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M1 Maths can be used by students for independent learning, by schools as a supplement or substitute for a textbook, or as the basis of a school program. Free support is offered to anyone thinking of trialling the materials with students.

 

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N1:     Number - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

N1-1 pdf   docx

Whole numbers

  • whole numbers to trillions

  • the terms: whole number, counting number, multiple, factor, even, odd, composite, prime, >, <

  • divisibility rules, products of prime factors

4 h
N1-2 pdf   docx   Fraction Meanings
  • understanding common fractions, decimal fractions and percentages

3 h
N1-3 pdf   docx

Fraction Conversions

  • converting between equivalent common fractions, between mixed numbers and improper fractions and between common fractions, decimal fractions and percentages

3 h N1-2
N1-4 pdf   docx   Negatives
  • understanding negative numbers and placing them on a number line

1 h
N1-5 pdf   docx

Calculators

  • using calculators to add, subtract, multiply and divide whole numbers, decimal fractions, common fractions and negative numbers

1 h N1-3 N1-4
N1-6 pdf   docx

Powers

  • whole number powers and square roots

  • expressing counting numbers as products of prime factors in power form

2 h N1-1 N1-5
N1-7 pdf   docx   Order of Operations
  • order of operations conventions

3 h
N1-8 pdf   docx

  Common Fraction

  Operations 1

  • mental methods to perform simple operations on common fractions

  • approximation to perform more difficult operations

2 h N1-3
N1-9 pdf   docx

  Decimal Operations

  1

  • exact and approximate mental/written methods to add and subtract whole numbers and decimal fractions and multiply and divide whole numbers

3 h N1-3
N1-10 pdf   docx

  Rounding and

  Approximation

  • rounding of numbers

  • approximate calculations

3 h N1-5 N1-9

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N2:     Number - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

N2-1 pdf   docx   Number Sets
  • the various sets of numbers

2 h
N2-2 pdf   docx

  Fractions of

  Numbers

  • finding fractions (common, decimal and percent) of numbers

  • adding and subtracting percentages to/from numbers, including by multiplying

2 h
N2-3 pdf   docx   Rates
  • rates

4 h
N2-4 pdf   docx   Ratios
  • ratios

2 h N2-3
N2-5 pdf   docx

  Decimal Operations

  2

  • exact and approximate mental/written methods to multiply and divide whole numbers and decimal fractions

  • predicting when decimal fractions will terminate, recur and continue without recurrence

3 h N2-2
N2-6 pdf   docx

Negative Operations

  • mental/written methods to perform operations on positive and negative numbers

3 h
N2-7 pdf   docx

  Common Fraction

  Operations 2

  • mental/written methods to add, subtract, multiply and divide common fractions

3 h

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N3:     Number - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

N3-1 pdf   docx   Scientific Notation
  • scientific notation

2 h
N3-2 pdf   docx   Simple Interest
  • simple interest

3 h
N3-3 pdf   docx   Proportion
  • direct proportion

  • inverse proportion

2 h

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N4:     Number - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

N4-1 pdf   docx   Compound Interest
  • compound interest

3 h

Return to Main Menu  

 

 

N5:     Number - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 5 modules.

N5-1 pdf   docx   Simplifying Surds
  • simplifying expressions containing surds

2 h A5-2

Return to Main Menu  

 

 

N6:     Number - Level 6

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.

N6-1 pdf   docx

Complex Numbers

  • plotting complex numbers on an Argand diagram

  • converting between Cartesian, polar and exponential form

  • adding, subtracting, multiplying and dividing complex numbers and finding powers and roots

  • application of complex numbers to trigonometric identities and fractals

9 h
N6-2 pdf   docx

Vectors

  • scalars and geometric vectors in 2 and 3 dimensions

  • addition, subtraction, multiplication by a scalar

  • scalar and vector products

  • applications of geometric vectors

  • storage vectors

8 h

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A1:     Algebra - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

A1-1 pdf   docx   Relations 1
  • using relations given as tables, as graphs and as sets of ordered pairs

3 h
A1-2 pdf   docx

Relations 2

  • the terms 'variable', 'independent' and 'dependent'

  • converting between different forms of a relation

3 h A1-1
A1-3 pdf   docx

Patterns

  • recognising patterns in sequences of numbers

  • determining whether a relation has a pattern (from both tables and graphs)

  • knowing that relations with patterns can be expressed as formulae

3 h A1-2
A1-4 pdf   docx

  Discrete vs

  Continuous Relations

  • distinguishing discrete and continuous relations

  • presenting them appropriately as tables and graphs

2 h A1-3
A1-5 pdf   docx

Substitution

  • substituting for the independent variable in a formula and doing the arithmetic to find the value of the dependent variable

  • converting from formulae to other forms of a relation

  • substituting into formulae with more than one independent variable

3 h A1-4
A1-6 pdf   docx

Equations

  • substituting for the dependent variable in a formula and solving the resulting equation to find the value of the independent variable

  • algebraic shorthand

7 h A1-5

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A2:     Algebra - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

A2-1 pdf   docx   Writing Equations
  • solving problems by modelling them with equations

3 h
A2-2 pdf   docx   Collecting Terms
  • collecting terms to solve equations

2 h A2-1
A2-3 pdf   docx   Expanding
  • expanding brackets to solve equations

3 h A2-2

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A3:     Algebra - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

A3-1 pdf   docx

  Undoing the

  Unknown

  • undoing the unknown to solve equations

3 h
A3-2 pdf   docx

  Choosing the

  Unknown

  • writing and solving equations where the choice of unknown is not obvious

2 h A3-1
A3-3 pdf   docx

  Squares and

  Fractions

  • solving equations with squares and fractions

4 h A3-2
A3-4 pdf   docx

  Rearranging

  Formulae

  • changing the subject of a formula

2 h A3-3
A3-5 pdf   docx   Solving by Graphing
  • using a graphics calculator or computer graphing program,

  • graphing relations and solving equations using a graphics calculator

2 h
A3-6 pdf   docx   Domain and Range
  • domain and range

2 h
A3-7 pdf   docx   Functions
  • functions and the language of functions

3 h A3-6
A3-8 pdf   docx   Linear Functions
  • general form and graph shape

  • using y=mx+c to convert between formulas, tables and graphs for linear functions

  • finding the formula for a linear function from the gradient and points on the line

  • equation solution methods

  • applications

  • finding equations of lines on the Cartesian plane

  • parallel and perpendicular lines

  • mid-point of a line segment

5 h A3-7 M3-3
A3-9 pdf   docx   Reciprocal Functions
  • general form and graph shape

  • equation solution methods

  • applications

2 h A3-8
A3-10 pdf   docx   Index Laws 1-5
  • using the index laws for natural number powers

4 h

Return to Main Menu  

 

 

A4:     Algebra - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

A4-1 pdf   docx   Factorising
  • factorising with circles

  • expanding and factorising quadratics

5 h
A4-2 pdf   docx   Quadratic Functions
  • general form and graph shape

  • equation solution methods

  • applications

  • writing and solving quadratic equations

6 h A4-1
A4-3 pdf   docx

  Simultaneous

  Equations - Linear

  • solving pairs of linear simultaneous equations by equating, graphing, substitution, elimination and calculator

6 h
A4-4 pdf   docx   Inequalities
  • solving single-unknown inequalities and graphing the solutions on a number line

1 h
A4-5 pdf   docx   Algebraic Fractions
  • manipulating algebraic fractions

3 h A4-1
A4-6 pdf   docx   Algebraic Proofs
  • algebraic proofs

2 h

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A5:     Algebra - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 5 modules.

A5-1 pdf   docx

  Polynomial

  Functions

  • general form and graph shape

  • equation solution methods

  • applications

3 h
A5-2 pdf   docx   Index Laws 6-10
  • zero, negative and fractional indices

  • converting between fractional indices and surds

3 h
A5-3 pdf   docx   Power Functions
  • general form and graph shape

  • equation solution methods

  • applications

2 h A5-2
A5-4 pdf   docx

  Exponential

  Functions and Logs

  • general form and graph shape

  • equation solution methods and logs

  • applications

5 h A5-2
A5-5 pdf   docx

  Simultaneous

  Equations - General

  • solving pairs of general simultaneous equations by equating, graphing and substitution

  • solving larger sets of simultaneous equations

6 h A5-3 A5-4
A5-6 pdf   docx

  Finding Formulae for

  Functions

  • finding formulae for functions from known value pairs

3 h A5-5
A5-7 pdf   docx   Model Functions
  • finding model functions for data using technology

3 h A5-6
A5-8 pdf   docx

  Calculator Equation

  Solving

  • the equation solving function of a graphics calculator

1 h A5-1
A5-9 pdf   docx

  Algebraic

  Transformations

  • how changes to formulae affect their graphs and vice versa

4 h
A5-10 pdf   docx   Further Relations
  • composition of functions

  • inverse functions and y^2 = x

  • discontinuities

  • rational functions

  • piecewise and step functions

  • absolute value functions

  • circles

5 h A5-1
A5-11 pdf   docx

  Trigonometric

  Functions

  • general form and graph shape of sinusoidal functions

  • applications of sinusoidal functions

  • drawing graphs of sinusoidal functions from the formulas and vice versa

  • non-sinusoidal trigonometric functions

5 h M5-1
A5-12 pdf   docx

  Trigonometric

  Equations

  • solving equations derived from trigonometric functions

5 h A5-11 M5-1
A5-13 pdf   docx   Logs
  • the meaning of logs

  • logarithmic functions

  • equations from logarithmic functions

  • the log laws

  • logarithmic scales

7 h A5-4

Return to Main Menu  

 

 

A6:     Algebra - Level 6

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.

A6-1 pdf   docx

  Combinations and

  the Binomial

  Expansion

  • multiplication principle

  • permutations and combinations

  • expansion of (x+y)^n

  • Pascal’s triangle

6 h
A6-2 pdf   docx

  Arithmetic

  Sequences

  • recursive and explicit formulae

  • sum to n terms

4 h
A6-3 pdf   docx

  Geometric

  Sequences

  • recursive and explicit formulae

  • sum to n terms

  • sum to infinity

3 h A6-2
A6-4 pdf   docx

Linear Programming

  • graphing formula inequalities on the Cartesian plane

  • solving linear programming problems

3 h
A6-5 pdf   docx

  Further Methods of

  Proof

  • proof by deduction

  • proof by exhaustion

  • proof by contradiction

  • proof by induction

3 h
A6-6 pdf   docx

  Loci and Conic

  Sections

  • loci

  • conic sections

4 h

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M1:     Measurement - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

M1-1 pdf   docx

  Dimensions, Size and

  Mass

  • dimensions and measures of size in 1D, 2D and 3D

  • measuring and estimating length, area, volume and mass

5 h
M1-2 pdf   docx   Time 1
  • reading and recording times to the nearest minute on digital and analogue clocks

  • the order of the months and how many days in each

  • calendars

  • simple timetables

2 h
M1-3 pdf docx   Unit Conversion
  • converting between units for mass and length, between L, mL and cm3 and between units for time

2 h M1-1 M1-2
M1-4 pdf   docx

  Length, Area and

  Volume 1

  • calculating perimeters of polygons

  • calculating areas of rectangles and volumes of rectangular prisms

2 h M1-1 M1-3

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M2:     Measurement - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

M2-1 pdf   docx   Graduated Scales
  • reading graduated scales

2 h
M2-2 pdf   docx

Time 2

  • determining start time, finish time and duration of events given the other two

  • measuring and estimating duration of events

  • converting between 12h and 24h time

  • at a given local time, finding the time in other parts of the country in winter and in summer

  • estimating times in other parts of the world

  • more difficult timetables

5 h
M2-3 pdf   docx

Length, Area and Volume 2

  • perimeters of circles and sectors of circles

  • approximating areas of non-rectangular shapes using an enveloping rectangle

  • areas of parallelograms, trapeziums, triangles, circles and sectors of circles

  • surface areas (flat faces only)

  • volumes of prisms and cylinders

6 h G2-4

Return to Main Menu  

 

 

M3:     Measurement - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

M3-1 pdf   docx   Pythagoras
  • using Pythagoras theorem to find any side of a right-angle triangle in 2- and 3-dimensional situations

3 h
M3-2 pdf   docx

Trigonometry

  • using tangent, sine and cosine ratios to find side lengths and angles in right-angle triangles

  • solving problems using trigonometry including those involving direction and angles of elevation/depression

6 h M3-1
M3-3 pdf   docx   Slope
  • slope as an angle

  • gradient

2 h M3-2
M3-4 pdf   docx

Length, Area and Volume 3

  • perimeters, areas and volumes of compound shapes

  • distinguishing length, area and volume formulae by inspection

  • the effect on length, area and volume of multiplying the dimensions of a shape

8 h M3-1

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M4:     Measurement - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

M4-1 pdf   docx

Length, Area and Volume 4

  • converting between different units for area and volume

  • volumes of pyramids, cones and spheres

  • surface areas of cylinders, cones and spheres

  • approximating volumes of irregular 3D shapes

4 h

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M5:     Measurement - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 5 modules.

M5-1 pdf   docx

  Unit Circle and Trig

  Identities

  • sines, cosines and tangents in terms of the unit circle

  • identities: tan theta = sin theta/cos theta, Pythagorean identity, sin theta = cos (90 - theta)

4 h
M5-2 pdf   docx   Solving Triangles
  • cosine and sine rules

  • area formulae

5 h M5-1

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M6:     Measurement - Level 6

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.

M6-1 pdf   docx   Radians
  • radians, conversion between radians and degrees and the radian values of common angles

5 h
M6-2 pdf   docx   Exact Trig Values
  • exact values of the trig functions of multiples of 30 and 45 degrees

3 h M6-1

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G1:     Geometry - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

G1-1 pdf   docx   Drawings
  • plans and elevations, perspective drawings, cross sections and nets

3 h M1-1
G1-2 pdf   docx   Angles
  • estimating, measuring and constructing angles

  • the meaning of turn and angle

2 h
G1-3 pdf   docx   Position
  • describing position using eight compass points, distance and bearing, coordinates and latitude and longitude

3 h G1-2

Return to Main Menu  

 

 

G2:     Geometry - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

G2-1 pdf   docx   Maps and Scales
  • making and reading maps and plans with legends and scales

2 h
G2-2 pdf   docx   Geometric Figures
  • conventions for labelling geometric figures

  • geometric theorems

5 h
G2-3 pdf   docx

  Properties of

  Polygons

  • polygon names

  • internal angles

  • types of triangles and their properties

  • types of quadrilateral and their properties

5 h
G2-4 pdf   docx

  Geometric

  Vocabulary

  • words used in geometry

2 h
G2-5 pdf   docx

  Transformations and

  Symmetry

  • translations, reflections, rotations and dilations of points and shapes

  • reflectional and rotational symmetry

3 h G2-2
G2-6 pdf   docx   Congruence
  • the meaning of congruence

  • tests for congruence of triangles

3 h G2-2

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G3:     Geometry - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

G3-1 pdf   docx   Similarity
  • the meaning of similarity

  • tests for similarity

  • applications of similar triangles

3 h

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G4:     Geometry - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

G4-1 pdf   docx   Geometric Proofs
  • proving geometric statements using chains of reasoning

  • circle theorems

4 h

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S1:     Statistics - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

S1-1 pdf docx   Data Displays 1
  • reading varied data displays

  • reading and drawing tables, picture graphs, dot plots, bar graphs, scatter graphs and line graphs

6 h
S1-2 pdf   docx   Data Summary
  • mean, median, mode and range

2 h

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S2:     Statistics - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

S2-1 pdf   docx   Data Collection
  • data and surveys

  • extracting data

2 h

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S3:     Statistics - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

S3-1 pdf   docx   xlsx   Spreadsheets
  • using spreadsheets to store data, to calculate and to produce graphs

4 h
S3-2 pdf   docx   Data Displays 2
  • reading varied data displays

  • reading and drawing grouped tables, compound bar graphs, histograms, stem and leaf plots and pie charts

5 h
S3-3 pdf   docx   Critiquing
  • critiquing data collection, data representation and conclusions drawn from data

3 h S3-2
S3-4 pdf   docx   Data Types
  • numerical, categorical and ordinal data

  • univariate, bivariate and multivariate data

  • time series

1 h
S3-5 pdf   docx   Data Distributions
  • distribution shape

  • unimodal and bimodal distributions

  • normal distributions

  • skewed distributions

2 h S3-2

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S4:     Statistics - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

S4-1 pdf   docx

Quantiles and Spread

  • quantiles and ogives

  • five-number summaries, box plots

  • inter-quartile range

  • standard deviation

5 h
S4-2 pdf   docx   Linear Regression
  • trends in data, regression lines, interpolation and extrapolation

  • correlation

  • causality

3 h

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S5:     Statistics - Level 5

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 5 modules.

S5-1 pdf   docx

  Grouped Data

  • calculating statistics from grouped data

3 h

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P1:     Probability - Level 1

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite modules.

P1-1 pdf   docx

Probability

  • the meaning of probability

  • finding approximate probabilities using data (from experiment and pre-existing) and understanding the reliability of the approximations

  • estimating probabilities by guesswork

  • finding exact probability using indifference, deciding when it applies

  • calculating expected frequency

8 h N1-3

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P2:     Probability - Level 2

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.

P2-1 pdf   docx   Compound Events
  • addition and multiplication rules

5 h
P2-2 pdf   docx   Two-way Tables
  • using two-way tables to determine probabilities

1 h P2-1
P2-3 pdf   docx   Venn Diagrams
  • using Venn diagrams to determine numbers and probabilities

3 h

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P3:     Probability - Level 3

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.

P3-1 pdf   docx   Tree Diagrams
  • using tree diagrams to determine probabilities

3 h

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P4:     Probability - Level 4

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.

P4-1 pdf   docx

  Complex

  Probabilities

  • using the addition and multiplication rules in combination

4 h

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P6:     Probability - Level 6

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.

P6-1 pdf   docx   Sets
  • set terminology and notation

2 h
P6-2 pdf   docx

  Conditional

  Probability

  • conditional probability

3 h
P6-3 pdf   docx

  Discrete Random

  Variables

  • discrete random variables

  • discrete probability distributions

  • expected value and variation

5 h
P6-4 pdf   docx

  Binomial

  Distributions

  • binomial probabilities

5 h P6-3 A6-1
P6-5 pdf   docx

  Continuous Random

  Variables

  • probability density functions

  • expected value, quantiles and spread

  • cumulative distribution functions

  • mean and variance of aX + b

5 h P6-3 C6-10
P6-6 pdf   docx   Normal Distributions
  • finding probabilities from values

  • finding values from probabilities

  • z-scores

5 h P6-5
P6-7 pdf   docx

  Confidence Intervals

  for Proportions

  • confidence intervals for proportions

4 h P6-4
P6-8 pdf   docx

  Confidence Intervals

  for Means

  • confidence intervals for means

3 h P6-7

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C6:     Calculus - Level 6

Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.

C6-1 pdf   docx

Velocity Graphically

  • displacement vs time graphs: high/low, rising/falling, steeper/flatter

  • gradient = velocity

  • gradient of secant = average velocity

  • gradient of tangent = instantaneous velocity

4 h
C6-2 pdf   docx

Velocity Algebraically

  • velocity at a given time using reducing intervals

  • velocity at given time using an unspecified interval, dt

  • velocity at any time

6 h C6-1
C6-3 pdf   docx   Velocity by Rule
  • differentiating at^n and sums of such terms by rule

6 h C6-2
C6-4 pdf   docx

Other Relations

  • calculus with relations other than between time, displacement and velocity

  • generic x-y relations

4 h C6-3
C6-5 pdf   docx

Applications of Derivatives

  • small increments

  • tangents and normals

  • finding a point with a given gradient

  • optimisation

  • turning points and curve sketching

8 h C6-4
C6-6 pdf   docx

  Chain, Product and

  Quotient Rules

  • chain, product and quotient rules

7 h C6-5
C6-7 pdf   docx   Other Derivatives
  • the derivatives of sin x, cos x, a^x, e^x, ln x

5 h C6-6
C6-8 pdf   docx

  Mastering

  Differentiation

  • differentiating all functions fluently

12 h C6-7
C6-9 pdf   docx

  Differential

  Equations

  • differential equations

10 h C6-8
C6-10 pdf   docx

Integration

  • definite integrals and the fundamental theorem of calculus

  • solving problems with integration

  • area under and between curves

  • trapezoidal rule

  • indefinite integrals

14 h C6-9
C6-11 pdf   docx   Pert
  • differential equations of the form dA/dt = rA

4 h C6-10
C6-12 pdf   docx

  Higher-orders

  Derivatives

  • second and higher-order derivatives

3 h C6-10
C6-13 pdf   docx   Graph Sketching
  • sketching graphs of polynomial and rational functions using knowledge of function shape, extreme behaviour, discontinuities, axis intercepts, stationary points and spot values

4 h C6-8
C6-14 pdf   docx   Optimisation
  • finding the value of a control quantity which gives the optimum value of an objective quantity

6 h C6-8
C6-15 pdf   docx

Simpson's Rule

  • finding the value of a control quantity which gives the optimum value of an objective quantity

2 h C6-10

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Skills

There is just one module for each of the skills. Each module covers all levels.

Click on the required format. Word documents need to be downloaded and opened in Word to display properly.

Mental Arithmetic pdf   docx     Problem Solving pdf   docx     Investigating pdf   docx     Communication pdf   docx

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Programs

Each country in the world, and often each state, specifies a different maths curriculum for its students. However, up to Year 10 at least, these curricula all tend to contain basically the same maths topics, just arranged in a different sequence and maybe assigned to different year levels.

So, for a school work program up to Year 10, it should be possible to assign the corresponding M1 Maths module to each topic in the curriculum and then to work through those modules accordingly. A possible program for the Australian Years 7-10 curriculum is given below under the Curriculum-paced link.

Alternatively, if there is some freedom regarding the internal structure of the school program used, it should be possible to work progressively through Levels 1, 2, 3 . . . over the Years up to Year 10.

The idea of calling them Levels 1 to 5 rather than 7 to 10 is that it is not necessary to lock-step the M1 Maths levels to the school year levels. Rather, it allows a program where students work through the levels at a pace which suits their background, ability, aspirations and dedication. Such a program would allow students to master concepts before moving on to other concepts which depend on them, a luxury often not afforded by lock-step programs. Clicking the Student-paced link below will lead to a suggestion for this type of program.

The Progress Tracker link below is a spreadsheet that could be used to record progress with such a student-paced program.

Click on the required format. Word documents and spreadsheets need to be downloaded and opened in Word or Excel to display properly.

Curriculum-paced   pdf   docx                       Student-paced   pdf   docx                       Progress Tracker   xlsx

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Level Tests

The links below are to Knowledge tests and Skills test for each level from Level 1 to Level 5. The tests were produced by writing a question or two from each of the modules at that level, plus a scattering of questions from earlier levels. There will eventually be four versions of each test. However, not all have been written to date.

These tests could be used as school tests. A version should be picked at random and minor changes made (e.g. changing some of the numbers, maybe changing the problems and the investigation). Students can then still use the versions below for test preparation / practice without invalidating the tests. The tests won't be high stakes after all. Alternatively, schools might decide to write their own tests from scratch. In that case, the tests below could be used as models.

Click on the required format. Word documents need to be downloaded and opened in Word to display properly.

    Version A Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx pdf   docx pdf   docx pdf   docx pdf   docx
    Skills pdf   docx pdf   docx pdf   docx pdf   docx pdf   docx

    Version B Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

    Version C Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

    Version D Level 1 Level 2 Level 3 Level 4 Level 5
    Knowledge pdf   docx        
    Skills pdf   docx        

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Curriculum Correlation

Being Australian, I have produced correlation tables showing which M1 Maths knowledge module corresponds to each of the syllabus elements for the Australian Years 7 to 10 syllabus and the Australian Years 11-12 Mathematical Methods syllabus. Being a Queenslander, I have done the same for the Queensland Years 11-12 syllabuses. The links below will take you to the various tables.

I'm afraid I haven't done the same for other places. But, if anyone would like to produce them for their country or state, I would gladly include them here.

Word documents need to be downloaded and opened in Word to display properly.

Australian Curriculum

Years 7-10 Maths   pdf   docx Years 11-12 Maths Methods   pdf   docx

Queensland Syllabuses

Years 11-12 Essential Maths  pdf   docx Years 11-12 Maths Methods   pdf   docx
Years 11-12 General Maths   pdf   docx Years 11-12 Specialist Maths   pdf   docx

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Fun and Games

These are fun activities and games which can be played as a class or by small groups. They help develop or reinforce the concepts addressed in the learning modules. Click the preferred format in the first column to download instructions and materials for that activity. Word documents need to be downloaded and opened in Word to display properly. The instructions are designed primarily for teachers to allow them to conduct the activity with a class.

Activity

Format

Relevance

Description

Bingo

pdf   docx

Mental arithmetic (all levels)

A game of bingo where students have to perform simple mental computations to work out the numbers called

Goodies and Baddies

pdf   docx

General

A quiz game between one half of the class and the other. The questions can be made up to suit the needs of the class.

Group Problem Solving

pdf   docx

Problem solving – persistence and cooperation

A competition in which students work in groups to try to solve more problems correctly than the other groups

  Mind Reading

pdf   docx

Problem solving

A simple magic trick for students to work out

Twenty

pdf   docx

Problem solving

A strategy game for students to work out so they can succeed in the challenge of beating the teacher

Last One Standing

pdf   docx

General

A quick class game that rehearses recollection of facts and mental arithmetic skills Can be used as a break and leg stretch

4-Corner Quiz

pdf   docx

General

This is a fun quiz involving movement that can be used to revise and reinforce any topic

Target

pdf   docx

Number sense, mental arithmetic, estimation, order of operations

A card game in which students use numbers to make an expression as close in value as possible to a given target number

Back to Back

pdf   docx

Geometry, Communication

An activity where students have to give clear and precise mathematical instructions

Protractor Golf

pdf   docx

Estimating and measuring angles and distances

A game for two in which students aim for holes on a paper golf course by estimating then measuring direction and distance

Walk the Plank

pdf   docx

Adding and subtracting positive and negative numbers

A simulation of walking the plank using addition and subtraction of positive and negative numbers to decide which direction and how far to go

Fraction Line

pdf   docx

Fraction meanings and fractions of numbers

A game where one half of the class competes against the other half to best estimate given fractions of the way along a line

Fraction Dominoes

pdf   docx

Fraction conversion

A game of dominoes to develop fluency with recognising different expressions of the same fraction and with fraction conversion

Millionaire

pdf   docx pdf   docx

Fractions of numbers

A board game that rehearses fractions among other things

Stomp

pdf   docx

Number facts and mental arithmetic

A board game for two

Greedy Pig

pdf   docx

Probability

A game mostly for fun, but which helps develop intuitive ideas of probability It can be used with all levels

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To search for a particular string, word or phrase on this web page, press Ctrl+F.

For more detailed instructions, see below for the browser you are using. To find modules which mention 'equation', search for 'equation'. If you want also to find 'equate', 'equating' etc., search for 'equat'.

  Chrome

Press Ctrl+F (or click on the white upward arrow on an orange background on the far right of the address bar, then choose 'Find...')

You will get a small dialogue box near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences.

  Safari

Press Ctrl+F

You will get a small box with a magnifying glass near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Enter key to scroll through other occurrences.

  Firefox

Press Ctrl+F (or click on the three horizontal bars on the far right of the address bar, then choose 'Find in This Page...')

You will get a small dialogue box near the bottom left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences.

  Edge

Press Ctrl+F (or click on the three dots on the far right of the address bar, then choose 'Find on Page...')

You will get a small dialogue box near the top left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Left and Right arrows in the dialogue box to move to other occurrences.

  Other Browsers

Most other browsers work in very similar ways. It shouldn't be hard to find the search function.

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