# Year 8 Mathematics – Australian Capital Territory (ACT)

### ACT 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 | 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. | |||

3 | 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. | |||

4 | 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. | |||

5 | 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. | |||

6 | Area | Area of a trapezium. | |

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||

7 | Area | Area of a rhombus. | |

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||

8 | Fractions | Multiplying and dividing to obtain equivalent fractions | |

Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. | |||

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

Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||

10 | 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. | |||

11 | 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. | |||

12 | 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. | |||

13 | Fractions | Multiplying fractions by whole numbers | |

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

14 | Fractions | Fractions of whole numbers | |

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

15 | 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). | |||

16 | Fractions | Dividing fractions | |

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

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

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

18 | 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. | |||

19 | 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. | |||

20 | 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. | |||

21 | 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. | |||

22 | 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. | |||

23 | 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. | |||

24 | Decimals | Multiplying decimals by whole numbers | |

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

25 | 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. | |||

26 | 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. | |||

27 | 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. | |||

28 | Percentages | Introduction to percentages, including relating common fractions to percentages | |

Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||

29 | 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. | |||

30 | 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. | |||

31 | 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. | |||

32 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

33 | Sign word problems | Solving Word Problems by recognising Sign Words | |

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division. | |||

34 | Equations | Problem solving strategies | |

Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||

35 | Number problems | Problems with numbers. | |

Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||

36 | Money | Problems involving money | |

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

37 | Length | Problems with length. | |

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

38 | Mass | Problems with mass. | |

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

39 | Area | Problems with area. | |

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

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

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

41 | 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. | |||

42 | Volume | Using the cubic metre to measure volume. | |

Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||

43 | 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. | |||

44 | 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. | |||

45 | 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. | |||

46 | 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. | |||

47 | 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. | |||

48 | Area | Area of regular polygons and composite figures. | |

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | 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. | |||

53 | 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. | |||

54 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |

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

55 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

56 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||

57 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. | |||

58 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | 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. | |||

66 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||

67 | Algebra-highest common factor | Highest common factor. | |

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||

68 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

69 | 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. | |||

70 | 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. | |||

71 | Geometry-angles | Parallel Lines. | |

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||

72 | Geometry-problems | Additional questions involving parallel lines | |

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||

73 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

74 | Algebraic equations | Solving equations containing binomial expressions | |

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

75 | 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. | |||

76 | 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. | |||

77 | 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. | |||

78 | 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. | |||

79 | Geometry-constructions | Geometric constructions | |

Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||

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

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

81 | Algebraic equations | Equations involving fractions. | |

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

82 | 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. | |||

83 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |

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

84 | 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. | |||

85 | 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. | |||

86 | 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. | |||

87 | Similar triangles | Using similar triangles to calculate lengths | |

Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||

88 | Overlapping triangles | Examples involving overlapping triangles | |

Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||

89 | 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. | |||

90 | Statistics | Frequency histograms and polygons | |

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

91 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

92 | 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. | |||

93 | 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. | |||

94 | 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. | |||

95 | 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 | |||

96 | Exam | Exam – Year 8 | |

Objective: Exam |