# Year 7 Mathematics – Australian Capital Territory (ACT)

### ACT Year 7 Mathematics

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

1 | Study Plan | Study plan – Year 7 | |

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

2 | Weight/mass | Introducing the concept of mass | |

Objective: On completion of the lesson the student will understand the concepts of mass. | |||

3 | 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. | |||

4 | Weight/mass | The kilogram | |

Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||

5 | Weight/mass | The gram and net mass | |

Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||

6 | 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. | |||

7 | 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. | |||

8 | Multiplication | Multiplication using extended algorithms. | |

Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||

9 | Multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |

Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication. | |||

10 | Division | Division with and without a remainder. | |

Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

14 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||

15 | 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. | |||

16 | 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. | |||

17 | 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. | |||

18 | 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. | |||

19 | Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map. | |||

20 | 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. | |||

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 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | 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. | |||

27 | Fractions | Multiplying fractions by whole numbers | |

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

28 | Fractions | Fractions of whole numbers | |

Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||

29 | 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). | |||

30 | Fractions | Dividing fractions | |

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

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

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

32 | 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. | |||

33 | 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. | |||

34 | 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. | |||

35 | 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. | |||

36 | 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 | |||

37 | 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. | |||

38 | 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. | |||

39 | Capacity | Using the cubic cm as a standard unit of measurement for volume and capacity | |

Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape. | |||

40 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |

Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||

41 | Capacity | Converting between volume and capacity using kilolitres and litres | |

Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity. | |||

42 | Capacity | Estimate, measure and compare the capacity of containers | |

Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||

43 | Capacity | Converting between volume and capacity using millilitres and litres | |

Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||

44 | Weight/mass | The tonne – converting units and problems | |

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||

45 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||

46 | 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. | |||

47 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |

Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||

48 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |

Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||

49 | Division/repeat subtraction | Repeated subtraction with divisors less than 20 with no remainders | |

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20. | |||

50 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders. | |||

51 | Division/repeat subtraction | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders. | |||

52 | Division/repeat subtraction | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders. | |||

53 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with remainders | |

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders. | |||

54 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||

55 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||

56 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||

57 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |

Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||

58 | Division/repeat subtraction | Using divide, multiply and subtraction in the bring down method | |

Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method. | |||

59 | Sign word problems | Solving Word Problems by recognising Sign Words | |

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division. | |||

60 | Equations | Problem solving strategies | |

Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||

61 | Number problems | Problems with numbers. | |

Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||

62 | Money | Problems involving money | |

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

63 | Length | Problems with length. | |

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

64 | Mass | Problems with mass. | |

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

65 | Area | Problems with area. | |

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

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

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

67 | 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. | |||

68 | 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. | |||

69 | 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. | |||

70 | 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. | |||

71 | 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. | |||

72 | 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. | |||

73 | 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. | |||

74 | Decimals | Multiplying decimals by whole numbers | |

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

75 | 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. | |||

76 | 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. | |||

77 | 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. | |||

78 | 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. | |||

79 | 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. | |||

80 | 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. | |||

81 | 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. | |||

82 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

83 | 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. | |||

84 | 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. | |||

85 | 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. | |||

86 | 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. | |||

87 | 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. | |||

88 | 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. | |||

89 | 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. | |||

90 | 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. | |||

91 | 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. | |||

92 | 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. | |||

93 | 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. | |||

94 | 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. | |||

95 | 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. | |||

96 | 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. | |||

97 | 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. | |||

98 | 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. | |||

99 | 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. | |||

100 | 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. | |||

101 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

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

102 | 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. | |||

103 | 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. | |||

104 | Geometry-angles | Parallel Lines. | |

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

105 | 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. | |||

106 | Algebraic equations | Solving two step equations | |

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

107 | Algebraic equations | Solving equations containing binomial expressions | |

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

108 | Geometry-triangles | Angle sum of a triangle | |

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||

109 | Geometry-triangles | Exterior angle theorem | |

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||

110 | Special triangles | Special triangles | |

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. | |||

111 | 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. | |||

112 | Geometry-constructions | Geometric constructions | |

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

113 | Exam | Exam – Year 7 | |

Objective: Exam |