# Year 8 Mathematics – Queensland

### QLD Year 8 Mathematics

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

1 | Study Plan | Study plan – Year 8 | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Addition | Addition up to the number 999 | |

Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers. | |||

3 | Subtraction | Subtraction up to the number 999 using the renaming method | |

Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers. | |||

4 | Counting and numeration | The numbers 10 000 to 99 999 | |

Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers. | |||

5 | Counting and numeration | Addition to 9999 and beyond | |

Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems. | |||

6 | Basic mathematics part 2 | Subtraction involving four-digit numbers and beyond | |

Objective: To subtract 4 or 5-digit numbers from 5-digit numbers using the Renaming Method | |||

7 | Multiplication | Multiplication – important facts. | |

Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences. | |||

8 | Division | Division with and without a remainder. | |

Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||

9 | Division | Dividing two and three digit numbers by a single digit number. | |

Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number. | |||

10 | Counting and numeration | Seven digit numbers | |

Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers. | |||

11 | Multiplication | Multiplication by 2 and 3 digits | |

Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form. | |||

12 | Division | Divide whole numbers by a 2 digit divisor | |

Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction. | |||

13 | Length | Using the metre as a formal unit to measure perimeter | |

Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||

14 | Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||

15 | 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 | |||

16 | Length | Compare and convert formal units of measurement | |

Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||

17 | Length | Problems with length. | |

Objective: On completion of the lesson the student will be able to solve problems with length. | |||

18 | Area | Introduction to the square centimetre. | |

Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly. | |||

19 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||

20 | Area | Finding the area of a triangle and other composite shapes. | |

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||

21 | Area | Larger areas: square metre, hectare, square kilometre. | |

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||

22 | Area | Problems with area. | |

Objective: On completion of the lesson the student will be able to solve problems with area. | |||

23 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |

Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||

24 | 3-D shapes | Constructing models. | |

Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms. | |||

25 | Volume | Using the cubic centimetre to measure volume. | |

Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting. | |||

26 | Volume | Introducing the formula for volume. | |

Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||

27 | Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: On completion of the lesson the student will know a way to find volume and capacity. | |||

28 | Capacity | Using the cubic cm as a standard unit of measurement for volume and capacity | |

Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape. | |||

29 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |

Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||

30 | Capacity | Converting between volume and capacity using kilolitres and litres | |

Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity. | |||

31 | Capacity | Estimate, measure and compare the capacity of containers | |

Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||

32 | Capacity | Converting between volume and capacity using millilitres and litres | |

Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||

33 | Volume/capacity | Problems with volume/capacity. | |

Objective: Problem Solving: problems involving volume/capacity | |||

34 | Volume | Finding the volume of prisms | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||

35 | Multiplication | Multiples and factors of whole numbers | |

Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||

36 | Fractions | Subtracting fractions from whole numbers | |

Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||

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

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

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

Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||

39 | Fractions | Multiplying fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||

40 | Fractions | Fractions of whole numbers | |

Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||

41 | Fractions | Multiplying fractions | |

Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||

42 | Fractions | Multiplying mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||

43 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). | |||

44 | Fractions | Dividing fractions | |

Objective: On completion of the lesson the student will be able to divide fractions. | |||

45 | Fractions | Dividing mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||

46 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |

Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||

47 | Decimals | Rounding decimals | |

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||

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

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||

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

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||

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

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand. | |||

51 | Decimals | Multiplying decimals by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||

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

Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||

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

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand. | |||

54 | Decimals | Dividing decimal fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||

55 | Decimals | Dividing numbers by a decimal fraction | |

Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||

56 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||

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

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||

58 | Percentages | One quantity as a percentage of another | |

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||

59 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||

60 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

61 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||

62 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||

63 | Rules for indices/exponents | Terms raised to the power of zero | |

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||

64 | Surds | Introducing surds | |

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||

65 | Graphs – Basic | Column Graphs | |

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

66 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

67 | Data | Pie and bar graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||

68 | Statistics | Frequency distribution table | |

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||

69 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

70 | Statistics part 1 | Relative Frequency | |

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

71 | Statistics | The range. | |

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||

72 | Statistic-probability | The mode | |

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||

73 | Statistic-probability | The mean | |

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||

74 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

75 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||

76 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

77 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

78 | Statistic-probability | Rolling a pair of dice | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||

79 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||

80 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||

81 | Time, 24-hour | 24 hour time | |

Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||

82 | Time, distance, speed | Average speed | |

Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. | |||

83 | Time zones | Time zones | |

Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||

84 | Area | Area of a circle. | |

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||

85 | Volume | Solving Problems about Volume – Part 1. | |

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||

86 | Volume | Solving Problems about Volume – Part 2. | |

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||

87 | Weight/mass | The gram and net mass | |

Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||

88 | Weight/mass | The tonne – converting units and problems | |

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||

89 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |

Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||

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

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

91 | 3-D shapes | Recognise and name pyramids according to spatial properties | |

Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||

92 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||

93 | 3-D shapes | Viewing 3-D shapes. | |

Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles. | |||

94 | Lines and angles | Mapping and grid references | |

Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places. | |||

95 | Geometry-angles | Measuring angles | |

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||

96 | Geometry-angles | Adjacent angles | |

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||

97 | Geometry-angles | Complementary and supplementary angles | |

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||

98 | Geometry-angles | Vertically opposite angles | |

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||

99 | Geometry-angles | Angles at a Point. | |

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||

100 | Geometry-triangles | Angle sum of a triangle | |

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||

101 | Geometry-triangles | Exterior angle theorem | |

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||

102 | Special triangles | Special triangles | |

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. | |||

103 | Geometry-quadrilaterals | Quadrilaterals | |

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||

104 | Geometry part 1 | Geometric Constructions | |

Objective: To bisect a line, bisect an angle and construct a perpendicular using a compass and ruler | |||

105 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||

106 | Geometry part 3 | Angles | |

Objective: To label and classify angles and calculate pronumeral values within angles | |||

107 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||

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

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

109 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||

110 | Geometry-congruence | Proofs and congruent triangles. | |

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent. | |||

111 | Similar triangles | Similar triangles | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||

112 | Algebraic expressions | Algebraic expressions. | |

Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||

113 | Algebraic expressions | Substitution into algebraic expressions. | |

Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||

114 | Algebraic expressions | Directed numbers: addition and subtraction. | |

Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||

115 | Algebraic expressions | Directed numbers: multiplication and division. | |

Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||

116 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |

Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||

117 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |

Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||

118 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||

119 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |

Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||

120 | Algebraic expressions | Simplifying algebraic expressions: division | |

Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||

121 | Algebraic expressions | Expanding algebraic expressions: multiplication | |

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||

122 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||

123 | Algebraic equations | Solving equations containing addition and subtraction | |

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||

124 | Algebraic equations | Solving equations containing multiplication and division | |

Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||

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

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

126 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

127 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

128 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

129 | Algebra- formulae | Equations resulting from substitution into formulae. | |

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||

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

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

131 | Exam | Exam – Year 8 – Level 5: Maths A | |

Objective: Exam |