maths Zone 7 VELS Edition.

Assessment

FT7 refers to questions on Heinemann Maths Zone 7 VELS Edition FlexiTest. Specific section references are provided.

Unit1: Whole numbersDimensions: Number; Working mathematicallyTime: 3 weeks

VELS standard / Course / Heinemann references / Assessment
Number problems
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / B Whole number problems / MZ7 p.8 (1.2) / B FT7 1.2 Short answer
B FT7 1.2 Multiple choice
C FT7 1.2 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / B Magic squares / MZ7 p.16 (1.3) / C MZ7 VELS Design task p.18
B FT7 1.3 Short answer
C FT7 1.3 Multiple choice
C FT7 1.3 Applications and analysis
Students develop simple mathematical models for real situations (e.g. using constant rates of change for linear models). They develop generalisations by abstracting the features from situations and expressing these in words and symbols. They predict using interpolation (working with what is already known) and extrapolation (working beyond what is already known). They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context. / Problems / MZ7 p.15 (Investigation)
MZ7 p.32 (Problem solving)
MZ7 p.40 (Investigation)
They solve simple equations (e.g. 5x + 7 = 23, 1.4x – 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations. / Number sentences / MZ7 p.36 (1.8) / C FT7 1.8 Short answer
C FT7 1.8 Multiple choice
C FT7 1.8 Applications and analysis
Estimating
Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (e.g. 925 ÷ 34 ≈ 900÷30=30). / Estimating and rounding / MZ7 p.21 (1.5)
MZ7 p.28 (Investigation)
MZ7 p.33 (Investigation) / C FT7 1.5 Short answer
C FT7 1.5 Multiple choice
C FT7 1.5 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.
Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (e.g. 925 ÷ 34 ≈ 900÷30=30). / B Mental maths strategies / MZ7 p.34 (1.7) / B FT7 1.7 Short answer
B FT7 1.7 Multiple choice
C FT7 1.7 Applications and analysis
Calculations
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Division / MZ7 p.19 (1.4) / C FT7 1.4 Short answer
C FT7 1.4 Multiple choice
C FT7 1.4 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Order of operations / MZ7 p.29 (1.6) / C FT7 1.6 Short answer
C FT7 1.6 Multiple choice
C FT7 1.6 Applications and analysis

Unit2: Number patternsDimensions: Number; Working mathematicallyTime: 3 weeks

VELS standard / Course / Heinemann references / Assessment
Divisibility, primes, factors, multiples
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Multiples / MZ7 p.53 (2.1) / C FT7 2.1 Short answer
C FT7 2.1 Multiple choice
E FT7 2.1 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Divisibility / MZ7 p.56 (2.2)
MZ7 p.58 (Problem solving) / C FT7 2.2 Short answer
B FT7 2.2 Multiple choice
C FT7 2.2 Applications and analysis
Students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes. / The sieve of Eratosthenes / MZ7 p.62 (Investigation)
Students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes. / Factors / MZ7 p.59 (2.3) / C FT7 2.3 Short answer
C FT7 2.3 Multiple choice
C FT7 2.3 Applications and analysis
Students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes. / Prime and composite numbers / MZ7 p.63 (2.4)
MZ7 p.65 (Investigation)
MZ7 p.69 (Maths in action) / C FT7 2.4 Short answer
C FT7 2.4 Multiple choice
C FT7 12.4 Applications and analysis
Students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes. / Prime factors and factor trees / MZ7 p.66 (2.5) / C FT7 2.5 Short answer
C FT7 2.5 Multiple choice
C FT7 2.5 Applications and analysis
Number types
Students develop simple mathematical models for real situations (e.g. using constant rates of change for linear models). They develop generalisations by abstracting the features from situations and expressing these in words and symbols. They predict using interpolation (working with what is already known) and extrapolation (working beyond what is already known). They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context. / Number systems and patterns / MZ7 p.3 (1.1)
MZ7 p.41 (Maths in action)
MZ7 p.76 (Computer investigation)
MZ7 p.78 (VELS Design task) / C FT7 1.1 Short answer
C FT7 1.1 Multiple choice
E FT7 1.1 Applications and analysis
Students use knowledge of perfect squares when calculating and estimating squares and square roots of numbers (e.g. 202 = 400 and 302 = 900 so √700 is between 20 and 30). They evaluate natural numbers and simple fractions given in base-exponent form (e.g. 54= 625 and ). They know simple powers of 2, 3, and 5 (e.g. 26 = 64, 34 = 81, 53= 125). They calculate squares and square roots of rational numbers that are perfect squares (e.g. √0.81 = 0.9 and ). They calculate cubes and cube roots of perfect cubes (e.g. 3√64 = 4). / Square and cube numbers / MZ7 p.70 (2.6) / C FT7 2.6 Short answer
C FT7 2.6 Multiple choice
C FT7 2.6 Applications and analysis
Students express natural numbers base 10 in binary form, (e.g. 4210 = 1010102), and add and multiply natural numbers in binary form (e.g. 1012 + 112 = 10002 and 1012 × 112 = 11112). / E Binary numbers / MZ7 p.73 (2.7) / C (Q1–6), E (Q7–9) FT7 2.7 Short answer
C FT7 2.7 Multiple choice
E FT7 2.7 Applications and analysis
They evaluate natural numbers and simple fractions given in base-exponent form (e.g. 54 = 625 and ). / Powers / MZ7 p.80 (2.8) / C FT7 2.8 Short answer
C FT7 2.8 Multiple choice
C FT7 2.8 Applications and analysis

Unit3: FractionsDimensions: Number; Working mathematicallyTime: 4 weeks

VELS standard / Course / Heinemann references / Assessment
Equivalence and operations
They write equivalent fractions for a fraction given in simplest form (e.g. 2/3 = 4/6 = 6/9 = …). / B Equivalence and reducing / MZ7 p.95 (3.1) / C FT7 3.1 Short answer
C FT7 3.1 Multiple choice
C FT7 3.1 Applications and analysis
They write equivalent fractions for a fraction given in simplest form (e.g. 2/3 = 4/6 = 6/9 = …).
They know the decimal equivalents for the unit fractions and find equivalent representations of fractions as decimals, ratios and percentages (e.g. a subset:set ratio of 4:9 can be expressed equivalently as ). / Comparing and ordering / MZ7 p.101 (3.2)
MZ7 p.104 (Problem solving) / C FT7 3.2 Short answer
C FT7 3.2 Multiple choice
C FT7 3.2 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Adding and subtracting fractions / MZ7 p.105 (3.3)
MZ7 p.107 (3.4)
MZ7 p.109 (VELS Design task)
MZ7 p.110 (Maths in action) / C FT7 3.3 Short answer
C FT7 3.3 Multiple choice
C FT7 3.3 Applications and analysis
C FT7 3.4 Short answer
C FT7 3.4 Multiple choice
E FT7 3.4 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / E Multiplying fractions / MZ7 p.112 (3.5)
MZ7 p.115 (Problem solving) / C FT7 3.5 Short answer
C FT7 3.5 Multiple choice
C FT7 3.5 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / E Dividing fractions / MZ7 p.115 (3.6) / C FT7 3.6 Short answer
C FT7 3.6 Multiple choice
C FT7 3.6 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Mixed operations / MZ7 p.118 (Investigation)
MZ7 p.120 (3.7) / E FT7 3.7 Short answer
C FT7 3.7 Multiple choice
E FT7 3.7 Applications and analysis
Students understand ratio as both set:set comparison (e.g. number of boys:number of girls) and subset:set comparison (e.g. number of girls:number of students), and find integer proportions of these, including percentages (e.g. ratio number of girls:number of boys is 2:3 = 4:6 = 40%:60%). / Problems with fractions / MZ7 p.123 (3.8) / C FT7 3.8 Short answer
C FT7 3.8 Multiple choice
E FT7 3.8 Applications and analysis

Unit4: DecimalsDimensions: Number; Working mathematicallyTime: 4 weeks

VELS standard / Course / Heinemann references / Assessment
Place value
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / B Place value, reading and writing decimals / MZ7 p.133 (4.1)
MZ7 p.138 (Problem solving) / B FT7 4.1 Short answer
B FT7 4.1 Multiple choice
C FT7 4.1 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.
They know the decimal equivalents for the unit fractions and find equivalent representations of fractions as decimals, ratios and percentages (e.g. a subset:set ratio of 4:9 can be expressed equivalently as ). They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy. / Comparing decimals, ordering / MZ7 p.138 (4.2) / C FT7 4.2 Short answer
C FT7 4.2 Multiple choice
C FT7 4.2 Applications and analysis
They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy. / Rounding decimals / MZ7 p.142 (4.3) / C FT7 4.3 Short answer
C FT7 4.3 Multiple choice
C FT7 4.3 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Converting decimals to fractions / MZ7 p.145 (4.4) / C FT7 4.4 Short answer
C FT7 4.4 Multiple choice
C FT7 4.4 Applications and analysis
They know the decimal equivalents for the unit fractions and find equivalent representations of fractions as decimals, ratios and percentages (e.g. a subset:set ratio of 4:9 can be expressed equivalently as ). / Common fractions to decimals / MZ7 p.168 (Investigation)
Calculations
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / B Addition and subtraction of decimals / MZ7 p.147 (4.5)
MZ7 p.150 (4.6)
MZ7 p.153 (Problem solving) / C VELS Design task (p.164)
C FT7 4.5 Short answer
C FT7 4.5 Multiple choice
C FT7 4.5 Applications and analysis
C FT7 4.6 Short answer
C FT7 4.6 Multiple choice
C FT7 4.6 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Multiplication by whole numbers / MZ7 p.155 (4.7) / C FT7 4.7 Short answer
C FT7 4.7 Multiple choice
C FT7 4.7 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Multiplication / MZ7 p.158 (4.8)
MZ7 p.161 (4.9) / C FT7 4.8 Short answer
C FT7 4.8 Multiple choice
C FT7 4.8 Applications and analysis
C FT7 4.9 Short answer
C FT7 4.9 Multiple choice
E FT7 4.9 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / Division by whole numbers / MZ7 p.165 (4.10)
MZ7 p.169 (4.11) / C FT7 4.10 Short answer
C FT7 4.10 Multiple choice
C FT7 4.10 Applications and analysis
C FT7 4.11 Short answer
C FT7 4.11 Multiple choice
C FT7 4.11 Applications and analysis
Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. / E Division by other decimals / MZ7 p.172 (4.12)
MZ7 p.175 (Maths in action) / E FT7 4.12 Short answer
E FT7 4.12 Multiple choice
E FT7 4.12 Applications and analysis

Unit 5: MeasurementDimensions: Measurement, chance and dataTime: 4 weeks

VELS standard / Course / Heinemann references / Assessment
Length
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / B Units / MZ7 p.185 (5.1)
MZ7 p.189 (5.2) / B FT7 5.1 Short answer
B FT7 5.1 Multiple choice
B FT7 5.1 Applications and analysis
C FT7 5.2 Short answer
C FT7 5.2 Multiple choice
C FT7 5.2 Applications and analysis
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / Metric units / MZ7 p.193 (5.3) / C FT7 5.3 Short answer
C FT7 5.3 Multiple choice
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / Measuring / MZ7 p.xxiii (Assignment) / MZ7 p.xxiii (Assignment)
Students develop simple mathematical models for real situations (e.g. using constant rates of change for linear models). / Problem solving / MZ7 p.195 (Problem solving) / C FT7 5.3 Applications and analysis
Perimeter
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. / Perimeter / MZ7 p.196 (5.4) / MZ7 p.201 (VELS Design task)
B (Q1–3); C (Q4–6) FT7 5.4 Short answer
C FT7 5.4 Multiple choice
C FT7 5.4 Applications and analysis
Area
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. / Understanding area / MZ7 p.203 (5.5)
MZ7 p.209 (5.6)
MZ7 p.216 (5.7)
MZ7 p.221 (Maths@work) / C FT7 5.5 Short answer
C FT7 5.5 Multiple choice
C FT7 5.5 Applications and analysis
B (Q1–3); C (Q4–6) FT7 5.6 Short answer
C FT7 5.6 Multiple choice
C FT7 5.6 Applications and analysis
C FT7 5.7 Short answer
C FT7 5.7 Multiple choice
E FT7 5.7 Applications and analysis
Volume
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. They calculate the surface area and volume of prisms and cylinders. / Understanding volume / MZ7 p.223 (5.8) / B FT7 5.8 Short answer
B FT7 5.8 Multiple choice
C FT7 5.8 Applications and analysis
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. They calculate the surface area and volume of prisms and cylinders. / Volume of rectangular prisms / MZ7 p.226 (5.9) / C FT7 5.9 Short answer
C FT7 5.9 Multiple choice
C FT7 5.9 Applications and analysis
Time
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / 24-hour time / MZ7 p.228 (5.10) / B FT7 5.10 Short answer
B FT7 5.10 Multiple choice
C FT7 5.10 Applications and analysis
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / Time-related calculations / MZ7 p.233 (5.11) / C FT7 5.11 Short answer
C FT7 5.11 Multiple choice
E FT7 5.11 Applications and analysis

Unit 6: AlgebraDimensions: Structure; Working mathematicallyTime: 4 weeks

VELS standard / Course / Heinemann references / Assessment
Rules and formulae
Students use variables in general mathematical statements. / Understanding rules and formulae / MZ7 p.251 (6.1)
MZ7 p.256 (6.2) / C FT7 6.1 Short answer
C FT7 6.1 Multiple choice
C FT7 6.1 Applications and analysis
C FT7 6.2 Short answer
C FT7 6.2 Multiple choice
C FT7 6.2 Applications and analysis
Using symbols
Students use variables in general mathematical statements. / Introduction to the use of pronumerals / MZ7 p.259 (6.3)
MZ7 p.281 (Graphics calculator investigation) / C FT7 6.3 Short answer
C FT7 6.3 Multiple choice
C FT7 6.3 Applications and analysis
Students develop simple mathematical models for real situations (e.g. using constant rates of change for linear models). They develop generalisations by abstracting the features from situations and expressing these in words and symbols. They predict using interpolation (working with what is already known) and extrapolation (working beyond what is already known). They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context. / Using number patterns and problem solving / MZ7 p.267 (6.4)
MZ7 p.269 (Problem solving)
MZ7 p.269 (6.5)
MZ7 p.274 (Investigation)
MZ7 p.279 (CAS investigation) / VELS Design task p.283
C FT7 6.4 Short answer
C FT7 6.4 Multiple choice
C FT7 6.4 Applications and analysis
C FT7 6.5 Short answer
C FT7 6.5 Multiple choice
C FT7 6.5 Applications and analysis
Students use variables in general mathematical statements. / Notation / MZ7 p.275 (6.6) / C FT7 6.6 Short answer
C FT7 6.6 Multiple choice
C FT7 6.6 Applications and analysis
Grid references
Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. / Battleships / MZ7 p.284 (6.7) / C FT7 6.7 Short answer
C FT7 6.7 Multiple choice
E FT7 6.7 Applications and analysis
Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. / E Chess pieces / MZ7 p.287 (Investigation)
Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. / Map coordinates / MZ7 p.289 (Maths@work)
Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. / The Cartesian plane / MZ7 p.292 (6.8) / C FT7 6.8 Short answer
C FT7 6.8 Multiple choice
C FT7 6.8 Applications and analysis

Unit 7: AnglesDimensions: Space; Working mathematicallyTime: 3 weeks

VELS standard / Course / Heinemann references / Assessment
Geometrical drawing
Students measure length, perimeter, area, surface area, mass, volume, capacity, angle, time and temperature using suitable units for these measurements in context. / Measuring and drawing angles / MZ7 p.309 (7.1)
MZ7 p.323 (7.3)
MZ7 p.325 (Investigation)
MZ7 p.337 (Problem solving) / C FT7 7.1 Short answer
C FT7 7.1 Multiple choice
C FT7 7.1 Applications and analysis
C FT7 7.3 Short answer
E FT7 7.3 Applications and analysis
Students estimate the accuracy of measurements and give suitable lower and upper bounds for measurement values. / Estimating angles / MZ7 p.318 (7.2)
MZ7 p.322 (Investigation) / C FT7 7.2 Short answer
C FT7 7.2 Multiple choice
C FT7 7.2 Applications and analysis
Students estimate the accuracy of measurements and give suitable lower and upper bounds for measurement values. / Looking at angles / MZ7 p.318 (Problem solving)
MZ7 p.326 (Maths in action)
Types of angles
They describe and apply the angle properties of regular and irregular polygons, in particular, triangles and quadrilaterals. / Describing angles / MZ7 p.328 (7.4)
MZ7 p.332 (Investigation) / MZ7 VELS Design task p.331
C FT7 7.4 Short answer
C FT7 7.4 Multiple choice
C FT7 7.4 Applications and analysis
They use the properties of parallel lines and transversals of these lines to calculate angles that are supplementary, corresponding, allied (co-interior) and alternate. / Complementary and supplementary / MZ7 p.333 (7.5) / C FT7 7.5 Short answer
C FT7 7.5 Multiple choice
E FT7 7.5 Applications and analysis
They describe and apply the angle properties of regular and irregular polygons, in particular, triangles and quadrilaterals. / Angles in a revolution / MZ7 p.338 (7.6) / C FT7 7.6 Short answer
C FT7 7.6 Multiple choice
E FT7 7.6 Applications and analysis
They use the properties of parallel lines and transversals of these lines to calculate angles that are supplementary, corresponding, allied (co-interior) and alternate. / Vertically opposite angles / MZ7 p.341 (7.7) / C FT7 7.7 Short answer
C FT7 7.7 Multiple choice
E FT7 7.7 Applications and analysis

Unit 8: EquationsDimensions: Structure; Working mathematicallyTime: 4 weeks