# Year 9 leading to A Mathematics – Queensland

### QLD Year 9 leading to A 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 | 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 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | Area | Problems with area. | |

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

27 | 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. | |||

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

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

29 | 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. | |||

30 | 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. | |||

31 | 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. | |||

32 | Fractions | Finding equivalent fractions | |

Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||

33 | 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. | |||

34 | 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. | |||

35 | Fractions | Comparing and ordering fractions greater than (>) 1 | |

Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||

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 | 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. | |||

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

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

49 | 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. | |||

50 | Decimals | Multiplying decimals by whole numbers | |

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

51 | 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. | |||

52 | 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. | |||

53 | 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. | |||

54 | 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. | |||

55 | 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. | |||

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 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | 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. | |||

71 | 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. | |||

72 | 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. | |||

73 | 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. | |||

74 | 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. | |||

75 | 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. | |||

76 | 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. | |||

77 | 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. | |||

78 | Lines and angles | Main and intermediate compass points | |

Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location. | |||

79 | 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. | |||

80 | 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. | |||

81 | 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. | |||

82 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

83 | 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. | |||

84 | 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. | |||

85 | Algebraic equations | Solving two step equations | |

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

86 | Algebraic equations | Solving equations containing binomial expressions | |

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

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

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

88 | Algebraic equations | Equations involving fractions. | |

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

89 | 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. | |||

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

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

91 | 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. | |||

92 | Statistic-probability | Experimental probability | |

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

93 | 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. | |||

94 | Statistics | Frequency histograms and polygons | |

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

95 | Statistics | Relative frequency | |

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

96 | 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. | |||

97 | 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. | |||

98 | 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. | |||

99 | 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 | |||

100 | Statistic-probability | Cumulative frequency | |

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

101 | 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. | |||

102 | 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. | |||

103 | 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. | |||

104 | Statistics – Range and dispersion | Range as a measure of dispersion | |

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||

105 | 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. | |||

106 | 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. | |||

107 | 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. | |||

108 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||

109 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |

Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||

110 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |

Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||

111 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |

Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||

112 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |

Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||

113 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |

Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||

114 | 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. | |||

115 | 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. | |||

116 | 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. | |||

117 | 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. | |||

118 | 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. | |||

119 | 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. | |||

120 | 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. | |||

121 | 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. | |||

122 | 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. | |||

123 | 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. | |||

124 | 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. | |||

125 | Exam | Exam – Year 9 – Level 5: Maths A | |

Objective: Exam |