# Grade 8 Mathematics – Canada

### Grade 8 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Grade 8 | |

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 | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

5 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

6 | Fractions | Reducing fractions to lowest equivalent form | |

Objective: To reduce a fraction to its lowest form | |||

7 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

8 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

9 | Fractions | Adding and subtracting fractions with the same denominator | |

Objective: To add and subtract fractions with the same denominator | |||

10 | Fractions | Adding and subtracting fractions with different denominators | |

Objective: To add fractions with different denominators and the answer is less than 1 | |||

11 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

12 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

13 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

14 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

15 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

16 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

17 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

18 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

19 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

20 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

21 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

22 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

23 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

24 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

25 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

26 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

27 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

28 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

29 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

30 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

31 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

32 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

33 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

34 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

35 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

36 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

37 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

38 | 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 | |||

39 | 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 | |||

40 | 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 | |||

41 | 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 | |||

42 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

43 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

44 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

45 | Measurement – Capacity | Converting between volume and capacity using kiloliters and liters | |

Objective: To know the formal units of measurement for volume and capacity for bigger objects | |||

46 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

47 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

48 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

49 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

50 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

51 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

52 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

53 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

54 | Space | Using the prefix to determine polygons | |

Objective: To continue sequences of shapes and recognise prefixes and name polygons | |||

55 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

56 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

57 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

58 | Space | Use grids to enlarge/reduce 2-D shapes | |

Objective: To recognise shapes that tessellate and specify position on a grid | |||

59 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

60 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

61 | 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 | |||

62 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

63 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

64 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

65 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

66 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

67 | Geometry part 1 | Measuring Angles | |

Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex | |||

68 | Geometry part 1 | Adjacent Angles | |

Objective: To recognise and calculate the size of adjacent angles | |||

69 | Geometry part 1 | Complementary and Supplementary Angles | |

Objective: To recognise and calculate the size of complementary and supplementary angles | |||

70 | Geometry part 1 | Vertically Opposite Angles | |

Objective: To determine values of pronumerals in vertically opposite angles | |||

71 | Geometry part 1 | Angles at a Point | |

Objective: To use angles at a point to calculate unknown angles | |||

72 | Geometry part 1 | Parallel Lines | |

Objective: To identify angle pairs and calculate angles formed by a transversal and parallel lines | |||

73 | Geometry part 1 | Additional questions involving parallel lines | |

Objective: To determine angle magnitude for angles formed by parallel lines and transversals | |||

74 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

75 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

76 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

77 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

78 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

79 | Quadrilaterals | Quadrilaterals 6 | |

Objective: To establish the properties of quadrilaterals in the number plane | |||

80 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

81 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

82 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

83 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

84 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

85 | Geometry part 2 | Examples involving overlapping triangles | |

Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles | |||

86 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

87 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

88 | 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 | |||

89 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

90 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

91 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

92 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

93 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

94 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

95 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

96 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

97 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

98 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

99 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

100 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

101 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

102 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

103 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

104 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

105 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

106 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

107 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

108 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

109 | Space | Main and intermediate compass points | |

Objective: To specify direction using the eight points of a compass | |||

110 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

111 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

112 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

113 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

114 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

115 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

116 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

117 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

118 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

119 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

120 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

121 | Exam | Exam – Grade 8 | |

Objective: Exam |