# Year 8 Mathematics – National Curriculum

### Year 8 Mathematics

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

1 | Self Assessment | Self Assessment – Year 8 | |

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 | Logarithms-Power of 2 | Powers of 2. | |

Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. | |||

8 | 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. | |||

9 | 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. | |||

10 | 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. | |||

11 | 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. | |||

12 | 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 | |||

13 | 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. | |||

14 | 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. | |||

15 | Decimals | Rounding decimals | |

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||

16 | 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. | |||

17 | Number theory – sets | Number sets and their members | |

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. | |||

18 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

19 | 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. | |||

20 | Length | Problems with length. | |

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

21 | Mass | Problems with mass. | |

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

22 | Area | Problems with area. | |

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

23 | 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. | |||

24 | Money | Problems involving money | |

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

25 | 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. | |||

26 | 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. | |||

27 | 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. | |||

28 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

29 | 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. | |||

30 | Factors by grouping | Factors by grouping. | |

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||

31 | 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. | |||

32 | 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. | |||

33 | 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. | |||

34 | 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. | |||

35 | 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. | |||

36 | 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. | |||

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

42 | Data | Line graphs. | |

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

43 | 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. | |||

44 | 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. | |||

45 | 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. | |||

46 | 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. | |||

47 | 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. | |||

48 | Number theory – equations | Transformations that produce equivalent equations | |

Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |

Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||

53 | Volume | Using the cubic centimetre to measure volume. | |

Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting. | |||

54 | 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 | |||

55 | 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. | |||

56 | 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. | |||

57 | 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. | |||

58 | 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. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | Area | Comparing and ordering areas. | |

Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||

63 | 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. | |||

64 | 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. | |||

65 | Volume | Solving Problems about Volume – Part 2. | |

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||

66 | 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. | |||

67 | 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. | |||

68 | 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. | |||

69 | Translations | Transformations – reflections | |

Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||

70 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |

Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||

71 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |

Objective: On completion of this lesson the student will perform translations in a number plane. | |||

72 | 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. | |||

73 | 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. | |||

74 | 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. | |||

75 | Geometry-constructions | Geometric constructions | |

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

76 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||

77 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

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

78 | 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. | |||

79 | 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. | |||

80 | 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. | |||

81 | 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. | |||

82 | 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. | |||

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

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

84 | Statistic-probability | The complementary result .. | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. | |||

85 | 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. | |||

86 | 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. | |||

87 | 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. | |||

88 | Statistic-probability | Experimental probability | |

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

89 | Statistic-probability | Experimental probability | |

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

90 | 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. | |||

91 | 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. | |||

92 | 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 | |||

93 | Exam | Exam – Year 8 | |

Objective: Exam |