Download Curriculum into the classroom (C2C)

Curriculum into the classroom (C2C)
Year level plan
Mathematics
Year level
Eight
This Year level plan is based on the Queensland Studies Authority Mathematics Year 8 plan
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.
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 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, areas of common shapes and their volumes and 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
Curriculum intent
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
Australian Curriculum: Mathematics for P(F)-10 Version 3.0
www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
[accessed on 27 September 2012].
Achievement
standard
By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational
and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems
relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of
quadrilaterals. 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.
Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph
linear relationships on the Cartesian plane. 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. Students determine complementary events and calculate
the sum of probabilities.
Australian Curriculum: Mathematics for P(F)-10 Version 3.0
www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
[accessed on 27 September 2012].
Curriculum into the classroom (C2C), Mathematics Year level plan Year 8
Education Queensland
Version 1, October 2012
TERM
1
Unit overviews Unit 1:
Sequencing teaching and learning
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
2
3
4
Unit 2:
Unit 3:
Unit 4:
Unit 5:
Unit 6:
Unit 7:
Unit 8:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
Through the proficiency
strands of —
Understanding,
Fluency, Problem
solving and Reasoning,
students have
opportunities to
develop
understandings of:
 Number and place
 Number and place
 Number and place
 Algebra — expand
 Measurement
 Statistics — collect,
 Measurement —
 Algebra — apply
value — revise
- calculate the
value — represent,
value — express
and factorise
organise and display
develop formulas for
number laws to
operations with
perimeter and area of
compare and order
rational numbers as
algebraic
data, interpret data
volume and capacity
algebraic expressions
integers
parallelograms,
integers, and solve
terminating or
expressions, apply
displayed in tables
of rectangular and
and equations,
 Real numbers —
problems involving
recurring decimals,
number laws to
rhombuses, kites and
and graphs, connect
triangular prisms and
expand and factorise
model situations
the four operations
appreciate that
algebraic expressions
circles (including
samples and
prisms, solve volume
algebraic
involving proportional
and rational numbers
irrational numbers
and equations, solve
semi- and quarterpopulations, identify
problems and convert
expressions, solve
relationships and
circles), use formulas
can be expressed as
linear equations
collection methods,
units of measurement
simple linear
 Financial
solve a range of
for perimeter and
problems involving
mathematics — make
infinite decimals
algebraically.
explore the effect of
equations
 Geometric reasoning
rates and ratios
area to solve
connections between  Probability — draw
sample size, calculate
— revise angle
algebraically and
 Number and place
 Linear and non-linear
percentages,
and interpret Venn
value — express
problems, and
measures of
properties, explore
graphically, connect
relationships —
fractions and
diagrams to assign
numbers in index,
generate formulas for
centrality, identify
congruence, with and
patterns, linear
interpret, model and
decimals and apply
probabilities, state the
establish the index
the circumference
outliers and their
without technology,
functions, tables of
formulate patterns
and area of a circle
this to percentage
complement of an
laws with whole
affect on measures of
identify the effect of
values, graphs and
and relationships;
and solve problems.
increase or decrease
event, use the
number bases and
centre, identifying
reflections,
rotations
worded statements,
represent patterns
situations, and
complement to
positive integral
sources of bias and
and translations on
plot coordinates on
and relationships as
problem solve in a
solving problems of
indices,
apply this knowledge
the shape and size of
the Cartesian plane
rules, functions,
range of contexts
probability, draw and
to make hypotheses
plane shapes,
and solve realistic
tables & graphs,
solve linear equations
including financial
use two-way tables to
and support
establish and apply
problems, and
using graphical
situations.
assign probabilities.
conclusions
the congruence tests,
investigate patterns to
techniques.
extend congruence of
develop an algebraic
 Measurement —
triangles to identify
rule
solve problems
the properties of a
 Number and place
involving time
range of
value — consolidate
duration, for 12 and
quadrilaterals and
the four operations
24 time formats,
solve problems using
with rational numbers.
within a single time
the properties of
zone.
congruent figures,
reasoning and
generalisations.
Curriculum into the classroom (C2C), Mathematics Year level plan Year 8
Education Queensland
Version 1, October 2012
General
e with:
Opportunities to engage
capabilities and
crosscurriculum
priorities
Key to general
capabilities and
cross-curriculum
priorities
Assessment
Literacy
Num
meracy
Opportunities to eng
gage with:
ICT comp
petence
Critical a
and creative thinking
Ethical behaviou
ur
Personal and social
s
competence
Intercultural unders
standing
Aboriginal and Torres Strait Isla
ander histories and culltures
a and Australia’s engag
gement with Asia
ASIA Asia
y
SUST Sustainability
Te
eachers and children organise
o
evidence of learning in individual fo
olios. The individual fo
olio is constructed jointly by a teacher, a child, parents/carers and
d other partners. It bec
comes a
dyynamic record of exam
mples of a child’s learn
ning and development.
Unit
1
Short answer questions
Students use percentage to
calculate com
mmission, mark-up,
profit and loss
s and make financial
decisions.
2
Written
Students dete
ermine
complementary events and use the
sum of probab
bilities to solve
problems.
Assessment
Making judgments
Feedback
Opportunities
s to engage with:
ASIA
Un
nit
Consistency of
teacher
judgments
Opportunities to engage with:
4
Unit
Unit
5
Short answ
wer questions
Students rrepresent linear
relationshiips, solve equations frrom
graphical rrepresentations, use
perimeter and area to solve
problems.
n
Written
Studen
nts collect representative
data an
nd explore the effect of
o
outliers
s on the median and mean.
m
6
Short answer
a
questions
Studen
nts solve problems inv
volving
volume
e, rates and ratios.
Te
eachers will initially ma
ake judgments on a
Teachers will discusss task-specific
sm
mall random sample to
o reach a common
descriptors of the qu
uality of student
un
nderstanding of the ex
xpected standard, and performance.
then grade their own cla
ass.
dually grade all studen
nt
Teachers will individ
responses, applying
g the shared
understanding achie
eved through this
calibration process.
Students will pee
er-review the conclusions of
their open-ended
d task.
8
Sh
hort answer questions
Students use congruenc
ce
pro
operties and volume fo
ormula to
so
olve problems, and write and
ma
anipulate algebraic eq
quations
an
nd expression .
Teachers will grade student respon
nses
individually and
a then select studen
nt samples
representativ
ve of the A–E qualities
s.
Teachers will inittially make judgments on a
small random sa
ample to reach a comm
mon
Teachers will meet to share samples and
understanding off the expected standard, and discuss judgm
ments based on evide
ence
then grade their own class.
provided in student
s
responses, aim
ming to
reach consen
nsus.
Curriculum
m into the classroom ((C2C), Mathematics Year
Y
level plan Year 8
Education
n Queensland
Version 1, Oc
ctober 2012
Content descriptions for Year 8 mathematics
Australian Curriculum: Mathematics for P(F)-10 Version 3.0
www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
[accessed on 27 September 2012].
Review for balance and coverage of content descriptions
Number and Algebra
Unit
1
2
3
4
5
Measurement and Geometry
6
7
8
Number and place value
Use index notation with numbers to
establish the index laws with positive
integral indices and the zero index.
1
2
3
4
5
Statistics and Probability
6
7
8
Using units of measurement
      
Choose appropriate units of
measurement for area and volume
and convert from one unit to
another.
Carry out the four operations with
      Find perimeters and areas of
rational numbers and integers, using
parallelograms, trapeziums,
efficient mental and written strategies
rhombuses and kites.
and appropriate digital technologies.
Real numbers
Investigate terminating and recurring
decimals.
       
Investigate the concept of irrational
numbers, including π.


Solve problems involving the use of
percentages, including percentage
increases and decreases, with and
without digital technologies.
       
Solve a range of problems involving
rates and ratios, with and without
digital technologies.
       
Investigate the relationship between
features of circles such as
circumference, area, radius and
diameter. Use formulas to solve
problems involving circumference
and area.
Develop the formulas for volumes of
rectangular and triangular prisms
and prisms in general. Use formulas
to solve problems involving volume.
Solve problems involving duration,
including using 12- and 24-hour
time within a single time zone.
      
Develop the conditions for
congruence of triangles.
Unit
1
2
3
4
5
6
7
8
Chance
       
Identify complementary events and       
use the sum of probabilities to solve
problems.
       
Describe events using language of
'at least', exclusive 'or' (A or B but
not both), inclusive 'or' (A or B or
both) and 'and'.

       
Represent events in two-way tables
and Venn diagrams and solve
related problems.

Data representation and Interpretation

       
Geometric reasoning
Define congruence of plane shapes
using transformations.
Money and financial mathematics
Solve problems involving profit and
loss, with and without digital
technologies.
Unit

Investigate techniques for collecting
data, including census, sampling
and observation.

Explore the practicalities and
implications of obtaining data
through sampling using a variety of
investigative processes.

Explore the variation of means and
proportions of random samples
drawn from the same population.

Investigate the effect of individual
data values , including outliers, on
the mean and median.

       
Curriculum into the classroom (C2C), Mathematics Year level plan Year 8
Education Queensland
Version 1, October 2012
Number and Algebra
Unit
1
2
3
4
5
Measurement and Geometry
6
7
8
Patterns and algebra
Use index notation with numbers to
establish the index laws with positive
integral indices and the zero index.
Unit
1
2
3
4
5
6
7
8
Geometric reasoning
      
Establish properties of
quadrilaterals using congruent
triangles and angle properties,
and solve related numerical
problems using reasoning.
       
       
Factorise algebraic expressions by
identifying numerical factors.
       

Simplify algebraic expressions
involving the four operations.
       

Plot linear relationships on the
Cartesian plane with and without the
use of digital technologies.
       

Solve linear equations using
algebraic and graphical techniques.
Verify solutions by substitution.
       

Linear and non-linear relationships
Curriculum into the classroom (C2C), Mathematics Year level plan Year 8
Education Queensland
Version 1, October 2012
Concepts for Year 8 mathematics
Review for balance and coverage of concepts
Number and Algebra
Unit
1
2
3
4
5
Measurement and Geometry
6
7
8
Unit
1
2
3
4
5
Statistics and Probability
6
7
8
Unit
1
2
3
4
5
6
7
8
Addition and subtraction
      Area
       
Data collection
     
Equivalence
      Length
       
Data representation
      
Financial mathematics
      
       
Data interpretation
      
Functions
       Transformation
       
Probability
       
Multiplication and division
       
Proportional reasoning
Time
Volume
       
       
     
       
       
Real numbers
   
       
       
Representations
     
       
       
Curriculum into the classroom (C2C), Mathematics Year level plan Year 8
Education Queensland
Version 1, October 2012