Download Mathematics: 3AB concurrent teaching program

Mathematics: 3AB concurrent teaching program - Year 11 MBA Raymond
Each semester is based on a 15 teaching week block.
Time placement
Unit
Time allocation (h)
Weeks 1–2
Weeks 2–3
Weeks 4–5
Weeks 5–6
3A
3A
3B
3A
6
5
6
8
Weeks 7–10
3B
Weeks 11
Content area
Topic
Assessment
Number and algebra
Number and algebra
Number and algebra
Number and algebra
Indices and exponential equations
Features of graphs
Interpret graphs
Solving equations
Investigation 1
15
Number and algebra
Calculus
3B
4
Number and algebra
Conjectures and Proofs
Weeks 12–13
Week 13–14
Semester 2
Week 1
Weeks 1–2
Week 2–3
Weeks 3–4
Weeks 4–5
Week 6
Weeks 7–8
Weeks 8–9
Week 10
Weeks 10–11
Week 12
Weeks 12–13
3A
3A
7
3
Chance and data
Chance and data
Quantify chance
Interpret chance
Test 3
Semester One Exam
3A
3A
3A
3A
3B
3A
3A
3A
3B
3B
3B
3B
1
5
4
3
5
4
5
5
2
4
2
8
Chance and data
Chance and data
Chance and data
Space and measurement
Number and algebra
Number and algebra
Number and algebra
Space and measurement
Space and measurement
Space and measurement
Space and measurement
Chance and data
Collect and organise data
Represent data 1
Interpret data 1
Rate
System of equations
Recursion
Finance
Triangles
Area and polynomials
Networks
Geometry
Represent data 2
Investigation 3
Weeks 13–14
3B
8
Chance and data
Interpret data 2
Semester 1
Test 1
Test 2
Investigation 2
Test 4
Test 5
Investigation 4
Test 6
Investigation 5
Weeks 15 - 16
Weeks 17 - 18
Revision
revision
Investigation 6
Semester Two Exam
Mathematics: 3AMAT and 3BMAT program
Program detail
Students will be provided with opportunities to:
 plan and carry through tasks:
▪ choose and use mathematical models and methods
▪ choose methods of processing—written, with a calculator.
 interpret solutions:
▪ check answers fit specifications
▪ link solutions to contexts
▪ generalise results.
 argue to support or contest mathematical conclusions
 communicate methods, reasoning and results.
The number formats for the unit are positive and negative numbers, recurring decimals, square roots, cube roots and numbers expressed with
integer powers.
Note: The program assumes that students will be familiar with linear and quadratic relationships.
Unit/
time
3A
6h
S1 Weeks
1–2
Topic/syllabus entry
Number and algebra: Indices and exponential
Equations
Embedded content to be addressed when it
arises
1.1.1 use mental strategies for estimation in
context
1.1.2 evaluate the absolute value of rational
numbers
1.1.3 use calculators efficiently
1.1.4 round numbers to a given number of
significant figures
1.1.5 round, truncate and choose appropriate
accuracy as part of calculation and
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
1.1.7 - See 3.1 in 3AMAS
Assessment
Investigation 1
1.2.6 Link 5
Unit/
time
Topic/syllabus entry
estimation
1.1.6 recognise the effects of rounding and
truncating on the accuracy of results
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
1.2.1 Link 1
1.2.3 Link 2
1.2.2 Link 3
1.1.7 use the laws of indices to simplify
numerical and algebraic expressions and
to solve equations.
1.2.6 use function notation
1.2.1 sketch graphs of:
y  bx , b  0 , b  e ,
y  x n , for n = 2, 3, ½, ⅓, -1
1.2.3 identify domain and range of functions
1.2.2 describe the effects of varying a , b , c
and d on the graph of
y  af [b( x  c)]  d where:
f ( x)  x n , for n = 2, 3, ½,⅓, -1
f ( x)  k x
(vary up to two parameters in any one
example)
Assessment
Unit/
time
Topic/syllabus entry
3A
5h
S1 Weeks
2–3
Number and algebra: Features of graphs
1.2.4 distinguish linear, quadratic, cubic,
exponential and reciprocal functions in
algebraic and graphical forms
1.2.5 describe the graphs of functions
qualitatively (calculations not required)
considering:
– intercepts
– lines of symmetry
– turning points
– asymptotes
– concavity
– points of inflection.
3B
6h
S1 Weeks
4–5
Number and algebra: Interpret graphs
1.1.1 apply polynomial, exponential and power
functions to practical situations including
optimisation and use numerical and
graphical techniques
1.1.2 interpret graphs:
– domain and range
– intercepts and points
– slope at a point
– local and global maxima and minima.
Specialist Mathematics related
content
3AMAS and 3BMAS
1.2.1, 1.2.2 – See 3.2 in 3AMAS
Resources
To use the links
use 'Control Click'.
1.2.4 Link 4
Assessment
Investigation option
Graph functions to determine
features of graphs and
determine any rules or
patterns associated with
these features and the rules
for the functions.
Investigation option
Interpreting graphs to solve
practical situations.
Test 1
Indices and exponential
equations
Features of graphs
Unit/
time
3A
8h
S1 Weeks
5–6
Specialist Mathematics related
content
3AMAS and 3BMAS
Topic/syllabus entry
Number and algebra: Solving equations
1.3.1 rearrange algebraic expressions into forms
useful for computation, including
1.3.2 - See 3.4, 3.5 in 3AMAS
Resources
To use the links
use 'Control Click'.
1.3.1 Link 6
factorising a x  b and x  bx  c
1.3.2 solve algebraically and graphically:
– quadratic equations in factored form
– cubic equations in factored form
2
2
2
– exponential equations ab
(logarithms not required)
2
kx
1.3.4
1.3.5
1.3.6
Investigation Options
Using the calculator,
investigate different
functions’ graphical features
and associate patterns with
the factored and expanded
form.
c, b0
– simple power equations x  c ,
n = 2, 3, ½, ⅓, -1.
solve simultaneous equations graphically,
including linear and quadratic equations
describe how one quantity varies with
another by inspecting the formula that
relates them, including quantities that are
inversely proportional
solve inverse proportion problems
relate the ideas of inverse proportion and
reciprocal functions.
n
1.3.3
Assessment
1.3.3 Link 7
Gather practical data to
investigate quantities which
are inversely proportional to
each other.
Unit/
time
3B
15h
S1
Weeks 7–
10
Topic/syllabus entry
Resources
To use the links
use 'Control Click'.
Number and algebra: Calculus
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.3.6
1.3.7
differentiate y  x n , n a whole number
use the sum and product rules to
differentiate polynomials
use differentiation to determine tangent
lines at a point for polynomial functions
use differentiation to sketch polynomial
functions (points of inflection not required)
use differentiation to solve optimisation
problems with polynomial functions
determine and interpret the anti-derivatives
of polynomial functions that are expressed
in expanded form
use notations for the derivative: y  , f ' ,
f ( x ) ,
3B
4h
S1 Week
11
Specialist Mathematics related
content
3AMAS and 3BMAS
1.3.1 Link 10
1.3.4 Link 11
Assessment
Test 2
Interpret Graphs
Solving Equations
Calculus
Investigation option
Using a calculator investigate
the gradient of different
functions at various points to
develop patterns which lead
to the process for
differentiating simple
functions.
1.3.5 Link 12
d
dy df
,
and
f (x)
dx dx
dx
Number and algebra: Conjectures and proofs
1.4.1 make conjectures about numbers such as
‘the sum of two odd numbers is even’
1.4.2 search for counter-examples to
conjectures in order to disprove them
1.4.3 construct simple deductive proofs using
algebra such as ‘prove that the sum of two
odd numbers is even’
1.4.4 follow algebraic deductive arguments and
ascertain their validity.
Investigation 2
Link 13
Test 3
Calculus
Unit/
time
3A
7h
S1 Weeks
12–13
3A
3h
S1 Weeks
13–14
Topic/syllabus entry
Chance and data: Quantify Chance
3.1.1 use lists, tree diagrams and two-way
tables to determine sample spaces for twoand three-stage events
3.1.2 use Venn diagrams to represent sample
spaces for two events and to illustrate
subset, intersection, union and
complement
3.1.3 use sample spaces to calculate simple
probabilities and probabilities for
compound events
3.1.4 use addition and multiplication principles
for counting, and use the counts to
calculate probabilities
3.1.5 use the relationship P(A) + P(A΄) = 1 to
calculate probabilities for complementary
events
3.1.6 use set and probability notation such as
n(U), n(A), n(A') or n( A ), n(A  B), n(A 
B), n(A|B), Ø and P(A), P(A'), P(A  B),
P(A'  B)
3.2.1 use probabilities to predict proportions and
number of outcomes that are likely to
satisfy provided criteria in n trials
3.2.2 estimate population size using the
capture/recapture technique
Chance and data: Interpret chance
3.1.7 calculate probabilities for normal
distributions with known mean  and
standard deviation 
3.1.8 use the 68%, 95%, 99.7% rule for data
one, two and three standard deviations
from the mean
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
Assessment
Investigation option
Estimation using the
capture/recapture technique
Investigation option
Analysis of simple games,
leading to sample spaces
and probabilities
Semester 1 examination
Unit/
time
Topic/syllabus entry
3.1.9
3.2.3
3.2.4
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
Assessment
use probability notation for normal random
variables such as P(X < x) .
calculate quantiles for normally distributed
data with known mean and standard
deviation
use number of standard deviations from
the mean (standard scores) to describe
deviations from the mean in normally
distributed data sets.
3A
1h
S2 Week 1
Chance and data: Collect and organise Data
3.3.1 plan sampling methods (systematic,
random, stratified, self-selection,
convenience) and justify choosing a
sample instead of a census.
Investigation 3
3A
5h
S2
Weeks 1–2
Chance and data: Represent data 1
3.4.1 construct frequency histograms for
grouped and ungrouped data
3.4.2 construct boxplots for ungrouped data,
outliers not distinguished
3.4.3 calculate mean, median and mode for
ungrouped frequency data and recognise
that averages indicate location of
frequency distributions
3.4.4 calculate weighted mean, mean for
grouped data, and median and modal
classes
3.4.5 describe spread between data displayed in
frequency tables and graphs using terms
such as gaps, clusters, more dense/less
dense regions, outliers, symmetry and
skewness
3.4.6 calculate cumulative frequency, quartiles
and interquartile range for ungrouped data
Investigation option
Use various statistical
measures to summarise
actual data and express
findings based on these
measures.
Unit/
time
Topic/syllabus entry
and use them to describe spread
3.4.7 determine the standard deviation for
grouped and ungrouped data using the
inbuilt facility on a calculator
3.4.8 identify extreme and unexpected values
3.4.9 calculate outliers (values more than
1.5  interquartile range beyond the upper
and lower quartiles).
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
Assessment
Unit/
time
3A
4h
S2
Weeks 2–3
Topic/syllabus entry
Chance and data: Interpret data 1
3.5.1 discern connections between frequency
histograms and boxplots, including the
shape of histograms for provided boxplots
3.5.2 discern the advantages/disadvantages of
using frequency histograms and boxplots
to display data
3.5.3 discern effects of different equal-sized
class intervals on histograms
3.5.4 discern viability of interquartile range,
range and standard deviation for ranking
datasets in order of spread
3.5.5 interpret spread summaries in terms of
their mathematical definitions
3.5.6 reason to include or exclude outliers
3.5.7 discern effects on summary statistics of
cropping data (including outliers)
3.5.8 compare datasets, combining
interpretation of mean, standard
deviation, and skewness or symmetry
about the mean
3.5.9 compare datasets, combining
interpretation of median, interquartile
range and skewness or symmetry about
the median
3.5.10 compare scores from two or more sets of
data using number of standard deviations
from the mean (standard scores)
3.5.11 infer results for populations from samples,
recognising possible chance variation
between them
3.5.12 show how data can be manipulated to
serve different purposes.
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
Assessment
Investigation option
Represent data in a variety
of ways and investigate the
advantages and
disadvantages of the
different approaches.
Unit/
time
Topic/syllabus entry
3A
3h
S2
Weeks 3–4
Space and measurement: Rate
2.1.1 convert between rate units such as
kilometres per hour and metres per second
2.1.2 interpret function of time relationships
y  f (t ) including distance and
displacement relationships
2.1.3 sketch and interpret graphs for y  f (t )
relationships
2.1.4 recognise that rate of change is constant
for linear relationships.
3B
5h
S2
Weeks 4–5
Number and algebra: Systems of Equations
1.2.1 formulate and solve one-variable
equations and inequalities (absolute value
terms not included)
1.2.2 formulate systems of linear equations and
inequalities in two variables from word
descriptions
1.2.3 solve systems of linear equations in two
variables by elimination
1.2.4 solve two-variable linear programming
problems graphically, without sensitivity
analysis.
3A
4h
S2 Week 6
Number and algebra - Recursion
1.4.1 use recursion to determine terms and
sums for sequences including arithmetic
and geometric sequences
1.4.2 use recursion to study growth and decay.
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
2.1 Link 9
1.4.2 Link 8
Assessment
Test 4
Collect and organise data
Represent data
Interpret data
Investigation option
A task involving sequences
to review recursion.
Unit/
time
3A
5h
S2
Weeks 7–8
3A
5h
S2
Weeks 8–9
Specialist Mathematics related
content
3AMAS and 3BMAS
Topic/syllabus entry
Number and algebra: Finance
1.5.1 use, construct and interpret spreadsheets
for making financial decisions
1.5.2 judge adequacy of spreadsheets and
make refinements if necessary
1.5.3 calculate loans with reducible interest,
including determining the number of years
for the balance to fall to a specified amount
1.5.4 calculate annuities using a spreadsheet
1.5.5 interpret and make decisions about loan
and repayment amounts with reducible
interest.
Space and measurement: Triangles
2.2.1 use the unit circle to identify sine and
cosine ratios for acute and obtuse angles
(degree measure only)
2.2.2 use the formula area ΔABC =
1
absin C
2
2.2.3 use the sine and cosine rules to determine
sides and angles of triangles (twodimensional contexts only).
Resources
To use the links
use 'Control Click'.
Assessment
Investigation option
Using a calculator, or
spreadsheets, students may
be provided with data to
determine the best loan from
a sample, or outcome for a
particular financial situation.
Test 5
Systems of equations
Rate
Patterns
2.2.1, 2.2.2, 2.2.3 - See 2.3, 2.5 in
3AMAS
Investigation option
Developing the patterns for
sine and cosine in the unit
circle
Extending right angle triangle
Trigonometry to sine and
cosine rule for non-right
angled triangles.
3B
2h
S2 Week
10
Space and measurement: Area and
polynomials
2.1.1 estimate the area between the x-axis and
graphs of simple polynomial functions
using the areas of circumscribed and
inscribed rectangles.
Investigation 4
3B
4h
S2 Weeks
Space and measurement: Networks
2.2.1 analyse project networks
2.2.2 construct project networks
Test 6
Finance
Unit/
time
Topic/syllabus entry
10–11
2.2.3
3B
2h
S2 Week
12
Space and measurement: Geometry
2.3.1 distinguish general geometric arguments
from those based on specific cases
2.3.2 follow and ascertain the validity of
geometric arguments.
3B
8h
S2 Weeks
12–13
Chance and Data: Represent data 2
3.1.1 describe association (positive, negative,
weak, strong or none)
3.1.2 determine Pearson’s correlation coefficient
r using a calculator
3.1.3 describe properties of regression lines
(least-squares relationship and passing
through ( x , y ) )
3.1.4 calculate and graph regression models for
data with linear trends
3.1.5 calculate residuals for linear models and
construct residual plots
3.1.6 calculate moving averages, regression
lines for moving averages, and seasonal
adjustments for periodic time-series data.
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
determine critical paths and minimum
completion times for projects with fixed
activity times.
Assessment
Measurement
Networks
Link 13
Unit/
time
Topic/syllabus entry
Specialist Mathematics related
content
3AMAS and 3BMAS
Resources
To use the links
use 'Control Click'.
Assessment
3B
8h
S2 Weeks
13–14
Chance and data: Interpret data 2
3.2.1 place expressions of association (weak,
strong etc.) on a scale from -1 to 1
3.2.2 recognise correlation does not imply
causality
3.2.3 discern ‘goodness of fit’ for regression
lines, using visual inspection of
scatterplots, residual plots and correlation
coefficient
3.2.4 consider regression lines:
– to include or crop outliers
– effects on the lines of cropping outliers
and other data
– whether intercepts are valid
– variables that explain data above and
below the lines
– alternative models that might fit data
better than a line including quadratic,
exponential.
3.2.5 predict from regression lines, recognising
the risks of extrapolation, and assess
reliability
3.2.6 explain why regression lines are used for
prediction, rather than data points and why
predicted and actual results are likely to
differ
3.2.7 recognise that regression lines for samples
and populations may differ due to chance
variation
3.2.8 predict from regression lines, making
seasonal adjustments for periodic data.
Investigation 5
S2 Weeks
15 - 16
Revision
Investigation 6
Unit/
time
S2 Weeks
17 - 18
Topic/syllabus entry
Specialist Mathematics related
content
3AMAS and 3BMAS
Revision
Assessment
Semester 2 Exam
Hours allocated
In this program*
Suggested in the syllabus
Resources
To use the links
use 'Control Click'.
Number and
Algebra
58
58
Space and
Measurement
16
16
Chance and
Data
36
36
Total
110
110