# Year 9 Mathematics – Australian Capital Territory (ACT)

### ACT Year 9 Mathematics

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

1 | Study Plan | Study plan – Year 9 | |

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

2 | 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. | |||

3 | 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. | |||

4 | 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 | |||

5 | Weight/mass | The kilogram | |

Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||

6 | 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. | |||

7 | Problems | Solve and record division using known facts and sharing | |

Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems. | |||

8 | 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. | |||

9 | 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. | |||

10 | Place value | The numbers 1000 to 9999 | |

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

14 | 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. | |||

15 | 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. | |||

16 | 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. | |||

17 | 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. | |||

18 | Multiplication | Multiplication using extended algorithms. | |

Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||

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

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

20 | 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. | |||

21 | 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. | |||

22 | 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. | |||

23 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||

24 | 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. | |||

25 | Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map. | |||

26 | 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. | |||

27 | 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. | |||

28 | Fractions | mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||

29 | Fractions | Improper fractions | |

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||

30 | 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. | |||

31 | 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. | |||

32 | 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. | |||

33 | 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. | |||

34 | 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. | |||

35 | 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. | |||

36 | 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. | |||

37 | 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. | |||

38 | Money | Problems involving money | |

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

39 | Length | Problems with length. | |

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

40 | Mass | Problems with mass. | |

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

41 | Area | Problems with area. | |

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

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

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

43 | 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. | |||

44 | 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 | |||

45 | 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. | |||

46 | 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. | |||

47 | 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. | |||

48 | 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. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | 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. | |||

53 | Surface area | Surface area of a cube/rectangular prism. | |

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

54 | Surface area | Surface area of a triangular/trapezoidal prism. | |

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

55 | Surface area | Surface area of a cylinder and sphere. | |

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||

56 | 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. | |||

57 | Volume | Volume of a cylinder and sphere. | |

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||

58 | 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. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | Fractions | Multiplying fractions by whole numbers | |

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

64 | Fractions | Fractions of whole numbers | |

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

65 | 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). | |||

66 | Fractions | Dividing fractions | |

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

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

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

68 | 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. | |||

69 | 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. | |||

70 | 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. | |||

71 | Decimals | Multiplying decimals by whole numbers | |

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

72 | 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. | |||

73 | 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. | |||

74 | 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. | |||

75 | 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. | |||

76 | 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. | |||

77 | 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. | |||

78 | 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. | |||

79 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

80 | 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. | |||

81 | 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. | |||

82 | 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. | |||

83 | 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. | |||

84 | 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. | |||

85 | 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. | |||

86 | 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. | |||

87 | 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. | |||

88 | 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. | |||

89 | 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. | |||

90 | 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. | |||

91 | 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. | |||

92 | 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. | |||

93 | 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. | |||

94 | 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. | |||

95 | 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. | |||

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

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

97 | 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. | |||

98 | 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. | |||

99 | 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. | |||

100 | 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. | |||

101 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

102 | 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. | |||

103 | 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. | |||

104 | Geometry-angles | Parallel Lines. | |

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

105 | 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. | |||

106 | 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. | |||

107 | 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. | |||

108 | 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. | |||

109 | 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. | |||

110 | Geometry-constructions | Geometric constructions | |

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

111 | 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. | |||

112 | 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. | |||

113 | 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. | |||

114 | 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. | |||

115 | 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. | |||

116 | 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. | |||

117 | 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. | |||

118 | 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. | |||

119 | Statistics | Frequency histograms and polygons | |

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

120 | Statistics | Relative frequency | |

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

121 | 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. | |||

122 | 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. | |||

123 | 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. | |||

124 | 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 | |||

125 | Trigonometry-ratios | Trigonometric ratios. | |

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||

126 | Trigonometry-ratios | Using the calculator. | |

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||

127 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||

128 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||

129 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||

130 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||

131 | Trigonometry-compass | Bearings – the compass. | |

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||

132 | Trigonometry-elevation | Angles of elevation and depression. | |

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||

133 | Exam | Exam – Year 9 | |

Objective: Exam |