| 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 |
