# Year 9 Mathematics – National Curriculum

### Year 9 Mathematics

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

1 | Self Assessment | Self Assessment – Year 9 | |

Objective: Assessment | |||

2 | 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. | |||

3 | 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. | |||

4 | 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. | |||

5 | 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. | |||

6 | 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. | |||

7 | 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. | |||

8 | 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. | |||

9 | 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. | |||

10 | 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. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

14 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

15 | Number theory – operations | Properties of real numbers using addition and multiplication | |

Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication. | |||

16 | 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. | |||

17 | 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. | |||

18 | 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. | |||

19 | 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. | |||

20 | 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. | |||

21 | 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. | |||

22 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | 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. | |||

27 | 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. | |||

28 | Algebraic equations | Solving two step equations | |

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

29 | Algebraic equations | Solving equations containing binomial expressions | |

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

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

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

31 | Geometry-circles | The equation of a circle: to find radii of circles | |

Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius. | |||

32 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||

33 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||

34 | Coordinate geometry | Solve by graphing | |

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||

35 | 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. | |||

36 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | 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. | |||

42 | 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. | |||

43 | 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. | |||

44 | 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. | |||

45 | 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. | |||

46 | 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. | |||

47 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |

Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||

48 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |

Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | Pythagoras | Pythagorean triples | |

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

53 | 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. | |||

54 | 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. | |||

55 | Pythagoras | Proofs of Pythagoras theorem | |

Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem | |||

56 | 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 | |||

57 | 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. | |||

58 | 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. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | Statistic-probability | Experimental probability | |

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

69 | 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. | |||

70 | 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. | |||

71 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. | |||

72 | Statistics | Relative frequency | |

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

73 | 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. | |||

74 | 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. | |||

75 | Statistics – Spread | Measures of spread | |

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||

76 | Statistics – Standard deviation | Standard deviation applications | |

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||

77 | Statistics | Frequency histograms and polygons | |

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

78 | 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. | |||

79 | Statistics | Frequency histograms and polygons | |

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

80 | Statistics | Relative frequency | |

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

81 | 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. | |||

82 | 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. | |||

83 | 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. | |||

84 | 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 | |||

85 | Statistic-probability | Cumulative frequency | |

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

86 | 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. | |||

87 | 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. | |||

88 | 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. | |||

89 | Statistics – Spread | Measures of spread | |

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||

90 | Statistics – Standard deviation | Standard deviation applications | |

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||

91 | Statistics – Standard deviation | Normal distribution | |

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. | |||

92 | Statistics – Interquartile range | Measures of spread: the interquartile range | |

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||

93 | 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. | |||

94 | Exam | Exam – Year 9 | |

Objective: Exam |