Download Year 8 Course Outline

CVC Year 8 Mathematics Program 2017
Week(s)
1-2
2-3
3-4
5
Australian Curriculum Content Description
“Getting to know you” statistics activities

Collecting data

Graphing data

Calculations (mean, mode, median, range)
Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)
Explore the practicalities and implications of obtaining data through sampling using a variety of
investigative processes (ACMSP206)
Explore the variation of means and proportions of random samples drawn from the same population
(ACMSP293)
Investigate the effect of individual data values, including outliers, on the mean and median (ACMSP207)
Carry out the four operations with rational numbers and integers, using efficient mental and written
strategies and appropriate digital technologies
(ACMNA183)
Investigate terminating and recurring decimals (ACMNA184)
Investigate the concept of irrational numbers, including π (ACMNA186)
Number &
Algebra
Statistics
&
Probability
Week(s)
6-7
Elaboration(s)
Identifying situations where data can be collected by census and those where a
sample is appropriate
Investigating the uses of random sampling to collect data
Using sample properties to predict characteristics of the population
Using displays of data to explore and investigate effects
Using patterns to assist in finding rules for the multiplication and division of integers
Using the number line to develop strategies for adding and subtracting rational
numbers
Recognising terminating, recurring and non terminating decimals and choosing their
appropriate representations
Understanding that the real number system includes irrational numbers
A
Excellent Achievement
Identifies equivalent forms of irrational numbers.
B
High Achievement
Identifies forms of numbers and classifies numbers as
rational or irrational.
Calculates the mean and the median of a data set,
explaining how the relationship between the two is
influenced by outliers and other values. Describes
different methods for the collection of data and explains
their impact on the collected data.
Calculates the mean and the median of a data set,
identifying outliers and explaining their influence on the
relationship between the two. Describes different methods
for the collection of data
C
Satisfactory Achievement
Calculates the mean and the median of a data set and
identifies how an outlier affects the relationship between
the two. Identifies issues related to the collection of data,
e.g. sample size, bias.
Australian Curriculum Content Description
Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
Investigate the relationship between features of circles such as circumference, area, radius and
diameter.
Elaboration(s)
Establishing and using formulas for areas such as trapeziums, rhombuses and kites
Investigating the circumference and area of circles with materials or by measuring, to
establish an understanding of formulas
Use formulas to solve problems involving circumference and area (ACMMG197)
Investigating the area of circles using a square grid or by rearranging a circle divided
into sectors
Identifying regions in Australia and countries in Asia that are in the same time zone
7-9
10
Solve problems involving duration, including using 12 and 24-hour time within a single time zone.
(ACMMG199)
Measurement
& Geometry
A
Excellent Achievement
Uses the correct relationship to solve multi-step problems,
including the inverse use of formulas, involving the
circumference and area of circles and uses numbers
expressed in exact form.
B
High Achievement
Uses the correct relationship to solve problems involving the
circumference and area of circles, e.g. perimeter of a sector.
C
Satisfactory Achievement
Names features of circles and calculates their circumference
and area. Converts between units of area.
Term 2
Week(s)
1-3
Australian Curriculum Content Description
Use index notation with numbers to establish the index laws with positive
integral indices and the zero index (ACMNA182)
Extend and apply the distributive law to the expansion of algebraic
expressions (ACMNA190)
Elaboration(s)
Evaluating numbers expressed as powers of positive integers
Applying the distributive law to the expansion of algebraic expressions using strategies such as the area model
Recognising the relationship between factorising and expanding
3-6
Factorise algebraic expressions by identifying numerical factors
(ACMNA191)
Identifying the greatest common divisor (highest common factor) of numeric and algebraic expressions and using a
range of strategies to factorise algebraic expressions
Understanding that the laws used with numbers can also be used with algebra
Simplify algebraic expressions involving the four operations (ACMNA192)
Number &
Algebra
Week(s)
A
Excellent Achievement
Simplifies algebraic expressions, including fractions with
numerical denominators, the four operations and multiple
uses of the distributive law.
B
High Achievement
Simplifies algebraic expressions involving the four
operations and the use of the distributive law twice.
Australian Curriculum Content Description
Choose appropriate units of measurement for area and volume and
convert from one unit to another (ACMMG195)
C
Satisfactory Achievement
Simplifies algebraic expressions with at most three
operations and the use of the distributive law once.
Elaboration(s)
Choosing units for area including mm2, cm2, m2, hectares, km2, and units for volume including mm3, cm3, m3
Recognising that the conversion factors for area units are the squares of those for the corresponding linear units
7-8
Develop the formulas for volumes of rectangular and triangular prisms and
prisms in general. Use formulas to solve problems involving volume
(ACMMG198)
Define congruence of plane shapes using transformations (ACMMG200)
9
10
Develop the conditions for congruence of triangles (ACMMG201)
Establish properties of quadrilaterals using congruent triangles and angle
properties, and solve related numerical problems using reasoning.
(ACMMG202)
Recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units
Investigating the relationship between volumes of rectangular and triangular prisms
Understanding the properties that determine congruence of triangles and recognising which transformations create
congruent figures.
Establishing that two figures are congruent if one shape lies exactly on top of the other after one or more
transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles
are equal.
Investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of
the conditions for congruence (SSS, SAS, ASA and RHS)
Solving problems using the properties of congruent figures
Constructing triangles using the conditions for congruence
Establishing the properties of squares, rectangles,
parallelograms, rhombuses, trapeziums and kites
Identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry
Measurement
& Geometry
A
Excellent Achievement
Extracts information and constructs a diagram from a
worded description, correctly using geometric symbols.
Identifies the congruent triangles and justifies the condition
of congruency with a full explanation. Solves related
numerical problems.
Uses congruency of triangles and related angle properties to
prove the properties of quadrilaterals. Uses properties of
quadrilaterals to solve numerical problems.
B
High Achievement
Identifies congruency in triangles of varying orientations,
naming the triangles. Justifies congruency by naming the
condition.
Uses congruency of triangles to justify the properties of
quadrilaterals.
C
Satisfactory Achievement
Identifies congruency in triangles, naming the triangles.
Justifies congruency by naming the condition.
Identifies and correctly names quadrilaterals, and applies
distinguishing properties.
Term 3
Week(s)
1-2
3
4-5
Australian Curriculum Content Description
Solve problems involving the use of percentages, including percentage
increases and decreases, with and without digital technologies (ACMNA187)
Elaboration(s)
Using percentages to solve problems, including those involving mark ups, discounts and GST
Using percentages to calculate population increases and decreases
Expressing profit and loss as a percentage of cost or selling price, comparing the difference
Solve problems involving profit and loss, with and without digital
technologies (ACMNA189)
Solve a range of problems involving rates and ratios, with and without digital
technologies (ACMNA188)
Investigating the methods used in retail stores to express discounts
Understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most
efficient form to solve a particular problem
Calculating population growth rates in Australia and Asia and explaining their difference
Number &
Algebra
Week(s)
6-7
8 - 10
A
Excellent Achievement
Applies percentages, rates and ratios in complex worded
problems requiring at least three calculations, including
inverse, with and without technology.
B
High Achievement
Applies percentages, rates and ratios in complex worded
problems requiring at most two calculations, including
inverse, with and without technology.
C
Satisfactory Achievement
Applies percentages, rates and ratios in simple worded
problems, requiring at most two calculations, with and
without technology.
Solves complex multi-step worded problems involving profit
and loss, including inverse calculations, with and without
technology.
Solves multi-step worded problems involving profit and loss,
with and without technology.
Solves simple worded problems involving profit and loss,
with and without technology.
Australian Curriculum Content Description
Plot linear relationships on the Cartesian plane with and without the use of
digital technologies (ACMNA193)
Solve linear equations using algebraic and graphical techniques. Verify
solutions by substitution (ACMNA194)
Number &
Algebra
Elaboration(s)
Completing a table of values, plotting the resulting points and determining whether the relationship is linear
Finding the rule for a linear relationship
Solving real life problems by using variables to represent unknowns
A
Excellent Achievement
Identifies relationships as linear or non-linear, justifying that a
relationship is linear by providing reasoning for the conclusion.
B
High Achievement
Compares and explains similarities and differences between
different linear relationships.
Solves multi-step linear equations, including the use of fractions
Solves multi-step linear equations, using algebraic techniques
C
Satisfactory Achievement
Plots points on the Cartesian plane, identifies and writes a linear
relationship, and solves associated equations using algebraic
conventions.
Term 4
Week(s)
1
Australian Curriculum Content Description
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)
Represent events in two way tables and Venn diagrams and solve related problems
(ACMSP292)
2-3
3-5
A
Excellent Achievement
Uses Venn diagrams and two- way tables to model more than two
choices and describes each region of the sample space. Writes
the associated probability in multiple number forms.
Number &
Algebra
Applies probability to solve problems. Interprets the sample
space using relevant language, including the distinction between
inclusive and exclusive ‘or’.
Elaboration(s)
Identifying the complement of familiar events
Understanding that probabilities range between 0 to 1 and that calculating the probability of an event
allows the probability of its complement to be found
Posing 'and', 'or' and 'not' probability questions about objects or people
Using Venn diagrams and two way tables to calculate probabilities for events, satisfying 'and', 'or' and
'not' conditions
Understanding that representing data in Venn diagrams or two way tables facilitates the calculation of
probabilities
Collecting data to answer the questions using Venn diagrams or two way tables
B
High Achievement
Uses Venn diagrams and two- way tables to model more than two
choices, showing that their probabilities sum to 1.
Interprets the sample space using relevant language, e.g. at least,
at most.
C
Satisfactory Achievement
Uses Venn diagrams and two- way tables to model authentic
situations. Indicates where events are complementary and shows
that probabilities sum to 1.
Interprets the sample space using relevant language, e.g. and, or,
not.
Week(s)
Review of topics – especially solving equations and algebraic manipulation
6 - 10
Introduction of some new topics – for example the Pythagorean Theorem
Cover some problem solving strategies – drawing a diagram, making a list, guess & check, simplifying the problem etc
CVC Year 8 Maths Assessment Outline 2017
Strand Weightings:
Strand
Number & Algebra
Measurement & Geometry
Weighting
39%
32%
Statistics & Probability
Observation
TOTAL
24%
5%
100%
Type Weightings:
Type
Investigation
Tests
Observation
TOTAL
Weighting
28%
67%
5%
100%
Timeline
Week 3
Term 1
Week 5
Week 10
Week 6
Term 2
Week 8
Week 10
Week 3
Week 5
Term 3
Week 7
Week 10
Term 4
Week 5
Name
Investigation 1
Test 1
Test 2
Test 3
Investigation 2
Test 4
Investigation 3
Test 5
Investigation 4
Test 6
Test 7
Observation
-
Strand
Statistics & Probability
N&A (5%) // S&P (6%)
Measurement & Geometry
Number & Algebra
Measurement & Geometry
Measurement & Geometry
Number & Algebra
Number & Algebra
Number & Algebra
Number & Algebra
Statistics & Probability
N&A (2%) // M&G (2%) //
S&P (1%)
Weighting
8%
11%
12%
8%
8%
12%
6%
7%
6%
7%
10%
5%