# Year 9 Extension Mathematics – South Australia

### SA Year 9 Extension Mathematics

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

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

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

2 | 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. | |||

3 | Area | Problems with area. | |

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

4 | 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. | |||

5 | 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. | |||

6 | 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. | |||

7 | 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. | |||

8 | 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. | |||

9 | 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 | |||

10 | 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. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

14 | 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. | |||

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

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

16 | 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. | |||

17 | 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. | |||

18 | 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. | |||

19 | 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). | |||

20 | Fractions | Dividing fractions | |

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

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

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

22 | 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. | |||

23 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

24 | 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. | |||

25 | 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. | |||

26 | Surds | Some rules for the operations with surds | |

Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||

27 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

28 | Surds | Creating entire surds | |

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds | |||

29 | Surds | Adding and subtracting like surds | |

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. | |||

30 | Surds | Expanding surds | |

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||

31 | Surds | Binomial expansions | |

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. | |||

32 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

33 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

34 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

35 | 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. | |||

36 | 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. | |||

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | 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. | |||

42 | 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. | |||

43 | Geometry-angles | Parallel Lines. | |

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

44 | 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. | |||

45 | 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. | |||

46 | Geometry-polygons | Angles of regular polygons | |

Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||

47 | 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. | |||

48 | 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. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | 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. | |||

53 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

54 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

55 | Pythagoras | Find the hypotenuse Part 2 | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||

56 | Pythagoras | Calculating a leg of a right-angled triangle | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||

57 | Data | Line graphs. | |

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

58 | 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. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

71 | 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. | |||

72 | 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. | |||

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 | Algebraic equations | Equations involving grouping symbols. | |

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

76 | Algebraic equations | Equations involving fractions. | |

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

77 | 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. | |||

78 | Algebra- formulae | Changing the subject of the formula. | |

Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||

79 | Money | Problems involving money | |

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

80 | 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. | |||

81 | Statistics | Frequency histograms and polygons | |

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

82 | Statistics | Relative frequency | |

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

83 | 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. | |||

84 | 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. | |||

85 | 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. | |||

86 | 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 | |||

87 | Statistic-probability | Cumulative frequency | |

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

88 | Statistic-probability | Calculating the median from a frequency distribution | |

Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||

89 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||

90 | Statistics using a calculator | Statistics and the student calculator | |

Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems. | |||

91 | 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. | |||

92 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

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

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

94 | 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. | |||

95 | Statistic-probability | Experimental probability | |

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

96 | 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. | |||

97 | 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. | |||

98 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

99 | Graphing binomials | Binomial products with negative multiplier | |

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. | |||

100 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

101 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

102 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

103 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

104 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

105 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

106 | 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. | |||

107 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

108 | Scientific notation | Scientific notation with small numbers | |

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||

109 | Scientific notation | Changing scientific notation to numerals | |

Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||

110 | Significant figures | Significant figures | |

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||

111 | Exam | Exam – Year 9 Extension | |

Objective: Exam |