Download 2017 Year8 Mathematics Extension Program

Irene McCormack Catholic College
Mathematics Learning Area
Year 8 Mathematics
Academic Extension Program
2017
Resource Materials
Excel Extension Revision and Exam Booklet Year 8
(MS) Mathspace (online)
Assessments
SEMESTER ONE
TESTS (3)
21%
EPW (2)
14%
EXAM (Semester 1 Content Only)
10%
SUB TOTAL
45%
SEMESTER TWO
TESTS (3)
24%
EPW (2)
16%
EXAM (Semester 1 & 2 Content)
15%
SUB TOTAL
55%
YEAR TOTAL
100%
Year 8 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 Mathematics Academic Extension Program, 2017
Term 1
Week
Content
Australian Curriculum Content Descriptors
Exercises and
Resources
Assessments
Integers and Indices
1-2
Integers Review
Integer multiplication
3-4
Integer Division
Combined operations
with integers
Multiplying and dividing
numbers in index form
4
Powers of powers,
products and quotients
Carry out the four operations with rational
numbers and integers, using efficient
mental and written strategies and
appropriate digital technologies
(ACMNA183)
Carry out the four operations with rational
numbers and integers, using efficient
mental and written strategies and
appropriate digital technologies
(ACMNA183)
Chapter 2
Chapter 2
Use index notation with numbers to
establish the index laws with positive
integral indices and the zero index
(ACMNA182)
Use index notation with numbers to
establish the index laws with positive
integral indices and the zero index
(ACMNA182)
Chapter 3
Investigate terminating and recurring
decimals (ACMNA184)
Chapter 1
Test 1
Fractions, decimals and
percentages
5
Working with fractions
and decimals
Investigate the concept of irrational
numbers, including π (ACMNA186)
5-6
Types of decimals
Negative fractions and
decimals
7
8-9
Estimating percentages
Writing fractions and
decimals as percentages
Writing percentages as
fractions and decimals
Writing one amount as a
percentage of another
Finding a percentage of
an amount
10
Increasing or decreasing
by a given percentages
Financial application of
percentages
Investigate terminating and recurring
decimals (ACMNA184)
Chapter 1
EPW 1
Investigate the concept of irrational
numbers, including π (ACMNA186)
No descriptors – cover anyway
Chapter 4
Solve problems involving the use of
percentages, including percentage
increases and decreases, with and
without digital technologies (ACMNA187)
Chapter 4
Solve problems involving the use of
percentages, including percentage
increases and decreases, with and
without digital technologies (ACMNA187)
Chapter 4
Solve problems involving profit and loss,
with and without digital technologies
(ACMNA189)
Test 2
Term 2
Week
Content
Australian Curriculum Content
Descriptors
Exercises and
Resources
Assessments
Algebra
1
Variables and
expressions
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 5
Substitution for variables
1-2
Using formulae
2-3
Simplifying expressions
Chapter 5
Simplify algebraic expressions involving
the four operations (ACMNA192)
Chapter 5
Extend and apply the distributive law to
the expansion of algebraic expressions
(ACMNA190)
Factorise algebraic expressions by
identifying numerical factors
(ACMNA191)
Chapter 5
Solve a range of problems involving
rates and ratios, with and without digital
technologies (ACMNA188)
Chapter 1
Solve a range of problems involving
rates and ratios, with and without digital
technologies (ACMNA188)
Chapter 1
EPW 2
Multiplying and dividing
algebraic terms
3-4
Expanding brackets
Factorising
Ratios
5
Writing ratios
Simplifying ratios
Unit ratio and scale
factors
6
Using ratios to find
amounts
Test 3
Sharing amounts in a
given
ratio
7
Revision
8
Exams
EXAM
Rates
9
Solve a range of problems involving
rates and ratios, with and without digital
technologies (ACMNA188)
Chapter 1
Perimeter
Find perimeters and areas of
parallelograms, trapeziums, rhombuses
and kites (ACMMG196)
Chapter 7
Circle relationships
Investigate the relationship between
features of circles such as
circumference, area, radius and
diameter. Use formulas to solve
problems involving circumference and
area (ACMMG197)
Rates
Measurement
10
Term 3
Week
Content
Australian Curriculum Content
Descriptors
Exercises and
resources
Assessments
Measurement cont.
1
Circumference
Area
Investigate the relationship between
features of circles such as
circumference, area, radius and
diameter. Use formulas to solve
problems involving circumference and
area (ACMMG197)
Chapter 7 / 8
Find perimeters and areas of
parallelograms, trapeziums, rhombuses
and kites (ACMMG196)
2
Area of a circle
Converting linear units
to squared and cubed
units
Investigate the relationship between
features of circles such as
circumference, area, radius and
diameter. Use formulas to solve
problems involving circumference and
area (ACMMG197). Include partial
circles and composite shapes.
Chapter 7/8
Choose appropriate units of
measurement for area and volume and
convert from one unit to another
(ACMMG195)
2–3
Volume and capacity
Develop the formulas for volumes of
rectangular and triangular prisms and
prisms in general. Use formulas to solve
problems involving volume
(ACMMG198)
Chapter 7/8
Test 4
4
Time
Solve problems involving duration,
including using 12- and 24-hour time
within a single time zone (ACMMG199)
Chapter 6
EPW 3
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 9
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 9
Linear graphs
5–6
Interpreting line graphs
Linear relationships
(only from a pattern in a
table).
6–7
Finding the rule (in
terms of change).
Using linear
relationships
Plot linear relationships on the Cartesian
plane with and without the use of digital
technologies (ACMNA193)
Linear equations
8
The language of
equations
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 10
Solving linear equations
(beyond 3 step must
use algebraic
balancing)
9
Solving more complex
equations
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 10
Solve linear equations using algebraic
and graphical techniques. Verify
solutions by substitution (ACMNA194)
Chapter 10
Solving equations
where the unknown
appears on both sides
10
Solving problems using
equations
Test 5
Term 4
Week
Content
Australian Curriculum Content
Descriptors
Exercises and
resources
Assessment
Geometry
1
Angles Review
No descriptors – cover anyway
Chapter 11
2D Shapes review
1–2
Congruent triangles
Develop the conditions for congruence
of triangles (ACMMG201)
Chapter 11
3
Congruence and
transformation
Establish properties of quadrilaterals
using congruent triangles and angle
properties, and solve related numerical
problems using reasoning
(ACMMG202)
Chapter 11
Identify complementary events and use
the sum of probabilities to solve
problems (ACMSP204)
Chapter 13
Statistics and probability
4
Population sampling
Using sample measures
of centre and spread
Explore the variation of means and
proportions in random samples drawn
from the same population (ACMSP293)
Investigate the effect of individual data
values , including outliers, on the mean
and median (ACMSP207)
5
Frequency graphs and
tables
Explore the practicalities and
implications of obtaining data through
sampling using a variety of investigative
processes (ACMSP206)
Chapter 13
6
Understanding
probability
Investigate the effect of individual data
values, including outliers, on the mean
and median (ACMSP207)
Chapter 12
Test 6
6–7
Theoretical probability
for single-step
experiments
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)
Represent events in two-way tables and
Venn diagrams and solve related
problems (ACMSP292)
Chapter 12
7
REVISION
8–9
EXAM
EXAMS
Year 8 Achievement Standard
Number and Algebra
By the end of Year 8, students solve everyday problems involving rates, ratios and
percentages. Students use efficient mental and written strategies to carry out the four
operations with integers. They describe index laws and apply them to whole numbers.
They describe rational and irrational numbers. Students solve problems involving profit and
loss. They simplify a variety of algebraic expressions. They solve linear equations and
graph linear relationships on the Cartesian plane. They make connections between
expanding and factorising algebraic expressions.
Measurement and geometry
Students solve problems relating to the volume of prisms. They make sense of time
duration in real applications. Students convert between units of measurement for area and
volume. They 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. They identify conditions for the congruence of triangles and
deduce the properties of quadrilaterals.
Statistics and probability
Students determine the probabilities of complementary events and calculate the sum of
probabilities. Students model authentic situations with two-way tables and Venn diagrams.
They choose appropriate language to describe events and experiments. They explain
issues related to the collection of data and the effect of outliers on means and medians in
that data.