11-19 PROGRESSION. For alternative Schemes of Work see

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1 11-19 PROGRESSION Our KS3 Maths Progress and Edexcel GCSE (9-1) Mathematics courses have been developed to provide you and your students with seamless progression to GCSE. This 5 Year Scheme of Work is for use with high attainers leading to the Higher GCSE. For alternative Schemes of Work see

2 5 year Scheme of Work (3 year KS3, 2 year KS4) Tests for the 3 year SoW for KS3 and the 2 year SoW for GCSE can be found on Pearson's ActiveLearn Digital Service, which combines front-of-class teaching resources with online homework and practice, as well as planning and assessment materials. YEAR 1 YEAR 2 YEAR 3 Delta 1 Delta 2 Delta 3 Unit 1 Analysing and displaying data Unit 1 Factors and powers Unit 1 Powers and roots Unit 2 Number skills Unit 2 Working with powers Unit 2 Quadratics Unit 3 Equations, functions and formulae Unit 3 2D shapes and 3D solids Unit 3 Inequalities, equations and formulae Unit 4 Fractions Unit 4 Real-life graphs Unit 4 Collecting and analysing data Unit 5 Angles and shapes Unit 5 Transformations Unit 5 Multiplicative reasoning Unit 6 Decimals Unit 6 Fractions, decimals and percentages Unit 6 Non-linear graphs Unit 7 Equations Unit 7 Constructions and loci Unit 7 Accuracy and measures Unit 8 Multiplicative reasoning Unit 8 Probability Unit 8 Graphical solutions Unit 9 Perimeter, area and volume Unit 9 Scale drawings and measurements Unit 9 Trigonometry Unit 10 Sequences and graphs Unit 10 Graphs Unit 10 Mathematical reasoning This scheme assumes 4 hours maths teaching per week in year 4 and year 5. There is some overlap between the KS3 course and the KS4 course, therefore the suggested teaching hours for KS4 assume that students have already covered some of the material in their 3-year KS3 course, and that some of the lessons can be combined, set as homework or not taught. Here are some suggestions for fitting the content into the suggested teaching times: Lessons where the content has previously been taught at KS3 can be combined, particularly in the earlier units. The Prior knowledge check, Check up and/or Unit test could be set as homework rather than taking up teaching time. It may not be necessary to cover all strategy problem-solving lessons in full with students who used our KS3 Maths Progress course as they will already be familiar with many of the strategies. The functional problem-solving lessons could be omitted, or saved for the revision period. These lessons provide richer activities in real-life contexts but do not contain any new teaching. YEAR 4 YEAR 5 GCSE (9-1) Higher GCSE (9-1) Higher Unit 1 Number Unit 16 Circle theorems Unit 2 Algebra Unit 3 Interpreting and representing data Unit 4 Fractions, ratio and proportion Unit 5 Angles and trigonometry Unit 6 Graphs Unit 7 Area and volume Unit 8 Transformation and constructions Unit 9 Equations and inequalities Unit 10 Probability Unit 11 Multiplicative reasoning Unit 12 Similarly and congruence Unit 13 More trigonometry Unit 14 Further statistics Unit 15 Equations and graphs Unit 17 More algebra Unit 18 Vectors and geometric proof Unit 19 Proportion and graphs

3 YEAR 1 KS3 Maths Progress Delta 1 TERM UNIT / LESSON HOURS GCSE (9-1) SPEC STEPS STEPS OBJECTIVES REFERENCE FROM TO AUTUMN 1 Analysing and displaying data 11 N1 S1 S2 S3 S4 S5 S Two-way tables and bar charts 2 5 Use two-way tables. Interpret and draw dual bar charts and compound bar charts. 1.2 Averages and range 3 6 Choose the most appropriate average for a set of data. Find the mode, median, mean and range for a set of data. Compare sets of data using averages and the range. 1.3 Grouped data 3 6 Group discrete and continuous data. Draw and interpret grouped frequency diagrams. 1.4 More graphs 3 6 Interpret and draw line graphs. Recognise when a graph is misleading. 1.5 Pie charts 5 6 Draw and interpret pie charts. 1.6 STEM: Scatter graphs and correlation AUTUMN 2 Number skills 11 N1 N2 N3 N4 N6 N7 N14 N Factors, primes and multiples 2.2 Using negative numbers Graph paper and draw scatter graphs. Describe the correlation between two sets of data. Draw a line of best fit and use it to estimate values. Understand the difference between multiples, factors and primes. Find all the factor pairs of any whole number. Find the HCF and LCM of two numbers. Add, subtract, multiply and divide positive and negative numbers. 2.3 Multiplying and dividing 4 5 Use mental and written strategies for multiplication. Divide a 3-digit integer by a single or 2-digit integer. 2.4 Squares and square roots 4 5 Use index notation for squares and square roots. 2.5 More powers and roots 5 6 Calculate with squares and square roots. Carry out calculations involving squares, cubes, square roots and cube roots. Use factorising to work out square roots and cube roots. Solve word problems using square roots and cube roots. 2.6 Calculations 5 6 Estimate answers to complex calculations. Carry out calculations involving brackets.

4 HALF-TERM TEST AUTUMN 3 Equations, functions and formulae 11 A1 A2 A3 A4 A5 A6 A7 3.1 Simplifying algebraic expressions Simplify expressions by collecting like terms. 3.2 Writing algebraic expressions 4 5 Construct expressions using four operations. 3.3 STEM: Using formulae 3 5 Substitute into formulae. 3.4 Writing formulae 4 6 Derive formulae from a description. 3.5 Brackets and powers 4 6 Expand expressions involving brackets. Substitute into expressions involving powers. 3.6 Factorising expressions 6 6 Factorise an algebraic expression. AUTUMN 4 Fractions 11 N1 N2 N3 N4 N6 N8 N10 N12 N15 R3 R Working with fractions 4 6 Compare and simplify fractions. 4.2 Adding and subtracting fractions 4.3 Fractions, decimals and percentages 4.4 Multiplying and dividing fractions Write one number as a fraction of another. Work out simple fractions of amounts. Write an improper fraction as a mixed number. Add and subtract fractions. Work with equivalent fractions, decimals and percentages. Use division to write a fraction as a decimal. Work out fractions of amounts. Divide an integer and a fraction by a fraction. Multiply a fraction by a fraction. 4.5 Working with mixed numbers 5 7 Add and subtract mixed numbers. END OF TERM TEST SPRING 5 Angles and shapes 9 G3 G4 G6 G Angles and parallel lines 4 6 Enter time as a mixed number into a calculator. Multiply and divide a mixed number. Work out unknown angles when two or more lines meet or cross at a point. Work out unknown angles involving parallel lines. 5.2 Triangles 4 6 Describe the line and rotational symmetry of triangles. Understand how to prove that a result is true. Use properties of a triangle to work out unknown angles.

5 Use the properties of isosceles and equilateral triangles to solve problems. 5.3 Quadrilaterals 4 5 Describe the line and rotational symmetry of quadrilaterals. Describe the properties of quadrilaterals. Solve problems involving quadrilaterals. 5.4 Polygons 5 7 Work out the interior and exterior angles of a polygon. SPRING 6 Decimals 11 N1 N2 N3 N4 N6 N10 N12 N14 N15 R Ordering decimals 5 7 Write decimals in ascending and descending order. 6.2 Rounding decimals 5 6 Round to decimal places. 6.3 Adding and subtracting decimals 4 6 Add and subtract decimals. 6.4 Multiplying decimals 4 6 Multiply a decimal by an integer. Use place value to multiply decimals. 6.5 Dividing decimals 4 6 Divide a decimal by a whole number. 6.6 Fractions, decimals and percentages 5 6 Divide a number by a decimal. Convert between fractions decimals and percentages. 6.7 FINANCE: Working with percentages 4 6 Compare different proportions using percentages. Calculate percentages with and without a calculator. Calculate percentage increases and decreases. Work backwards to solve a percentage problem. HALF-TERM TEST SPRING 7 Equations 9 A1 A2 A4 A5 A Solving one-step equations 4 5 Write and solve simple equations. Solve problems using equations. 7.2 Solving two-step equations 5 6 Write and solve two-step equations. Write and solve equations that have brackets. 7.3 More complex equations 6 6 Write and solve equations with letters on both sides. 7.4 Trial and improvement 6 8 Solve equations that include x ² and x 3 Use trial and improvement to find solutions to 1 decimal place. END OF TERM TEST SUMMER 8 Multiplicative reasoning 11 R4 R5 R6 R7 R8 R STEM: Metric and imperial units 4 5 Convert between metric and imperial units.

6 Use metric units. 8.2 Writing ratios 4 6 Write a ratio in its simplest form. Simplify a ratio expressed in fractions or decimals. 8.3 Sharing in a given ratio 4 5 Share a quantity in 2 or more parts in a given ratio. 8.4 Proportion 5 5 Understand the relationship between ratio and proportion. 8.5 Proportional reasoning 5 6 Solve simple word problems involving ratio and direct proportion. Solve simple word problems involving ratio and inverse proportion. 8.6 Using the unitary method SUMMER 9 Perimeter, area and volume 11 N13 R1 G1 G12 G13 G14 G15 G16 G Triangles, parallelograms and trapeziums 9.2 Perimeter and area of compund shapes Solve problems involving ratio and proportion using the unitary method. Write ratios in the form 1 : n Solve best buy problems. Calculate the area of triangles. Calculate the area of parallelograms. Calculate the area of trapeziums. Calculate the perimeter of shapes made from rectangles and triangles. Calculate the area of shapes made from rectangles and triangles. 9.3 Properties of 3D solids 4 5 Identify nets of different 3D shapes. Know the properties of 3D shapes. 9.4 Surface area 4 6 Calculate the surface area of a cube. Calculate the surface area of a cuboid. 9.5 Volume 5 6 Calculate the volume of a cube. 9.6 STEM: Measures of area and volume HALF-TERM TEST SUMMER 10 Sequences and graphs 10 A8 A9 A10 A23 A24 A Sequences Calculate the volume of a cuboid. Convert between different units of volume: cm³, ml and litres. Convert between metric measures for area and volume. Work out the terms of an arithmetic sequence using the term-to-term rule. Work out a given term in a simple arithmetic sequence.

7 END OF TERM TEST END OF YEAR TEST 10.2 The nth term Work out and use expressions for the n th term in an arithmetic 5 6 sequence Pattern sequences 4 6 Generate sequences and predict how they will continue. Recognise geometric sequences and work out the term-to-term rule Coordinates and line segments 4 6 Use positive and negative coordinates. Work out the midpoint of a line segment Graphs 4 6 Draw straight-line graphs. Recognise straight-line graphs parallel to the axes. Recognise graphs of y = x and y = x

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13 YEAR 2 KS3 Maths Progress Delta 2 TERM UNIT / LESSON HOURS GCSE (9-1) SPEC STEPS FROM STEPS TO OBJECTIVES REFERENCE AUTUMN 1 Factors and powers 9 N2 N4 N6 N7 N14 N Prime factor decomposition 4 6 Write the prime factor decomposition of a number. Use prime factor decomposition to find the HCF or LCM or two numbers. 1.2 Laws of indices 6 8 Work out the laws of indices for positive powers. Show that any number to the power of zero is 1. Use the laws of indices for multiplying and dividing. 1.3 STEM: Powers of Use and understand powers of 10. Use the prefixes associated with powers of 10. Understand the effect of multiplying and dividing by any integer power of Calculating and estimating 6 7 Calculate with powers. Round to a number of significant figures. AUTUMN 2 Working with powers 10 A1 A3 A4 A simplifying expressions 6 6 Simplify expressions involving powers and brackets. Understand the meaning of an identity. 2.2 More simplifying 6 8 Use the index laws in algebraic calculations and expressions. Simplify expressions with powers. 2.3 Expanding and simplfying Write and simplify expressions involving brackets and powers. 6 7 Factorise an algebraic expression. 2.4 Substituting and solving 7 7 Substitute integers into expressions. Construct and solve equations. HALF-TERM TEST AUTUMN 3 2D shapes and 3D solids 12 G6 G9 G11 G13 G16 G17 G Plans and elevations 4 6 Use 2D representations of 3D solids. 3.2 Surface area of prisms 7 7 Sketch nets of 3D solids. Calculate the surface area of prisms. 3.3 Volume of prisms 5 8 Calculate the volume of right prisms. 3.4 Circumference of a circle 6 7 Name the different parts of a circle. Calculate the circumference. Calculate the radius or diameter when you know the circumference. 3.5 Area of a circle 6 7 Calculate the area of a circle. Calculate the radius or diameter when you know the area. 3.6 Cylinders 8 8 Calculate the volume and surface area of a cylinder. 3.7 Pythagoras' theorem 5 8 Use Pythagoras theorem in right-angled triangles. AUTUMN 4 Real life graphs 10 A8 A9 A10 R10 R14 R Direct proportion 5 6 Recognise when values are in direct proportion. Plot graphs and read values to solve problems. 4.2 FINANCE: Interpreting financial graphs 5 6 Interpret graphs from different sources. Understand financial graphs. 4.3 Distance-time graphs 5 7 Draw and interpret distance time graphs. Use distance time graphs to solve problems. 4.4 Rates of change 6 7 Interpret graphs that are curved. Interpret real-life graphs. 4.5 Misleading graphs 7 7 Understand when graphs are misleading. END OF TERM TEST SPRING 5 Transformations 11 R2 G4 G6 G7 G8 G24 G Reflection and translation 3 5 Describe and carry out translations. Describe and carry out reflections. 5.2 Rotation 3 8 Describe and carry out rotations. 5.3 Enlargement 5 6 Enlarge a shape. Describe an enlargement. 5.4 More enlargement 5 8 Enlarge a shape using negative scale factors. Enlarge a shape using fractional scale factors. 5.5 STEM: Combining transformations Transform 2D shapes using a combination of reflection, rotation, 5 8 enlargement and translation D shapes and 3D solids 5 9 Identify planes of reflection symmetry in 3D solids. Find the perimeter and area of 2D shapes after enlargement. Find the volume of 3D solids after enlargements. SPRING 6 Fractions, decimals and percentages 9 N3 N10 N12 R9 R Recurring decimals Recognise fractional equivalents to important recurring decimals 5 7 Recognise which denominators of simple fractions produce recurring decimals Change a recurring decimal into a fraction. 6.2 Using percentages 6 7 Calculate percentages Work out an original quantity before a percentage increase or decrease 6.3 Percentage change 8 8 Calculate percentage change.

14 6.4 FINANCE: Repeated percentage Calculate the effect of repeated percentage changes. change 9 9 HALF-TERM TEST SPRING 7 Constructions and loci 11 G1 G2 G Accurate drawings 4 5 Draw triangles accurately using a ruler and protractor. Draw diagrams to scale. 7.2 Constructing shapes 6 7 Draw accurate nets of 3D solids. Construct triangles using a ruler and compasses. Construct nets of 3D solids using a ruler and compasses. 7.3 Constructions Bisect a line using a ruler and compasses. Construct perpendicular lines using a ruler and compasses. 7.4 Constructions Bisect angles using a ruler and compasses. Draw accurate diagrams to solve problems. 7.5 Loci 5 8 Draw a locus. Use loci to solve problems. END OF TERM TEST SUMMER 8 Probability 11 P1 P2 P3 P4 P5 P6 P7 P8 P Comparing probabilities 3 6 Calculate and compare probabilities. Decide if a game is fair. 8.2 Mutually exclusive events 4 7 Identify mutually exclusive outcomes and events. Find the probabilities of mutually exclusive outcomes and events. Find the probability of an event not happening. 8.3 Estimating probability 4 5 Calculate the relative frequency of a value. Use relative frequency to make estimates. Use relative frequency to estimate the probability of an event. Use estimated probability to calculate expected frequencies. 8.4 Experimental probability 3 8 Carry out a probability experiment. Estimate probability using data from an experiment. Work out the expected results when an experiment is repeated. 8.5 Probability diagrams Tree diagrams 8 10 SUMMER 9 Scale drawings and measures 10 R2 G2 G3 G4 G5 G6 G7 G15 G HALF-TERM TEST SUMMER 10 Graphs 12 A8 A9 A10 A12 A14 A24 R10 R END OF TERM TEST END OF YEAR TEST List all the possible outcomes of one or two events in sample space diagrams or Venn diagrams. Calculate probabilities of repeated events. Use tree diagrams to find the probabilities of two or more events.

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16 YEAR 3 KS3 Maths Progress Delta 3 TERM UNIT / LESSON HOURS GCSE (9-1) SPEC STEPS STEPS REFERENCE FROM TO AUTUMN 1 Powers and roots 11 N3 N6 N7 N8 N9 A4 A OBJECTIVES 1.1 Reciprocals 7 8 Find the reciprocal of a number. Work with reciprocals. 1.2 Indices 7 8 Use negative indices. Work out powers of fractions. 1.3 Standard form 7 8 Write numbers using standard form. Order numbers written in standard form. 1.4 STEM: Calculating with standard Calculate with numbers written in standard form. 7 8 form 1.5 Fractional indices 9 9 Calculate with fractional indices. 1.6 Surds 9 10 Use surds. Understand the difference between rational and irrational numbers. AUTUMN 2 Quadratics 10 A4 A23 A24 A Sequences 6 9 Generate sequences using quadratic expressions. Find an expression for the nth term of a quadratic sequence. 2.2 Expanding 7 8 Multiply pairs of brackets. Square a linear expression. Use quadratic identities. 2.3 Factorising 9 9 Factorise quadratic expressions into two brackets. 2.4 Solving quadratic equations 9 9 Solve quadratic equations by factorising. HALF-TERM TEST AUTUMN 3 Inequalities, equations and formulae 11 A3 A5 A6 A17 A18 A19 A20 A21 A Inequalities 7 7 Solve linear equations and represent the solution on a number line. Multiply both sides of an inequality by a negative number. 3.2 Using index laws 6 7 Use index laws with zero and negative powers. 3.3 Solving equations 6 8 Explain the difference between equations, formulae and functions. Construct and solve complex equations. 3.4 Changing the subject 7 8 Change the subject of a formula 3.5 Algebraic fractions 8 9 Change algebraic fractions to equivalent fractions. Solve problems with fractions in formulae. AUTUMN 4 Collecting and analysing data 12 S1 S2 S3 S4 S5 S STEM: Data collection 4 8 Identify sources of primary and secondary data. Choose a suitable sample size. Understand how to reduce bias in sampling and questionnaires. Identify a random sample. 4.2 Presenting and comparing data 5 7 Draw and interpret stem and leaf diagrams. Construct and interpret frequency polygons. Use frequency polygons to compare data. 4.3 Estimating statistics 8 8 Estimate the mean and range from a grouped frequency table. Draw conclusions from tables and charts. 4.4 Box plots 7 9 Interpret statistics. Draw and interpret box plots. Compare data using box plots. 4.5 Cumulative frequency graphs 9 9 Draw cumulative frequency graphs for grouped data. Interpret cumulative frequency graphs. 4.6 Histograms Construct and interpret histograms. END OF TERM TEST SPRING 5 Multiplicative reasoning 10 R10 R13 G9 G17 G SPRING 6 Non-linear graphs 10 A11 A12 A13 A14 R Graphs of quadratic functions 7 8 Understand and draw graphs of quadratic functions Identify quadratic graphs and their features. Solve problems using quadratic graphs. 6.2 Solving quadratic equations 8 9 Use quadratic graphs to solve equations. 6.3 Graphs of cubic functions 7 9 Understand and draw graphs of cubic functions. Identify cubic graphs and their features. 6.4 STEM: Graphs of reciprocal functions 9 9 Identify and draw graphs of reciprocal functions HALF-TERM TEST SPRING 7 Accuracy and measures 9 N15 N16 R1 R11 R Solve problems using reciprocal graphs 7.1 Rates of change 8 8 Solve problems involving rates of change. Convert units with compound measures. 7.2 Density and pressure 8 8 Calculate density and pressure. Solve problems involving compound measures. 7.3 Upper and lower bounds 7 7 Understand the effects of rounding. Find upper and lower bounds. 7.4 Calculating with bounds 9 9 Calculate the lower and upper bound of areas and volumes.

17 7.5 STEM: Accurate measures in real life 9 9 Calculate the lower and upper bounds of compound measures. Use upper and lower bounds to solve complex problems. END OF TERM TEST SUMMER 8 Graphical solutions 11 A3 A9 A14 A Simultaneous equations 7 8 Solve a pair of simultaneous equations. 8.2 Using y = mx + c Rearrange equations of graphs to find the gradient and the y intercept. Find the equation of the line between two points. 8.3 More simultaneous equations 8 9 Solve more complex simultaneous equations. 8.4 Graphs and simultaneous equations 7 10 Solve simultaneous equations by drawing graphs. 8.5 Solving inequalities 8 8 Solve inequalities by graphing straight lines. Solve inequalities that involve quadratic graphs. SUMMER 9 Trigonometry 12 A12 G20 G21 G22 G The tangent ratio 7 9 Use conventions for naming sides of a right angled triangle. Work out the tangent of any angle. Use the tangent ratio to work out an unknown side of a right-angled triangle. 9.2 The sine ratio 7 9 Work out the sine of any angle. Use the sine ratio to work out an unknown side of a right-angled triangle. 9.3 The cosine ratio 7 9 Work out the cosine of any angle. Use the cosine ratio to work out an unknown side in a right-angled triangle. 9.4 Using trigonometry to find angles Use the trigonometric ratios to work out an unknown angle in a rightangled 7 9 triangle. 9.5 Solving problems using trigonometry Use trigonometry to solve problems involving missing lengths and 9 9 angles. 9.6 Trigonometric graphs Plot and sketch graphs of the trigonometric functions. Use the trigonometric ratios with any angle from 0 to 360 HALF-TERM TEST SUMMER 10 Mathematical reasoning 9 A6 A14 G6 G Explain, show and justify 8 9 Explain, show and justify a mathematical solution MODELLING: Real-life situations 8 9 Draw graphs to solve mathematical problems Proof Identify the difference between giving an example and proving a 8 9 theory. Understand how to use mathematical proof More proof 9 9 Present a logical argument using algebra. END OF TERM TEST END OF YEAR TEST

18 YEAR 4 Edexcel GCSE (9-1) Mathematics Higher Student Book TERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC REFERENCE STEPS FROM STEPS TO Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching. AUTUMN 1 Number 11 N2 N3 N4 N5 N6 N7 6th 12th N8 N9 N14 N15 Have a firm grasp of place value and be able to order integers and decimals and use the four operations. OBJECTIVES Know integer complements to 10 and to 100, multiplication facts to 10 10, strategies for multiplying and dividing by 10, 100 and Have encountered squares, square roots, cubes and cube roots and have knowledge of classifying integers. 1.1 Number problems and reasoning Multiply numbers in a similar format to questions N3 N5 6th 9th Work out the total number of ways of performing a series of tasks. later in the section. List possible outcomes from two events. 1.2 Place value and estimating Estimate the value of a square root. N3 N6 N14 N15 6th 7th Estimate an answer. Round numbers to a specified degree of accuracy. Use place value to answer questions. Apply the four operations. 1.3 HCF and LCM Multiply prime factors together. N3 N4 7th 8th Write a number of the product of its prime factors. List the factors of a number. Find the HCF and LCM of two numbers. 1.4 Calculating with powers (indices) Work out simple powers. N3 N6 N7 6th 8th Use powers and roots in calculations. 1.5 Zero, negative and fractional indices Apply the four operations. Multiply and divide using index laws. Work out a power raised to a power. Convert between fractions and decimals. N3 N6 N7 8th 12th Use negative indices. Use the laws of indices for positive indices. 1.6 Powers of 10 and standard form Multiply by powers of 10 when the number is written as an ordinary number and not an index. Use fractional indices. N3 N6 N9 7th 9th Write a number in standard form. Review different ways to divide by 10. Use negative indices. 1.7 Surds Review the meaning of the dot in the recurring notation. Identify the missing multiple which practices the skills of searching for a perfect square factor. Calculate with numbers in standard form. N3 N8 10th 11th Understand the difference between rational and irrational numbers. Simplify a surd. AUTUMN 2 Algebra 12 N1 N3 N8 N9 A1 A2 6th A3 A4 A5 A6 A7 A17 A21 A22 A23 A24 A25 10th Rationalise a denominator. AUTUMN 3 Interpreting and representing data 11 G14 S1 S2 S3 S4 S5 S6 4th 8th Read scales on graphs, draw circles, measure angles and plot coordinates in the first quadrant. Have experience of tally charts. Use inequality notation. Find midpoint of two numbers. Find the range, mean, median and mode of a data set. 3.1 Statistical diagrams 1 Work out mode, median and range from a list of numbers. 3.2 Time series Identify trends by noticing whether sequences of numbers increase, decrease or oscillate. 3.3 Scatter graphs Recognise when a line has a positive, negative or zero gradient. Plot points on a coordinate grid, and identify points that do not lie on a straight line. 3.4 Line of best fit Understand and be able to define the meaning of correlation. Read values from graphs. S1 S2 S3 4th 7th Construct and use back-to-back stem and leaf diagrams. Construct and use frequency polygons and pie charts. S2 6th 6th Plot and interpret time series graphs. Use trends to predict what might happen in the future. S6 6th 7th Plot and interpret scatter graphs. Determine whether or not there is a linear relationship between two variables. S6 6th 7th Draw a line of best fit on a scatter graph. Use the line of best fit to predict values. 3.5 Averages and range Find the range of a list of numbers. S4 S5 5th 8th Decide which average is best for a set of data. Find the midpoint of two numbers. Estimate the mean and range from a grouped frequency table. Find the modal class and the group containing the median. 3.6 Statistical diagrams 2 Use subtraction to find missing values. S2 5th 6th Construct and use two-way tables. Draw a bar chart. Choose appropriate diagrams to display data. Draw a pie chart. Recognise misleading graphs. AUTUMN 4 Fractions, ratio and percentages 10 N2 N3 N8 N10 N11 N12 N13 R3 R4 R5 R6 6th 10th Know the four operations of number. Find common factors. Have a basic understanding of fractions as being parts of a whole. Define percentage as number of parts per hundred. Be aware that percentages are used in everyday life. Use ratio notation, and to write a ratio in its simplest form. 4.1 Fractions Identify unit fractions, improper fractions and mixed numbers. Multiply a whole number by a fraction. Know the priority of operations. 4.2 Ratios Multiply a fraction by its reciprocal for a product of 1. Simplify ratios. Write ratios in the form n : 1. R7 R8 R9 R Ratio and proportion Write one number as a proportion of the total. N13 R4 R5 R6 R7 R8 R10 Identify equivalent ratios. N2 N3 6th 8th Add, subtract, multiply and divide fractions and mixed numbers. Find the reciprocal of an integer, decimal or fraction. N11 N13 R4 R5 6th 7th Write ratios in the form 1 : n or n : 1. Compare ratios. Find quantities using ratios. Solve problems involving ratios. 6th 8th Convert between currencies and measures. Recognise and use direct proportion. Solve problems involving ratios and proportion. 4.4 Percentages Find a percentage of a given amount. N12 N13 R9 6th 9th Work out percentage increases and decreases. Work out percentage multipliers. Solve real-life problems involving percentages. 4.5 Fractions, decimals and percentages Convert between fractions, decimals and percentages. Solve simple equations. AUTUMN 5 Angles and trigonometry 12 N7 N8 N15 G1 G3 G4 G6 G20 G21 N2 N8 N10 R3 R6 R9 6th 10th Work out percentage increases and decreases. 6th 9th Solve real-life problems involving percentages.

19 5.1 Angle properties of triangles and quadrilaterals Rearrange simple formulae and equations, as preparation for rearranging trig formulae. Recall basic angle facts. Understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents. Recall the properties of special types of triangles and quadrilaterals. Recognise special types of triangle and quadrilateral. G1 G3 G4 G6 6th 6th Derive and use the sum of angles in a triangle and in a quadrilateral. Recall basic angle facts. 5.2 Interior angles of a polygon Name polygons and understand the meaning of regular polygon. Substitute numbers into an expression. Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. G3 6th 7th Calculate the sum of the interior angles of a polygon. Use the interior angles of polygons to solve problems. Find missing angles in triangles, quadrilaterals and at a point. 5.3 Exterior angles of a polygon Find missing angles on a straight line. G3 6th 8th Know the sum of the exterior angles of a polygon. Calculate the sum of interior angles of a polygon. Use the angles of polygons to solve problems. 5.4 Pythagoras theorem 1 Recall square numbers and square roots. N15 G20 7th 7th Calculate the length of the hypotenuse in a right-angled triangle. Find the area of a square. Solve problems using Pythagoras theorem. 5.4 Pythagoras theorem 1 Find square roots. N7 N8 G20 8th 8th Calculate the length of a shorter side in a right-angled triangle. Recognise perfect squares. Solve problems using Pythagoras theorem. Use Pythagoras' theorem to find the length of the hypotenuse. 5.6 Trigonometry 1 Convert fractions to decimals. G20 6th 9th Use trigonometric ratios to find lengths in a right-angled triangle. Identify the hypotenuse. Use trigonometric ratios to solve problems. Use the angle sum of a triangle to work out missing angles. 5.7 Trigonometry 2 Identify the opposite and adjacent sides of a given angle in right-angled triangles. G20 G21 6th 9th Use trigonometric ratios to calculate an angle in a right-angled triangle. Use the trigonometric ratios to find lengths in rightangled triangles. Find angles of elevation and angles of depression. Use trigonometric ratios to solve problems. Know the exact values of the sine, cosine and tangent of some angles. END OF TERM 1 TEST SPRING 6 Graphs 11 N13 A8 A9 A10 A11 A12 A14 A15 A16 A17 G11 R8 R10 R11 6th 10th SPRING 7 Area and volume 10 N8 N13 N14 N15 N16 6th 12th R1 G1 G9 G12 G14 G16 G17 G18 Know the names and properties of 3D shapes. Know the concept of perimeter and area by measuring lengths of sides. Substitute numbers into an equation and give answers to an appropriate degree of accuracy. Know the various metric units. Identify planes of symmetry of 3D solids. Sketch a net of a 3D shape. Work out the volume of a 3D solid made of cuboids. Recall Pythagoras' theorem. 7.1 Perimeter and area Recognising units of length (perimeter) and area. G16 G17 6th 6th Find the perimeter and area of compound shapes. Work out the area and perimeter of rectangles, triangles and parallelograms. 7.2 Units and accuracy Recall the formulae for the area of quadrilaterals N13 N14 N15 N16 R1 and triangles. Identify the possible integer values of G14 G16 x from an inequality. Round numbers to a specified degree of accuracy. Recall and use the formula for the area of a trapezium. 6th 10th Convert between metric units of area. Calculate the maximum and minimum possible values of a measurement. Work out percentages of quantities. 7.3 Prisms Calculate the volume and surface area of a cuboid. N13 N14 N15 R1 G16 7th 9th Convert between metric units of volume. Calculate the volume of a shape made from cuboids. Calculate volumes and surface areas of prisms. 7.4 Circles Understand radius and diameter. N8 G9 G17 6th 8th Calculate the area and circumference of a circle. Solve and rearrange simple equations. Calculate area and circumference in terms of π. 7.5 Sectors of circles Work out fractions of a circle given the angle of a N8 N16 G9 G17 G18 8th 12th Calculate the perimeter and area of semicircles and quarter circles. sector. Simplify equations. Calculate arc lengths, angles and areas of sectors of circles. 7.6 Cylinders and spheres Find the area and circumference of a circle in terms N16 G16 G17 7th 11th Calculate volume and surface area of a cylinder and a sphere. of π. Sketch a net of a cylinder. Solve problems involving volumes and surface areas. Solve simple equations. 7.7 Pyramids and cones Find the volume of a cube. G17 6th 12th Calculate volume and surface area of pyramids and cones. Find the side length of a cube given its volume. Solve problems involving pyramids and cones. Calculate the area of a triangle. Use Pythagoras' theorem to work out the length of the hypotenuse. SPRING 8 Transformations and constructions 10 R2 R6 G1 G2 G7 G8 G12 G13 G15 G24 G25 6th 10th Recognise 2D shapes. Plot coordinates in four quadrants and linear equations parallel to the coordinate axes. Convert metric measures. Recognise congruent and similar shapes. Transform shapes using translation, reflection, rotation and enlargement D solids Draw 3D shapes on an isometric grid. G12 G13 6th 7th Draw plans and elevations of 3D solids. Recognise dimensions of a cuboid. 8.2 Reflection and rotation Draw simple straight lines on a coordinate grid. G8 6th 7th Refl ect a 2D shape in a mirror line. Know whether the image is congruent to the original following a reflection or a rotation. Rotate a 2D shape about a centre of rotation. Describe refl ections and rotations. 8.3 Enlargement Enlarge shapes on a coordinate grid in one quadrant. R2 R6 6th 10th Enlarge shapes by fractional and negative scale factors about a centre of enlargement. 8.4 Transformations and combinations of transformations Describe translations. G7 G24 G25 7th 8th Translate a shape using a vector. Carry out and describe combinations of transformations. 8.5 Bearings and scale drawings Convert metric measures and apply to scales. R2 G1 G15 6th 7th Draw and use scales on maps and scale drawings. Accurate drawing of right-angled triangle. Solve problems involving bearings.

20 8.6 Constructions 1 Accurate drawings of triangles given SSS and ASA. G1 G2 6th 7th Construct triangles using a ruler and compasses. Know the meaning of the terms perpendicular, Construct the perpendicular bisector of a line. bisect, arc. Construct the shortest distance from a point to a line using a ruler and compasses. 8.7 Constructions 2 Draw angles with a protractor. R2 G1 G2 7th 8th Bisect an angle using a ruler and compasses. Construct triangles and deduce infomration from them. Construct angles using a ruler and compasses. Construct shapes made from triangles using a ruler and compasses. 8.8 Loci R2 G1 G2 7th 10th Draw a locus. Use loci to solve problems. SPRING 9 Equations and inequalities 9 N1 N8 A3 A4 A5 A9 A11 A18 A19 A21 A22 6th 12th Understand the and symbols. Substitute into, solve and rearrange linear equations. Factorise simple quadratic expressions. Recognise the equation of a circle. 9.1 Solving quadratic equations 1 Know that a square has two possible roots A3 A4 A11 A18 7th 9th Find the roots of quadratic functions. Find the factors of a given number. Rearrange and solve simple quadratic equations. Factorise expressions. Solve simple equations containing a squared term. 9.2 Solving quadratic equations 2 Understand the term quadratic N8 A3 A4 A18 8th 10th Solve more complex quadratic equations. Find positive and negative square roots. Use the quadratic formula to solve a quadratic equation. Solve quadratic equations by factorising. Expand two pairs of brackets. Simplify surds. 9.3 Completing the square Expand and simplify a square bracket. A3 A4 A5 A18 7th 12th Complete the square for a quadratic expression. Simplify surds. Solve quadratic equations by completing the square. Solve simple equations, giving the answer in surd form. 9.4 Solving simple simultaneous Substitute into simple algebraic expressions. A3 A4 A5 A19 A21 8th 10th Solve simple simultaneous equations. equations Rearrange equations. Solve simultaneous equations for real-life situations. 9.5 More simultaneous equations Recall the equation of a straight line. A3 A4 A5 A9 A19 A21 9th 9th Use simultaneous equations to find the equation of a straight line. Solve simple simultaneous equations. Solve linear simultaneous equations where both equations are multiplied. Interpret real-life situations involving two unknowns and solve them. 9.6 Solving linear and quadratic Identify different types of equations. A3 A4 A5 A19 A21 10th 12th Solve simultaneous equations with one quadratic equation. simultaneous equations Solve quadraric equations. Use real-life situations to construct quadratic and linear equations and solve them. 9.7 Solving linear inequalities Understand inequality signs A3 A4 A5 A22 6th 9th Solve inequalities and show the solution on a number line and using set notation. Construct correct inequalities from given information SPRING 10 Probability 9 N1 P1 P2 P3 P4 P5 P6 5th 12th P7 P8 P9 Understand that a probability is a number between 0 and 1, and distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur. Mark events and/or probabilities on a probability scale of 0 to 1. Know how to add and multiply fractions and decimals. Express one number as a fraction of another. List all outcomes for a single event systematically. Make predictions from experimental data. Complete a two-way table Combined events List all outcomes for a single event systematically. N5 P7 P8 5th 8th Use the product rule for finding the number of outcomes for two or more events. List all outcomes for two events systemaically. List all the possible outcomes of two events in a sample space diagram Mutually exclusive events Add decimals. Subtract decimals and fractions from P4 P8 6th 7th Identify mutually exclusive outcomes and events. 1. Understand the relationship between ratios and fractions. Find the probabilities of mutually exclusive outcomes and events. Find the probability of an event not happening Experimental probability Simplify fractions. P1 P2 P3 P5 6th 8th Work out the expected results for experimental and theoretical probabilities. Multilply whole numbers by decimals. Compare real results with theoretical expected values to see if a game is fair Independent events and tree diagrams Add and multiply fractions and decimals. P1 P4 P8 P9 7th 10th Draw and use frequency trees. Calculate probabilities of repeated events. Draw and use probability tree diagrams Conditional probability Know that the probability of something not P4 P8 P9 8th 12th Decide if two events are independent. happening is 1 minus the probability of the event happening. Draw and use probability tree diagrams. Draw and use tree diagrams to calculate conditional probability. Draw and use tree diagrams without replacement. Use two-way tables to calculate conditional probability Venn diagrams and set notation Interpret inequalities. P4 P6 P8 P9 6th 10th Use Venn diagrams to calculate conditional probability. Use Venn diagrams. END OF TERM 2 TEST SUMMER 11 Multiplicative reasoning 8 N12 N13 A2 A9 R1 R6 6th R9 R10 R11 R13 R14 R16 9th Use set notation. Find a percentage of an amount and relate percentages to decimals. Rearrange equations and use these to solve problems. Know speed = distance/time, density = mass/volume. Convert between metric units. Solve simple direct and indirect proportion problems, including currency conversion Growth and decay Understand the use of indices. N12 R9 R16 8th 9th Find an amount after repeated percentage changes. Work out the decimal multiplier for a percentage increase/decrease. Solve growth and decay problems.

21 11.2 Compound measures Calculate simple rates. A2 R1 R11 6th 7th Calculate rates. Substitute numbers into equations, and solve for the Convert between metric speed measures. unknown. Use speed = distance/time to solve problems. Use a formula to calculate speed and acceleration More compound measures Convert between metric units. N13 R1 R11 6th 8th Solve problems involving compound measures. Recall the formulae for the area of a circle and volume of a prism Ratio and proportion Rearrange formulae. A9 R6 R10 R13 R14 6th 9th Use relationships involving ratio. Recognise graphs of y = x and y = 1/x. Find the gradient of a line given its equation. Decide whether quantities are in direct proportion. Use direct and indirect proportion. SUMMER 12 Similarity and congruence 8 R6 R12 G5 G6 G7 G17 6th G19 Recognise and enlarge shapes and calculate scale factors. Know how to calculate area and volume in various metric measures. Measure lines and angles, and use compasses, ruler and protractor to construct standard constructions. 12th Recognise congruent shapes. Know basic angle facts Congruence Know the angle sum of interior angles of a triangle. G5 G6 6th 10th Show that two triangles are congruent. Recognise congruent shapes. Recall basic angle facts. Find missing lengths using Pythagoras' theorem Geometric proof and congruence Know the conditions of congruence and use correct mathematical notation for equal angles and sides. Know the conditions of congruence. G5 G6 12th 12th Prove shapes are congruent. Recall the properties of special triangles and Solve problems involving congruence. quadrilaterals Similarity Use geometric properties to find similarities and R6 R12 G6 G7 5th 9th Use the ratio of corresponding sides to work out scale factors. differences between given polygons. Calculate scale factors. Find missing lengths on similar shapes More similarity Find area scale factor, given length scale factor. G6 G7 G19 9th 11th Use similar triangles to work out lengths in real life. Use the link between linear scale factor and area scale factor to solve problems Similarity in 3D solids Work out the volume and surface area of a cube. G6 G17 G19 9th 12th Use the link between scale factors for length, area and volume to solve problems. Convert between metric units. Work out cubes and cube roots. SUMMER 13 More trigonometry 13 N16 A8 A12 A13 G20 G22 G23 9th 12th Use axes and coordinates to specify points in all four quadrants. Recall and apply Pythagoras Theorem and trigonometric ratios. Substitute into formulae Accuracy Find upper and lower bounds of a given measurement Graph of the sine function Know the exact values of sin θ for θ = 30, 45, 60 and 90 Use Pythagoras' theorem. Find angles using the sin function Graph of the cosine function Know the exact values of cos θ for θ = 30, 45, 60 and 90 Use Pythagoras' theorem. N16 10th 11th Understand and use upper and lower bounds in calculations involving trigonometry. A8 A12 G21 10th 12th Understand how to find the sine of any angle. Know the graph of the sine function and use it to solve equations. A8 A12 G21 10th 12th Understand how to find the cosine of any angle. Know the graph of the cosine function and use it to solve equations. Find angles using the cos function The tangent function Know the exact values of tan θ for θ = 30, 45, 60 A8 A12 G21 10th 12th Understand how to fi nd the tangent of any angle. Use Pythagoras' theorem. Know the graph of the tangent function and use it to solve equations. Find angles using the tan function Calculating areas and the sine rule Calculate the area of a triangle using (1/2)b h G22 G23 9th 12th Find the area of a triangle and a segment of a circle. Know the formula for calculating the area of a circle. Use the sine rule to solve 2D problems The cosine rule and 2D trigonometric problems Use trigonometry Use bearings G22 G23 10th 12th Use the cosine rule to solve 2D problems. Calculate the area of a triangle. Solve bearings problems using trigonometry. Solve calculations Solving problems in 3D Use the sine and cosine rule. G20 12th 12th Use Pythagoras theorem in 3D. Use trigonometry in 3D Transforming trigonometric Reflect and rotate a coordiante point. A8 A13 12th 12th Recognise how changes in a function affect trigonometric graphs. graphs 1 Know the exact values of sin θ and cos θ for θ = 0, 30, 45, 60 and 90 ; know the exact value of tan θ for θ = 0, 30, 45 and 60 Sketch y = sinx, y = cosx and y= tanx for x from 0 to Transforming trigonometric Translate coordinate points by column vectors. A8 A13 12th 12th Recognise how changes in a function affect trigonometric graphs. graphs 2 Understand negative translations. SUMMER 14 Further statistics 10 S1 S3 S4 6th 12th Understand the different types of data: discrete/continuous. Have experience of inequality notation. Multiply a fraction by a number. Understand the data handling cycle Sampling Use fractions and percentages to work out data from S1 6th 10th Understand how to take a simple random sample. a table. Understand how to take a stratifi ed sample Cumulative frequency Find the median of a data set. S3 9th 9th Draw and interpret cumulative frequency tables and diagrams Box plots Find the median and range from a stem-and-leaf diagram. Work out the median, quartiles and interquartile range from a cumulative frequency diagram. S4 9th 9th Find the quartiles and the interquartile range from stem-and-leaf diagrams. Draw and interpret box plots Drawing histograms Division calculations S3 10th 11th Understand frequency density. Draw a frequency diagram. Draw histograms. Write the modal class

22 Estimate the mean mass Interpreting histograms Write the modal class S3 11th 12th Interpret histograms. Estimate the mean mass Comparing and describing Work out the mean, median and mode of data sets. S4 9th 10th Compare two sets of data. populations Work out the mean and range from a table. SUMMER 15 Equations and graphs 9 N8 A4 A11 A12 A18 A19 A20 A21 A22 6th 12th Solve quadratics and linear equations. Solve simultaneous equations algebraically Solving simultaneous equations Know and draw graphs of circles. A19 A21 9th 10th Solve simultaneous equations graphically. graphically 15.2 Representing inequalities Know which integers satisfy an inequality A22 6th 12th Represent inequalities on graphs. graphically Solve inequalitites with one variable and show Interpret graphs of inequalities. solution using set notation Graphs of quadratic functions Solve quadratic equations by factorising. N8 A11 A12 8th 12th Recognise and draw quadratic functions. Sketch simple quadratic graphs Find coordinates of maximum point Solving quadratic equations Understand manimum and minimum points. N8 A18 A20 9th 12th Find approximate solutions to quadratic equations graphically. graphically Find roots of an equation by completing the square Solve quadratic equations using an iterative process. and using the quadratic formula Graphs of cubic functions Know where a graph will cross the x-axis A4 A12 A20 10th 12th Find the roots of cubic equations. Expand and simplify double brackets Sketch graphs of cubic functions. Find roots of a quadratic equation by completing the Solve cubic equations using an iterative process. square END OF TERM 3 TEST END OF YEAR TEST

23 YEAR 5 Edexcel GCSE (9-1) Mathematics Higher Student Book TERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC REFERENCE STEPS FROM STEPS TO OBJECTIVES Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching. AUTUMN 16 Circle theorems 10 A16 G9 G10 7th 11th Have practical experience of drawing circles with compasses. Recall the words, centre, radius, diameter, circumference, arc, sector and segment Recall the relationship of the gradient between two perpendicular lines. Find the equation of the straight line, given a gradient and a coordinate Radii and chords Recall the properties of an isosceles triangle and the G9 G10 7th 12th Solve problems involving angles, triangles and circles. language of a circle. Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Tangents Recall that the line drawn from the centre of a circle to the midpoint of a chord is at right angles to the chord. Understand and use facts about chords and their distance from the centre of a circle. Solve problems involving chords and radii. G9 G10 9th 12th Understand and use facts about tangents at a point and from a point. Know that the sum of the angles in a triangle must Give reasons for angle and length calculations involving tangents. be 180 Recall the correct maths language for parts of a circle 16.3 Angles in circles 1 Recall simple maths facts. G10 9th 10th Understand, prove and use facts about angles subtended at the centre and the circumference of circles. Recall the correct maths language for parts of a circle. Understand, prove and use facts about the angle in a semicircle being a right angle. Find missing angles using these theorems and give reasons for answers Angles in circles 2 Recall sum of angles of a triangle and a quadrilateral. G10 9th 10th Understand, prove and use facts about angles subtended at the circumference of a circle. Recall correct maths language for parts of a circle. Understand, prove and use facts about cyclic quadrilaterals. Prove the alternate segment theorem Applying circle theorems Understand that x² + y² = r² is the equation of a circle A16 G10 9th 11th Solve angle problems using circle theorems. with centre at the origin. Find the gradient of a line from its equation and know the gradient of a line perpendicular to it. Give reasons for angle sizes using mathematical language. Find the equation of the straight line, given a gradient and a coordinate. Recall circle theorems AUTUMN 17 More algebra 13 N8 A4 A5 A6 A7 A18 8th 12th Find the equation of the tangent to a circle at a given point. Simplify surds. Use negative numbers with all four operations. Add and multiply numeric fractions. Recall and use the hierarchy of operations. Manipulate algebraic expressions. Recall and use the quadratic formula Rearranging formulae Substitute into linear equations. A5 9th 11th Change the subject of a formula where the power of the subject appears. Change the subject of a formula. Change the subject of a formula where the subject appears twice. Factorise linear expressions Algebraic fractions Simplify numeric fractions and fractions containing simple algebraic terms. Add and multiply numeric fractions Simplifying algebraic fractions Factorise expressions by identifying the common factor between two terms. Simplify fractions containing simple algebraic terms. A4 A5 8th 10th Add and subtract algebraic fractions. Multiply and divide algebraic fractions. Change the subject of a formula involving fractions where all the variables are in the denominators. A4 9th 12th Simplify algebraic fractions. Factorise quadratic expressions of the form x2 + bx + c 17.4 More algebraic fractions Simplify algebraic fractions by cancelling common factors. Add, subtract, divide and multiply fractions containing simple algebraic terms Surds Decide whether each number is rational or irrational Solving algebraic fraction Find the lowest common multiple of two algebraic equations fractions. Solve quadratic equations by factorising. Manipulate expressions containing simple algebraic fractions Functions Calculate the output from a function machine for three different inputs. A4 9th 12th Add and subtract more complex algebraic fractions. Multiply and divide more complex algebraic fractions. N8 A4 10th 12th Simplify expressions involving surds. Expand expressions involving surds. Rationalise the denominator of a fraction. A18 10th 12th Solve equations that involve algebraic fractions. A7 8th 12th Use function notation. Solve simple equations Find composite functions. Write expressions using function machines Find inverse functions Proof Identify an odd number and an even number written A6 8th 12th Prove a result using algebra. algebraically. Recall the definitions of equations and identities. AUTUMN 18 Vectors and geometric proof 10 G25 9th 12th Use vectors to describe translations. Recall and use Pythagoras Theorem. Recall the properties of triangles and quadrilaterals. Express the relationship between two quantities as a ratio. Simplify surds Vectors and vector notation Use vectors to describe translations. G25 9th 10th Understand and use vector notation. Recall and use Pythagoras' Theorem. Work out the magnitude of a vector. Simplify surds Vector arithmetic Understand the components of a vector and use G25 10th 10th Calculate using vectors and represent the solutions graphically. vectors to describe translations. Recall properties of triangles and quadrilaterals. Calculate the resultant of two vectors More vector arithmetic Use properties of a parallelogram to identify equal G25 10th 11th Solve problems using vectors. and parallel lines. Add two column vectors. Use the resultant of two vectors to solve vector problems Parallel vectors and collinear Identify parallel column vectors. G25 10th 12th Express points as position vectors. points Add and subtract column vectors. Prove lines are parallel. Prove points are collinear.