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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)
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