LESMURDIE SENIOR HIGH SCHOOL
Mathematics 2AMAT/2BMAT PROGRAM
Students will be provided with opportunities to:
 plan and carry through tasks:

identify and organise information

develop systematic approaches

partition problems into sub-problems

identify simpler, related problems

choose and use mathematical methods

choose methods of processing—mental, written, with a calculator.
 interpret solutions:

check answers fit specifications

link solutions to contexts and reach conclusions

generalise results.
 communicate methods, reasoning and results.
The number formats for the units are decimals, fractions, percentages, positive and negative numbers, numbers expressed with positive integer powers, square roots, cube roots, simple ratios and rates.
References: Unit 2A and 2B Mathematics by Alan Sadler
Time
Topic/Syllabus entry
Resources
Number, algebra and calculator skills
2A 12 hours
2AMAT
Syllabus entries:
1.1.6 use calculators to calculate with integers, decimals, fractions
1.3.1 recognise that letters stand for variable numbers in algebra, including when translating between word and algebraic statements
1.3.2 use algebraic conventions such as 2  k  2k , and k  k  k 2
2A/2B Preliminary
Work, (number &
Algebra)
2A Chpt 1 (Number)
1.3.3
1.3.4
2A Cpt 5 (Algebra)
2A Chpt 6(Algebra)
2B 4hours
collect like terms in algebraic expressions
use the distributive property:
– to expand expressions of the form
(ax  b)(cx  d )
– to factorise linear expressions such as 8k  4 .
1.3.5 solve linear equations graphically and algebraically, expanding and gathering like terms where appropriate.
2BMAT
Syllabus entries:
1.1.2 use calculators to calculate, powers, square roots and cube roots
1.3.1 without a calculator solve equations with one algebraic term such as 2 x 2  1  19 , 3 x 3  24
1.3.2 solve linear equations and simple linear inequalities algebraically
1.1.3 convert numbers to and from scientific notation.
2B Chpt 2 (Integer
Powers)
Response Item
(Test 1)
Weekly skills test (Mental) — Ongoing
assessment
Week 1/4
Assessment
Time
Week 5
2B 4hours
Topic/Syllabus entry
Chance
2BMAT
Syllabus entries:
3.2.2 list sample spaces for one-stage events, with repetition to reflect possible outcomes
3.2.3 calculate simple probabilities, using sample spaces and the number of favourable outcomes divided by the total number of
outcomes, for one-stage events
3.2.4 use fractions, decimals and percentages to describe probability and move freely between them
3.2.5 use the fact that probabilities sum to 1 to calculate probabilities for complementary events
3.2.6 use the facts that probabilities sum to 1 and range from 0 to 1 to check probabilities
3.3.5 order outcomes from least likely to most likely, using fractional, decimal and percentage probabilities
3.3.6 explain probability statements in common usage
3.3.8 use chance terminology when describing events (‘probability of’, ‘complement of’).
Finance
2A 5 hours
2AMAT
Percentages
Syllabus entries:
1.1.6 use calculators to calculate with percentages
1.4.1 calculate profit, loss, discount and commission
1.4.2 determine ‘best buys’, use comparison, ratio and proportion
Proportion
1.3.7 solve direct proportion problems
.
2B 4 hours
Terms and sequences
2BMAT
Syllabus entries:
1.4.1 state recursive word rules for number sequences, identifying starting numbers
1.4.2 describe number sequences recursively using algebraic notation such as Tn 1  Tn  3 , T1  4
1.4.3 use recursive rules to continue sequences, including rules that involve simple percentages
1.4.4 investigate numbers
 identify patterns
 conjecture generalisations
 test conjectures with further cases
 provide explanations that support or refute
conjectures

use mathematical language to explain patterns.
Preliminary 2B
2B Chpt 5
2A Preliminary
2A Chpt 2
2A Chpt 3
2B Chpt 10
Assignments ongoing
Week 7/8
Assessment
Assignments ongoing
Week 6/7
Resources
Time
Week 8/9/10
2A 4 hours
Topic/Syllabus entry
Linear relationships
Resources
2A Chpt 4
2AMAT
Syllabus entries:
1.2.1 locate, plot and interpret points in the four quadrants of the Cartesian plane; reason whether or not to join the points
1.2.2 recognise that continuous lines and curves on a graph consist of points
1.2.3 sketch and interpret graphs that represent relationships in contexts such as water filling a vase
1.2.4
1.3.8
2B 4 hours
Week 2
2B Chpt 1
2BMAT
Syllabus entries:
2.3.1 represent information using network diagrams and interpret the diagrams (basic networks only, project networks not included)
2.3.2 investigate the traversability of networks
2.3.3 develop systematic methods to determine the shortest path between two vertices of a network.
Triangles/Pythagoras
2AMAT
Syllabus entries:
2.1.1
2.1.2
1.3.6
use direct proportion to estimate where direct measurement is not possible
use Pythagoras’s theorem to calculate the length of sides of right triangles
solve equations arising from application of Pythagoras’s theorem.
2A Chpt 9
Assignments ongoing
2A 4 hours
Networks
Response Item
(Test 2)
Assignments ongoing
identify linear relationships in the form y  mx  c
formulate linear rules for tables of values
determine tables of values for linear rules, recognise many values are possible besides the ones chosen
use tables of values to graph linear rules
read points from a line graph and recognise they satisfy the rule for the line
read gradient and vertical intercept of line graphs and link gradient to difference pattern in tables
formulate linear rules from graphs
graph lines from rules using gradient and vertical intercept.
relate the ideas of proportion and direct variation to linear functions
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Term 2
Week 1
Assessment
Time
Week 3/4
2B 4 hours
2B 4 hours
Week 5
Week 6/7
Week 8
Resources
Assessment
Coordinate geometry
2BMAT
Syllabus entries:
2.2.1 determine:
– distance between two points
– the gradient of a line joining two points
2.2.2 determine the equation of a line given:
– a point on the line and the gradient
– two points on the line.
1.3.3 set up simultaneous linear equations, using the forms y  mx  c and ax  by  c , and solve the equations algebraically
(unique solution only)
1.3.4
solve simultaneous linear equations graphically.
2A Chpt 11
2B Chpt 3
Response Item
(Test 3)
Exam Revision
Semester 1
Data collection and representation
2AMAT
Syllabus entries:
3.1.1 plan the collection of measurement data and fair (unbiased) samples to investigate situations specified by the teacher
3.1.2 plan recording sheets
3.1.3 collect and record data, and check and edit the record
3.1.4 group data in tables with provided equal-sized class intervals
3.2.1 construct one- and two-way frequency tables and dot frequency plots
3.2.2 construct frequency histograms frequency histograms for ungrouped data and data grouped in equal-sized class intervals
3.2.3 sketch the notional shape of frequency graphs (not from points).
2A Chpt 7
Assignments ongoing
2A 4 hours
Topic/Syllabus entry
Time
Term 2
Week 9/10
2A 8 hours
Topic/Syllabus entry
Prliminary Work
2A PW
2AMAT
Syllabus entries:
3.2.4 calculate mean, median and mode for ungrouped frequency data
3.2.5 calculate mean for grouped data and median and modal classes
3.2.6 calculate relative frequency, and proportions of data in fractional, decimal and percentage forms
3.2.7 describe spread of datasets informally, using terms such as data are spread out, tightly packed, clusters, gaps, more/less dense
regions, outliers
3.2.8 describe spread using range and lowest and highest scores
3.3.1 read information from tables, circle graphs (pie charts) with simple percentages, and frequency graphs, reading between
calibrations on scales
3.3.2 discern advantages/ disadvantages of using frequency graphs rather than tables to display data
3.3.3 discern the relative advantages and disadvantages of the various ‘averages’ (mean, median, mode)
3.3.4 compare datasets by describing spread of graphed data, and using mean, median, lowest and highest scores and range
3.3.5 use mathematical words that acknowledge uncertainty when comparing data sets such as ‘scores for … tend to be more spread
than scores for …’
3.3.6 calculate numbers of data in categories from relative frequency and proportions
2A Chpt 8
Response Item
(Test 1)
report on collected data (to include justifying sampling methods and explaining what graphs and summary values show) .
Trigonometry
2BMAT
Syllabus entries:
2.1.2 use sine, cosine and tangent ratios to calculate sides and angles (degree measure) of right triangles (two-dimensional contexts
only; exact trigonometric ratios involving surds are not required).
Assignments
ongoing
2B Chpt 12
Exponential functions
Investigation 5
Review Indices
2BMAT
Syllabus entries:
1.2.1
1.2.3
1.2.2
1.3.5
2B Chpt 9
x
graph exponential relationships, y  b for b  1 , x  0
interpret linear and exponential functions for practical situations.
recognise linear and exponential functions from equations, tables and graphs
solve exponential equations graphically and algebraically (simple cases with no leading coefficients e.g. 2 x  64 ).
Assignments (ongoing)
Week 3/4//5
2B 12 hours
Assessment
Analysing data
3.3.7
Term 3
Week 1/2
2B 6 hours
Resources
Time
2B 8 hours
Resources
Assessment
3D shapes
2BMAT
Syllabus entries:
2.1.1 use surface area and volume formulas directly and inversely for
– cubes, right prisms and pyramids
– cylinders, cones and spheres
(decimal answers only).
2B Chpt 4
Response Item
(Test 2)
Term 4
Week 1
2B 12 hours
Time series and bivariate data
2BMAT
Syllabus entries:
3.4.1 plan the collection of bivariate or time-series data to investigate situations specified by the teacher
3.4.2 predict what data will show
3.4.3 collect and record data, and check and edit the record
3.5.1 plot points and construct line graphs for time-series data, plotting between calibrations on scales, if necessary
3.5.2 construct scatterplots for bivariate data, plotting between calibrations on scales, if necessary
3.5.3 describe trend as increasing or decreasing, for bivariate data and time-series data
3.5.4 sketch notional increasing and decreasing trends (not from points)
3.5.5 fit trend lines ‘by eye’ over plotted points.
3.6.1 read information from scatterplots and plots of time series data, reading between calibrations on scales
3.6.2 predict using interpolation and extrapolation and trend lines fitted by eye, recognising the dangers of extrapolation
3.6.3 report on collected data (to include assessing how to improve data collection and handling).
Term 4
Week 2
Transformations
2A 4 hours
2AMAT
Syllabus entries:
2.2.1 identify translations, reflections and rotations of figures in two dimensions
2.2.2 produce patterns which exhibit symmetries, rotations, reflections and translations
2.2.3
use geometric conventions in drawing and geometric language to describe figures and patterns.
2B Chpt 7
2B Chpt 8
2B PW
Preliminary Work
2A Chpt 10
Assignments (ongoing)
Week 8/9/10
Assignments {ongoing)
Week 6/7
Topic/Syllabus entry
Time
Topic/Syllabus entry
Resources
Assessment
Simulations
Week 3
Week 4 &5
Revision of course
Week 6
Semester 2 Examinations
2B Chpt 6
Response Item
(Test 3)
Total hours
Combined 2A and 2B
Number and algebra
Space and measurement
Chance and data
In this program
44
24
32
100
Suggested in the syllabus
49
26
35
110
Text resources:
 FOM – Foundation of Mathematics (Alan Sadler)
 MQA – Maths Quest 11 General Mathematics A (Nolan/Jacaranda - www.jaconline.com.au)
 MQB – Maths Quest 11 General Mathematics B (Nolan/Jacaranda - www.jaconline.com.au)
 Working Mathematically with Chance and Data Levels 5-7, Mark Charlesworth (Ed.) (2000), MAWA: http://www.mawainc.org.au/
 Access to Algebra Series, Willis, S., Kissane, B., Johnston J . (1993), Curriculum Corporation: http://www.curriculum.edu.au/
 WestOne Services  Mathematics 2A & 2B, WestOne Services (DET): http://www.westone.gov.au/
Calculator references:
 Texas Instruments: http://education.ti.com
Thousands of activities can be found under ‘Classroom Activities’. Click on either ‘Activities Exchange’ or ‘EXPLORATIONS Series Book’.
 Casio: www.casioed.net.au
Several activities can be found under ‘activity books for graphics calculators’ (bottom–right) and at ‘ClassPad Corner’ (bottom–left).
 Hewlett–Packard: www.hpcalculators.com.au
Training modules can be found under ‘Graphic Calculators’ section. Scroll down to find the appropriate calculator.
Assignments (ongoing)
2B 4 hours
2BMAT
Syllabus entries:
3.1.1 simulate everyday chance events with outcomes that are not equally likely
3.2.1 use long-run relative frequency to estimate probabilities
3.3.1 predict the results for repetition of simulations with the same number of trials
3.3.2 use probabilities to predict proportions and number of outcomes that are likely to satisfy provided criteria in n trials
3.3.3 recognise predictions are not always realised
3.3.4 recognise the law of large numbers (that individual outcomes of chance events are unpredictable but the relative frequency
stabilises as the number of trials becomes large)
3.3.7 identify factors that could compromise a simulation of everyday chance events
3.3.8 Use chance terminology when describing events (‘probability of’, ‘complement of’).
Specific online and calculator activities:
Ref 1 Online learning activity: (Virtual manipulatives, grades 9–12) – http://nlvm.usu.edu. Under the ‘9–12’ heading click on the ‘Algebra’ cell, scroll down and
click on ‘Algebra Balance Scales’.
Ref 2 Online learning activity: (Virtual manipulatives, grades 9–12) – http://nlvm.usu.edu. Under the ‘9–12’ heading click on the ‘Algebra’ cell, scroll down and
click on ‘Algebra Balance Scales – negative’.
Ref 3 Calculator activity (Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘Algebra Tools’.
Ref 4 Online learning activity (Shodor) – www.shodor.org/interactivate1.0. Click on ‘Activities’, ‘Probability and Data Analysis Concepts’ and scroll down and
click on ‘Racing Game with One Dice’.
Ref 5 Online learning activity (Shodor) – www.shodor.org/interactivate1.0. Click on ‘Activities’, ‘Number and Operation’ and scroll down and click on
‘Sequencer’.
Ref 6 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’11–12’ heading choose the ‘Number’ cell, scroll down and then click on ‘The Old Swamp’.
Ref 7 Online learning activity: (Virtual manipulatives) – http://nlvm.usu.edu. Under the ‘9–12’ choose the ‘Algebra’ cell, scroll down and click on ‘Function
Machine’.
Ref 8 Online learning activity (Shodor) – www.shodor.org/interactivate1.0. Click on ‘Activities’, ‘Function and Algebra Concepts’, scroll down and click on
‘General Coordinates Game’.
Ref 9 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’7–8’ heading choose the ‘Algebra’ cell, scroll down and then click on ‘Guess my rule’.
Ref 10 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’7–8’ heading choose the ‘Algebra’ cell, scroll down and then click on ‘Describing and additive problem (linear)’.
Ref 11 Calculator activity ((Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘Sky Scrapers’.
Ref 12 Calculator activity ((Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘Beach Race’.
Ref 13 Calculator activity ((Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘The
Pythagorean Theoremand more’.
Ref 14 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’7–8’ heading choose the ‘Algebra’ cell, scroll down and then click on ‘Using Pythagoras to find the best position’.
Ref 15 Online learning activity (Shodor) – www.shodor.org/interactivate1.0. Click on ‘Activities’, ‘Probability and Data Analysis Concepts’ and scroll down and
click on ‘Plop It!’
Ref 16 Calculator activity ((Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘What Do You
Mean?’
Ref 17 Calculator activity (Texas Instruments): http://education.ti.com Choose ‘Classroom Activities’, ‘Activities Exchange’ and then type in ‘How High Does
A Ball Bounce?’
Ref 18 Online learning activity (Shodor) – www.shodor.org/interactivate1.0 .Click on ‘Activities’, ‘Geometry and Measurement Concepts’ and scroll down and
click on ‘Surface Area and Volume’.
Ref 19 Online learning activity: (Virtual manipulatives, grades 9–12) – http://nlvm.usu.edu. Under the ‘9–12’ heading choose ‘Geometry’, scroll down and click
on ‘Space Blocks’.
Ref 20 Online learning activity: (Virtual manipulatives, grades 9–12) – http://nlvm.usu.edu. Under the ‘9–12’ heading choose ‘Measurement’, scroll down and
click on ‘How High?’
Ref 21 Online learning activity: (Virtual manipulatives, grades 9–12) – http://nlvm.usu.edu. Under the ‘9–12’click on the ‘Probability and Data Analysis’ scroll
down, click on ‘Scatterplot’.
Ref 22 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’9–10’ heading choose the ‘Algebra’ cell, scroll down and then click on ‘How good was Bob Beamon?’
Ref 23 Online learning activity (Shodor) – www.shodor.org/interactivate1.0 Choose ‘Activities’, ‘Probability and Data Analysis Concepts’ and then click on
‘Rabbits and Wolves’.
Ref 24 Calculator activity (Casio’s Graphics Calculator 9860): www.casioed.net.au . Scroll down and click on ‘activity books for graphic calculators’. Under
the’11–12’ heading choose the ‘Chance/Data’ cell, scroll down and then click on ‘Raindrops Keep Falling On My Head’.
Other online resources:
• MEP (Mathematics Enhancement Programme), Centre for Innovation in Mathematics Teaching: http://www.cimt.plymouth.ac.uk/ Note: materials are
free, apply for a free access code to obtain solutions).
• Hot Maths www.hotmaths.com.au Login as teacher, Select topics and lessons, Pythagoras’ theorem (Pythagorean result developed through demonstration,
practice. A working mathematically idea investigating any links between areas of semi–circles and right triangles.
• Maths Forum – Maths Tools (National Science Foundation): http://mathforum.org/mathtools/ Use the drop–down boxes to choose course, resource and
technology then click ‘go’. Note: materials are free.