-
New Century Maths 8 teaching program (p. 1)
Teaching program New Century Maths 8 for the Australian
Curriculum
Year 8 topics
Week SEMESTER 1 Week SEMESTER 2
Term 1 1
1. Pythagoras theorem (Measurement and Geometry)
Term 3 1
7. Investigating data (Statistics and Probability)
2
2
3
3
4
2. Working with numbers (Number and Algebra)
4
8. Congruent figures (Measurement and Geometry)
5
5
6
6
9. Probability (Statistics and Probability)
7
3. Algebra (Number and Algebra)
7
8
8
9
9
Lost time
10
Lost time
10
Term 2 1
4. Geometry (Measurement and Geometry)
Term 4 1
10. Equations (Number and Algebra)
2
2
3
3
4
5. Area and volume (Measurement and Geometry)
4
11. Ratios, rates and time (Number and Algebra,
5
5
Measurement and Geometry)
6
6
7
6. Fractions and percentages (Number and Algebra)
7
12. Graphing linear equations
8
8
(Number and Algebra)
9
9
10
Lost time
10
Lost time
CURRICULUM STRANDS Number and Algebra Measurement and Geometry
Statistics and Probability
-
New Century Maths 8 teaching program (p. 2)
Year 7 topics
Week SEMESTER 1 Week SEMESTER 2 Term 1
1 1. Integers
(Number and Algebra) Term 3
1 7. Decimals
(Number and Algebra) 2
2
3
3
4
2. Angles (Measurement and Geometry)
4
8. Area and volume (Measurement and Geometry)
5
5
6
6
7
3. Whole numbers (Number and Algebra)
7
9. The number plane (Number and Algebra,
8
8
Measurement and Geometry)
9
9
Lost time
10
Lost time 10
Term 2 1
4. Fractions and percentages (Number and Algebra)
Term 4 1
10. Analysing data (Statistics and Probability)
2
2
3
3
4
5. Algebra and equations (Number and Algebra)
4
11. Probability (Statistics and Probability)
5
5
6
6
12. Ratios, rates and time (Number and Algebra,
7
6. Geometry (Measurement and Geometry)
7
Measurement and Geometry)
8
8
9
9
Lost time
10
Lost time 10
CURRICULUM STRANDS Number and Algebra Measurement and Geometry
Statistics and Probability
-
New Century Maths 8 teaching program (p. 3)
1. PYTHAGORAS THEOREM Time: 3 weeks (Term 1, Week 1) Text: New
Century Maths 8, Chapter 1, p.2 NSW and Australian Curriculum
references: Measurement and Geometry Right-angled triangles
(Pythagoras) / Real numbers
investigate the concept of irrational numbers, including
(8NA186) Right-angled triangles (Pythagoras) / Pythagoras and
trigonometry
investigate Pythagoras theorem and its application to solving
simple problems involving right-angled triangles (NSW Stage 4 /
9MG222)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-16 MG
applies Pythagoras theorem to calculate side lengths in
right-angled triangles and solves related problems
INTRODUCTION This is the first time students meet Pythagoras
theorem. This is a Year 9 topic in the Australian curriculum but a
Stage 4 (Years 7-8) topic in the NSW syllabus: Students should gain
an understanding of Pythagoras theorem, rather than just being able
to recite the formula. Emphasis should be placed upon understanding
the theorem and using it to solve problems involving the sides of
right-angled triangles. CONTENT 1 Square roots and surds 8NA186 U 2
Discovering Pythagoras theorem 9MG222 U F R C
identify the hypotenuse as the longest side in any right-angled
triangle and also as the side opposite the right angle establish
the relationship between the lengths of the sides of a right-angled
triangle in practical ways, including using
digital technologies 3 Finding the hypotenuse 9MG222 U F
solve practical problems involving Pythagoras theorem,
approximating the answer as a decimal and giving an exact answer as
a surd
4 Finding a shorter side 9MG222 U F 5 Mixed problems 9MG222 F 6
Testing for right-angled triangles 9MG222 U F R
use the converse of Pythagoras theorem to establish whether a
triangle has a right angle 7 Pythagorean triads 9MG222 U F
identify a Pythagorean triad as a set of three numbers such that
the sum of the squares of the first two equals the square of the
third
8 Pythagoras theorem problems 9MG222 F PS 9 Revision and mixed
problems RELATED TOPICS Year 7: Whole numbers, Algebra and
equations, Geometry Year 8: Working with numbers, Geometry, Area
and volume, Congruent figures Year 9: Pythagoras theorem,
Trigonometry, Coordinate geometry PROFICIENCY STRANDS / WORKING
MATHEMATICALLY U = Understanding (knowing and relating maths):
Understanding how the sides of a right-angled triangle are related
by
Pythagoras theorem F = Fluency (applying maths): Selecting
appropriate techniques involving Pythagoras theorem PS = Problem
solving (modelling and investigating with maths): Using Pythagoras
theorem to solve measurement
problems R = Reasoning (generalising and proving with maths):
Proving that a triangle is right-angled given the lengths of
its
sides C = Communicating (describing and representing maths):
Describing and explaining Pythagoras theorem in words and
-
New Century Maths 8 teaching program (p. 4)
as a formula EXTENSION IDEAS
Perigals dissection and other formal proofs of Pythagoras
theorem Pythagoras and the Pythagoreans, history of Pythagoras
theorem Harder problems: two-stage or in three-dimensions, for
example, longest diagonal in a rectangular prism Word problems
History of Pythagorean triads, properties of Pythagorean triads
Length of an interval on the number plane Irrational numbers,
graphing surds on a number line, simplifying surds The real number
system, proof that 2 is irrational
TEACHING NOTES AND IDEAS Pythagoras theorem was actually
discovered by others, centuries before Pythagoras was born around
580 BCE. Use knotted rope to show how ancient Egyptians builders
made a 3-4-5 triangle to create a right angle. State Pythagoras
theorem in words and as a formula. Stress that it works for
right-angled triangles only. Emphasise correct
setting-out of solutions. Check answers. Obviously its wrong if
the hypotenuse is shorter than one of the other sides.
There are different formulas for creating Pythagorean triads,
such as (p2 q2, 2pq, p2 + q2), (n,2
12 n , 2
12 +n ) for odd n, (2n
+ 1, 2n2 + 2n, 2n2 + 2n + 1). Multiplying or dividing a triad by
a constant gives another triad: we can use this to create decimal
triads such as (2.8, 9.6, 10).
Pythagorean triads (useful for triangle problems): (3, 4, 5) (5,
12, 13) (6, 8, 10) (7, 24, 25) (8, 15, 17) (9, 12, 15) (9, 40, 41)
(10, 24, 26) (11, 60, 61) (12, 16, 20) (12, 35, 37) (13, 84, 85)
(14, 48, 50) (15, 20, 25) (15, 36, 39) (16, 30, 34) (16, 63, 65)
(18, 24, 30) (18, 80, 82) (20, 21, 29) (20, 48, 52) (20, 99, 101)
(21, 28, 35) (21, 72, 75) (24, 32, 40) (24, 45, 51) (24, 70, 74)
(25, 60, 65) (27, 36, 45) (28, 45, 53) (28, 96, 100) (30, 40, 50)
(30, 72, 78) (32, 60, 68) (33, 44, 55) (33, 56, 65) (35, 84, 91)
(36, 48, 60) (36, 77, 85) (39, 52, 65) (39, 80, 89) (40, 42, 58)
(40, 75, 85) (40, 96, 104) (42, 56, 70) (45, 60, 75) (48, 55, 73)
(48, 64, 80) (48, 90, 102) (51, 68, 85) (54, 72, 90) (56, 90, 106)
(57, 76, 95) (60, 63, 87) (60, 80, 100) (60, 91, 109) (63, 84, 105)
(65, 72, 97) (66, 88, 110) (69, 92, 115) (72, 96, 120) (80, 84,
116).
ASSESSMENT IDEAS Research assignment on Pythagoras and
Pythagoras theorem. Matching activities: Pythagoras theorem to
diagrams. Writing activity explaining Pythagoras theorem.
TECHNOLOGY Spreadsheets can be used to find unknown sides or
generate Pythagorean triads. Use the Internet to research the
history of Pythagoras and irrational numbers. Use dynamic geometry
software to explore and prove Pythagoras theorem. LANGUAGE
Hypotenuse is an ancient Greek word: hypo means under while
teinousa means stretching because the hypotenuse
stretches under a right angle. Explain and reinforce the logic
behind the converse of Pythagoras theorem. From the NSW syllabus:
The meaning of exact answer will need to be taught explicitly.
Students may find some of the
terminology/vocabulary encountered in word problems involving
Pythagoras theorem difficult to interpret, for example, foot of a
ladder, inclined, guy wire.
-
New Century Maths 8 teaching program (p. 5)
2. WORKING WITH NUMBERS Time: 3 weeks (Term 1, Week 4) Text: New
Century Maths 8, Chapter 2, p.36 NSW and Australian Curriculum
references: Number and Algebra Indices / Number and place value
Use index notation with numbers to establish the index laws with
positive integral indices and the zero index (8NA182) Investigate
index notation and represent whole numbers as products of powers of
prime numbers (7NA149)
Computation with Integers / Number and place value Carry out the
four operations with rational numbers and integers, using efficient
mental and written strategies and
appropriate digital technologies (8NA183) Fractions, Decimals
and Percentages / Real numbers
Investigate terminating and recurring decimals (8NA184) NSW
Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-4 NA compares, orders and calculates with integers, applying a
range of strategies to aid computation MA4-5 NA operates with
fractions, decimals and percentages MA4-9 NA operates with
positive-integer and zero indices of numerical indices
INTRODUCTION This topic revises and extends basic operations
with whole numbers, integers, decimals, powers, roots and prime
factors, then explores properties of squares and square roots (ab)2
and ab and the index laws. This is a short refresher topic that
reinforces mental, pen-and-paper and calculator skills so dont
dwell too long on particulars. Keep it simple and make the revision
suitable to the ability and experience of your Year 8 class. You
may even like to set part of this topic as a revision assignment
rather than re-teach it all. Ensure that estimating and checking of
answers are reinforced during lessons. CONTENT 1 Mental calculation
7NA151 U F R
apply the associative, commutative and distributive laws to aid
mental computation 2 Adding and subtracting integers 8NA183 U F PS
R 3 Multiplying integers 8NA183 U F R 4 Dividing integers 8NA183 U
F R 5 Order of operations 8NA183 U F
apply the order of operations to evaluate expressions involving
directed numbers mentally, including where an operator
is contained within the numerator or denominator of a fraction,
for example, 15 915 3+
6 Decimals 8NA183 U F round decimals to a specified number of
decimal places
7 Multiplying and dividing decimals 8NA183 U F PS R 8
Terminating and recurring decimals 8NA184 U F R C
use the notation for recurring (repeating) decimals, for
example, 0.33333 = 0.3 , 0.345345345 = 0.345 , 0.266666 = 0.26
9 Powers and roots 7NA149 U F R C find square roots and cube
roots of any non-square whole number using a calculator, after
first estimating apply the order of operations to evaluate
expressions involving indices, square and cube roots, with and
without a
calculator
determine through numerical examples the properties of square
roots of products: (ab)2 and ab 10 Prime factors 7NA149 U F R
express a number as a product of its prime factors to determine
whether its square root or cube root is an integer 11 Index laws
for multiplying and dividing 8NA182 U F R
use index notation with numbers to establish the index laws with
positive integral indices and the zero index use index laws to
simplify expressions with numerical bases, for example, 52 54 5 =
57
-
New Century Maths 8 teaching program (p. 6)
12 More index laws 8NA182 U F R 13 Revision and mixed problems
RELATED TOPICS Year 7: Integers, Whole numbers, Fractions and
percentages, Decimals, Ratios, rates and time Year 8: Algebra,
Fractions and percentages, Ratios, rates and time Year 9: Working
with numbers, Indices PROFICIENCY STRANDS / WORKING MATHEMATICALLY
U = Understanding (knowing and relating maths): Understanding
operations with numbers, including powers, roots and
the index laws F = Fluency (applying maths): Using appropriate
methods for evaluating numerical expressions PS = Problem solving
(modelling and investigating with maths): Using operations with
integers and decimals to solve
real-life problems R = Reasoning (generalising and proving with
maths): Discovering general properties of numbers and operations
with
numbers C = Communicating (describing and representing maths):
Using correct notation for recurring decimals, powers and
roots EXTENSION IDEAS Investigate the square root of quotients
Investigate the history of calculation methods, for example,
Italian multiplication Irrational numbers, surds, graphing surds on
a number line, simplifying surds. Investigate the value of 0.9 . Is
it really equal to 1? Convert recurring decimals to fractions (Year
9, Stage 5.3). Investigate scientific notation. How did
mathematicians find square roots before calculators and computers?
Investigate Newtons method. TEACHING NOTES AND IDEAS Revise number
and calculator skills through problems, puzzles and games.
Encourage students to develop number sense. Analysing properties of
numbers leads to the study of pattern and early algebra work.
Fractions, percentages, ratios and rates will be covered later this
year. The NSW syllabus says that written multiplication and
division of decimals may be limited to operators with two digits.
When teaching rounding decimals, include more difficult examples,
such as rounding 4.8971 to two decimal places. Investigate patterns
in the recurring decimals of the fraction families of the sixths,
sevenths and ninths. Some decimals are neither terminating nor
recurring. Their digits run endlessly, but without repeating, for
example, 2 =
1.4142135 and = 3.1415926 Investigate finding higher powers on
the calculator. As an alternative to factor trees, prime factors
can also be extracted by repeated division. See the Skillsheet
Prime factors
by repeated division.
Common mistake: 9 = 3. The square root of a number is a single
positive value, so 9 = 3 only. However, 9 = -3 and the equation x2
= 9 has two solutions, x = 3 or -3.
In Year 8, the index laws are applied to numerical expressions
only. The index laws in algebraic form will be covered in Year 9 or
in the Year 8 topic Algebra as extension work.
ASSESSMENT IDEAS Non-calculator test. Revision assignment.
TECHNOLOGY Not all calculators are the same: teachers will need to
look for subtle differences in the locations and functions of keys.
Use calculators to evaluate mixed expressions, including the use of
the parentheses and ANS keys, but beware of cheap calculators that
do not follow order of operations rules. Students can use the
spreadsheet to round or order decimals, or convert fractions to
terminating and recurring decimals.
-
New Century Maths 8 teaching program (p. 7)
LANGUAGE -3 is read negative 3, not minus 3. Students should not
confuse the negative sign with the minus operation. Reinforce the
language of approximation: approximate, write correct to, round to,
n decimal places, nearest tenth.
Note that the NSW syllabus now prefers the term rounding to
rounding off. Terminating means stopping; recurring means
repeating.
-
New Century Maths 8 teaching program (p. 8)
3. ALGEBRA Time: 3 weeks (Term 1, Week 7) Text: New Century
Maths 8, Chapter 3, p.88 NSW and Australian Curriculum references:
Number and Algebra Algebraic Techniques 1 and 2 / Patterns and
algebra
Extend and apply the distributive law to the expansion of
algebraic expressions (8NA190) Factorise algebraic expressions by
identifying numerical factors (8NA191) Factorise algebraic
expressions by identifying algebraic factors (NSW Stage 4) Simplify
algebraic expressions involving the four operations (8NA192)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-8 NA generalises number properties to operate with algebraic
expressions
INTRODUCTION The Australian curriculum introduces algebra by
generalising number laws and patterns, and in the Year 7 topic
Algebra and equations students met elementary concepts such as
variables, translating worded statements to algebraic expressions,
algebraic abbreviations and substitution. In this Year 8 topic,
students meet more formal operations with algebraic terms such as
simplifying algebraic expressions, including the processes of
expanding and factorising. This topic is fairly technical and
abstract so each skill should be taught with care and precision as
students may will the concepts difficult. Students should practise
and master each skill before moving onto the next one. CONTENT 1
Variables 7NA175 U F R C
introduce the concept of variables as a way of representing
numbers using letters extend and apply the laws and properties of
arithmetic to algebraic terms and expressions
2 From words to algebraic expressions 7NA177 U F PS R C move
fluently between algebraic and word representations as descriptions
of the same situation
3 Substitution 7NA176 U F PS create algebraic expressions and
evaluate them by substituting a given value for each variable
4 Collecting variables 8NA192 U F R C 5 Adding and subtracting
terms 8NA192 U F R C 6 Multiplying terms 8NA192 U F R C 7 Dividing
terms 8NA192 U F R C 8 Extension: The index laws 9NA212 U F R C
extend and apply the index laws to variables, using positive
integer indices and the zero index 9 Expanding expressions 8NA190 U
F R 10 Factorising algebraic terms 8NA191 U F R
factorise a single algebraic term, for example, 6ab = 3 2 a b 11
Factorising expressions 8NA191 U F R 12 Factorising with negative
terms 8NA191 U F R 13 Revision and mixed problems RELATED TOPICS
Year 7: Algebra and equations Year 8: Working with numbers,
Equations, Graphing linear equations Year 9: Algebra, Indices,
Equations PROFICIENCY STRANDS / WORKING MATHEMATICALLY U =
Understanding (knowing and relating maths): Learning algebraic
concepts and operations F = Fluency (applying maths): Applying
general rules effectively to simplify algebraic expressions PS =
Problem solving (modelling and investigating with maths): Using
expressions and formulas to represent and solve
problems
-
New Century Maths 8 teaching program (p. 9)
R = Reasoning (generalising and proving with maths): Using
algebra to represent, generalise and simplify pattern in
numbers
C = Communicating (describing and representing maths):
Describing and representing general properties of numbers
algebraically
EXTENSION IDEAS More challenging problems involving substitution
and translating worded statements into algebraic expressions
Binomial expansions (Year 9/Stage 5.2), for example (x + 3)(x 2),
(x + 5)(x 5), (x + 2)2 Factorising by grouping in pairs Negative or
fractional indices TEACHING NOTES AND IDEAS Resources: counters,
cubes, cups, blocks, envelopes and other concrete materials for
modelling variables From the NSW syllabus: To gain an understanding
of algebra, students must be introduced to the concepts of
pronumerals,
expressions, unknowns, equations, patterns, relationships and
graphs in a wide variety of contexts. For each successive context,
these ideas need to be redeveloped. Students need gradual exposure
to abstract ideas as they begin to relate to algebraic terms to
real situations.
Stress that a variable does not stand for an object but for the
number of objects. Even though we do not know the value of a
variable or term, we can still collect them. For example, 3 lots of
x plus 4 lots of x equals 7 lots of x.
Some students believe 4a + 2b a = [4a +] [2b ] a = 5a 2b.
Encourage them to group each term with the sign before it: 4a [+
2b] [ a] = 3a + 2b.
Determine and justify whether a simplified or equivalent
expression is correct by substituting a number. Common mistakes: 2a
a = 2, 3b2 = 3b 3b. Explain that the index 2 belongs to the b only.
Application of collecting like terms: the formulas for the
perimeter of the square and rectangle. Show that variables
provide
a powerful shorthand in this regard. For simplifying algebraic
terms, include mixed exercises so that students experience all four
operations and identify which
rule to use. Include terms that are constants or which have
powers. NSW syllabus: Check expansions and factorisations by
performing the reverse process. Include examples involving
negative terms. ASSESSMENT IDEAS Writing activity on the use of
variables and simplifying algebraic expressions Research assignment
or poster on the algebraic rules or the history/meaning of algebra
Vocabulary test TECHNOLOGY Note that spreadsheet formulas are
written differently to algebraic formulas. CAS (Computer Algebra
Systems) can be used to simplify, expand or evaluate algebraic
expressions. LANGUAGE Reinforce the meanings of variable, term,
expression, simplify, evaluate, substitute, expand and factorise.
An algebraic term consists of a number and/or a variable, for
example, 4p2. An algebraic expression is a phrase containing
terms and one or more arithmetic operation, for example, 5x + 6.
An equation is a sentence containing an expression, an = sign and
an answer, for example, 5x + 6 = 26.
The word expand comes from writing out an expression the long
way without brackets. Draw a diagram using rectangles and an array
of dots to show equivalences such as 3(n + 2) = 3n + 6. Students
are not required to learn the phrase distributive law.
NSW syllabus: Recognise the role of grouping symbols and the
different meanings of expressions, such as 2a + 1 and 2(a + 1).
Emphasise the difference between expand and factorise, as
students will often do the opposite of what is requested.
-
New Century Maths 8 teaching program (p. 10)
4. GEOMETRY Time: 3 weeks (Term 2, Week 1) Text: New Century
Maths 8, Chapter 4, p.130 NSW and Australian Curriculum references:
Measurement and Geometry Properties of Geometrical Figures 1 /
Geometric reasoning
Identify corresponding, alternate and co-interior angles when
two straight lines are crossed by a transversal, and the
relationships between them (7MG164)
Investigate conditions for two lines to be parallel and solve
simple numerical problems using reasoning (7MG165) Classify
triangles according to their side and angle properties and describe
quadrilaterals (7MG165) Demonstrate that the angle sum of a
triangle is 180 and use this to find the angle sum of a
quadrilateral (7MG166)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-17 MG classifies, describes and uses the properties of
triangles and quadrilaterals, and determines congruent
triangles to find unknown lengths and angles MA4-18 MG
identifies and uses angle relationships, including those related to
transversals on sets of parallel lines
INTRODUCTION This topic revises geometrical concepts introduced
in Year 7, namely relating to angles, triangles and quadrilaterals,
in a more formal way. However, practical activities and correct
geometrical terminology should be promoted throughout this topic.
From the NSW syllabus: At this stage in geometry, students should
write reasons without the use of abbreviations to assist them in
learning new terminology, and in understanding and retaining
geometrical concepts. CONTENT 1 Angle geometry 6MG141 U F PS R
C
investigate angles on a straight line, angles at a point and
vertically opposite angles, and use results to find unknown
angles
2 Angles on parallel lines 7MG163, 7MG164 U F PS R C 3 Line and
rotational symmetry 7MG181 U F C
identify line and rotational symmetries 4 Classifying triangles
7MG165 U F R C
classify triangles according to their side and angle properties
5 Classifying quadrilaterals 7MG165 U F R C
distinguish between convex and non-convex quadrilaterals (the
diagonals of a convex quadrilateral lie inside the figure) describe
squares, rectangles, rhombuses, parallelograms, kites and
trapeziums
6 Properties of quadrilaterals 7MG165 U F R C investigate the
properties of special quadrilaterals classify special
quadrilaterals on the basis of their properties
7 Angle sums of triangles and quadrilaterals 7MG166 U F PS R
justify informally that the interior angle sum of a triangle is
180, and that any exterior angle equals the sum of the two
interior opposite angles use the angle sum of a triangle to
establish that the angle sum of a quadrilateral is 360
8 Extension: Angle sum of a polygon NSW STAGE 5.2 U F PS R apply
the result for the interior angle sum if a triangle to find, by
dissection, the interior angle sum of polygons with
more than three sides 9 Revision and mixed problems RELATED
TOPICS Year 7: Angles, Geometry Year 8: Pythagoras theorem, Area
and volume, Congruent figures Year 9: Geometry, Congruent and
similar figures
-
New Century Maths 8 teaching program (p. 11)
PROFICIENCY STRANDS / WORKING MATHEMATICALLY U = Understanding
(knowing and relating maths): Learning geometrical concepts,
definitions, terminology and notation F = Fluency (applying maths):
Applying correct procedures, language and notation to solve
geometrical problems PS = Problem solving (modelling and
investigating with maths): Finding unknown angles in geometrical
problems R = Reasoning (generalising and proving with maths): Using
logic and reasoning to explore and deduce geometrical
ideas and properties C = Communicating (describing and
representing maths): Classifying angles, triangles and
quadrilaterals and describing
their properties, including symmetries EXTENSION IDEAS
Investigate the history of geometry and Euclid. From NSW syllabus:
Students who recognise class inclusivity and minimum requirements
for definitions may address this
Stage 4 content concurrently with content in Stage 5 Properties
of Geometrical Figures where properties of triangles and
quadrilaterals are deduced from formal definitions. For example, is
a parallelogram a trapezium?
The formal definitions and tests for special quadrilaterals
(Stage 5.3). See the NSW syllabus (Stage 5.3 Properties of
Geometrical Figures) on introducing more formal definitions of the
special triangles and quadrilaterals.
Find the size of one angle in a regular polygon, or the exterior
angle sum of a convex polygon. Formal proofs in deductive
geometry.
TEACHING NOTES AND IDEAS Resources: rulers, set squares,
protractors, paper and scissors, charts and posters, geometry and
drawing software. From syllabus: Students should give reasons when
finding unknown angles. For some students, formal setting-out could
be
introduced. For example, PQR = 70 (corresponding angles, PQ ||
SR). Give examples and counter-examples of the types of triangles
and quadrilaterals and ask students to describe them in their
own words. You may like to give the meaning first, then the
name. Properties of triangles and quadrilaterals should be
demonstrated informally (by symmetry, paper-folding, protractor
and
ruler measurement), rather than by congruent triangle proofs.
From NSW syllabus: A range of examples of the various triangles and
quadrilaterals should be given, including
quadrilaterals containing a reflex angle and figures presented
in different orientations. The properties of special quadrilaterals
allow us to develop formulas for finding their areas in the topic
Area and volume,
for example, the diagonal properties of the kite and rhombus. In
how many different ways can you demonstrate the angle sum of a
triangle (or quadrilateral)? Proving properties of quadrilaterals
by similar triangles will be covered in the topic Congruent
figures. ASSESSMENT IDEAS Writing activity or poster summary on the
properties of angles, triangles or quadrilaterals Vocabulary test
What quadrilateral am I puzzles Research/investigation assignment
on properties of triangles or quadrilaterals Assignment on setting
out a geometry proof TECHNOLOGY There is much scope in this topic
to use dynamic geometry software such as GeoGebra. The Internet is
full of dynamic geometry animations and applets that demonstrate
the properties of angles, triangles and quadrilaterals shown in
this topic. LANGUAGE Equilateral comes from the Latin aequus latus,
meaning equal sides, isosceles comes from the Greek isos skelos,
meaning
equal legs, and scalene comes from the Greek skalenos skelos,
meaning uneven leg. Avoid using the term base angles for isosceles
triangles because it may be misleading, depending upon the
orientation of
the triangle. Instead, use the angles opposite the equal sides
or the two angles next to the uneven side. From the NSW syllabus:
The diagonals of a convex quadrilateral lie inside the figure.
-
New Century Maths 8 teaching program (p. 12)
5. AREA AND VOLUME Time: 3 weeks (Term 2, Week 4) Text: New
Century Maths 8, Chapter 5, p.170 NSW and Australian Curriculum
references: Measurement and Geometry Area / Using units of
measurement
Choose appropriate units of measurement for area and volume and
convert from one unit to another (8MG195) Find perimeters and areas
of parallelograms, trapeziums, rhombuses and kites (8MG196)
Investigate the relationship between features of circles such as
circumference, area, radius and diameter; use formulas to
solve problems involving circumference and area (8MG197) Volume
/ Using units of measurement
Develop the formulas for volumes of rectangular and triangular
prisms and prisms in general; use formulas to solve problems
involving volume (8MG198)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-12 MG
calculates the perimeter of plane shapes and the circumference of
circles MA4-13 MG uses formulas to calculate the area of
quadrilaterals and circles, and converts between units of area
MA4-14 MG uses formulas to calculate the volume of prisms and
cylinders, and converts between units of volume
INTRODUCTION This topic revises and extends perimeter, area and
volume concepts, with new content including the areas of special
quadrilaterals and circles, and conversions between metric units
for area and volume. Circle measurement is formally introduced, and
after examining the parts and geometrical properties of a circle,
students discover the special number and its role in calculating
perimeters and areas of circles and circular shapes. CONTENT 1
Perimeter 8MG196 U F PS R 2 Metric units for area 8MG195 U F PS R C
3 Areas of rectangles, triangles and parallelograms 7MG159 U PS
R
establish the formulas for areas of rectangles, triangles and
parallelograms and use these in problem solving 4 Areas of
composite shapes 7MG159 U F PS 5 Area of a trapezium 8MG196 U PS R
6 Areas of kites and rhombuses 8MG196 U PS R 7 Parts of a circle
8MG197 U C
investigate the line symmetries and the rotational symmetry of
circles and of diagrams involving circles, such as a sector and a
circle with a marked chord or tangent
8 Circumference of a circle 8NA186, 8MG197 U F PS R investigate
the concept of irrational numbers, including find the perimeter of
quadrants, semi-circles, sectors and composite figures
9 Area of a circle 8MG197 U F PS R calculate the area of
quadrants, semi-circles, sectors and composite figures
10 Metric units for volume 8MG195 U F PS R C 11 Volume of a
prism 8MG198 U F PS R C
determine if a solid has a uniform cross-section 12 Volume of a
cylinder 8MG198 U F PS R 13 Volume and capacity 6MG138 U F PS
connect volume and capacity and their units of measurement
recognise that 1 mL is equivalent to 1 cm3 solve problems involving
volume and capacity of right prisms and cylinders
14 Revision and mixed problems RELATED TOPICS Year 7: Geometry,
Area and volume Year 8: Pythagoras theorem, Geometry Year 9:
Geometry, Surface area and volume, Congruent and similar
figures
-
New Century Maths 8 teaching program (p. 13)
PROFICIENCY STRANDS / WORKING MATHEMATICALLY U = Understanding
(knowing and relating maths): Learning measurement concepts,
terminology and techniques F = Fluency (applying maths): Selecting
correct strategies to convert between metric units and calculate
areas and
volumes PS = Problem solving (modelling and investigating with
maths): Solving problems involving measurement, perimeter,
area and volume R = Reasoning (generalising and proving with
maths): Introducing formulas to generalise the rule for
calculating
perimeters, areas and volumes; analyse relationships for
converting between metric units for length, area and volume C =
Communicating (describing and representing maths): Describing
metric units of area and volume and labelling the
parts of a circle EXTENSION IDEAS Herons formula for the area of
a triangle with sides of length a, b and c. Areas of irregular
figures: traverse surveys, Simpsons rule. Surface area of a cube,
prism and cylinder. History of , formulas for generating the value
of . Area formula involving d rather than r. Area of an ellipse.
Calculate the perimeter of a regular hexagon inscribed in a circle
with the circles circumference to demonstrate that > 3.
Circumference of the Earth, latitude and longitude (small and great
circles) on the Earths surface. Volume of a pyramid or cone (Year
10 Stage 5.3). TEACHING NOTES AND IDEAS Resources: 1 cm grid paper,
cube blocks, cardboard grid diagrams of plane shapes, nets and
models of prisms, discs, coins,
cups, CDs and lids for circumference measurement activities,
compasses, string, measuring tape, ruler, trundle wheel, paper and
scissors for dissection activities, geometry/drawing software.
Areas may be found by paper-cutting activities and grid
overlays: print out the Worksheet 1 cm grid paper and photocopy it
onto an overhead transparency.
Estimate areas of windows, noticeboards, blackboards, desktop,
postage stamps. Mark a square metre or hectare on school
grounds.
Examples of composite shapes: L-shape, T-shape, U-shape,
trapezium, semi-circles, annuli and pipes. The area of a rhombus or
a kite can be cut up and rearranged into two congruent triangles or
one rectangle. The area
formula actually works for any quadrilateral with perpendicular
diagonals. The area of a trapezium can be cut up and rearranged
into two triangles or one rectangle. When proving the formulas for
areas of special quadrilaterals, demonstrate the usefulness and
power of variables in algebra. Emphasise how area involves
multiplying two dimensions or powers of 2 while volume involves
three dimensions or
powers of 3. Compare the area formula for a circle to that of a
square: both involve powers of 2. Draw each part of the circle on
the board and ask students to describe it in their own words, for
example, a sector is like a
slice of pizza or cake. From the NSW syllabus: The number is
known to be irrational At this stage, students only need to know
that the digits
in its decimal expansion do not repeat (all this means is that
it is not a fraction), and in fact have no known pattern. 3.141 592
653 589 793
With composite area problems, encourage students to look for
opportunities for combining two semi-circles. ASSESSMENT IDEAS
Practical activity/assignment/test on perimeter/circumference, area
and volume. Research assignment on the history/progress of and
finding the circumference/area of a circle. Open-ended and
back-to-front questions: A triangular prism has a volume of 36 cm3.
What could its dimensions be? TECHNOLOGY Drawing and animation
software may be used to demonstrate area and volumes of geometrical
figures. Also search for animations and applets from the Internet.
LANGUAGE From NSW syllabus: Volume refers to the space occupied by
an object or substance. The abbreviation m3 is read cubic
metre(s) and not metres cubed. Ensure that students use the
correct units for area and volume. Express area formulas in words
as well as algebraically.
-
New Century Maths 8 teaching program (p. 14)
From NSW syllabus: The names for some parts of the circle
(centre, radius, diameter, circumference, sector, semi-circle and
quadrant) are first introduced in Stage 3 Pi () is the Greek letter
equivalent to p, and is the first letter of the Greek word
perimetron, meaning perimeter. In 1737, Euler used the symbol for
pi for the ratio of the circumference to the diameter of a
circle.
Concentric means same centre, an annulus is a ring shape bounded
by two concentric circles.
-
New Century Maths 8 teaching program (p. 15)
6. FRACTIONS AND PERCENTAGES Time: 3 weeks (Term 2, Week 7)
Text: New Century Maths 8, Chapter 6, p.234 NSW and Australian
Curriculum references: Number and Algebra Fractions, Decimals and
Percentages / Real numbers
Solve problems involving the use of percentages, including
percentage increases and decreases, with and without digital
technologies (8NA187)
Financial Mathematics / Money and financial mathematics Solve
problems involving profit and loss, with and without digital
technologies (8NA189) Investigate and calculate Goods and Services
Tax (GST), with and without digital technologies (NSW Stage 4)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-5 NA operates with fractions, decimals and percentages MA4-6 NA
solves financial problems involving purchasing goods
INTRODUCTION This topic revises Year 7 concepts in fractions and
percentages before introducing operations with percentages and
problems involving percentages. Students have been calculating
percentages of quantities since primary school but here they will
learn the skills necessary for applying percentages to financial
situations, including percentage change, the unitary method, and
calculating profit, loss and GST. Although the advancement of
computers and the metric system has made decimals more practical
than fractions, fraction skills are still applied in areas such as
algebraic fractions, solving equations, ratios and similar figures.
CONTENT 1 Fractions 7NA152 U F
compare fractions using equivalence 2 Adding and subtracting
fractions 7NA153 U F R
solve problems involving addition and subtraction of fractions,
including those with unrelated denominators 3 Multiplying and
dividing fractions 7NA154 U F PS
multiply and divide fractions using efficient written strategies
and digital technologies 4 Percentages, fractions and decimals
7NA157 U F C
connect fractions, decimals and percentages and carry out simple
conversions 5 Fraction and percentage of a quantity 7NA158 U F
C
find fractions and percentages of quantities and express one
quantity as a fraction or percentage of another, with and without
digital technologies
6 Expressing amounts as fractions and percentages 7NA155, 7NA158
U F C express one quantity as a fraction of another, with and
without digital technologies
7 Percentage increase and decrease 8NA187 U F PS C 8 Percentages
without calculators 8NA187 U F PS R 9 The unitary method 8NA187 U F
PS R C 10 Profit, loss and GST 8NA189 U F PS R C 11 Percentage
problems 8NA187 U F PS C 12 Revision and mixed problems RELATED
TOPICS Year 7: Fractions and percentages, Decimals, Ratios, rates
and time Year 8: Working with numbers, Probability, Equations,
Ratios, rates and time PROFICIENCY STRANDS / WORKING MATHEMATICALLY
U = Understanding (knowing and relating maths): Learning the
concepts, notations and operations of fractions and
percentages F = Fluency (applying maths): Applying appropriate
fraction and percentage operations to different situations
-
New Century Maths 8 teaching program (p. 16)
PS = Problem solving (modelling and investigating with maths):
Solve a variety of real-life problems using fractions and
percentages, including financial problems
R = Reasoning (generalising and proving with maths): Finding
shortcuts for calculating with fractions and percentages by looking
for general patterns
C = Communicating (describing and representing maths):
Converting between fractions, decimals and percentages;
interpreting and writing worded answers to problems
EXTENSION IDEAS Repeated percentage changes, for example,
successive discounts. What percentage change is equivalent to an
increase of
10% followed by a decrease of 10%? Investigate interest rates
and the method and formula for calculating simple and compound
interest. TEACHING NOTES AND IDEAS Resources: newspaper cuttings of
applications of percentages, for example, interest rates, GST,
statistical graphs, opinion
polls. Have students make a collage of newspaper clippings on
the applications of percentages. Examine an advertising claim
that
uses percentages. Encourage students to know the percentage
equivalents of commonly-used fractions and be able to use their
mental
computation skills on these. Students should recognise
equivalences when calculating, for example, multiplication by 1.05
will increase a number by 5%, multiplication by 0.87 will decrease
it by 13%.
Investigate the percentage forms of fraction families such as
the eighths and the sixths. What are 32 , 16 % and 37.5% as
fractions? Encourage students to develop a number sense rather
than rely upon the calculator too often. Check that answers
make
sense. Estimate first. Applications of percentages: interest
rates, cricket statistics (for example, run rate), exam marks,
discount, GST, inflation,
unemployment, commission, ingredients in food and drink. Does
taking off 10% followed by adding 10% give the original number? The
unitary method is a powerful skill that can be applied to
percentages, fractions, decimals, ratios and rates. From the NSW
syllabus: The GST is levied at a flat rate of 10% on most goods and
services, apart from GST-exempt items
(usually basic necessities such as milk and bread). ASSESSMENT
IDEAS Collage/poster on the applications of percentages. Revision
assignment on applications of percentages. TECHNOLOGY Use
spreadsheets to convert between fractions, decimals and percentages
and to order fractions, decimals and percentages. You could
investigate the percentage format on a spreadsheet. Some
calculators have a [%] key: 16 [] 25 [%] gives 25% of 16; 5 [] 40
[%] gives 5 out of 40 as a percentage; 150 [] 13 [%] [] decreases
150 by 13%. LANGUAGE The word cent comes from the Latin centum
meaning one hundred, so per cent means out of one hundred. The
%
symbol is a modified form of 100
.
When expressing quantities as percentages, reinforce the
importance of identifying what follows of in the question, for
example, Calculate the discount as a percentage of the marked
price. Students should also be able to differentiate between cost
price and selling price.
Why does the unitary method have that name?
-
New Century Maths 8 teaching program (p. 17)
7. INVESTIGATING DATA Time: 3 weeks (Term 3, Week 1) Text: New
Century Maths 8, Chapter 7, p.282 NSW and Australian Curriculum
references: Statistics and Probability Data Collection and
Representation / Data representation and interpretation
Identify and investigate issues involving numerical data
collected from primary and secondary sources (7SP169) Construct and
compare a range of data displays including stem-and-leaf plots and
dot plots (7SP170) Explore the practicalities and implications of
obtaining data through sampling using a variety of investigative
processes
(8SP206) Investigate techniques for collecting data, including
census, sampling and observation (8SP284)
Single Variable Data Analysis / Data representation and
interpretation Calculate mean, median, mode and range for sets of
data, and interpret these statistics in the context of data
(7SP171) Describe and interpret data displays using median, mean
and range (7SP172) Investigate the effect of individual data
values, including outliers, on the mean and median (8SP207) Explore
the variation of means and proportions of random samples drawn from
the same population (8SP293)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-19 SP collects, represents and interprets single sets of data,
using appropriate statistical displays MA4-20 SP analyses single
sets of data using measures of location and range
INTRODUCTION This topic revises and extends statistical concepts
introduced in Year 7, introducing the techniques involved in
collecting data. This is a practical topic, and it is expected that
some data will be generated from surveys undertaken in class, which
can then be used for calculation and analysis. The mass media,
including the Internet, is also a rich source of data for
statistical investigation. CONTENT 1 Organising and displaying data
7SP170 U F PS R C
interpret and construct divided bar graphs, sector graphs and
line graphs with and without ICT use a tally to organise data into
a frequency distribution table
2 Types of data 8SP284 U F R C recognise data as numerical
(either discrete or continuous) or categorical
3 The mean and mode 7SP171 U F PS R 4 The median and range
7SP171 U F PS R 5 Analysing frequency tables 7SP170, 7SP172 U F PS
R 6 Dot plots and stem-and-leaf plots 7SP170, 7SP172 U F PS R C 7
Frequency histograms and polygons 7SP170, 7SP172 U F PS R C
draw and interpret frequency histograms and polygons 8 Sampling
8SP206, 8SP284, 7SP169 U F C 9 Designing survey questions 8SP206,
7SP169 U F PS C
construct appropriate survey questions and a related recording
sheet to collect both numerical and categorical data about an issue
of interest
10 Comparing samples and populations 8SP293, 7SP169 U F PS R C
11 Analysing data 7SP172, 8SP207 U F PS R C 12 Revision and mixed
problems RELATED TOPICS Year 7: Fractions and percentages,
Analysing data Year 8: Fractions and percentages Year 9:
Investigating data
-
New Century Maths 8 teaching program (p. 18)
PROFICIENCY STRANDS / WORKING MATHEMATICALLY U = Understanding
(knowing and relating maths): Knowing the various types of data
displays and statistical measures F = Fluency (applying maths):
Reading and interpreting graphs, calculating and analysing
statistics, comparing data sets PS = Problem solving (modelling and
investigating with maths): Analysing data to solve problems,
drawing conclusions R = Reasoning (generalising and proving with
maths): Making generalizations and drawing conclusions from
statistical
displays and measures C = Communicating (describing and
representing maths): Classify and represent data in different forms
and make
conclusions about data sets after analysing them EXTENSION IDEAS
(Year 10 Stage 5.2) Interquartile range, box-and-whisker plots.
Grouped data, class intervals, median class. Replicate or implement
a major statistical investigation. TEACHING NOTES AND IDEAS
Resources: ruler, compasses, graph paper, graphs and tables from
newspapers, statistical yearbooks and census data from
the Australian Bureau of Statistics, spreadsheets, statistical
and graphing software, accident statistics. From NSW syllabus: Dot
plots and line graphs are first introduced in Stage 3. Students
construct, describe and interpret
column graphs in Stages 2 and 3; however, Stage 4 is the first
Stage in which histograms, divided bar graphs and sector (pie)
graphs are encountered.
Applications of mean: sports averages, rainfall or temperatures,
number of matches in a matchbox, market research. Applications of
mode: number of people in Australian family, most popular
Australian car, ordering stock for a shop. Applications of median:
wages, home prices. Read and comprehend a variety of data displays
used in the media and in other school subject areas. Compare the
strengths
and weaknesses of different forms of data display. Each graph
should have a title and key or scale. A histogram is a special type
of column graph. Leave a half-column gap at the vertical axis, as
the columns are centred on
the scores on the horizontal axis. Newspapers, magazines and the
Internet are useful sources of statistical information. Replicate a
newspaper survey. Examples of surveys: TV/radio ratings, opinion
polls, phone polls, CD sales, quality control. Survey the number of
left-
handed or blue-eyed students in the class or Year group and use
this to estimate the number with the same feature in the school or
whole of Australia.
The class may be surveyed on a number of characteristics:
height, arm span, shoe size, heartbeat rate, reaction time, number
of children in family, number of people living at home, hours slept
last night, number of letters in first name, number of cars or
mobile phones owned at home, make/colour of car, mode of travel to
school, favourite TV/radio station, reaction time, eye/hair colour,
birth month or star sign.
Question when it is more appropriate to use the mode or median,
rather than the mean, when analysing data. Which is higher, the
mean or median price of Australian homes?
Do more surnames begin with AM or NZ? Sometimes, a sample is
biased because it is too small or does not represent the population
accurately, for example, men
only, adults only. ASSESSMENT IDEAS Include open-ended
questions: The range of a set of eight scores is 10 and the mode is
3. What might the scores be? Plan, implement and report on a
statistical investigation. Vocabulary test. Investigate the use and
abuse of statistics and statistical graphs in the media. Research
the role of the Australian bureau of Statistics. TECHNOLOGY Explore
the statistical and graphing features of a spreadsheet, GeoGebra,
Fx-Stat, graphics/CAS calculators or software. Visit the Australian
Bureau of Statistics CensusAtSchool website
www.abs.gov.au/censusatschool or purchase their CD-ROMs. LANGUAGE
This topic contains much statistical jargon, so a student-created
glossary may be useful. Median = middle, for example, median strip
on a highway, or sounds like medium, mode (French) = fashionable,
popular. Population may refer to a collection of items as well as
people. Spend considerable time explaining the difference between
discrete and continuous data.
-
New Century Maths 8 teaching program (p. 19)
8. CONGRUENT TRIANGLES Time: 2 weeks (Term 3, Week 4) Text: New
Century Maths 8, Chapter 8, p.342 NSW and Australian Curriculum
references: Measurement and Geometry Properties of Geometrical
Figures 2 / Geometric reasoning
Define congruence of plane shapes using transformations (8MG200)
Develop the conditions for congruence of triangles (8MG201)
Establish properties of quadrilaterals using congruent triangles
and angle properties, and solve related numerical
problems using reasoning (8MG202) NSW Stage 4 outcomes A
student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-18 MG indentifies and uses angle relationships, including those
related to transversals on sets of parallel lines
INTRODUCTION This topic introduces the concepts and language
associated with congruent figures (especially triangles), building
on knowledge learned in past geometry topics. The properties of
congruent triangles are to be discovered through construction and
measurement, with more formal work such as congruent triangle
proofs to be taught in Year 9 as a Stage 5.3 topic. The geometrical
constructions are included here because they are based on the
properties of special triangles and quadrilaterals, especially the
diagonal properties of a rhombus. CONTENT 1 Transformations 7MG181
U F R C
describe translations, reflections in an axis, and rotations of
multiples of 90 on the Cartesian plane using coordinates 2
Congruent figures 8MG200 U F R C
name the vertices in matching order when using the symbol in a
congruence statement 3 Constructing triangles 8MG201 U F PS R
construct triangles using the conditions for congruence 4 Tests
for congruent triangles 8MG201 U F PS R C
investigate the minimum conditions needed, and establish the
four tests, for two triangles to be congruent (the SSS, SAS, AAS
and RHS rules)
5 Proving properties of triangles and quadrilaterals 8MG202 U F
PS R C use transformations of congruent triangles to verify some of
the properties of special quadrilaterals, including properties
of the diagonals 6 Extension: Bisecting intervals and angles U F
R 7 Constructing parallel and perpendicular lines 7MG163 U F
construct parallel and perpendicular lines using their
properties, a pair of compasses and a ruler, and dynamic geometry
software
8 Revision and mixed problems RELATED TOPICS Year 7: Geometry
Year 8: Pythagoras theorem, Geometry Year 9: Geometry, Congruent
and similar figures PROFICIENCY STRANDS / WORKING MATHEMATICALLY U
= Understanding (knowing and relating maths): Understanding the
concepts of transformation and congruence F = Fluency (applying
maths): Identifying congruent figures and their properties,
applying correct transformations,
geometrical constructions and congruent triangle tests PS =
Problem solving (modelling and investigating with maths): Using
geometry to test congruent triangles and prove
properties of triangles and quadrilaterals R = Reasoning
(generalising and proving with maths): Generalising properties of
congruent triangles and using them to
-
New Century Maths 8 teaching program (p. 20)
prove properties of triangles and quadrilaterals C =
Communicating (describing and representing maths): Using correct
notation and terminology for congruent
triangles EXTENSION IDEAS Similar figures (Year 9) Formal
congruent triangle proofs (Year 9 Stage 5.3) TEACHING NOTES AND
IDEAS Resources: geometrical instruments, dynamic geometry
software, reference and summary charts. Investigate congruence in
cultural and religious design patterns. From NSW syllabus:
Congruent figures are embedded in a
variety of designs, for example, tapa cloth, Aboriginal designs,
Indonesian ikat designs, Islamic designs, designs used in ancient
Egypt and Persia, window lattice, woven mats and baskets.
Students should be encouraged to prove results orally before
writing them up. Introduce scaffolds of proofs where students fill
in the blanks.
ASSESSMENT IDEAS Research assignment on congruent and similar
figures and their history Test/assignment on formal setting-out of
geometry proof Vocabulary test TECHNOLOGY The Math Open Reference
website www.mathopenref.com contains animations demonstrating
geometrical constructions and the tests for congruent triangles.
From NSW syllabus: Dynamic geometry software or prepared applets
are useful tools for investigating properties of congruent figures
through transformations. LANGUAGE Use matching angles for congruent
figures rather than corresponding to avoid confusion with
corresponding angles found
when a transversal crosses two lines. From the NSW syllabus:
This syllabus has used matching to describe angles and sides in the
same position: however, the use of the word corresponding is not
incorrect.
Encourage students to set out their geometrical answers
logically, step-by-step and giving reasons. The mathematical symbol
means is identical to in algebra and is congruent to in
geometry.
-
New Century Maths 8 teaching program (p. 21)
9. PROBABILITY Time: 3 weeks (Term 3, Week 6) Text: New Century
Maths 8, Chapter 9, p.384 NSW and Australian Curriculum references:
Statistics and Probability Probability 1 / Chance
Identify complementary events and use the sum of probabilities
to solve problems (8SP204) Probability 2 / Chance
Describe events using language of at least, exclusive or (A or B
but not both), inclusive or (A or B or both) and and (8SP205)
Represent events in two-way tables and Venn diagrams and solve
related problems (8SP292) NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-21 SP represents probabilities of simple and compound
interest
INTRODUCTION This short topic revises and extends probability
concepts learned in Year 7, introducing Venn diagrams and two-way
tables as methods of representing sample spaces of more complicated
chance situations. There are many opportunities here for class
discussion, practical lessons and language activities. CONTENT 1
Probability 7SP168 U F PS C
assign probabilities to the outcomes of events and determine
probabilities for events 2 Complementary events 8SP204 U F R C 3
Venn diagrams 8SP205, 8SP292 U F PS R C
recognise the difference between mutually exclusive and
non-mutually exclusive events 4 Two-way tables 8SP205, 8SP292 U F
PS R C
convert representations of the relationship between two
attributes in Venn diagrams to two-way tables 5 Probability
problems 8SP205, 8SP292 U F PS R
solve probability problems involving single-step experiments
such as card, dice and other games 6 Experimental probability
6SP146 U F PS R
compare observed frequencies across experiments with expected
frequencies 7 Revision and mixed problems RELATED TOPICS Year 7:
Analysing data, Probability Year 8: Fractions and percentages,
Interpreting data Year 9: Probability PROFICIENCY STRANDS / WORKING
MATHEMATICALLY U = Understanding (knowing and relating maths):
Knowing the terminology, concepts and notations of probability F =
Fluency (applying maths): Applying probability theory and
techniques to solve problems PS = Problem solving (modelling and
investigating with maths): Using probability theory to investigate
problems,
determining sample spaces, analysing the results of a chance
experiment R = Reasoning (generalising and proving with maths):
Making generalisations and inferences about probability
situations and experiments, including complementary events C =
Communicating (describing and representing maths): Expressing
probabilities as fractions, decimals and
percentages, describing complementary events, representing
sample spaces on Venn diagrams and two-way tables EXTENSION IDEAS
Two-stage or three-stage experiments: making lists, tables, tree
diagrams (Year 9) Counting techniques More complex Venn diagrams,
set notation (union vs intersection)
-
New Century Maths 8 teaching program (p. 22)
Investigate probability expressed as odds (ratio) The addition
rule of probability
TEACHING NOTES AND IDEAS Resources: Dice, coins, counters,
spinners, playing cards, probability simulation software. Do not
assume that all students have had experience with the properties of
playing cards: suits, colours, deck of 52. Be
sensitive to religious and cultural differences in attitudes
towards gambling. Reinforce the ideas of randomness and equally
likely outcomes. Discuss the claim: Since traffic lights can show
red, amber
or green, the probability that a light shows red is 1/3.
Investigate common misconceptions about chance, such as if a coin
is tossed repeatedly and heads comes up five times in a
row then, for the next toss, tails has a better chance than
heads. Explore Venn diagrams using attributes of students in the
class, for example, brown hair, walks to school. See the NSW
syllabus for examples of Venn diagrams and two-way tables. From
the NSW syllabus: Students are expected to be able to interpret
Venn diagrams involving three attributes; however
students are not expected to construct Venn diagrams involving
three attributes. Collect newspaper or Internet articles involving
chance, or test a chance game to see if it is fair. Investigate the
frequency of each letter of the alphabet in print or the Scrabble
game. Investigate games involving dice (Craps, Yahtzee), coins
(Two-Up), cards, raffles, spinners, Roulette. Play calculator
cricket
or noughts-and-crosses on the computer/Internet. Use real or
simulated experiments to find probabilities of winning and compare
with theoretical probabilities. Investigate the data from past
Lotto draws using the NSW Lotteries website
(www.nswlotteries.com.au).
Do not fall into the trap of thinking of (or teaching)
probability as being all about games of chance and gambling.
Investigate the applications of probability in insurance, for
example, car accidents, home burglaries, life expectancy, quality
control or sampling. Use the Internet to find quotes on premiums.
What factors affect the chances of a particular car being
stolen?
ASSESSMENT IDEAS Vocabulary test or writing activities involving
probability. Research/investigation on listing and counting the
outcomes of a sample space using Venn diagrams and/or two-way
tables. TECHNOLOGY Random numbers can be generated on a calculator,
graphics or CAS calculator, or spreadsheet. The Internet,
spreadsheets and other software may be used ti simulate a chance
situation such as a lotto draw, coin tosses or dice throws.
LANGUAGE How is the word complementary used in this topic similar
to its use with complementary angles or its everyday English
meaning? Carry out language activities on identifying the
complement of an event, such as there are fewer than 3 children in
a family. This could be done as a matching pairs memory card
game.
What is the difference between more than 3 and 3 or more? The
NSW syllabus lists the following terms that can be used to describe
compound events: at least, at most, not, and, both,
not both, or and neither. Also from the NSW syllabus: An event
is one or a collection of outcomes. For instance, an event might be
that we roll an
odd number [on a die], which would include the outcomes 1, 3 and
5. A simple event has outcomes that are equally likely A compound
event is an event which can be expressed as a combination of simple
events, for example, drawing a card that is black or a King;
throwing at least 5 on a fair six-sided die.
-
New Century Maths 8 teaching program (p. 23)
10. EQUATIONS Time: 3 weeks (Term 4, Week 1) Text: New Century
Maths 8, Chapter 10, p.418 NSW and Australian Curriculum
references: Number and Algebra Equations / Linear and non-linear
relationships
Solve simple linear equations (7NA179) Solve linear equations
using algebraic and graphical techniques, and verify solutions by
substitution (8NA194) Solve simple quadratic equations (NSW Stage
4)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-10 NA uses algebraic techniques to solve simple linear and
quadratic equations
INTRODUCTION This short topic revises and builds upon the
concept of equations and the algebraic methods for solving them.
Students were introduced to equations in the Year 7 topic Algebra
and equations, while the algebraic operations of collecting like
terms and expanding expressions were learned earlier this year in
the Algebra topic. Like many algebra skills, the process of
equation-solving is detailed and technical, requiring careful and
precise understanding and practice. Aim to teach this topic at a
level appropriate to the ability of your class. Solving linear
equations graphically will be covered in the topic Graphing linear
equations later this year. CONTENT 1 One-step equations 7NA179 U F
R
solve linear equations using algebraic methods that involve one
or two steps in the solution process and which may have non-integer
solutions
2 Two-step equations 7NA179 U F R 3 Equations with variables on
both sides 8NA194 U F R
solve linear equations using algebraic methods that involve at
least two steps in the solution process and which may have
non-integer solutions
4 Equations with brackets 8NA194 U F R 5 Simple quadratic
equations x2 = c NSW U F R C 6 Equation problems 8NA194 U F PS R
C
solve real-life problems by using pronumerals to represent
unknowns 7 Revision and mixed problems RELATED TOPICS Year 7:
Algebra and equations Year 8: Algebra Year 9: Equations PROFICIENCY
STRANDS / WORKING MATHEMATICALLY U = Understanding (knowing and
relating maths): Learning the techniques for solving equations F =
Fluency (applying maths): Selecting correct techniques for solving
equations PS = Problem solving (modelling and investigating with
maths): Solving real-life problems by modeling with equations R =
Reasoning (generalising and proving with maths): Using algebraic
operations to solve equations C = Communicating (describing and
representing maths): Describing the solution to real-life problems
in words after
solving an equation EXTENSION IDEAS
Equations involving x2 or 1x
Harder formulas and word problems, constructing formulas
-
New Century Maths 8 teaching program (p. 24)
Equations with the unknown in the denominator Non-linear
equations, for example, squares and square roots Simultaneous
equations TEACHING NOTES AND IDEAS Resources: counters, cups,
cubes, blocks, envelopes, two-pan balance scales and other concrete
materials for modelling
variables in equations. From the NSW syllabus: Distinguish
between algebraic expressions where pronumerals are used as
variables, and
equations where pronumerals are used as unknowns Include
two-step equations where the variable appears in the second term,
for example, 15 2x = 7. Stress that the goal of solving an equation
is to have the variable on its own on the left side of the equation
and the value on
the right side. The balancing and backtracking methods of
solving equations are quite similar when written algebraically; the
difference is
in their models (and explanation). The process of undoing
(backtracking) or balancing needs to be explained and reinforced
early. Use a putting on socks
and shoes analogy to explain why undoing an equation must take
place in reverse order. We undo the last thing first. When solving
a word problem, identify the unknown quantity and call it x, say.
After solving, check that its solution sounds
reasonable. ASSESSMENT IDEAS Writing activity comparing and
evaluating the different methods of solving an equation. TECHNOLOGY
Spreadsheets, graphics calculators and GeoGebra can be used to
guess, check and improve solutions to equations. CAS calculators
can be used to solve equations. LANGUAGE Algebra comes from the
Arabic word al-jabr, meaning restoration or the process of adding
the same amount to both sides
of an equation. In 825 CE, the Arabic mathematician al Khwarizmi
wrote a book called Hisab al-jabr wal-muqabala (The science of
equations).
An algebraic expression refers to a phrase containing terms and
arithmetic operations, such as 2a + 5, while an algebraic equation
refers to a sentence involving an expression and an equals sign,
such as 2a + 5 = 13.
Encourage students to set out their solutions to equations
neatly with equals signs aligned in the same column.
-
New Century Maths 8 teaching program (p. 25)
11. RATIOS, RATES AND TIME Time: 3 weeks (Term 4, Week 4) Text:
New Century Maths 8, Chapter 11, p.444 NSW and Australian
Curriculum references: Number and Algebra, Measurement and Geometry
Proportion / Real numbers
Solve a range of problems involving rates and ratios, with and
without digital technologies (8NA188) Proportion / Linear and
non-linear relationships
Investigate, interpret and analyse graphs from authentic data
(7NA180) Time / Using units of measurement
Solve problems involving duration, including using 12- and
24-hour time within a single time zone (8MG199) Solve problems
involving international time zones (NSW Stage 4)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-2 WM applies
appropriate mathematical techniques to solve problems MA4-3 WM
recognises and explains mathematical relationships using reasoning
MA4-7 NA operates with ratios and rates, and explores graphical
representation MA4-15 MG performs calculations of time that involve
mixed units, and interprets time zones
INTRODUCTION This topic revised and extends concepts in ratios,
rates and time calculations. Ratios compare parts or shares of
something, while rates compare quantities expressed in different
units, for example, speed compares distance travelled with the time
taken. Travel graphs and time calculations are included here
because travel graphs also compare distance with time, while many
rates include units of time. The new content of this topic are
scale maps and plans, dividing a quantity in a given ratio,
sketching informal graphs and international time zones. Note that
this topic links together concepts in Number, Measurement and
Statistics (graphs, timetables). CONTENT 1 Ratios 8NA188 U C 2
Simplifying ratios 8NA188 U F 3 Ratio problems 8NA188 U F PS C
recognise and solve problems involving simple ratios 4 Scale
maps and plans 8NA188 U F PS C 5 Dividing a quantity in a given
ratio 8NA188 U F
divide a quantity in a given ratio 6 Rates 8NA188 U C
convert given information rates 7 Best buys 7NA174 U F PS R
C
investigate and calculate best buys 8 Rate problems 8NA188 U F
PS C 9 Speed 8NA188 U F PS C 10 Travel graphs 7NA180 U F PS R C
use travel graphs to investigate and compare the distance
travelled to and from school interpret features of travel graphs
such as the slopes of lines and the meaning of horizontal lines
11 Sketching informal graphs 7NA180 U F PS R C sketch informal
graphs to model familiar events, for example, noise level during
the lesson
12 Time differences 8MG199 U F PS C 13 International time zones
NSW U F PS C 14 Revision and mixed problems RELATED TOPICS Year 7:
Ratios, rates and time Year 8: Fractions and percentages, Graphing
linear equations Year 9: Working with numbers
-
New Century Maths 8 teaching program (p. 26)
PROFICIENCY STRANDS / WORKING MATHEMATICALLY U = Understanding
(knowing and relating maths): Learning the concepts and operations
involving ratios, rates and time F = Fluency (applying maths):
Applying appropriate concepts and skills to situations PS = Problem
solving (modelling and investigating with maths): Solving real-life
problems using ratios, rates, travel
graphs and time calculations R = Reasoning (generalising and
proving with maths): Making generalizations and inferences about
best buys and travel
graphs C = Communicating (describing and representing maths):
Describing and interpret relationships using ratios, scale
diagrams, rates and travel graphs, and represent time and time
differences in various ways EXTENSION IDEAS Investigate the golden
ratio and the golden rectangle: see Just for the Record on page 456
and the NSW syllabus under
Proportion Solve harder rate problems, for example, fuel
consumption, converting rates to different units, for example, from
km/h to
m/s Investigate speed records and other units of speed such as
Mach Research the history of the calendar and/or time measurement:
Julian, Gregorian, Islamic, Chinese, Jewish calendars,
daylight saving, International Date Line TEACHING NOTES AND
IDEAS Resources: supermarket catalogues for best buys, tables of
data showing rates such as fuel consumption or birth rates,
stopwatch, 24-hour clock, calendars, timetables, map with world
time zones Encourage the class to list instances of ratios, when
the parts or shares of a mixture are important: cordial, punch,
cake mix,
lawn mower fuel, concrete, paste (flour and water), lemonade,
milkshake, fertiliser, gear ratios, slopes of hills, probability
and betting odds.
Investigate the aspect ratios of TV, computer and cinema
screens. For scale drawings, liaise with the TAS and HSIE faculties
for plans and maps. Investigate on a map distances between
suburbs, towns, world cities. For rates, stress that the slash
(/) indicates the division process and means per or out of.
Encourage students to list examples of rates and the two units
being compared: birth rate, population growth, heartbeat,
typing speed, fuel consumption, postage rates, metric and
currency conversions, download speed, filling a tank, mobile phone
costs, classified ads, cost of petrol, meat or fruit, population
density, cricket run rate (runs/over), batters strike rate
(runs/100 balls), bowlers strike rate (balls/wicket) and other
sports statistics.
Investigate population density, population growth, birth rate,
death rate, speed, fuel consumption. Investigate unit pricing on
supermarket shelves, and how sometimes the unit is 100 mL rather
than 1 mL (why?). Discuss
why the best buy is usually the largest item. Since 2009, unit
pricing has been compulsory in all Australian supermarkets.
Applications of time calculations: bus/plane trip using timetables,
length of movie, payroll (hours worked), sunrise to
sunset, length of school or work day ASSESSMENT IDEAS Design a
map or scale drawing. Poster assignment on applications of ratios
or rates Travel graph tell me a story writing activities Problems
involving travel times and time zones. Plan a holiday and create a
travel schedule with the times written in 12- or 24-hour time
TECHNOLOGY Ratios can be entered into a calculator using the
[ab/c] fraction key. However, when simplifying improper ratios, use
the [d/c] key to convert the mixed numeral answer to a proper
ratio. Students should be introduced to the calculators
degrees-minutes-seconds key for time calculations. Use the Internet
to find airline, train and cinema timetables. Put itineraries onto
a spreadsheet and calculate different times. Visit Google Maps and
analyse its scale. LANGUAGE The symbol for minute is . The symbol
for second is . Their abbreviations are min and s respectively.
-
New Century Maths 8 teaching program (p. 27)
The word minute comes from the Latin pars minuta prima, meaning
the first (prima) division (minuta) of an hour. In this way, it is
related to the alternative meaning and pronunciation of the word
minute as tiny. The word second comes from pars minuta secunda,
meaning the second (secunda) division of an hour.
The parts of a ratio are called its terms. Why does the unitary
method have that name?
-
New Century Maths 8 teaching program (p. 28)
12. GRAPHING LINEAR EQUATIONS Time: 3 weeks (Term 4, Week 7)
Text: New Century Maths 8, Chapter 12, p.500 NSW and Australian
Curriculum references: Number and Algebra Linear Relationships /
Linear and non-linear relationships
Plot linear relationships on the Cartesian plane with and
without the use of digital technologies (8NA193) Solve linear
equations using algebraic and graphical techniques, and verify
solutions by substitution (8NA194)
NSW Stage 4 outcomes A student:
MA4-1 WM communicates and connects mathematical ideas using
appropriate terminology, diagrams and symbols MA4-3 WM recognises
and explains mathematical relationships using reasoning MA4-11 NA
creates and displays number patterns; graphs and analyses linear
relationships; and performs
transformations on the Cartesian plane
INTRODUCTION This algebra topic provides an introduction to
coordinate geometry. Students were introduced to the number plane
in Years 6-7, but this is the first time they link tables of values
and algebraic rules to graphing on a number plane. This topic
demonstrates how patterns in number can be represented visually and
graphically. More formal coordinate geometry will be examined in
Year 9. CONTENT 1 Tables of values 8NA193 U F 2 Finding the rule
8NA193 U F R C 3 Finding rules for number patterns 8NA193 F PS R
C
use objects to build a geometric pattern, record the results in
a table of values, describe the pattern in words and algebraic
symbols and represent the relationship on a number grid
4 The number plane 7NA178 U F C given coordinates, plot points
on the Cartesian plane and find coordinates for a given point
5 Graphing number patterns 8NA194 U F R C recognise a given
number pattern (including decreasing patterns), complete a table of
values, describe the pattern in words
or algebraic symbols, and represent that relationship on a
number grid 6 Graphing linear equations 8NA193 U F R C
form a table of values for a linear relationship by substituting
a set of appropriate values for either of the pronumerals and graph
the number pairs on the Cartesian plane
extend the line joining a set of points to show that there is an
infinite number of ordered pairs that satisfy a linear
relationship
7 Finding the equation of a line 8NA194 U F R C derive a rule
for a set of points that has been graphed on a number plane
8 Comparing linear equations NSW U F PS R C graph more than one
line on the same set of axes using ICT and compare the graphs to
describe similarities and differences,
for example, parallel, pass through the same point use ICT to
graph linear and simple non-linear relationships such as y = x3
9 Solving linear equations graphically 8NA194 U F R C 10
Intersecting lines 8NA194 U F R C
graph two intersecting lines on the same set of axes and read
off the point of intersection 11 Revision and mixed problems
RELATED TOPICS Year 7: Algebra and equations, The number plane Year
8: Algebra, Equations Year 9: Equations, Coordinate geometry
PROFICIENCY STRANDS / WORKING MATHEMATICALLY U = Understanding
(knowing and relating maths): Understanding and relating linear
equations, tables of values and the
number plane F = Fluency (applying maths): Using correct
strategies to find the equation of a line or number pattern,
plotting points on a
number plane
-
New Century Maths 8 teaching program (p. 29)
PS = Problem solving (modelling and investigating with maths):
Identifying similarities and differences between two or more
lines
R = Reasoning (generalising and proving with maths): Finding a
general rule for a number pattern or line, solving linear equations
graphically
C = Communicating (describing and representing maths):
Representing number patterns algebraically and graphically
EXTENSION IDEAS The gradient of a line Graphing of curves:
parabola, cubic, exponential, hyperbola. Use of a graphics
calculator or GeoGebra. Simultaneous equations Elementary
coordinate geometry: distance and midpoint Applications of linear
functions, for example, profit function TEACHING NOTES AND IDEAS
Resources: number plane grid paper and activities/puzzles, graphics
calculators or software, spreadsheet software. Students should be
reminded to label the axes and the graphs. All points that lie on
the line have coordinates that satisfy the linear equation. Points
that dont lie on the line do not satisfy the
equation. Graphing a linear equation demonstrates how a
numerical pattern can be converted to a
graphical pattern. Convert the classroom into a coordinate grid
system, then ask stand up/hand up all those people whose two
coordinates add up to 5 for a good visual demonstration.
ASSESSMENT IDEAS Report on investigating the graphs of linear
equations Given the line, find the equation Practical test using a
graphics calculator or computer Graphing test
TECHNOLOGY Use a graphics calculator, GeoGebra or spreadsheet
software to graph and compare a range of linear equations. LANGUAGE
From the NSW syllabus under Stage 3, Patterns and Algebra 2: The
Cartesian plane (commonly referred to as the number
plane) is named after [Ren] Descartes who was one of the first
to develop analytical [coordinate] geometry on the number
plane.
From the NSW syllabus under Linear Relationships: In Stage 3,
students use position in pattern and value of term when describing
a pattern from a table of values, for example, the value of the
term is three times the position in the pattern.
Time: 3 weeks (Term 1, Week 1) Text: New Century Maths 8,
Chapter 1, p.2INTRODUCTIONCONTENTRELATED TOPICSPROFICIENCY STRANDS
/ WORKING MATHEMATICALLYEXTENSION IDEASTEACHING NOTES AND
IDEASASSESSMENT IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 1, Week
4) Text: New Century Maths 8, Chapter 2,
p.36INTRODUCTIONCONTENTRELATED TOPICSPROFICIENCY STRANDS / WORKING
MATHEMATICALLYEXTENSION IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 1, Week 7) Text: New
Century Maths 8, Chapter 3, p.88INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 2, Week 1) Text: New
Century Maths 8, Chapter 4, p.130INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 2, Week 4) Text: New
Century Maths 8, Chapter 5, p.170INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 2, Week 7) Text: New
Century Maths 8, Chapter 6, p.234INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 3, Week 1) Text: New
Century Maths 8, Chapter 7, p.282INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 2 weeks (Term 3, Week 4) Text: New
Century Maths 8, Chapter 8, p.342INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 3, Week 6) Text: New
Century Maths 8, Chapter 9, p.384INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 4, Week 1) Text: New
Century Maths 8, Chapter 10, p.418INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 4, Week 4) Text: New
Century Maths 8, Chapter 11, p.444INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT
IDEASTECHNOLOGYLANGUAGETime: 3 weeks (Term 4, Week 7) Text: New
Century Maths 8, Chapter 12, p.500INTRODUCTIONCONTENTRELATED
TOPICSPROFICIENCY STRANDS / WORKING MATHEMATICALLYEXTENSION
IDEASTEACHING NOTES AND IDEASASSESSMENT IDEASTECHNOLOGYLANGUAGE