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Mathematics Scheme of Work Year 8 New Mathematics Framework Year 8 Mathematics – Scheme of Work (22-06-2010) 1 YEAR 8: Overview of year 8 scheme of work YEAR 8 Term 1 Term 2 Term 3 Number & Algebra 1 Integers, powers and roots; sequences, functions and graphs (8 hours) Statistics 1 Probability (6 hours) Geometry and Measures 2 Measures and mensuration (5 hours) Geometry and Measures 3 Transformations, Geometrical reasoning: lines, angles and shapes (5 hours) Number 4 Geometry and Measures 1 Geometrical reasoning: lines, angles and shapes; constructions (5 hours) Number 2 Fractions, decimals, percentages, ratio and proportion (6 hours) Algebra 3 Integers, powers and roots; sequences, functions and graphs (6 hours) Algebra 4 Calculations, measures (6 hours) Geometry and Measures 4 Equations and formulae, graphs (6 hours) Algebra 5 Sequences, functions and graphs, equations and graphs (7 hours) Statistics 3 Geometrical reasoning: lines, angles and shapes; transformations, mensuration (9 hours) Statistics, including probability (7 hours) Year 8 Mathematics – Scheme of Work (22-06-2010) 2 Assessment Tests Test 1 Algebra 2 Test 2 Equations and formulae (6 hours) Number 3 Test 3 Place value, calculations, calculator methods, fractions, decimals, percentages, ratio and proportion, solving problems (7 hours) Statistics 2 Test 4 Statistics (6 hours) Solving problems Including fractions, decimals, percentages, ratio and proportion (5 hours) Test 5 End of year test YEAR 8: AUTUMN TERM MATHEMATICAL TOPIC - Context Algebra 1 (8 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 1.1 Multiplying and dividing negative numbers 1.2 HCF and LCM 1.3 Powers and roots 1.4 Prime factors 1.5 Sequences 1 1.6 Sequences 2 1.7 Solving problems FM Blackpool Tower 1.1 Multiplying and dividing negative numbers 1.2 HCF and LCM 1.3 Powers and roots 1.4 Prime factors 1.5 Sequences 1 1.6 Sequences 2 1.7 Solving problems FM Blackpool Tower Geometry & Measures 1 (5 hours) 2.1 Alternate and corresponding angles 2.2 Angles in triangles and quadrilaterals 2.3 Geometric proof 2.4 The geometric properties of quadrilaterals 2.5 Constructions 1.1 Add, subtract, multiply and divide integers. 1.2 Use multiples, factors, common factors, highest common factors, lowest common multiples and primes. 1.3 Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers. 1.4 Find the prime factor decomposition of a number, for example, 8000 = 26 × 53. 1.5 Generate terms of a linear sequence using termto-term and position-to-term rules. 1.6 Use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated. 1.7 Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. FM Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. 2.1 Identify alternate angles and corresponding angles. 2.2 Understand that: the angle sum of a triangle is 180° and of a quadrilateral is 360°; the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 2.3 Understand a proof that: the angle sum of a triangle is 180° and of a quadrilateral is 360°; the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 2.4 Solve geometrical problems using side and angle properties of special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties. 2.5 Use a straight edge and compasses to construct: the mid-point and perpendicular bisector of a line segment; the bisector of an angle; the perpendicular from a point to a line; the perpendicular from a point on a line. 1.1 Multiply and divide integers. 1.2 Use multiples, factors, common factors, highest common factors, lowest common multiples and primes. 1.3 Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers. 1.4 Find the prime factor decomposition of a number, for example, 8000 = 26 × 53. 1.5 Generate terms of a linear sequence using termto-term and position-to-term rules. 1.6 Use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated. 1.7 Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. FM Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. 2.1 Identify alternate angles and corresponding angles. 2.2 Explain how to find, calculate and use: the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; the interior and exterior angles of regular polygons (Year 9 Framework Objective). 2.3 Understand a proof that: the angle sum of a triangle is 180° and of a quadrilateral is 360°; the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 2.4 Solve geometrical problems using side and angle properties of special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties. 2.5 Use a straight edge and compasses to construct: the mid-point and perpendicular bisector of a line segment; the bisector of an angle; the perpendicular from a point to a line; the perpendicular from a point on a line. Use ICT to explore these constructions. Use straight edge and compasses to construct triangles, given right angle, hypotenuse and side (RHS) (Year 9 Framework Objective). Year 8 Mathematics – Scheme of Work (22-06-2010) 3 2.1 Alternate and corresponding angles 2.2 Interior and exterior angles of polygons 2.3 Geometric proof 2.4 The geometric properties of quadrilaterals 2.5 Constructions YEAR 8: AUTUMN TERM MATHEMATICAL TOPIC - Context Statistics 1 (6 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 3.1 Probability 3.2 Probability scales 3.3 Mutually exclusive events 3.4 Calculating probabilities 3.5 Experimental probability FM Fun in the fairground 3.1 Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable. 3.2 Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p. 3.3 Use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events. 3.4 Use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events. 3.5 Collect data using a suitable method (for example, observation, controlled experiment, and data logging using ICT). Compare estimated experimental probabilities with theoretical probabilities, recognising that: if an experiment is repeated the outcome may, and usually will, be different; increasing the number of times an experiment is repeated generally leads to better estimates of probability. FM Interpret the results of an experiment using the language of probability. Compare estimated experimental probabilities with theoretical probabilities, recognising that: if an experiment is repeated the outcome may, and usually will, be different; increasing the number of times an experiment is repeated generally leads to better estimates of probability. 3.1 Probability 3.2 Probability scales 3.3 Mutually exclusive events 3.4 Calculating probabilities 3.5 Experimental probability FM Fun in the fairground 3.1 Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable. 3.2 Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p. 3.3 Use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events. 3.4 Use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events. 3.5 Compare estimated experimental probabilities with theoretical probabilities, recognising that: if an experiment is repeated the outcome may, and usually will, be different; increasing the number of times an experiment is repeated generally leads to better estimates of probability. FM Interpret the results of an experiment using the language of probability. Compare estimated experimental probabilities with theoretical probabilities, recognising that: if an experiment is repeated the outcome may, and usually will, be different; increasing the number of times an experiment is repeated generally leads to better estimates of probability. Year 8 Mathematics – Scheme of Work (22-06-2010) 4 YEAR 8: AUTUMN TERM MATHEMATICAL TOPIC - Context Number 2 (6 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 4.1 Fractions and decimals 4.2 Adding and subtracting fractions 4.3 Multiplying and dividing fractions 4.4 Percentages 4.5 Percentage increase and decrease 4.6 Real-life problems FM Going on holiday 4.1 Refine own findings and approaches on the basis of discussions with others; recognise efficiency in an approach; relate the current problem and structure to previous situations. Order decimals. Recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals. 4.2 Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers). 4.3 Multiply and divide an integer by a fraction. 4.4 Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another. 4.5 Calculate percentages and find the outcome of a given percentage increase or decrease. Use the equivalence of fractions, decimals and percentages to compare proportions. 4.6 Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8. FM Identify the mathematical features of a context or problem. Calculate percentages and find the outcome of a given percentage increase or decrease. Carry out more difficult calculations effectively and efficiently. Know rough metric equivalents of imperial measures in common use. Interpret tables and diagrams. 4.1 Fractions and decimals 4.2 Adding and subtracting fractions 4.3 Multiplying and dividing fractions 4.4 Percentages 4.5 Percentage increase and decrease 4.6 Real-life problems FM Going on holiday Algebra 2 (6 hours) 5.1 Algebraic shorthand 5.2 Like terms 5.3 Expanding brackets 5.4 Using algebra with shapes 5.5 Use of index notation with algebra 5.1 Recognise that letter symbols play different roles in equations, formulae and functions. 5.2 Simplify or transform linear expressions by collecting like terms. 5.3 Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic. Multiply a single term over a bracket. 5.4 Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic. Multiply a single term over a bracket. 5.5 Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers. 5.1 Algebraic shorthand 5.2 Like terms 5.3 Expanding brackets and factorising 5.4 Using algebra with shapes 5.5 Index notation with algebra 4.1 Recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals. Order decimals. 4.2 Add and subtract fractions by writing them with a common denominator. 4.3 Calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction. 4.4 Interpret percentage as the operator 'so many hundredths of' and express one given number as a percentage of another. 4.5 Calculate percentages and find the outcome of a given percentage increase or decrease. Use the equivalence of fractions, decimals and percentages to compare proportions. 4.6 Refine own findings and approaches on the basis of discussions with others; recognise efficiency in an approach; relate the current problem and structure to previous situations. Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8. FM Interpret tables and diagrams. Identify the mathematical features of a context or problem. Know rough metric equivalents of imperial measures in common use. Carry out calculations effectively and efficiently when using a calculator. Calculate percentages and find the outcome of a given percentage increase or decrease. 5.1 Recognise that letter symbols play different roles in equations, formulae and functions. 5.2 Simplify or transform linear expressions by collecting like terms. 5.3 Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic. Multiply a single term over a bracket. 5.4 Multiply a single term over a bracket. 5.5 Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers. 31 Hours Teaching Year 8 Mathematics – Scheme of Work (22-06-2010) 5 YEAR 8: SPRING TERM MATHEMATICAL TOPIC - Context Geometry & Measures 2 (5 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 6.1 Area of a triangle 6.2 Area of a parallelogram 6.3 Area of a trapezium 6.4 Volume of a cuboid 6.5 Imperial units 6.1 The circle 6.2 Circumference of a circle 6.3 Area of a circle 6.4 Surface area and volume of prisms 6.5 Imperial units 6.1 Make accurate mathematical diagrams, graphs and constructions. Know the definition of a circle and the names of its parts (Year 9 Framework Objective). 6.2 Know and use the formula for the circumference of a circle (Year 9 Framework Objective). 6.3 Know and use the formula for the area of a circle (Year 9 Framework Objective). 6.4 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts. Convert between area measures (for example, mm2 to cm2, cm2 to m2, and vice versa) and between volume measures (for example, mm3 to cm3, cm3 to m3, and vice versa) (Year 9 Framework Objective). Calculate the surface area and volume of right prisms (Year 9 Framework Objective). 6.5 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of imperial measures in common use, such as miles, pounds (lb) and pints. Algebra 3 (6 hours) 7.1 Linear functions 7.2 Finding a function from its inputs and outputs 7.3 Graphs from functions 7.4 Gradient of a straight line (steepness) 7.5 Real-life graphs FM M25 6.1 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts. Derive and use formulae for the area of a triangle; calculate areas of compound shapes. 6.2 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts. Derive and use formulae for the area of a parallelogram. 6.3 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts. Derive and use formulae for the area of a trapezium; calculate areas of compound shapes. 6.4 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts. Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids. 6.5 Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of imperial measures in common use, such as miles, pounds (lb) and pints. 7.1 Express simple functions algebraically and represent them in mappings or on a spreadsheet. 7.2 Express simple functions algebraically and represent them in mappings or on a spreadsheet. 7.3 Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT. 7.4 Recognise that equations of the form y = mx + c correspond to straight-line graphs. 7.5 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, for example, distance–time graphs. FM Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. 7.1 Linear functions 7.2 Finding a function from inputs and outputs 7.3 Graphs from functions 7.4 Gradient of a straight line 7.5 Real-life graphs FM M25 7.1 Express simple functions algebraically and represent them in mappings or on a spreadsheet. 7.2 Express simple functions algebraically and represent them in mappings or on a spreadsheet. 7.3 Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT. 7.4 Recognise that equations of the form y = mx + c correspond to straight-line graphs. 7.5 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, for example, distance–time graphs. FM Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. Year 8 Mathematics – Scheme of Work (22-06-2010) 6 YEAR 8: SPRING TERM MATHEMATICAL TOPIC - Context Number 3 (7 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 8.1 Powers of 10 8.2 Large numbers 8.3 Estimations 8.4 Adding and subtracting decimals 8.5 Efficient calculations 8.6 Multiplying and dividing decimals FM Taxes 8.1 Read and write positive integer powers of 10, multiply and divide integers and decimals by 0.1, 0.01. Round decimals to the nearest whole number or to one or two decimal places. Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, and cubes and cube roots; solve problems mentally. 8.2 Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places. 8.3 Make and justify estimates and approximations of calculations. Select from a range of checking methods, including estimating in context and using inverse operations. 8.4 Use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal places. 8.5 Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memory. 8.6 Use efficient written methods for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. FM Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; calculate percentages and find the outcome of a given percentage increase or decrease. 8.1 Powers of 10 8.2 Large numbers 8.3 Estimations 8.4 Working with decimals 8.5 Efficient calculations 8.6 Multiplying and dividing decimals FM Taxes 8.1 Read and write positive integer powers of 10, multiply and divide integers and decimals by 0.1, 0.01. Round decimals to the nearest whole number or to one or two decimal places. Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, and cubes and cube roots; solve problems mentally. 8.2 Round positive numbers to any given power of 10. 8.3 Make and justify estimates and approximations of calculations. Select from a range of checking methods, including estimating in context and using inverse operations. 8.4 Round decimals to the nearest whole number or to one or two decimal places. Use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal places. Use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes. 8.5 Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memory. Enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time). 8.6 Use efficient written methods for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. FM Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; calculate percentages and find the outcome of a given percentage increase or decrease. Year 8 Mathematics – Scheme of Work (22-06-2010) 7 YEAR 8: SPRING TERM MATHEMATICAL TOPIC - Context Geometry & Measures 3 (5 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 9.1 Congruent shapes 9.2 Combinations of transformations 9.3 & 9.4 Enlargements 9.5 Shape and ratio 9.1 Know that if two 2-D shapes are congruent, corresponding sides and angles are equal. Identify all the symmetries of 2-D shapes. 9.2 Transform 2-D shapes by rotation, reflection and translation, on paper and using ICT. Try out mathematical representations of simple combinations of these transformations. 9.3 & 9.4 Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive integer scale factor; explore enlargement using ICT. 9.5 Apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units, recognising links with fraction notation. 9.1 Congruent shapes 9.2 Combinations of transformations 9.3 Enlargements 9.4 Planes of symmetry 9.5 Shape and ratio 9.1 Know that if two 2-D shapes are congruent, corresponding sides and angles are equal. Identify all the symmetries of 2-D shapes. 9.2 Transform 2-D shapes by rotation, reflection and translation, on paper and using ICT. Try out mathematical representations of simple combinations of these transformations. 9.3 Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive integer scale factor; explore enlargement using ICT. 9.4 Identify reflection symmetry in 3-D shapes (Year 9 Framework Objective). 9.5 Apply understanding of the relationship between ratio and proportion; simplify ratios, including those expressed in different units, recognising links with fraction notation. Algebra 4 (6 hours) 10.1 Solving equations 10.2 Equations involving negative numbers 10.3 Equations with unknowns on both sides 10.4 Substituting into expressions 10.5 Substituting into formulae 10.6 Creating your own expressions and formulae 10.1 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.2 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.3 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.4 Substitute integers into simple formulae, including examples that lead to an equation to solve; substitute positive integers into expressions involving small powers, for example, 3x2 + 4 or 2x3. 10.5 Substitute integers into simple formulae, including examples that lead to an equation to solve; substitute positive integers into expressions involving small powers, for example, 3x2 + 4 or 2x3. 10.6 Derive simple formulae. 10.1 Solving equations 10.2 Equations involving negative numbers 10.3 Equations with unknowns on both sides 10.4 Substituting into expressions 10.5 Substituting into formulae 10.6 Creating your own expressions and formulae 10.1 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.2 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.3 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 10.4 Substitute positive integers into expressions involving small powers, for example, 3x2 + 4 or 2x3. 10.5 Substitute integers into simple formulae, including examples that lead to an equation to solve. 10.6 Derive simple formulae. Year 8 Mathematics – Scheme of Work (22-06-2010) 8 YEAR 8: SPRING TERM MATHEMATICAL TOPIC - Context Statistics 2 (6 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 11.1 Stem-and-leaf diagrams 11.2 Pie charts 11.3 More about pie charts 11.4 Scatter graphs 11.5 More about scatter graphs FM Football attendances 11.1 Calculate statistics for sets of discrete and continuous data, including with a calculator; recognise when it is appropriate to use the range, mean, median and mode. Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include stem-and-leaf diagrams. 11.2 Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored. 11.3 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: pie charts for categorical data; bar charts and frequency; diagrams for discrete and continuous data; simple scatter graphs. 11.4 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: pie charts for categorical data; bar charts and frequency; diagrams for discrete and continuous data; simple scatter graphs. Interpret tables, graphs and diagrams for discrete data, relating summary statistics and findings to the questions being explored. 11.5 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: pie charts for categorical data; bar charts and frequency; diagrams for discrete and continuous data; simple scatter graphs. Interpret tables, graphs and diagrams for discrete data, relating summary statistics and findings to the questions being explored. FM Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. 11.1 Statistical surveys 11.2 Stem-and-leaf diagrams 11.3 Interpreting graphs and diagrams 11.4 Scatter graphs 11.5 Analysing data FM Football attendances 11.1 Discuss a problem that can be addressed by statistical methods and identify related questions to explore. Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources; consider appropriate sample size. Plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data and two-way tables for recording discrete data. Collect data using a suitable method (for example, observation, controlled experiment and data logging using ICT). 11.2 Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include stem-and-leaf diagrams. 11.3 Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored. Discuss how different sets of data relate to the problem; identify possible primary or secondary sources; determine the sample size and most appropriate degree of accuracy (Year 9 Framework Objective). Gather data from specified secondary sources, including printed tables and lists, and ICTbased sources, including the internet (Year 9 Framework Objective). 11.4 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: pie charts for categorical data; bar charts and frequency; diagrams for discrete and continuous data; simple scatter graphs. Interpret tables, graphs and diagrams for discrete data, relating summary statistics and findings to the questions being explored. 11.5 Write about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used. FM Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. 35 Hours Teaching Year 8 Mathematics – Scheme of Work (22-06-2010) 9 YEAR 8: SUMMER TERM MATHEMATICAL TOPIC - Context Number 4 (6 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 12.1 Fractions 12.2 Adding and subtracting fractions 12.3 Order of operations 12.4 Multiplying decimals 12.5 Dividing decimals FM Shopping for bargains 12.1 Use the equivalence of fractions, decimals and percentages to compare proportions. 12.2 Add and subtract fractions by writing them with a common denominator. Understand and use the rules of arithmetic and inverse operations in the context of integers and fractions. 12.3 Use the order of operations, including brackets, with more complex calculations. 12.4 Use efficient written methods for multiplication of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. 12.5 Use efficient written methods for division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. FM Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. 12.1 Fractions 12.2 Adding and subtracting fractions 12.3 Order of operations 12.4 Multiplying decimals 12.5 Dividing decimals FM Shopping for bargains Algebra 5 (7 hours) 13.1 Expand and simplify 13.2 Solving equations 13.3 Constructing equations to solve 13.4 Problems with graphs 13.5 Real-life graphs 13.6 Change of subject FM Train timetable 13.1 Refine own findings and approaches on the basis of discussions with others; recognise efficiency in an approach; relate the current problem and structure to previous situations. Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. 13.2 Solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 13.3 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 13.4 Plot the graphs of linear functions, where y is given explicitly in terms of x. 13.5 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, for example, distance–time graphs. Simplify or transform linear expressions by collecting like terms. FM Identify the mathematical features of a context or problem. 13.1 Expand and simplify 13.2 Solving equations by trial and improvement 13.3 Constructing equations 13.4 Problems with graphs 13.5 Real-life graphs 13.6 Change of subject FM Train timetable 12.1 Use the equivalence of fractions, decimals and percentages to compare proportions. 12.2 Add and subtract fractions by writing them with a common denominator. Understand and use the rules of arithmetic and inverse operations in the context of integers and fractions. 12.3 Use the order of operations, including brackets, with more complex calculations. 12.4 Strengthen and extend mental methods of calculation, working with decimals. Use efficient written methods for multiplication of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. 12.5 Strengthen and extend mental methods of calculation, working with decimals. Use efficient written methods for division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations. FM Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. 13.1 Refine own findings and approaches on the basis of discussions with others; recognise efficiency in an approach; relate the current problem and structure to previous situations. Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. 13.2 Within the appropriate range and content manipulate numbers, algebraic expressions and equations. 13.3 Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (for example, inverse operations, transforming both sides in same way). 13.4 Plot the graphs of linear functions, where y is given explicitly in terms of x. 13.5 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, for example, distance–time graphs. Simplify or transform linear expressions by collecting like terms. FM Identify the mathematical features of a context or problem. Year 8 Mathematics – Scheme of Work (22-06-2010) 10 YEAR 8: SUMMER TERM MATHEMATICAL TOPIC - Context Solving Problems (5 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 14.1 Number and measures 14.2 Using algebra, graphs and diagrams to solve problems 14.3 Logic and proof 14.4 Proportion 14.5 Ratio 14.1 Within the appropriate range and content: make accurate mathematical diagrams, graphs and constructions on paper and on screen; calculate accurately, selecting mental methods or calculating devices as appropriate; manipulate numbers, algebraic expressions and equations, and apply routine algorithms; use accurate notation, including correct syntax when using ICT; record methods, solutions and conclusions; estimate, approximate and check working. 14.2 Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. Use graphs and set up equations to solve simple problems involving direct proportion. 14.3 Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. Conjecture and generalise; move between the general and the particular to test the logic of an argument; identify exceptional cases or counterexamples; make connections with related contexts. 14.4 Apply understanding of the relationship between ratio and proportion. Enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time). 14.5 Simplify ratios, including those expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple problems involving ratio and direct proportion. 14.1 Number and measures 14.2 Using algebra, graphs and diagrams to solve problems 14.3 Logic and proof 14.4 Proportion 14.5 Ratio 14.1 Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. Move between the general and the particular to test the logic of an argument. 14.2 Identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate procedures and tools, including ICT. Use graphs and set up equations to solve simple problems involving direct proportion. 14.3 Conjecture and generalise; move between the general and the particular to test the logic of an argument; identify exceptional cases or counterexamples; make connections with related contexts. Use logical argument to interpret the mathematics in a given context or to establish the truth of a statement; give accurate solutions appropriate to the context or problem; evaluate the efficiency of alternative strategies and approaches. 14.4 Apply understanding of the relationship between ratio and proportion. Enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time). Use proportional reasoning to solve problems, choosing the correct numbers to take as 100%, or as a whole (Year 9 Framework Objective). 14.5 Simplify ratios, including those expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple problems involving ratio and direct proportion. Year 8 Mathematics – Scheme of Work (22-06-2010) 11 YEAR 8: SUMMER TERM MATHEMATICAL TOPIC - Context Geometry & Measures 4 (9 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 15.1 & 15.2 Plans and elevations 15.3 Scale drawings 15.4 Finding the mid-point of a line segment 15.5 To construct a triangle given three sides 15.6 Circumference and area of a circle 15.7 Bearings 15.8 A cube investigation FM Photographs 15.1 & 15.2 Use geometric properties of cuboids and shapes made from cuboids; use simple plans and elevations. 15.3 Make scale drawings. 15.4 Find the midpoint of the line segment AB, given the coordinates of points A and B. 15.5 Use straight edge and compasses to construct a triangle, given three sides (SSS). Use ICT to explore this construction. 15.6 Use formulae from mathematics and other subjects; substitute integers into simple formulae. 15.7 Use bearings to specify direction. 15.8 Calculate surface areas of cuboids and shapes made from cuboids. FM Identify the mathematical features of a context or problem. Calculate percentages and find the outcome of a given percentage increase or decrease. Use the unitary method to solve simple problems involving ratio. Understand and use the language and notation associated with enlargement. Know rough metric equivalents of imperial measures in common use. Calculate areas of compound shapes. Interpret tables and diagrams. 15.1 & 15.2 Plans and elevations 15.3 Scale drawings 15.4 Finding the mid-point of a line segment 15.5 Map scales 15.6 Loci 15.7 Bearings 15.8 A cube investigation FM Photographs 15.1 & 15.2 Use geometric properties of cuboids and shapes made from cuboids; use simple plans and elevations. Visualise and use 2-D representations of 3-D objects (Year 9 Framework Objective). 15.3 Make scale drawings. 15.4 Find the mid-point of the line segment AB, given the coordinates of points A and B. 15.5 Use and interpret maps and scale drawings in the context of mathematics and other subjects (Year 9 Framework Objective). 15.6 Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, for example, an equilateral triangle. 15.7 Use bearings to specify direction. 15.8 Calculate surface areas of cuboids and shapes made from cuboids. FM Interpret tables and diagrams. Identify the mathematical features of a contextual problem. Know rough metric equivalents of imperial measures in common use. Calculate areas of compound shapes. Understand and use the language associated with enlargement. Calculate percentages and find the outcome of a given percentage increase or decrease. Use the unitary method to solve simple problems involving ratio Year 8 Mathematics – Scheme of Work (22-06-2010) 12 YEAR 8: SUMMER TERM MATHEMATICAL TOPIC - Context Statistics 3 (7 hours) ►OVERVIEW – Teacher Pack 2 ► FRAMEWORK OBJECTIVES – Teacher Pack 2 ►OVERVIEW – Teacher Pack 3 ► FRAMEWORK OBJECTIVES – Teacher Pack 3 16.1 Frequency tables 16.2 Assumed mean and working with statistics 16.3 Drawing frequency diagrams 16.4 Comparing data 16.5 Which average to use? 16.6 Experimental and theoretical probability FM Questionnaire 16.1 Discuss a problem that can be addressed by statistical methods and identify related questions to explore. Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. Plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data. Collect data using a suitable method (for example, observation, controlled experiment, data logging using ICT). 16.2 Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. 16.3 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: bar charts and frequency; diagrams for discrete and continuous data; simple line graphs for time series. 16.4 Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored. Compare two distributions using the range and one or more of the mode, median and mean. 16.5 Recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. 16.6 Write about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used. Compare estimated experimental probabilities with theoretical probabilities. FM Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet. Interpret the results of an experiment using the language of probability. 16.1 Collecting data for frequency tables 16.2 Assumed mean and working with statistics 16.3 Drawing frequency diagrams 16.4 Comparing data 16.5 Comparing sets of data 16.6 Experimental and theoretical probability FM Questionnaire 16.1 Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. Plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data. Discuss how different sets of data relate to the problem; identify possible primary or secondary sources; determine the sample size and most appropriate degree of accuracy (Year 9 Framework Objective). Design a survey or experiment to capture the necessary data from one or more sources; design, trial and if necessary refine data collection sheets (Year 9 Framework Objective). 16.2 Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class. 16.3 Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: bar charts and frequency; diagrams for discrete and continuous data; simple line graphs for time series. 16.4 Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to the questions being explored. Compare two distributions using the range and one or more of the mode, median and mean. 16.5 Compare two or more distributions and make inferences, using the shape of the distributions and appropriate statistics (Year 9 Framework Objective). 16.6 Write about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used. Compare estimated experimental probabilities with theoretical probabilities. FM Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet. Interpret the results of an experiment using the language of probability. 34 Hours Teaching Year 8 Mathematics – Scheme of Work (22-06-2010) 13