# S5 – Access Level Mathematics – Scotland

### S5 – Access Level Mathematics

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

1 | Study Plan | Study plan – S5 – HNQ – Access Level | |

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

2 | Addition | Addition to 99 | |

Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99. | |||

3 | Subtraction | Subtraction up to the number 99 | |

Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences. | |||

4 | Subtraction | Subtraction with borrowing | |

Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method | |||

5 | Subtraction | Subtraction of two-digit numbers Involving comparison. | |

Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct. | |||

6 | 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. | |||

7 | 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. | |||

8 | Problems | Solve and record division using known facts and sharing | |

Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems. | |||

9 | Place value | The numbers 1000 to 9999 | |

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999. | |||

10 | 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. | |||

11 | 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. | |||

12 | Multiplication | Multiplication using extended algorithms. | |

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

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

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

14 | 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. | |||

15 | 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. | |||

16 | 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. | |||

17 | 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. | |||

18 | 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. | |||

19 | 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. | |||

20 | 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. | |||

21 | Length | Compare length by using informal units of measurement | |

Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object. | |||

22 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | 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. | |||

27 | 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. | |||

28 | 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. | |||

29 | 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. | |||

30 | 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 | |||

31 | 3-D shapes | Constructing models. | |

Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms. | |||

32 | 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. | |||

33 | 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. | |||

34 | 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 | |||

35 | 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. | |||

36 | 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. | |||

37 | Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: On completion of the lesson the student will know a way to find volume and capacity. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | 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. | |||

42 | 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. | |||

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

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

44 | 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. | |||

45 | 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. | |||

46 | 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. | |||

47 | 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. | |||

48 | 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. | |||

49 | 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. | |||

50 | 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. | |||

51 | 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. | |||

52 | 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. | |||

53 | 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. | |||

54 | 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. | |||

55 | 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. | |||

56 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole. | |||

57 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects. | |||

58 | Fractions | Comparing and ordering fractions | |

Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||

59 | Fractions | mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||

60 | Fractions | Improper fractions | |

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||

61 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | Decimals | Introduction to decimals | |

Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||

66 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places. | |||

67 | Decimals | Decimals with whole numbers 10th and 100th | |

Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals. | |||

68 | 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) | |||

69 | 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) | |||

70 | 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. | |||

71 | 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. | |||

72 | Time, months | Months and seasons of the year | |

Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season. | |||

73 | Time, days of week | Days of the week | |

Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary. | |||

74 | Time, duration | Duration | |

Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units. | |||

75 | Time, minutes | Analogue – Telling time – minutes in the hour | |

Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock. | |||

76 | Time, units | Units of time | |

Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars. | |||

77 | Time, a.m. p.m. | AM and PM time | |

Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time. | |||

78 | Time, quarter to, past | Quarter past and quarter to | |

Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’. | |||

79 | Time, minutes past the hour | Minutes past | |

Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock. | |||

80 | Time, minutes to the hour | Minutes to | |

Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock. | |||

81 | Time, digital, analogue | Comparing analogue and digital time | |

Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks. | |||

82 | Time, digital | O’clock and half past using digital time | |

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock. | |||

83 | Time, analogue | O’clock and half past on the analogue clock | |

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock. | |||

84 | 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. | |||

85 | 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. | |||

86 | 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. | |||

87 | 2-D shapes | Using the prefix to determine polygons | |

Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||

88 | 2-D shapes | Spatial properties of quadrilaterals | |

Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||

89 | Angles | Measure and classify angles | |

Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||

90 | 2-D shapes | Recognise and name triangles | |

Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||

91 | 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. | |||

92 | 3-D shapes | Recognise and name prisms according to spatial properties | |

Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||

93 | 3-D shapes | Recognise and name pyramids according to spatial properties | |

Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||

94 | Lines and angles | Describing position. | |

Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||

95 | 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. | |||

96 | 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. | |||

97 | Lines and angles | Informal coordinate system | |

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper. | |||

98 | Data | Pictograms | |

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

99 | Data | Bar Charts | |

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

100 | Data | Line graphs. | |

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

101 | Data | Pie and bar graphs. | |

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

102 | Multiplication | Multiplying 2-digit numbers by multiple of 10 | |

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication. | |||

103 | 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. | |||

104 | 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. | |||

105 | 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. | |||

106 | 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. | |||

107 | 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. | |||

108 | 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. | |||

109 | 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. | |||

110 | 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. | |||

111 | 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. | |||

112 | 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 | |||

113 | 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. | |||

114 | 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. | |||

115 | 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. | |||

116 | 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. | |||

117 | 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. | |||

118 | 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. | |||

119 | 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. | |||

120 | Money | Problems involving money | |

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

121 | Length | Problems with length. | |

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

122 | Mass | Problems with mass. | |

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

123 | Area | Problems with area. | |

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

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

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

125 | Exam | Exam – S5 – HNQ – Access Level | |

Objective: Exam |