# Grade 9 – Principles of Mathematics (Academic) Mathematics – Canada

### 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 |