Skip to main content

Grade 9 – Principles of Mathematics (Academic)

# TOPIC TITLE
1 Study Plan Study plan – Grade 9 – Principles of Mathematics (Academic)
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Algebra – Basic Directed Numbers: Addition and Subtraction
Objective: To add/subtract numbers using a number line – first number and answer can be negative
3 Algebra – Basic Directed Numbers: Multiplication and Division
Objective: To multiply and divide directed numbers and evaluate powers of directed numbers
4 Fractions BODMAS
Objective: To calculate answers for fraction and mixed number questions using BODMAS
5 Decimals Rounding Decimals
Objective: To round a number with one or two decimal places to the nearest whole number
6 Decimals Multiplication of decimals by decimals to two decimal places
Objective: To multiply decimals to two digits
7 Decimals Dividing numbers by decimals
Objective: To divide a whole number by a decimal fraction
8 Percentages Changing percentages to fractions and decimals
Objective: To change percentages to fractions and decimals
9 Percentages One Quantity as a Percentage of Another
Objective: To determine what one quantity is as a percentage of another
10 Uniform motion The Speed Formula
Objective: To calculate speed, distance or time using speed = distance/time
11 Algebra – Basic Simplifying Algebraic Expressions: Combining Addition and Subtraction
Objective: To simplify expressions containing addition and subtraction and two unlike terms
12 Algebra – Basic Simplifying Algebraic Expressions: Multiplication
Objective: To simplify algebraic products using (but not stating) the commutative law
13 Algebra – Basic Simplifying Algebraic Expressions: Division
Objective: To divide algebraic terms where the divisor is a factor of the dividend
14 Algebra – Basic Expanding Algebraic Expressions: multiplication
Objective: To remove grouping symbols from an expression where the multiplier is monomial
15 Algebra – Basic Expanding Algebraic Expressions: Negative multiplier
Objective: To expand parentheses when there is a negative multiplier
16 Algebra – Basic Expanding and simplifying algebraic expressions
Objective: To expand and simplify algebraic expressions involving grouping symbols
17 Algebra – Basic Solving Equations containing Addition and Subtraction
Objective: To solve one-step equations involving addition or subtraction
18 Algebra – Basic Solving Equations containing Multiplication and Division
Objective: To solve one-step equations involving multiplication or division
19 Algebra – Basic Solving Two-Step Equations
Objective: To solve two-step equations without division in the initial problem
20 Algebra – Basic Solving Equations Containing Binomial Expressions
Objective: To solve equations with binomial expressions on each side
21 Algebra – Basic Equations involving Grouping Symbols
Objective: To solve equations containing grouping symbols on each side
22 Algebra – Basic Equations involving fractions
Objective: To solve fraction equations with the unknown in either the numerator or denominator
23 Algebra – Basic Equations Resulting from Substitution into Formulae
Objective: To solve equations created by substituting values into formulae
24 Algebra – Basic Changing the Subject of the Formula
Objective: To change the subject of algebraic formulae using equation-solving techniques
25 Indices/Exponents Adding indices when multiplying terms with the same base
Objective: To add indices when multiplying powers that have the same base
26 Indices/Exponents Subtracting indices when dividing terms with the same base
Objective: To subtract indices when dividing powers of the same base
27 Indices/Exponents Multiplying indices when raising a power to a power
Objective: To multiply indices when raising a power to a power
28 Indices/Exponents Multiplying indices when raising to more than one term
Objective: To raise power products to a power
29 Indices/Exponents Terms raised to the power of zero
Objective: To evaluate expressions where quantities are raised to the power 0
30 Space Informal coordinate system
Objective: To specify location using a map coordinate system – origin top left
31 Graphs – Basic Line Graphs
Objective: To read and interpret line graphs
32 Graphs – Basic Pie and Bar Graphs
Objective: To read and interpret pie and bar graphs
33 Statistics part 1 Frequency distribution table
Objective: To construct a frequency distribution table for raw data and to interpret the table
34 Statistics part 1 Frequency histograms and polygons
Objective: To construct and interpret frequency histograms and polygons
35 Statistics part 1 Relative Frequency
Objective: To extend the frequency distribution table to include a relative frequency column
36 Statistics part 1 The Scatter plot
Objective: To make a valid interpretation of data presented as a scatter plot
37 Co-ordinate geometry part 1 The Gradient
Objective: To find the gradient of a line given its angle of inclination or given rise and run
38 Co-ordinate geometry part 1 The Gradient Formula
Objective: To use the gradient formula to find the gradient of straight lines
39 Co-ordinate geometry part 1 The Straight Line
Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b
40 Co-ordinate geometry part 1 Lines Through the Origin
Objective: To state the equation of lines passing through the origin and to graph y = mx
41 Co-ordinate geometry part 1 General Form of a Line and the x and y Intercepts
Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area
42 Co-ordinate geometry part 1 Slope Intercept Form of a Line
Objective: To change equation to slope intercept form and graph it and to find equation given graph
43 Co-ordinate geometry part 1 Point Slope Form of a Line
Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1)
44 Co-ordinate geometry part 2 Two Point Formula: equation of a line which joins a pair of points
Objective: To find the equation of the line which joins a pair of points
45 Co-ordinate geometry part 2 Intercept form of a straight line: find the equation when given x and y
Objective: To find the equation of a line given the x-axis and y-axis intercepts
46 Co-ordinate geometry part 2 Parallel Lines: identify equation of a line parallel to another
Objective: To change the standard form of a straight line equation to the y = mx + b form
47 Co-ordinate geometry part 2 Perpendicular Lines
Objective: To identify the equation of a line that is perpendicular to a given linear equation
48 Space Recognise and name prisms according to spatial properties
Objective: To name prisms according to the shape of the base
49 Space Recognise and name pyramids according to spatial properties
Objective: To name pyramids according to the shape of the base
50 Space Recognise nets for prisms, pyramids, cubes and cones
Objective: To match a net with a solid and determine whether a given net forms a solid
51 Space Viewing 3-D Shapes
Objective: To recognise what a solid looks like when viewed from a given direction
52 Measurement – Length Read and calculate distances on a map using the formal unit kilometre
Objective: To read distances (km) from a map and calculate total distances between locations
53 Measurement – Length Compare and convert formal units of measurement
Objective: To change cm to mm and then convert mm, cm, m and km from one to another
54 Measurement – Area Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram
Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height
55 Measurement – Area Finding the Area of a Triangle and Other Composite Shapes
Objective: To calculate the area of triangles and measure and calculate composite shape area
56 Measurement – Capacity Converting between volume and capacity using milliliters and liters
Objective: To solve capacity problems involving mixed dimensional units
57 Measurement – Capacity Estimate, measure and compare the capacity of containers
Objective: To understand estimation and a way to go about it
58 Measurement – Advanced area Area of a Trapezium
Objective: To calculate the area of trapezia using A=(h/2)(a+b)
59 Measurement – Advanced area Area of a Rhombus
Objective: To calculate the area of a rhombus using diagonal products
60 Measurement – Advanced area Area of a Circle
Objective: To calculate the area of circles and sectors and to solve circle problems
61 Measurement – Advanced area Area of Regular Polygons and Composite Figures
Objective: To calculate area of composite figures and solve problems using correct formulae
62 Problem solving Word Problems with Area
Objective: To solve area word problems using + – x and /
63 Measurement – Advanced volume Finding the volume of prisms
Objective: To calculate the volume of prisms using V=Ah and solve volume problems
64 Measurement – Advanced volume Volume of a Cylinder and Sphere
Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each
65 Measurement – Advanced volume Volume of Pyramids and Cones
Objective: To calculate the volumes of pyramids and cones
66 Measurement – Advanced volume Composite Solids
Objective: To calculate the volume of composite figures using appropriate formulae
67 Problem solving Word Problems with Volume/Capacity
Objective: To solve volume and capacity word problems using + – x and /
68 Surface area Surface Area of a Cube/Rectangular Prism
Objective: To calculate the surface area of cubes and rectangular prisms
69 Surface area Surface Area of a Triangular/Trapezoidal Prism
Objective: To calculate the surface area of triangular and trapezoidal prisms
70 Surface area Surface Area of a Cylinder and Sphere
Objective: To calculate the surface area of cylinders and spheres
71 Surface area Surface Area of Pyramids
Objective: To calculate the surface area of pyramids
72 Pythagoras Pythagoras’ Theorem: Finding the Hypotenuse
Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem
73 Pythagoras Using Pythagorean Triples to Identify Right Triangles
Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem
74 Pythagoras Calculating the Hypotenuse of a right-angled Triangle
Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals
75 Pythagoras Calculating a Leg of a right-angled Triangle
Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem
76 Geometry part 1 Angle Sum of a Triangle
Objective: To use the angle sum for a triangle to calculate unknown angles
77 Geometry part 1 Exterior angle theorem
Objective: To use the external angle of a triangle theorem to calculate unknown angles
78 Geometry part 1 Special triangles
Objective: To use the properties of equilateral and isosceles triangles to calculate angle size
79 Geometry part 1 Quadrilaterals
Objective: To use the angle sum of a quadrilateral to calculate unknown angles
80 Quadrilaterals Quadrilaterals 1
Objective: To recognise, name and describe the properties of quadrilaterals
81 Quadrilaterals Properties of Parallelograms – Opposite Angles Equal
Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’
82 Quadrilaterals Properties of Parallelograms – Diagonals, Sides and Angles
Objective: To prove parallelogram properties and calculate unknown angles and lengths
83 Quadrilaterals The Parallelogram Umbrella
Objective: To prove properties of specific parallelograms and find angles and lengths
84 Quadrilaterals Properties of Trapezoids
Objective: To prove properties of trapezoids and find unknown lengths and angles
85 Exam Exam – Grade 9 – Principles of Mathematics (Academic)
Objective: Exam