Mathematics Learning Area Year 8 Western Australian Curriculum 8... · Mathematics Learning Area...
Transcript of Mathematics Learning Area Year 8 Western Australian Curriculum 8... · Mathematics Learning Area...
Mathematics Learning Area
Year 8
Western Australian Curriculum
General Capabilities:
• Literacy
• Numeracy
• ICT
• Critical and Creative Thinking
• Ethical Behaviour
• Personal and Social Competence
• Intercultural Understanding
Resources: Cambridge Essential Mathematics Year 8
Outcomes:
1. Students recognise that everyone has the right to feel valued and safe, and, in this regard, understand their
rights and obligations and behave responsibly.
2. Students are self-motivated and confident in their approach to learning and are able to work individually and
collaboratively.
3. Students appreciate the role mathematics has had, and continues to have, in their own and other communities.
4. Students use mathematics thinking processes and skills in interpreting and dealing with mathematical and non-
mathematical situations.
Cross-Curriculum Priorities
Aboriginal and Torres Strait Islander histories and cultures
Students will explore connections between representations of number and pattern and how they relate to aspects of Aboriginal and Torres Strait Islander cultures. They will investigate time, place, relationships
and measurement concepts in Aboriginal and Torres Strait Islander contexts. Students will deepen their understanding of the lives of Aboriginal and Torres Strait Islander Peoples through the application and evaluation of statistical data.
Asia and Australia’s engagement with Asia
Students investigate the concept of chance using Asian games. They explore the way Asian societies apply other mathematical concepts such as patterns and symmetry in art and architecture. Investigations involving data collection and representation can be used to examine issues pertinent to the Asia region.
Sustainability
Mathematical understandings and skills are necessary to monitor and quantify both the impact of human activity on ecosystems and changes to conditions in the biosphere. Actions to improve sustainability involve students in processes such as auditing, reading measures
and gauges, and interpreting data on invoices and accounts. Mathematical and statistical analysis enables informed decision making about present and future action.
Year 8 Syllabus
Year Level Description
The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.
At this year level:
• understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area
• fluency includes calculating accurately with simple decimals, indices and integers; recognising equivalence of common decimals and fractions including recurring decimals; factorising and simplifying basic algebraic expressions and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects
• problem-solving includes formulating and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes and using two-way tables and Venn diagrams to calculate probabilities
• reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.
Year 8 Achievement Standard
Number and Algebra
At Standard, students solve everyday problems involving rates, ratios and percentages. They describe index laws and apply them to whole numbers. Students describe rational and irrational numbers. They solve problems involving profit and loss. Students make connections between expanding and factorising algebraic expressions. They use efficient mental and written strategies to carry out the four operations with integers. Students simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane.
Measurement and Geometry
Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. Students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. They convert between units of measurement for area and volume. Students perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles.
Statistics and probability
Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. Students explain issues related to the collection of data and the effect of outliers on means and medians in that data. They determine the probabilities of complementary events and calculate the sum of probabilities.
Week Western Australian
Curriculum
Content Description
At the end of this section of work the student
should be able to
Literacy words Resources Assessment
1 Revise number skills from Year 7 course
2 Carry out the four operations
with rational numbers and
integers, using efficient mental
and written strategies and
appropriate digital technologies
(ACMNA183)
Integers
• Evaluate using whole numbers and the four
operations
• Calculate multiples of numbers
• Find the HCF and LCM of pairs of numbers
Integer
Multiples
Number
Factor
Ex 1A, 1B, 1C
3 Compare, order, add and
subtract integers (ACMNA280)
Carry out the four operations
with integers, using efficient
mental and written strategies
and appropriate digital
technologies (ACMNA183)
• Test for divisibility
• Find the prime factors of numbers
• Add and subtract negative numbers
Prime
Subtract
Negative
Divisibility
Ex 1D, 1E, 1F
4 Compare, order, add and
subtract integers (ACMNA280)
Carry out the four operations
with integers, using efficient
mental and written strategies
and appropriate digital
technologies (ACMNA183)
• Multiply and divide using integers
• Use order of operations to evaluate
problems
Order
Multiply
Divide
Evaluate
Operation
Ex 1G, 1H Test Chapter 1
5
Lines, shapes and solids
• Find angles at a point
• Find sizes of angles within parallel lines
Angle
Parallel
Ex 2A, 2B
6 • Find sizes of angles within triangles
• Test for similarity in triangles
Triangle
Similarity
Ex 2C, 2D
7 Establish properties of
quadrilaterals using congruent
triangles and angle properties,
and solve related numerical
problems using reasoning
(ACMMG202)
• Find the size of angles in a quadrilateral
• Find the size of angles in various polygons
Quadrilateral
Polygon
Ex 2E, 2F
8 • Develop and use Euler’s rule Euler Ex 2G Test Chapter 2
9 Compare fractions using
equivalence. Locate and
represent fractions and mixed
numerals on a number line
(ACMNA152)
Investigate terminating and
recurring decimals
(ACMNA184)
Solve problems involving
addition and subtraction of
fractions, including those with
unrelated denominators
(ACMNA153) Multiply and
divide fractions and decimals
using efficient written strategies
and digital technologies
(ACMNA154)
Fractions, Decimals and Percentages
• Write equivalent fractions
• Use the four operations with fractions
Fraction
Decimal
Percentage
Equivalent
Ex 3A, 3B
10 Compare fractions using
equivalence. Locate and
represent fractions and mixed
numerals on a number line
(ACMNA152)
Investigate terminating and
recurring decimals
(ACMNA184)
• Use the four operations with negative
fractions
• Compare and convert fractions and decimals
Compare
Fraction
Decimal
Ex 3C, 3D
11 Compare fractions using
equivalence. Locate and
represent fractions and mixed
numerals on a number line
• Use the four operations with decimals
• Understand and use terminating, recurring
and rounding decimals
Terminating
Recurring
Rounding
Ex 3E, 3F
(ACMNA152)
Investigate terminating and
recurring decimals
(ACMNA184)
12 Express one quantity as a
fraction of another with and
without the use of digital
technologies (ACMNA155)
Solve problems involving the
use of percentages, including
percentage increases and
decreases, with and without
digital technologies
(ACMNA187)
• Convert percentages to fractions and
decimals and vice versa
• Express one quantity as a percentage of
another and find the percentage of quantity
Quantity
Percentage
Convert
Ex 3G, Ex 3H
13
Solve problems involving the
use of percentages, including
percentage increases and
decreases, with and without
digital technologies
(ACMNA187)
• Decrease and increase amounts by a
percentage
• Calculate percentage change
• Calculate percentage using the unitary
method
FA1 – The right to be safe
Topic 2: Warning signs and emergencies
2.4 Explore a range of emergencies, research
statistics and percentages, discuss strategies to
solve problems (P56)
2.5 As above (P57)
FA2 - Relationships
Topic 3: Bullying as an abuse of power
3.1 Research bullying statistics and
percentages, discuss strategies to solve
problems (P68) (display as data – see bottom
cell)
3.2 As above (P68)
FA3 – Recognising and reporting abuse
Topic 2: Identifying abuse and neglect
2.1 Research abuse statistics and percentages,
discuss strategies to solve problems (P78)
2.3 Sexual abuse – as above (P81)
2.5 Domestic violence – as above (P84)
Decrease
Increase
Unitary
Ex 3I, 3J, 3K Test Chapter 3
FA4 – Protective strategies
Topic 1: Problem – solving strategies
1.1 Use trust, take, control problem solving
strategy (P93) for activities FA1: 2.2, 2.5 FA2:
3.1, 3.2 FA3: 2.1, 2.3, 2.5
14 Find perimeters and areas of
parallelograms, rhombuses and
kites (ACMMG196)
Measurement and Pythagoras’ Theorem
• Convert between measures of length and
calculate perimeter of shapes
• Calculate the circumference of a circle
Length
Perimeter
Circumference
Circle
Ex 4A, 4B
15 Find perimeters and areas of
parallelograms, rhombuses and
kites (ACMMG196)
• Convert between area measurements and
calculate the area of shapes
• Calculate the area of special quadrilaterals
Area
Measurement
Quadrilateral
Ex 4C, 4D
16 Investigate the relationship
between features of circles such
as circumference, area, radius
and diameter. Use formulas to
solve problems involving
circumference and area
(ACMMG197)
• Calculate the area of a circle
• Calculate the area of sectors and composite
shapes
Sector
Composite
Shape
Ex 4E, 4F
17 Choose appropriate units of
measurement for area and
volume and convert from one
unit to another (ACMMG195)
Develop the formulas for
volumes of rectangular and
triangular prisms and prisms in
general. Use formulas to solve
problems involving volume
(ACMMG198)
• Calculate the surface area of a prism
• Calculate the volume and capacity of
rectangular prisms
• Calculate the volume of other prisms,
including cylinders
Surface
Volume
Rectangular
Prism
Cylinder
Ex 4G, 4H, 4I
18 Solve problems involving
duration, including using 12-
and 24-hour time within a single
• Convert between units of time
• Understand the rule of Pythagoras
Convert
Unit
Time
Ex 4J, 4K
time zone (ACMMG199)
Pythagoras
19 • Use Pythagoras’ theorem to calculate the
length of the hypotenuse and one of the
shorter sides
Theorem
Hypotenuse
Ex 4L, 4M Chapter 4 Test
20 Extend and apply the laws and
properties of arithmetic to
algebraic terms and expressions
(ACMNA177) Create algebraic
expressions and evaluate them
by substituting a given value for
each variable (ACMNA176))
Algebra
• Recognise terms, coefficients and algebraic
expressions
• Substitute numerical values into algebraic
expressions
• Add and subtract like terms
Term
Coefficient
Numerical
Ex 5A, 5B, 5C
21
Simplify algebraic expressions
involving the four operations
(ACMNA192)
• Multiply and divide algebraic terms
• Add and subtract algebraic fractions
Algebraic
Fractions
Ex 5D, 5E
22 Extend and apply the
distributive law to the expansion
of algebraic expressions
(ACMNA190)
• Multiply and divide algebraic fractions
• Expand brackets involving algebraic
expressions
Expand
Bracket
Expression
Ex 5F, 5G
23 Factorise algebraic expressions
by identifying numerical factors
(ACMNA191)
• Factorise algebraic expressions
• Applying algebra to various problems
Factorise
Algebra
Ex 5H, 5I
24 Use index notation with
numbers to establish the index
laws with positive integral
indices and the zero index
(ACMNA182)
• Multiply and divide terms with powers
• Simplify expressions using raising of
powers
Powers
Simplify
Ex 5J, 5K Chapter 5 Test
25 Recognise and solve problems
involving simple ratios
(ACMNA173)Investigate and
calculate 'best buys', with and
without digital technologies
(ACMNA174)
Rates and Ratios
• Understand basic ratios
• Simplify ratios
• Divide a quantity in a given ratio
Rate
Ratio
Ex 6A, 6B, 6C
26 Solve a range of problems
involving rates and ratios, with
and without digital technologies
(ACMNA188)
• Convert scale distance to actual distance and
vice versa
• Simplify rates
Distance
Rates
Convert
Ex 6D, 6E
27 Solve a range of problems
involving rates and ratios, with
and without digital technologies
(ACMNA188)
• Use the unitary method with ratios and rates
• Solve rate problems
• Convert speed into various units
Unitary
Speed
Unit
Ex 6F, 6G, 6H Chapter 6 Test
28 Solve linear equations using
algebraic and graphical
techniques. Verify solutions by
substitution (ACMNA194)
Equations
• Review equations
• Solve equations algebraically
Equation
Solve
Ex 7A, 7B
29 Solve linear equations using
algebraic and graphical
techniques. Verify solutions by
substitution (ACMNA194)
• Solve equations with fractions
• Solve equations with variables on both sides
• Solve equations with brackets
Variable
Bracket
Ex 7C, 7D, 7E
30 Solve linear equations using
algebraic and graphical
techniques. Verify solutions by
substitution (ACMNA194)
• Use formula in algebra
• Solve problems involving algebra
Formula
Problem
Algebra
Ex 7F, 7G Chapter 7 Test
31 Explore the practicalities and
implications of obtaining
representative data using a
variety of investigative
processes (ACMSP206)
Probability and Statistics
• Interpret graphs and tables
• Draw frequency tables
• Interpret histograms containing data
Probability
Statistics
Frequency
Histogram
Ex 8A, 8B, 8C
32 Explore the practicalities and
implications of obtaining
representative data using a
variety of investigative
processes (ACMSP206)
Investigate the effect of
individual data values ,
including outliers, on the mean
and median (ACMSP207)
• Calculate the mean, mode and median of
data
• Calculate the range and interquartile range
of data
FA2: Relationships
Topic 2: Power in relationships
2.1 Research powerful people and display
positive a negative effects (P64)
2.2 As above (P65)
FA2 - Relationships
Topic 3: Bullying as an abuse of power
3.1 Use bullying statistics and percentages
(from top cell) and display as data (P68)
3.2 As above (P68)
Mean
Mode
Median
Interquartile
Range
Ex 8D, 8E
FA4: Protective strategies
Topic 2: Network review and community
support
2.1 Display and investigate data using the
network review challenge (P98)
33 Explore the variation of means
and proportions in
representative data
(ACMSP293)
Identify complementary events
and use the sum of probabilities
to solve problems (ACMSP204)
Describe events using language
of 'at least', exclusive 'or' (A or
B but not both), inclusive 'or' (A
or B or both) and 'and'.
(ACMSP205)
• Understand and use surveying and sampling
• Calculate the probability of events
• Construct two-way tables of events
FA1 – The right to be safe
Topic 2: Warning signs and emergencies
2.4 Explore a range of emergencies, research
statistics and percentages, discuss strategies to
solve problems (P56)
2.5 As above (P57)
FA3 – Recognising and reporting abuse
Topic 2: Identifying abuse and neglect
2.1 Research abuse statistics and probabilities,
discuss strategies to solve problems (P78)
2.3 Sexual abuse – as above (P81)
2.5 Domestic violence – as above (P84)
Survey
Sample
Construct
Event
Ex 8F, 8G, 8H
34 Represent such events in two-
way tables and Venn diagrams
and solve related problems
(ACMSP292)
• Construct and interpret tree diagrams
• Interpret events using Venn diagrams and
two-way tables
• Calculate experimental probabilities
Construct
Interpret
Experimental
Ex 8I, 8J, 8K Chapter 8 Test
35 Plot linear relationships on the
Cartesian plane with and
without the use of digital
technologies (ACMNA193)
Straight Line Graphs
• Plot points on the number plane
• Draw tables from rules given
• Finding a rule from a graph and table
Plane
Rule
Graph
Ex 9A, 9B, 9C
36 Plot linear relationships on the
Cartesian plane with and
without the use of digital
technologies (ACMNA193)
• Calculate the gradient of a line
• Drawing graphs and finding equations using
gradient – intercept form
• Finding the x-intercept of a graph
Gradient
Intercept
Ex 9D, 9E, 9F
37 Plot linear relationships on the
Cartesian plane with and
without the use of digital
technologies (ACMNA193)
• Finding rules to applying linear graphs Linear
Ex 9G Chapter 9 Test
38 Transformations Reflection Ex 10A, 10B, 10C
• Draw images involving reflections,
translations and rotations
Translation
Rotation
transformation
Assessment Schedule
Assessment Week Weighting
Chapter 1 - Integers 4 1
Chapter 2 – Lines, shapes and
solids
8 1
Chapter 3 – Fractions, decimals
and percentages
13 1
Chapter 4 – Measurement and
Pythagoras’ Theorem
19 1
Chapter 5 – Algebra 24 1
Chapter 6 – Rates and ratios 27 1
Chapter 7 – Equations 30 1
Chapter 8 – Probability and
statistics
34 1
Chapter 9 – Straight line graphs 37 1