# Year 10 – Stage 5.2 Mathematics – New South Wales (NSW)

### NSW Year 10 – Stage 5.2 Mathematics

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

1 | Study Plan | Study plan – Year 10 Core | |

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

2 | 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. | |||

3 | 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. | |||

4 | 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. | |||

5 | 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 | |||

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

Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||

7 | 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. | |||

8 | Fractions | Multiplying fractions by whole numbers | |

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

9 | 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. | |||

10 | 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. | |||

11 | 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). | |||

12 | Fractions | Dividing fractions | |

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

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

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

14 | 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. | |||

15 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

16 | Algebraic equations | Solving equations containing binomial expressions | |

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

17 | Decimals | Adding decimals to two decimal places | |

Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places) | |||

18 | Decimals | Subtracting decimals to two decimal places | |

Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places) | |||

19 | Decimals | Using decimals – shopping problems | |

Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||

20 | Decimals | Using decimals to record length | |

Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements. | |||

21 | Decimals | Decimals to three decimal places | |

Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||

22 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | 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. | |||

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 | Algebraic equations | Equations involving grouping symbols. | |

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

33 | Algebraic equations | Equations involving fractions. | |

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

34 | Algebra-inequalities | Solving Inequalities. | |

Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||

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

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

36 | 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. | |||

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | 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. | |||

42 | 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. | |||

43 | Fractional indices/exponents | Fractional indices | |

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

44 | 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. | |||

45 | 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. | |||

46 | 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. | |||

47 | 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. | |||

48 | 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. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||

53 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||

54 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||

55 | 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. | |||

56 | 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. | |||

57 | Geometry-constructions | Geometric constructions | |

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

58 | Geometry-reasoning | Further difficult exercises involving formal reasoning | |

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | Geometry – triangles | Triangle inequality theorem | |

Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | 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. | |||

71 | 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. | |||

72 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

73 | Surface area | Surface area of cones | |

Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||

74 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

75 | Volume | Volume of pyramids and cones. | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||

76 | Volume | Composite solids. | |

Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. | |||

77 | Coordinate Geometry-the plane | Distance formula. | |

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||

78 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

79 | Coordinate Geometry-gradient | Gradient | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||

80 | Coordinate Geometry-gradient | Gradient formula. | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||

81 | Coordinate Geometry-straight line | The straight line. | |

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||

82 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||

83 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||

84 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||

85 | Coordinate Geometry-point slope | Point slope form of a line | |

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||

86 | 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. | |||

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 | 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. | |||

90 | 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. | |||

91 | Exam | Exam – Year 10 – Stage 5.2 | |

Objective: Exam |