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VELS Standards & Progression Points
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(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).
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Level
Standard/Progression point
Chapter 1
Integers
MathsWorld 8
Number
4.0
4.0
4.25
4.5
They model integers (positive and negative whole
numbers and zero), common fractions and decimals.
* Chapter pre-test Questions 2, 4, 5,
6, 8
Warm-up: Protons and antiprotons
They place integers, decimals and common fractions * Chapter pre-test Questions 9, 10
on a number line.
1.1: Numbers on the other side of
zero: negative numbers
Exercise 1.1: Questions 3, 5, 9
They use knowledge of perfect squares to determine 1.7: Powers and roots of integers
exact square roots.
Exercise 1.7 Questions 4 – 8
Students use a model to subtract one integer,
positive or negative, from another and show its
equivalence to adding the opposite (additive
inverse).
4.5
They estimate the square roots of whole numbers
using nearby perfect squares.
4.75
They estimate and use a calculator to find squares,
cubes, square and cube roots of any numbers.
4.75
5.0
5.0
5.0
5.0
5.0
Warm-up: Protons and antiprotons
1.1: Numbers on the other side of
zero: negative numbers
Try this! Temperature (p. 5)
1.3: Adding and subtracting
integers
Try this!: Flexitime (p. 14)
1.4: More addition and subtraction
of integers
Try this! Ships and sharks (p. 19)
Analysis task 2: Integers as rational
numbers
1.7: Powers and roots of integers
Exercise 1.7
Analysis task 2: Integers as rational
numbers parts a, b
They multiply negative numbers together, and give a 1.5: Multiplying integers
reasonable explanation of the result.
Try this! (p. 24)
Exercise 1.5
Analysis task 1: 1, 2, 3, 4, what
numbers are we heading for?
Students use knowledge of perfect squares when
Analysis task 2: Integers as rational
calculating and estimating squares and square roots
numbers (p. 34)
of numbers
(for example, 202 = 400 and 302 = 900 so √700 is
between 20 and 30).
They evaluate natural numbers and simple fractions 1.7: Powers and roots of integers
given in base-exponent form (for example, 54 = 625 Example 1 (p. 31)
and (2/3)2 = 4/9).
Exercise 1.7 Questions 2, 3, 4, 10, 11,
12, 14, 15
They calculate squares and square roots of rational
1.7: Powers and roots of integers
numbers that are perfect squares (for example, √0.81 Exercise 1.7 Questions 5 – 9
= 0.9 and √(9/16) = ¾).
They calculate cubes and cube roots of perfect cubes 1.7: Powers and roots of integers
(for example, 3√64 = 4).
Exercise 1.7 Questions 12, 13
Using technology they find square and cube roots of
rational numbers to a specified degree of accuracy
(for example, 3√200 = 5.848 to three decimal
places).
Analysis task 2: Integers as rational
numbers, parts a, b (p. 35)
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Structure
5.0
5.0
5.0
At Level 5 students identify collections of numbers
as subsets of natural numbers, integers, rational
numbers and real numbers.
They use Venn diagrams and tree diagrams to show
the relationships of intersection, union, inclusion
(subset) and complement between the sets.
They recognise and use inequality symbols.
Analysis task 2: Integers as rational
numbers
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 Warm-up Try this!
MicroWorlds HTML: Protons and
antiprotons
1.4: More addition and subtraction
of integers
MicroWorlds HTML: Ships and
sharks
1.5: Multiplying integers
MicroWorlds HTML: Train travel
multiplication
Analysis task 2: Integers as rational
numbers
1.2: Comparing and ordering
integers
Example 1 (p. 11)
Exercise 1.2 Question 4
Chapter 5: Algebra toolbox
5.7: Solving with algebra
Example 7 (p. 251)
Exercise 5.7 Questions 17, 27
Working
mathematically
5.0
Chapter 2
Mathematical thinking
Structure
4.75
Students extend number patterns based on square
numbers, and generalise the patterns using symbols,
such as the next square is found by adding the next
odd number
(n + 1)2 = n2 + (2n + 1).
2.4: Developing strategies to think
about my thinking
Problem set 2.4 Question 5
Students develop and test conjectures.
2.5: Mathematical reasoning:
conjecturing
Example investigation 1 Try this! pp.
82, 84
Practice investigation
Investigation 1: Quotient patterns in
100 grids
Investigation 2: Kites and
boomerangs
Investigation 4: Beprisque number
investigation
Chapter 2: Mathematical thinking
Working
mathematically
4.0
4.0
Students use the mathematical structure of problems
to choose strategies for solutions.
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4.0
They explain their reasoning and procedures and
interpret solutions.
2.5: Mathematical reasoning:
conjecturing
Example investigation 1 Try this! pp.
82, 84
Practice investigation
Investigation 1: Quotient patterns in
100 grids
Investigation 2: Kites and
boomerangs
Investigation 4: Beprisque number
investigation
4.0
They create new problems based on familiar
problem structures.
2.3: Problem posing
Example problems 1 – 3
Practice problems 1 – 3
4.25
Students develop generalisations inductively, from
examples such as angle sums in triangles.
2.2: Developing problem-solving
strategies
Problem set 2.2 Questions 6, 8
They find patterns and relationships by looking at
examples and recording the outcomes
systematically.
2.2: Developing problem-solving
strategies
Try this!
Example problem 2 (p. 52)
Practice problem 2 Try this! (p. 53)
Example problem 3 Try this! (p. 55)
Practice problem 3 Try this! (p. 55)
Example problem 4
Practice problem 4
Example problem 5
Example problem 6
Practice problem 5
Problem set 2.2
Students develop generalisations inductively, from
examples such as angle sums in triangles.
2.2: Developing problem-solving
strategies
Problem set 2.2 Questions 6, 8
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.
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).
2.5: Mathematical reasoning:
conjecturing
Practice investigation 1: Areas of
midpoint figures in quadrilaterals
4.25
4.25
5.0
Chapter 3
2.5: Mathematical reasoning:
conjecturing
Example investigation 1 Try this! pp.
82, 84
Practice investigation
Investigation 1: Quotient patterns in
100 grids
Investigation 2: Kites and
boomerangs
Investigation 4: Beprisque number
investigation
Angles, parallel lines and polygons
Space
4.25
They identify congruent shapes and solids when
appropriately aligned.
3.2: Triangles
Examples 10, 11, 12
Exercise 3.2 Question 11
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Students use a wide range of geometric language
correctly when describing or constructing shapes
and solids.
4.25
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.
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.
4.5
4.5
5.0
5.0
5.0
5.0
3.2: Triangles
3.3: Quadrilaterals
3.4 Other polygons
3.5 Star polygons
3.2: Triangles
Examples 3, 4, 5 (pp. 108 – 9)
Exercise 3.2 Questions 4, 5, 6
3.2: Triangles
Examples 10 – 12
Exercise 3.2 Question 11
3.2: Triangles
Examples 6 – 9
Exercise 3.2 Questions 8 – 10
Analysis task 2: Constructing dragresistant shapes
Analysis task 3: Drawing star
polygons in MicroWorlds
They use the properties of parallel lines and
transversals of these lines to calculate angles that are
supplementary, corresponding, allied (co-interior)
and alternate.
They describe and apply the angle properties of
regular and irregular polygons, in particular,
triangles and quadrilaterals.
3.1: Angles and parallel lines
Examples 3, 4, 5 (pp. 97 – 98)
Exercise 3.1 Questions 5 - 10
They recognise congruence of shapes and solids.
3.2: Triangles
Examples 10 – 12 (pp. 113 – 115)
They measure angles in degrees.
3.2: Triangles
Examples 7 – 9 pp. 111 – 113
Exercise 3.2 Questions 9, 10
Further angle work in sections 3.3 –
3.5
3.2: Triangles
Try this p. 104
Examples 3, 4, 5
3.3: Quadrilaterals
Examples 1, 2
Exercise 3.3 Questions 8, 11, 12, 13,
14, 20
3.4: Other polygons
Examples 1 – 6
Exercise 3.4 Questions 1 – 14
3.5: Star polygons
Example 1
Exercise 3.5 Questions 10, 11
Measurement,
Chance and
Data
4.0
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Working
mathematically
4.0
4.5
4.5
4.5
4.5
4.5
4.75
5.0
5.0
5.0
5.0
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 explain mathematical relationships by
extending patterns.
3.2: Triangles
Try this! p. 105
Example 2 (p. 105)
Exercise 3.2 Question 2
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.
3.2: Triangles
Try this! p. 104
3.3: Quadrilaterals
Exercise 3.3 Question 20
Analysis task 1: Polygon diagonals
They independently plan and carry out an
investigation with several components and report the
results clearly using mathematical language.
Students use computer drawing tools, such as MS
Word, Geometer’s Sketchpad, MicroWorlds and
Cabri Geometry, to explore geometric situations.
Analysis task 2: Constructing dragresistant shapes
They link known facts together logically, such as
parallelograms have rotational symmetry, therefore
they have equal opposite angles.
3.2 Triangles
Try this! p. 104
Exercise 3.2 Question 15
3.3 Quadrilaterals
Try this! p. 121
Try this! p. 123
Exercise 3.3 Questions 6, 7, 9, 10, 15
– 20
Students explain geometric propositions (for
example, by varying the location of key points
and/or lines in a construction).
3.5: Star polygons
Exercise 3.5 Question 8
Analysis task 2: Constructing dragresistant shapes
Analysis task 3: Drawing star
polygons in MicroWorlds
Analysis task 1: Polygon diagonals
Analysis task 3: Drawing star
polygons in MicroWorlds
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.
Analysis task 1: Polygon diagonals
Analysis task 2: Constructing dragresistant shapes
Analysis task 3: Drawing star
polygons in MicroWorlds
3.4: Polygons
Exercise 3.4 Question 8
Try this! (p. 123)
3.3: Polygons
Exercise 3.3 Questions 6b, 16b, c,
20b
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5.0
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.
Chapter 4
Fractions, decimals and percentages
5.0
Analysis task 1: Polygon diagonals
3.4: Other polygons
Exercise 3.4 Question 8
Analysis task 2: Constructing dragresistant shapes
Analysis task 3: Drawing star
polygons in MicroWorlds
Number
4.0
4.0
They create sets of number multiples to find the
lowest common multiple of the numbers.
4.1: Common denominators and
comparing fractions
Example 1 (p. 158)
Students use decimals, ratios and percentages to find * Chapter pre-test Question 10
equivalent representations of common fractions (for 4.9: Interchanging fractions,
example, ¾ = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8).
decimals and percentages
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 3, 4, 7, 8
4.2: Multiplying and dividing
fractions
Examples 1 – 4 (pp. 161 – 163)
Exercise 4.2
4.3: Adding and subtracting mixed
numbers
Examples 1, 2 (pp. 166, 167)
Exercise 4.3
They use estimates for computations and apply
criteria to determine if estimates are reasonable or
not.
4.6 Operations with decimals
Students should be encouraged to
check their answers as demonstrated
in Examples 3 – 5 (pp. 178 – 179)
4.25
They know that the position of the digit zero affects
the size of numbers, such as 00.070 = 0.07.
4.5: Place value, comparing
decimals and rounding
Examples 1, 2 (pp. 172, 173)
4.6: Operations with decimals
Example 1b (p. 177): writing a zero
after 35.9 does not alter the size of the
number. Similarly in Example 6 (p.
179)
4.25
Students use mental estimation to check the result of
calculator computations.
4.6 Operations with decimals
Students should be encouraged to
check their answers as demonstrated
in Examples 3 – 5 (pp. 178 – 179)
4.0
4.0
4.25
4.25
They use written and/or mental methods to divide
4.6 Operations with decimals
decimals by single digit whole numbers, interpreting Exercise 4.6 Question 6
the remainder.
They use knowledge of perfect squares to determine * Chapter pre-test Questions 5c, d
exact square roots.
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4.25
4.5
4.75
4.75
4.75
4.75
5.0
5.0
5.0
5.0
Students convert between fraction, decimal and
percentage forms, and use them to calculate and
estimate, such as estimate 63% of 300 by finding
two thirds.
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.
Students use equal multiplication by 10 to divide by
decimals, such as 0.24 ÷ 0.04 = 24 ÷ 4 = 6.
4.10: Finding a given percentage of
a quantity
Exercise 4.10 Questions 1 - 3
They use a range of strategies for estimating
multiplication and division calculations with
decimals, fractions and integers.
4.6: Operations with decimals
Students should be encouraged to
check their calculations as in
Examples 1 – 5 (pp. 177 – 179)
* Chapter pre-test Questions 8a – d
4.6: Operations with decimals
Example 5 (p. 179)
* Chapter pre-test Question 8i
4.6: Operations with decimals
Example 5 (p. 179)
Students use efficient mental and/or written methods 4.6: Operations with decimals
to multiply or divide by two-digit numbers.
Example 45 (p. 178)
They convert between decimals, ratios, fractions and 4.8: What is a percentage?
percentages, such as compare 3 out of 4 to 5 out of
Examples 1 – 3
7.
Exercise 4.8
4.9: Interchanging fractions,
decimals and percentages
Examples 1 – 3
Exercise 4.9
4.10: Finding a percentage of a
given quantity
Examples 1 – 5
Exercise 4.10
4.11: Expressing one quantity as a
percentage of another
Examples 1, 2
Exercise 4.11
They use technology for arithmetic computations
4.6: Operations with decimals
involving several operations on rational numbers of Exercise 4.6 Questions 13 – 20
any size.
They calculate squares and square roots of rational
4.4: Squares and square roots of
numbers that are perfect squares (for example, √0.81 fractions
= 0.9 and √(9/16) = ¾).
Examples 1, 2 (pp. 169 – 170)
Exercise 4.4 Questions 1 – 4
4.7: Squares and square roots of
decimals
Examples 1 – 3 (pp. 182 – 183)
Exercise 4.7 Questions 1, 2
They write equivalent fractions for a fraction given
4.3: Adding and subtracting mixed
in simplest form (for example, 2/3 = 4/6 = 6/9 =…). numbers
Examples 1, 2
They know the decimal equivalents for the unit
4.9: Interchanging fractions,
fractions ½, 1/3, ¼, 1/5, 1/8, 1/9 and find equivalent decimals and percentages
representations of fractions as decimals, ratios and
Examples 1 – 3 (pp. 190 – 191)
percentages (for example, a subset: set ratio of 4:9
Exercise 4.9 Question 1
can be expressed equivalently as 4/9 = 0.4 ≈
44.44%).
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5.0
5.0
5.0
5.0
Chapter 5
They write the reciprocal of any fraction and
calculate the decimal equivalent to a given degree of
accuracy.
4.2: Multiplying and dividing
fractions
Example 3 (p. 163)
4.9: Interchanging fractions,
decimals and percentages
Exercise 4.9
Analysis task 1: Pizza fractions
They evaluate natural numbers and simple fractions
given in base-exponent form (for example, 54 = 625
and (2/3)2 = 4/9).
4.4: Squares and square roots of
fractions
Example 1 (p. 169)
Exercise 4.4 Questions 1, 2, 5 – 9, 11,
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.
4.6: Operations with decimals
See checking in Examples 1 - 6
4.2: Multiplying and dividing
fractions
Examples 1 – 4
Exercise 4.2
4.3 Adding and subtracting mixed
numbers
Examples 1, 2
Exercise 4.3
4.6: Operations with decimals
Examples 1 – 6
Exercise 4.6
Algebra toolbox
Structure
4.0
4.0
4.0
4.25
4.25
4.5
4.5
Students identify relationships between variables
and describe them with language and words (for
example, how hunger varies with time of the day).
Students recognise that addition and subtraction, and
multiplication and division are inverse operations.
Analysis task 3: Generalising the
number laws
They solve equations by trial and error.
5.6 Solving equations: arithmetic
strategies
Example 1 (pp. 241 – 242)
Analysis task 2: Odds and evens
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 .
They recognise equivalence between simple
equivalent expressions, such as a + a + a = 3 x a =
3a.
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 inequalities showing the solutions on
number lines, such as x + 4 > 7.
5.6: Solving equations: arithmetic
strategies
Examples 2, 3 (pp. 242 – 243)
Exercise 5.6 Questions 6 – 10
5.1: Algebraic expressions
Examples 1 – 5 (pp. 216 – 219)
Exercise 5.1 Questions 1 – 15
5.6: Solving equations: arithmetic
strategies
Examples 1 – 3 (pp. 241 – 243)
Exercise 5.6 Questions 1 – 10
5.7: Solving with algebra
Example 1 (p. 251)
Exercise 5.7 Questions 17, 27
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4.5
4.5
4.75
4.75
5.0
5.0
5.0
5.0
Chapter 6
They use inverses to rearrange simple formulas,
including
p = c + m becomes m = p – c, and to find equivalent
algebraic expressions.
They use the distributive law to find and check
equivalent expressions, such as 2(m + 5) = 2m + 10.
5.7: Solving with algebra
Exercise 5.7 Question 22
Students use linear and other functions such as f(x) =
2x – 4, xy = 24, y = 2x and y = 4 – x2 to model
situations, such as the trajectory when diving into a
pool.
They rearrange simple formulas, such as s = d/t, so
t = d/s .
5.8: Solving equations: Formulating
Try this! p. 256
They identify the identity element and inverse of
rational numbers for the operations of addition and
multiplication
(for example, ½ + − ½ = 0 and 2/3 × 3/2 = 1).
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).
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.
They solve simple inequalities such as y ≤ 2x+ 4 and
decide whether inequalities such as x2 > 2y are
satisfied or not for specific values of x and y.
5.7: Solving with algebra
Examples 1 – 6 (pp. 247 – 250)
Exercise 5.7 Questions 1 – 20
5.3: Expanding algebraic
expressions
Try this! p. 227
Examples 1, 2 (p. 228)
Exercise 5.3 Questions 1 – 14
5.3: Factorising algebraic expressions
Try this! p. 231
Examples 2, 3 (pp. 232 – 233)
Exercise 5.3 Questions 3 – 7
5.7: Solving with algebra
Exercise 5.7 Questions 23 – 25
5.7: Solving with algebra
Exercise 5.7 Questions 23 – 26
5.7: Solving with algebra
Examples 1 – 6 (pp. 247 – 250)
Try this! p. 246
5.7: Solving with algebra
Example 1 (p. 251)
Exercise 5.7 Questions 17, 27
Transformations and tessellations
Space
4.0
4.0
4.25
4.5
4.5
They describe the features of shapes and solids that
remain the same (for example, angles) or change
(for example, surface area) when a shape is enlarged
or reduced.
They apply a range of transformations to shapes and
create tessellations using tools (for example,
computer software).
Students use a wide range of geometric language
correctly when describing or constructing shapes
and solids.
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.
They understand similarity as preserving shape
(angles and proportion) including resizing a photo
on a computer.
6.2: Congruency and similarity
Exercise 6.2 Questions 1 – 10
6.3: Tessellations
Exercise 6.3 Questions 1, 4, 8
6.2: Congruency and similarity
Examples 1, 2, 4, 5, 6, 7
6.3: Tessellations
Examples 1, 2 (p. 311)
Exercise 6.3 Questions 3, 5, 6, 7
6.2: Congruency and similarity
Enlarging and reducing: nonisometric transformations p. 294
Exercise 6.2 Questions 1 – 14
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5.0
5.0
5.0
5.0
They recognise congruence of shapes and solids.
Analysis task 1: Federation Square
They relate similarity to enlargement from a
common fixed point.
6.2: Congruency and similarity
Analysis task 1: Pantographs
They make tessellations from simple shapes.
6.3: Tessellations
Exercise 6.3 Questions 1, 2, 4
Analysis task 2: Federation Square
Analysis task 3: RMIT Storey Hall
Students use coordinates to identify position in the
plane.
6.1: Isometric transformations
Examples 2, 3, 4 (pp. 278 – 280)
Exercise 6.1 Questions 8, 11, 12
Students recognise and apply simple geometric
transformations of the plane such as translation,
reflection, rotation and dilation and combinations of
the above, including their inverses.
6.1: Isometric transformations
Examples 1 – 4 (pp. 277 – 280)
Exercise 6.1 Questions 1 – 14
6.2: Congruency and similarity
Exercise 6.2
Students use computer drawing tools, such as MS
Word, Geometer’s Sketchpad, MicroWorlds and
Cabri Geometry, to explore geometric situations.
6.1: Isometric transformations
Exercise 6.1 Questions 5, 6
6.2: Congruency and similarity
Exercise 6.2 Question 8
6.3: Tessellations
Exercise 6.3 Questions 4, 8c
Analysis task 1: Pantographs
They link known facts together logically, such as
parallelograms have rotational symmetry, therefore
they have equal opposite angles.
6.2: Congruency and similarity
Exercise 6.2 Question 14
6.3: Tessellations
Examples 1,2 (p. 311)
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.
6.2: Congruency and similarity
Exercise 6.2 Questions 8, 9
6.3: Tessellations
Exercise 6.3 Question 8
Structure
5.0
Working
mathematically
4.5
4.75
5.0
Chapter 7
Polyhedra and networks
Space
4.0
4.0
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.
They create two-dimensional representations of
three dimensional shapes and objects found in the
surrounding environment.
They develop and follow instructions to draw shapes
and nets of solids using simple scale.
* Chapter pre-test Questions 1, 2
7.1: Polyhedra and nets
Exercise 7.1 Questions 4, 7, 10
7.1: Polyhedra and nets
Examples 2, 3 (pp. 346 – 347)
Exercise 7.1 Questions 1 – 3
* Chapter pre-test Questions 5, 8
7.1: Polyhedra and nets
Exercise 7.1 Questions 8, 9
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4.0
4.25
4.5
5.0
5.0
5.0
Students use network diagrams to show
relationships and connectedness such as a family
tree and the shortest path between towns on a map.
Students use a wide range of geometric language
correctly when describing or constructing shapes
and solids.
They visualise a polyhedron from its net and vice
versa.
*Chapter pre-test Question 10
7.3: Networks
Exercise 7.3 Questions 1 – 13
They use two-dimensional nets to construct a simple
three-dimensional object such as a prism or a
platonic solid.
7.1: Polyhedra and nets
Investigating polyhedra (p. 344)
Analysis task 3: Truncated
octahedron
They use single-point perspective to make a twodimensional representation of a simple threedimensional object.
7.1: Polyhedra and nets
Try this! p. 348
Example 4 (p. 349)
Exercise 7.1 Questions 1, 2
They use network diagrams to specify relationships.
7.3: Networks
Exercise 7.3 Questions 1 – 10
7.1: Polyhedra and nets
Exercise 7.1 Questions 4, 7
* Chapter pre-test Question 4
7.1: Polyhedra and nets
Exercise 7.1 Questions 7, 13
Analysis task 1: Truncated
octahedron
They consider the connectedness of a network, such * Chapter pre-test Questions 9, 10
as the ability to travel through a set of roads between 7.3: Networks
towns.
Exercise 7.3 Questions 10, 11, 12
Analysis task 2: Flight paths
Analysis task 3: Locating a power
station
5.0
Working
mathematically
5.0
Chapter 8
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: Polyhedra and nets
Exercise 7.1 Questions 5, 8, 9
Indices
Number
4.25
5.0
5.0
5.0
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 know simple powers of 2, 3, and 5 (for
example, 26 = 64, 34 = 81, 53 = 125).
8.1: Numbers in index form
Examples 4, 5 (p. 391)
8.1: Numbers in index form
Exercise 8.1 Questions 11, 12
Analysis task 1: Population explosion
They calculate cubes and cube roots of perfect cubes 8.2: Exploring sums of squares and
(for example, 3√64 = 4).
cubes
Exercise 8.2 Question 11
Using technology they find square and cube roots of 8.2: Investigating sums of squares
rational numbers to a specified degree of accuracy
and cubes
(for example, 3√200 = 5.848 to three decimal
Exercise 8.2 Question 11
places).
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Students express natural numbers base 10 in binary
form, (for example, 4210 = 1010102), and add and
multiply natural numbers in binary form (for
example, 1012 + 112 = 10002 and 1012 × 112 =
11112).
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).
8.3: Binary numbers
Examples 1 – 10
Exercise 8.3
Students use linear and other functions such as f(x) =
2x – 4, xy = 24, y = 2x and y = 4 – x2 to model
situations, such as the trajectory when diving into a
pool.
They use exponent laws for multiplication and
division of power terms (for example 23 × 25 = 28, 20
= 1, 23 ÷ 25 = 2−2, (52)3 = 56 and (3 × 4)2 = 32 × 42).
Analysis task 1: Population explosion
Students generalise from perfect square and
difference of two square number patterns
(for example, 252 = (20 + 5)2 = 400 + 2 × (100) + 25
= 625. And 35 × 25 = (30 + 5) (30 - 5) = 900 − 25 =
875)
8.2: Exploring sums of squares and
cubes
See note in MathsWorld 8 Teacher
Edition
4.25
Students develop generalisations inductively, from
examples such as angle sums in triangles.
8.2: Exploring sums of squares and
cubes
Exercise 8.2 Question 8
5.0
Students use variables in general mathematical
statements.
8.4: Index form with pronumerals
Examples 1 – 5 (pp. 412 – 414)
Exercise 8.4 Questions 1 – 12
They develop generalisations by abstracting the
features from situations and expressing these in
words and symbols.
8.4: Index form with pronumerals
Examples 1 – 5 (pp. 412 – 414)
Exercise 8.4 Questions 1 – 12
Analysis task 3: Tower of Hanoi
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.
8.2: Exploring sums of squares and
cubes
Exercise 8.2 Question 8
Analysis task 2: Mersenne primes
5.0
5.0
8.1: Numbers in index form
Examples 4, 5 (p. 392)
Exercise 8.1 Questions 7, 8
Structure
4.75
5.0
5.0
8.1: Numbers in index form
Examples 6, 7, 8
Exercise 8.1 Question 12
8.4: Index form with pronumerals
Examples 1 – 5 (pp. 412 – 414)
Exercise 8.4 Questions 1 – 12
Working
mathematically
5.0
5.0
Chapter 9
Exploring chance
Measurement,
Chance and
Data
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.
9.1: Probability
Example 1 (pp. 433 – 434)
Exercise 9.1 Question 4
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13
4.25
4.25
4.5
4.75
5.0
5.0
5.0
5.0
They can identify empirical probability as long-run
relative frequency including random number
generator to simulate rolling two dice.
9.2: Simulating random processes
Try this! p. 441
Examples 1, 2 (pp. 442 – 444)
Exercise 9.2 Questions 2 – 5
They design simulations for simple chance events,
such as designing a spinner to simulate a probability
of two out of five.
Students use a two way table to display the
outcomes for a two-event experiment such as using
a 3-by-4 table to show the outcomes when students
are randomly allocated a drink (orange, pineapple or
apple juice) and a sandwich (salad, cheese, ham or
vegemite).
Students use a tree diagram to calculate theoretical
probabilities, such as drawing a tree diagram for the
experiment of spinning a red-blue-yellow-green
spinner twice and find from the sixteen equally
likely outcomes the probability that at least one is
blue.
Students use appropriate technology to generate
random numbers in the conduct of simple
simulations.
9.1: Probability
Exercise 9.1 Question 5
Students identify empirical probability as long-run
relative frequency.
9.2: Simulating random processes
Try this! p. 441
Try this! p. 443
Exercise 9.2 Questions 1 – 5
9.3: Estimating probability using
relative frequency
Examples 1, 2, 3 (p. 449 – 453)
Exercise 9.3 Questions 1 – 15
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.
9.1: Probability
Example 1 (pp. 433 – 434)
Exercise 9.1 Questions 8 – 14
They use Venn diagrams and Karnaugh maps to test
the validity of statements using the words none,
some or all (for example, test the statement ‘all the
multiples of 3, less than 30, are even numbers’).
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.
9.4: Two-way tables
Examples 1 – 3 (pp. 459 – 465)
Exercise 9.4 Questions 1 – 11
9.4: Two-way tables
Examples 1, 2, 3 (pp. 459 – 465)
Exercise 9.4 Questions 1 – 11
9.5: Tree diagrams and tables
Example 2 (p. 473)
Exercise 9.5 Questions 8, 9
9.5: Tree diagrams and tables
Example 1 (p. 472)
Exercise 9.5 Questions 1 – 6, 11, 12
Analysis task 1: Hopping frogs
9.2: Simulating random processes
Try this! p. 441
Try this! p. 443
Exercise 9.2 Questions 3, 5
9.5 Tree diagrams and tables
Example 1 (p. 471)
Exercise 9.5 Questions 1 – 6, 11, 12
Structure
4.0
5.0
5.0
9.4: Two-way tables
Example 1, 2, 3 (pp. 459 – 465)
Exercise 9.4 Questions 1 – 10
9.4: Two-way tables
Examples 1 – 3 (pp. 459 – 465)
Exercise 9.4 Questions 1 – 10
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Working
mathematically
4.25
4.75
5.0
Chapter 10
They independently plan and carry out an
investigation with several components and report the
results clearly using mathematical language.
Students organise problem solving using Venn
diagrams, tree diagrams and two way tables, for
clarifying relationships.
Analysis task 2: Winning at the fair
Analysis task 3: Stick or switch to
win a car
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.
9.2: Simulating chance
Try this! p. 441
Exercise 9.2 Questions 1 – 5
9.4: Two-way tables
Exercise 9.4
9.5: Tree diagrams and tables
Exercise 9.5
Ratios and rates
Number
4.25
4.25
4.5
4.75
5.0
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.
They find equivalent ratios.
10.1: Ratio
Exercise 10.1 Questions 1 – 3, 8 – 10
Students describe ratio as a comparison of either
subset to subset or subset to set, where the scale
factor is greater than 1 such as 2 : 5 = 1 : 2.5.
10.1: Ratio
Example 4 (p. 492)
Exercise 10.1 Questions 7, 10, 13, 14
10.3: Proportion
Exercise 10.3 Question 11
Students describe ratio as a comparison of either
subset to subset or subset to set, where the scale
factor is less than 1, such as 5 : 2 = 1 : 0.4.
10.1: Ratio
Example 4 (p. 492)
Exercise 10.1 Questions 12, 13
Students understand ratio as both set: set
comparison (for example, number of boys : number
of girls) and subset: set comparison (for example,
number of girls : number of students), and find
integer proportions of these, including percentages
(for example, the ratio number of girls: the number
of boys is 2 : 3 = 4 : 6 = 40% : 60%).
10.1: Ratio
Examples 1, 2 (p. 489)
Example 3 (p. 491)
Exercise 10.1 Questions 1 – 15
10.2: Dividing quantities in given
ratios
Examples 1, 2 (p. 497)
Exercise 10.2 Questions 1 – 10
They understand similarity as preserving shape
(angles and proportion) including resizing a photo
on a computer.
They use scales on maps and plans, whether
presented graphically or as comparison of units such
as 1cm = 1km, or as a ratio such as 1:100000, to
accurately convert between map measurements and
real distances.
Chapter Warm-up (p. 487)
10.1: Ratio
Exercise 10.1 Question 5
Space
4.5
4.5
10.3: Proportion
Examples 3, 4
Exercise 10.3 Questions 5, 6
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15
Students use coordinates to identify position in the
plane.
10.6: Rates of change
Examples 2, 3 (pp. 529, 532)
Exercise 10.6 Questions 2 – 9
Analysis task 1: Phone cards
They use lines, grids, contours, isobars, scales and
bearings to specify location and direction on plans
and maps.
10.5: Gradients and rates
Example 2
Try this! p. 521
Exercise 10.5 Questions 4 – 9
Analysis task 2: Rivergum National
Park
Analysis task 3: Highs, lows and
tropical cyclones
They can calculate with time using a calculator.
10.4: Rates
Examples 2, 3 (p. 504)
Examples 6, 7, 8 (pp. 507 – 508)
Exercise 10.4 Questions 1 – 4, 6, 7
Analysis task 1: Phone cards
They determine the independent variable and
specify the allowable values for both variables when
describing a function relating two variables.
They identify a steady rate of change in terms of the
steady slope of a linear graph.
10.6: Rates of change
Example 2 (p. 529)
Exercise 10.6 Questions 2 – 9
They describe and specify the independent variable
of a function and its domain, and the dependent
variable and its range.
10.6: Rates of change
Example 2 (p. 529)
Exercise 10.6 Questions 2 – 6
Chapter 13: Functions and models
They use linear and other functions such as f(x) = 2x
− 4, xy = 24, y = 2x and y = x2 − 3 to model various
situations.
10.6: Rates of change
Exercise 10.6 Questions 2 – 6
4.5
They identify situations with constant rate of change
and represent with a linear graph, such as taxi fares.
10.6: Rates of change
Examples 1, 2 (pp. 528, 529)
Exercise 10.6 Questions 2 – 10
5.0
They identify situations with constant rate of change
and represent with a linear formula.
10.6: Rates of change
Examples 1, 2 (pp. 528, 529)
Exercise 10.6 Questions 2 – 10
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.
10.6: Rates of change
Exercise 10.6 Questions 2 – 7, 9
Analysis task 1: Phone cards
5.0
5.0
Measurement,
Chance and
Data
4.75
Structure
4.25
4.75
5.0
5.0
10.6: Rates of change
Example 1 (p. 528)
Working
mathematically
5.0
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16
Chapter 11
Length, area and volume
Number
They use approximations to π in related
measurement calculations
(for example, π × 52 = 25π = 78.54 correct to two
decimal places).
5.0
They use technology for arithmetic computations
involving several operations on rational numbers of
any size.
5.0
* Chapter pre-test Question 8
11.1: Measuring and calculating
length
Try This! pp. 555, 556
Examples 8 – 10 (pp. 556 – 558)
Exercise 11.1 Questions 11 – 19
11.3: Area of a circle
Examples 1 – 4 (pp. 578 – 579)
Exercise 11.3 Questions 1 – 12
11.5: Surface area
Examples 2, 3 (p. 593)
Exercise 11.5 Questions 2, 6, 7, 9
11.6: Volume
Example 6 (p. 602)
Exercise 11.6 Question 8, 9, 10c,d,
11, 12a, b, 13, 14, 15
Most questions in all exercises
Measurement,
chance and
data
4.0
4.0
4.0
4.25
4.25
4.5
At Level 4, students use metric units to estimate and
measure length, perimeter, area, surface area, mass,
volume, capacity time and temperature.
They measure as accurately as needed for the
purpose of the activity.
All sections
They convert between metric units of length,
capacity and time (for example, L–mL, sec–min).
* Chapter pre-test Question 1
11.1: Measuring and calculating
length
Examples 1, 2 (p. 551)
Exercise 11.1 Question 5
11.2 Area of polygons
Examples 1, 2 (p. 565)
Example 4 (p. 566)
Exercise 11.2 Question 1
11.6: Volume
Examples 1 – 3 (pp. 599 – 600)
Exercise 11.6 Question 1
Chapter Warm-up Try this!
Students estimate length, perimeter, area of
rectangles and time providing suitable lower and
upper bounds for estimates.
They use measurement formulas for perimeter and
area of a rectangle and use correct units.
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.
11.6: Volume
Exercise 11.6 Question 6
11.1: Measuring and calculating
length
Examples 6, 7 (p. 554)
Exercise 11.1 Questions 6, 7
11.2: Area of polygons
Examples 3, 4, 5 (pp. 565 – 566)
Exercise 11.2 Question 2
Chapter Warm-up Try this!
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17
4.5
They use measurement formulas for the area and
perimeter of triangles and parallelograms.
11.1 Measuring and calculating
length
Exercise 11.1
11.2 Area of polygons
Exercise 11.2
11.3: Area of a circle
Exercise 11.3
4.5
They calculate areas of simple composite shapes,
such as the floor area of a house.
11.4 Composite areas
Examples 1, 2, 3 (pp. 584 – 586)
Exercise 11.4 Questions 1 – 9
4.75
Students convert between a wide range of metric
units.
11.1: Area of polygons
Examples 1, 2 (p. 565)
Exercise 11.2 Question 1
11.6: Volume
Examples 1, 2 (p. 599)
Exercise 11.6
Question 1
4.75
They explain the links between metric units such as
mL and cm3, 1 litre of water and 1 kg.
11.6: Volume
Units of capacity p. 599
4.75
They use measurement formulas for the area and
circumference of circles and composite shapes.
11.1: Measuring and calculating
length
Examples 8, 9, 10 (pp. 557 – 58)
Exercise 11.1
11.3: Area of a circle
Examples 1 – 4 (pp. 578 – 579)
Exercise 11.2
11.4: Composite shapes
Examples 1, 2 (pp. 584 – 585)
Exercise 11.4
4.75
They calculate volumes from estimates of lengths
providing suitable lower and upper bounds.
11.6: Volume
Exercise 11.6 Question 6
See note in MathsWorld 8 Teacher
Edition p. 605
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.
They distinguish absolute and percentage error, such
as a speed camera is accurate to within 2 km/hr or an
underwater pressure meter is accurate to within
0.01%.
11.2: Area of polygons
See pp. 566 – 567, 568 – 569
4.75
5.0
5.0
5.0
11.1: Measuring and calculating
length
Try this! p. 550
Examples 3 – 5 (pp. 551 – 553)
Exercise 11.1 Questions 1 – 4
At Level 5, students measure length, perimeter, area, All sections and analysis tasks
surface area, mass, volume, capacity, angle, time
and temperature using suitable units for these
measurements in context.
They interpret and use measurement formulas for
11.1: Length, area and volume
the area and perimeter of circles, triangles and
11.2: Area of polygons
parallelograms and simple composite shapes.
11.3: Area of a circle
11.4: Composite area
Analysis task 1: Floral clock
Analysis task 3: Snowflake fractal
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18
5.0
5.0
5.0
They calculate the surface area and volume of
prisms and cylinders.
11.5: Surface area
Examples 1 – 4 (pp. 592 – 595)
Exercise 11.5 Questions 3, 4
11.6: Volume
Examples 5, 6 (pp. 600 – 601)
Exercise 11.6 Questions 2 – 16
Analysis task 2: Cake boxes
Students estimate the accuracy of measurements and
give suitable lower and upper bounds for
measurement values.
11.1: Measuring and calculating
length
Try this! p. 550
Examples 3, 4 (pp. 551 – 553)
Exercise 11.1 Questions 1 – 4
They calculate absolute percentage error of
estimated values.
11.1: Measuring and calculating
length
Try this! p. 550
Example 4 (p. 552)
Exercise 11.1 Questions 3, 4
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.
11.3: Area of a circle
Exercise 11.3 Question 3
11.6: Volume
Exercise 11.6 Question 5
Analysis task 2: Cake boxes
Working
mathematically
5.0
Chapter 12
Investigating data
Number
5.0
They use technology for arithmetic computations
involving several operations on rational numbers of
any size.
e.g., Exercise 12.2
They distinguish between categorical and numerical
data and classify numerical data as discrete (from
counting) or continuous (from measurement).
12.1: Types of data
Examples 1, 2 (pp. 622, 623)
Example 3 (p. 625)
Exercise 12.1
They calculate and interpret measures of centrality
(mean, median, and mode) and data spread (range).
12.6: Measures of centre and
spread
Examples 1 – 4 (pp. 662 – 664)
Exercise 12.6 Questions 1 – 7
Students organise and tabulate univariate data,
including grouped and ungrouped, continuous and
discrete.
12.2: Organising data using tables
Example 1 (p. 631)
Exercise 12.2 Questions 1 – 8
Measurement,
Chance and
Data
4.0
4.0
4.25
MathsWorld 8 Teacher edition
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19
4.5
4.75
4.75
4.75
4.75
5.0
5.0
5.0
Students represent uni-variate data in appropriate
graphical forms such as stem and leaf plots, bar
charts and histograms.
12.3: Displaying data using stem
plots and dot plots
Examples 1 – 3 (p. 636)
Exercise 12.3
12.4: Pie charts and column graphs
Examples 1 – 3
Exercise 12.4
12.5: Line graphs and histograms
Example 1 (p. 654)
Exercise 12.5 Questions 3, 4, 5
Students interpret graphical forms and summary
statistics in context, including recognising
misleading presentations of data or informally
identify skewed distributions.
They describe how summary statistics for measures
of centre and spread are affected by outliers and
distribution and make appropriate choices, such as
choosing the size when ordering one sized caps to
sell at a fair.
They organise and tabulate continuous data
(grouped and ungrouped) using appropriate
technology for larger data sets.
They calculate mean, median and mode for grouped
data, such as age to nearest month, and make
inferences.
12.5: Line graphs and histograms
Try this! (p. 654)
Exercise 12.5 Question 9
Students organise, tabulate and display discrete and
continuous data (grouped and ungrouped) using
technology for larger data sets.
They represent uni-variate data in appropriate
graphical forms including dot plots, stem and leaf
plots, column graphs, bar charts and histograms.
12.2: Organising data using tables
See note in MathsWorld 8 Teacher
Edition p. 626
12.5: Line graphs and histograms
Example 1 (pp. 654 – 655)
Exercise 12.5 Questions 4, 5
12.6: Measures of centre and
spread
Try this! p. 662
Examples 1, 2, 3 (pp. 662 – 664)
Example 8 (p. 669 – 670)
Exercise 12.6 Questions 8, 9, 10
They calculate summary statistics for measures of
centre (mean, median, mode) and spread (range, and
mean absolute difference), and make simple
inferences based on this data.
12.3: Displaying data using stem
plots and dot plots
12.4: Pie charts and column graphs
12.5: Line graphs and histograms
12.6: Measures of centre and
spread
Example 6 (p. 667)
Exercise 12.6
Students use the terms intersection, union and
complement of sets correctly.
See note in MathsWorld 8 Teacher
Edition
Students use a spreadsheet as a database, to sort and
categorise data and generate statistical graphs.
Analysis task2: Be careful on the
road!
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 1: Scrabble
Analysis task 2: Be careful on the
road!
Structure
4.75
Working
mathematically
4.0
5.0
MathsWorld 8 Teacher edition
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20
Chapter 13
Functions and models
Space
5.0
Students use coordinates to identify position in the
plane.
13.1: Mapping diagrams and
functions
Example 2 (p. 693)
Exercise 13.1 Questions 3 – 6
Students use linear and other functions such as f(x) =
2x – 4, xy = 24, y = 2x and y = 4 – x2 to model
situations, such as the trajectory when diving into a
pool.
Chapter Warm-up Try this! p. 686
13.1: Mapping diagrams and
functions
Exercise 13.1 Questions 13 – 15, 17,
18
13.3: Mathematical models
Example 1 (p. 715)
Exercise 13.3 Questions 1 – 10
Analysis task 1: How high will it
bounce?
Analysis task 2: Advertising and sales
Analysis task 3: Fencing a guinea pig
enclosure
They create graphs (all four quadrants of the
Cartesian coordinate system) and tables of values for
linear functions (e.g. f(x) = 0.2x– 4) expressed
symbolically and describe how features of the
function are reflected in the table or graph.
13.2: Investigating linear functions
Example 1 (pp. 706 – 707)
Exercise 13.2 Questions 1 – 10
Exercise 13.1 Questions 13 – 15, 17,
18
13.3: Mathematical models
13.2: Investigating linear functions
Structure
4.75
4.75
4.75
5.0
5.0
5.0
5.0
They name situations that might be modelled by a
linear function, such as profit as a function of the
number of units sold, explaining why by identifying
the constant rate of change.
Students identify a function as a one-to-one
correspondence or a many-to-one correspondence
between two sets.
13.1: Mapping diagrams and
functions
Try this! p. 687
Examples 1, 2 (p. 691 – 3)
Exercise 13.1 Questions 1, 4, 5, 6, 16
They represent a function by a table of values, a
graph, and by a rule.
13.1: Mapping diagrams and
functions
Example 2 (p. 693)
Exercise 13.1 Questions 5, 6, 11 – 18
They describe and specify the independent variable
of a function and its domain, and the dependent
variable and its range.
13.1: Mapping diagrams and
functions
MR GLTS in action (p. 692)
Example 2 (p. 693)
Examples 3, 4, 5 (pp. 695 – 697)
Exercise 13.1
Analysis task 3: Fencing a guinea pig
enclosure
They use linear and other functions such as f(x) = 2x
− 4, xy = 24, y = 2x and y = x2 − 3 to model various
situations.
13.3: Mathematical models
Exercise 13.3 Questions 1 – 16
Analysis task 2: How high will it
bounce?
Analysis task 3: Fencing a guinea pig
enclosure
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21
Working
mathematically
4.5
They identify situations with constant rate of change
and represent with a linear graph, such as taxi fares.
13.3: Mathematical models
Example 1 (p. 714)
Exercise 13.3 Questions 1 – 9
5.0
They identify situations with constant rate of change
and represent with a linear formula.
13.2: Investigating linear functions
Try this! pp. 704 – 706
Example 1 (pp. 706 – 707)
Exercise 13.2 Questions 1 – 8
13.3: Mathematical models
Example 1 (p. 714)
Exercise 13.3 Questions 1 – 9
Students develop simple mathematical models for
real situations (for example, using constant rates of
change for linear models).
13.3: Mathematical models
Example 1 (p. 714)
Exercise 13.3 Questions 1 – 9
Analysis task 1: How high will it
bounce?
Analysis task 2: Advertising and sales
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.
13.1: Mapping diagrams and
functions
Exercise 13.1 Questions 5, 13, 17, 18
13.3: Mathematical models
Exercise 13.3 Questions 6, 7, 10
Analysis task 1: How high will it
bounce?
Analysis task 2: Advertising and sales
Analysis task 3: Fencing a guinea pig
enclosure
5.0
5.0
MathsWorld 8 Teacher edition
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