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GCSE EDEXCEL Linear Higher Tier SOW for W1 Functional Maths: Functional maths must be embedded in all lessons throughout Year 10 and Year 11 – many of the new exam style questions will be functional maths based. The interactive textbooks have some good functional maths questions that can be used in lessons. Functional maths tasks are hyperlinked on the SOW and can be printed directly from there – these tasks must be carried out. Financial Capability: All year 10 will have 4 financial capability tasks. There is one task per half term. These are detailed below and hyperlinked to the appropriate folder. Please familiarise yourself with the content prior to delivery. There is one per half term – it des not really matter where in the half term they are delivered; but they MUST be delivered. First half of Autumn Term – Financial Capability task 1 Second half of Autumn Term – Financial Capability task 2 Spring Term – Financial Capability task 3 Summer Term – Financial Capability task 4 Investigations: Using and applying mathematics is done throughout the lessons and SOW in Year 10 and Year 11; however – there are three investigations to be carried out during Year 10 – one per term. They can be completed at any time during the term; but towards the end of each term is usually preferable. The investigations are “Borders”, Number Stairs and Manhattan Cops GCSE Mathematics - Medium Term Plan GCSE EDEXCEL Linear Higher Tier SOW for W1 YEAR 10 The number of lessons allocated is a guide. It is important to enrich the curriculum and ensure Functional Mathematics is embedded throughout the topics. Financial capability task 1 and task2 must be covered during the autumn term (Click on task for hyperlink) Investigation – “Borders” must be completed this term General Topic No. of lesson s Number – Calculations: Whole numbers 6 Number Decimals 6 Objectives Autumn Term Fractions: Addition and subtraction Fractions: Multiplication and division 4 6 Students should be able to … Long multiplication and long division of positive integers, including word problems and knowing to round up or down after a remainder. Add, subtract, multiply and divide negative numbers and solve word problems involving negative numbers Round decimals to 1, 2 and 3 of decimal places Round integers and decimals to 1, 2 and 3 significant figures Estimate solutions by first rounding to 1 significant figure Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 d.p.), e.g. 43.2 1.2 & 266.22 0.34 Know that e.g. 13.5 0.5 = 135 5 Compare the sizes of fractions using a common denominator Add and subtract fractions, including mixed numbers – different denominators Convert a fraction to a decimal, or a decimal to a fraction Find the reciprocal of whole numbers, fractions, and decimals Multiply a fraction by an integer, by a unit fraction and by a general fraction including finding a fraction of a quantity Divide a fraction by an integer, by a unit fraction and by a general fraction (expressing the answer in its simplest form) Grade Notes D D-C FM style questions must be taught. D/C C D-C Include calculating before estimating, writing down all numbers on calculator display FM solving problems involving money D D D/C D C C C GCSE Mathematics - Medium Term Plan Need to be able to communicate why one fraction is bigger than another using equivalence eg: 1/3 or 2.5? Revisits simplifying, equivalent and converting between mixed and improper. Include solving word problems using fractions Suggested Enrichment / FM NRICH - Tug of war – a game for two involving adding / subtracting negative numbers GCSE EDEXCEL Linear Higher Tier SOW for W1 General Topic Geometry & measures Coordinates No. of lesson s 4 Objectives Grade Students should be able to … Identify the coordinates of the vertex of a cuboid on a 3-D grid Writing down the coordinates of the midpoint of the line connecting two points. Calculate the gradient of the line segment joining two points in the plane (all four quadrants) - change in vertical/change in horizontal. C D Notes Suggested Enrichment / FM Review Plotting and reading coordinates in all four quadrants if needed. B Learning Review 1 Algebra Introduction to algebra 4-6 AUTUMN TERM Geometry: Lines, angles and reasoning: Angles, properties of triangles and quadrilaterals Statistics Representing & interpreting data. Algebra Factors and multiples 6-8 8 o o o o 4 Simplify algebraic expressions in one or more like terms by addition and subtraction Multiply and divide powers of the same letter to simplify algebraic expressions (e.g. a x a x a = a3, 2a x 3a2 = 6a3, a3/a2 = a) Expand a single bracket and factorise algebraic expressions involving one pair of brackets D Use angle properties of quadrilaterals to calculate unknown angles. (Include algebra to find missing angles). Identify and list the properties of special quadrilaterals (including kites) and use these to find missing angles. Find missing angles on parallel lines using properties of corresponding angles, supplementary angles and alternate angles, giving reasons. D-C Draw and read information from an ordered stem-and-leaf diagram. Draw pie charts (for categorical data) working out angle sizes, and percentages. Draw a Frequency polygon for grouped data Calculate and use the mean and range to compare distributions. Draw and produce a scatter graph Appreciate that correlation is a measure of the strength of association between two variables and distinguish between positive, negative and no correlation. Draw a line of best fit by eye and understand what it represents Use a line of best fit to interpolate/ extrapolate Find the HCF and the LCM of numbers by listing factors or multiples. Write a number as a product of its prime factors, e.g. 108 = 22 33 Find the HCF and LCM of two numbers from their prime factor decompositions. Review 2 XMAS BREAK D C 3(y + 4) and 2y(3y – 4) type 12a – 18 and 20a2 + 35a type. Remind (-2)2 must go in brackets in calculator C D Reason: Candidates do poorly on explanations. Cannot give Z, F, C angle as reasons – must use correct terminology. Use ICT to draw charts and graphs too. C C C GCSE Mathematics - Medium Term Plan If asked for relationship in exam – word correlation must appear. Note – check understanding of what a prime number, a factor and a multiple is. FM: Reporting the weather and FM Teacher notes GCSE EDEXCEL Linear Higher Tier SOW for W1 Financial capability task 3 must be completed during the Spring term (Click on task for hyperlink) Investigation – “Number Stairs” must be completed this Spring term General Topic Geometry: Constructions and loci Spring Term Statistics Collecting data No. of lesson s 4-6 2 Objectives Grade Suggested Enrichment / FM Students should be able to … o o o o o o o o o Construct: An equilateral triangle with a given side The mid-point and perpendicular bisector of a line segment The perpendicular from a point on a line The bisector of an angle The angles 60, 30 and 45 degrees A regular hexagon inside a circle, etc A path equidistant from 2 points or 2 line segments, etc Draw a locus for a given rule. Solve practical problems using loci. Design a suitable question for a questionnaire and criticize a questionnaire. Understand the difference between: primary and secondary data; discrete and continuous data Choose and justify an appropriate sampling scheme, including random and stratified sampling, including understanding about bias in sampling 3 Understand and use bearings Algebra: Patterns and sequences 3–4 Find the nth term of a number sequence as an algebraic expression and use this to find any term in the sequence. Find the nth term from a sequence of patterns Investigate special number sequences (Fibonacci) Geometry & Measures: Properties of polygons 4-6 Geometry: Lines, angles and reasoning: Notes D C C C D Remind candidates construction lines must not be erased FM: Intruder – uses loci and constructions to secure premises C C C D Candidates generally answer poorly in exams on criticising questionnaires and writing better question / responses C D/C Calculate and use the sums of the interior angles of polygons of sides 3, 4, 5, 6, 8, 10 Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles Know that the sum of the exterior angles of any polygon is 360 degrees Find the size of each exterior/interior angle of a regular polygon Solve problems involving angles of regular and irregular polygons NCETM-The Ant – Visualising and constructing the loci of an ant C C C D D D C Review 3 GCSE Mathematics - Medium Term Plan FM: Get OS maps from Geography, using bearings plan a route from A to B. Students could be able to give a reasoned argument to support conclusions. NRICH – Fibs – investigating the Fibonacci sequence GCSE EDEXCEL Linear Higher Tier SOW for W1 General Topic Number Percentages No. of lesson 8 Objectives SPRING TERM Geometry & measures: 2D shapes – perimeter, area including circles. 6-8 Algebra: Solving linear equations 6 Grade Notes … Write a percentage as a decimal; or as a fraction in its simplest terms Write one number as a percentage of another number Calculate the percentage of a given amount – using multiplier Find a percentage increase/decrease of an amount – using multiplier Calculate simple and compound interest for two, or more, periods of time. Find a reverse percentage, e.g. find the original cost of an item given the cost after a 10% deduction Given two quantities – find the percentage change. D C C C Students need to learn how to use a multiplier. B B Need to be able to compare two saving / borrowing options where one uses simple interest and the other compound. Must solve FM problems involving area and perimeter. Solve problems of compound shapes involving rectangles, triangles. Calculate the area of a trapezium, areas of more complex shapes that involve trapeziums. Convert between units of area (e.g. 4m2 into cm2). Use and recall formulae to calculate perimeters and areas of circles, and parts of circles (semi circle, quarter circle – not arc length and sector area) Find the perimeter and area of shapes made up from triangles, rectangles and parts of circles Solve word problems involving area and circumference of circles – including working backwards to find ‘r ‘or‘d’ if area or circumference given. Calculate circumference and area of circles, giving answers in terms of ∏ D/C C Solve linear equations with one, or more, operations (including fractional coefficients) with unknowns on both sides. Solve linear equations involving a brackets Solve quadratic and cubic equations using trial and improvement method to 1 d.p. Set up and solve linear equations Easter Break C Must solve FM style questions D/C C Check students can name all parts of circles, tangents too. Review expanding a single bracket D Year 10 Exams are a few weeks after Easter break GCSE Mathematics - Medium Term Plan Suggested Enrichment / FM FM – Get job section of local paper. Obtain income tax rates, NI rates and ask students to use these to work out take home pay. FM: Understanding VAT & FM: Teacher notes NRICH Race track – A good problem involving circumference of circles. FM: Plan a bedroom. Give area, use Argos catalogues for cost / dimensions of items including carpet; draw 2D plan of bedroom – include cost. FM: Naismith’s Rule and FM – Teacher notes GCSE EDEXCEL Linear Higher Tier SOW for W1 Spri ng Ter m General Topic No. of lesson s Objectives Grade Notes Suggested Enrichment / FM Students should be able to … Year 10 Exams are 2nd week back Financial capability task 4 must be completed during the Summer term (Click on task for hyperlink) Investigation – “Manhattan Cops” must be completed this Summer term Geometry & measures: 3-D shapes and tessellation Transformations 4-6 5–7 Draw and interpret plans and elevations Draw 3D solids onto isomeric paper. Draw planes of symmetry in 3-D shapes Tessellate a shape and recognise which regular polygons tessellate. Use a vector to describe and draw a translation. Rotate a 2D shape about a point and fully describe a rotation Reflect shapes in a given mirror line; parallel to the coordinate axes and then y = x or y = –x Enlarge shapes by a given scale factor from a given point; using positive and negative scale factors greater than one Enlarge shapes by a given fractional scale factor, e.g. 1/2, 3/2, 1/4 Understand that shapes produced by translation, rotation and reflection are congruent to its image Combine transformations and describe combined transformations. Use the relationship between distance, speed and time to draw, interpret and solve problems of distance–time graphs including finding the gradient and knowing that average speed is the gradient of the line. Convert between hours and fractions of an hour to minutes, and form fractions of a minute to seconds. Convert between metric units of speed e.g. km/h to m/s Draw and solve problems using real life graphs (Car hire, bills with fixed charges, conversion graphs etc) Know that density is found by mass ÷ volume Use the relationship between density, mass and volume to solve problems, e.g. find the mass of an object with a given volume and density Convert between metric units of density e.g. kg/m to g/cm Substitute positive and negative numbers into simple algebraic formulae including formulae involving powers and roots Change “word” formulae into algebra Change the subject of a formula (Use function machine to help) Generate a formula by working backwards through a problem e.g. given y = 3d + 4, find d. Summer Term Measures: Speed, density and conversion graphs 6-8 Algebra: Formulae 4–6 C D D D/C C Candidates must tessellate at least 6 shapes Candidates lose marks because they do not describe properly or fully, or they confuse transformation. C NRICH Tessellating transformations a very interesting activity on combined transformations C C C B C B GCSE Mathematics - Medium Term Plan Link to science – gradient gives average speed or velocity. Candidates frequently cannot convert 3.4 hrs into hours and minutes, or 3.4 minutes into minutes and seconds. Like wise – they also have difficulty with km/h to m/s It is important that students know where formula are used, and the cross curricular link with science is made FM: Mobile phones and FM: Teacher notes GCSE EDEXCEL Linear Higher Tier SOW for W1 General Topic Summer Term, Year 10 Number: Ratio, proportion and scale No. of lesson 8-10 Geometry & measures: Surface area and volume 6 Objectives Students should be able to … Appreciate that e.g. the ratio 1:2 represents 1/3 and 2/3 of a quantity and write a ratio as a fraction. Divide quantities in a given ratio, e.g. divide £20 in the ratio 2:3 Work backwards to find a quantity e.g. Jack and Jill shared a lottery win in the ratio of 4:7; Jill got £560, what was the total lottery win? Write ratio’s in the form 1:n and n:1 Solve problems involving unitary ratio, e.g. Best buys and recipes. Solve problems involving indirect proportion. Work out the real distance from a map, e.g. Find the real distance represented by 4 cm on a map with scale 1:25 000 Work out the distance on a map for a given real distance and scale Solve problems involving scale drawing. Use formulae to calculate the volumes of cuboids and right-prisms. Use formulae to calculate the surface area of cuboids and right-prisms. Use formulae to calculate the volume and surface area of a cylinder. Solve a range of problems involving surface area and volume, e.g. given the volume and length of a cylinder find the radius Convert between units of volume (e.g. m3 to cm3) Grade D/C Notes FM style questions must be practiced. D/C Suggested Enrichment / FM NRICH The Garrison – problem involving direct proportion C FM: Planning a dinner party and Teacher notes C B B B YEAR 10 WORK EXPERIENCE – 1 WEEK Summer Holiday GCSE Mathematics - Medium Term Plan FM questions – best packaging, better volume. Candidates classically convert m3 to cm3 wrong. They think they just add two zeros. GCSE EDEXCEL Linear Higher Tier SOW for W1 YEAR 11 The number of lessons allocated is a guide. It is important to enrich the curriculum and ensure Functional Mathematics is embedded throughout the topics. YEAR 11 Mock Exams are first week of December General Topic Statistics: Averages for large sets of data. Probability No. of lesson 4-5 6-8 Autumn Term Year 11 Objectives Students should be able to … Find the mean and median of data given - ungrouped frequency table Find an estimate for the mean of data - grouped frequency table Find the modal class and the class which the median lies in a grouped frequency table. List all the outcomes from mutually exclusive events, e.g. from two coins, two dice using sample space diagrams (SSD) Know that if the probability of an event occurring is p than the probability of it not occurring is 1 – p Find estimates of probabilities by considering relative frequency in experimental results and know that the more an experiment is repeated the better the estimate of probability Complete two way tables and calculate probabilities from these. Know that the probability of A or B is P(A) + P(B) Know that the probability of A and B is P(A) P(B) Draw and use tree diagrams to solve probability problems (including examples of non-replacement) Grade D C C Notes Estimated mean from grouped frequency – candidates of ten lose marks as they forget to do the mid class interval C Candidates often give probabilities as a ratio – they lose all marks for this C D B B Need to know that SSD and tree diagrams are ways of recording all outcomes, and can be used to find probabilities Suggested Enrichment / FM FM: Fishing competition NRICH The Better Bet NCETM Fair game? – Activity involving a game where relative frequency can be calculated. FM: Fairground and FM: Teacher notes Candidate may have to draw tree from scratch now Geometry: Pythagoras’ theorem 4-6 Use Pythagoras’ theorem to find unknown lengths in right angled triangles. Use Pythagoras to find the height of an isosceles triangle. Solve word problems involving right angled triangles, including height of isosceles triangles. C Review squares and square roots. B Teacher discretion for h of triangle in isosceles. GCSE Mathematics - Medium Term Plan One old Greek – discovering Pythagoras GCSE EDEXCEL Linear Higher Tier SOW for W1 General Topic Algebra: Linear functions y = mx + c No. of lesson 8 Algebra: Index notation 4–5 Autumn Term Number: Standard form 4-6 Objectives Students should be able to … Substitute values of x into linear functions to find corresponding values of y, by completing a table of values. Plot points for linear functions on a coordinate grid and draw the corresponding straight lines where y is given explicitly in terms of x (y = 3x + 4), x + y = k, and ax + by = K types using cover up method. Interpret m and c as gradient and y-intercept in linear functions, and understand effects of changing these values. Understand that the graphs of linear functions are parallel if they have the same value of m Name equation of line direct from graph, draw graph using gradient and intercept method. Calculate the gradient using difference in y/difference in x Identify if points lie on a given straight line Solve simultaneous equations graphically. Know squares and roots up to 20, and cubes and roots up to 10 Know that square numbers have two square toots, one positive and one negative. Use index notation for squares, cubes and powers of 10. Use index rules to simplify and calculate numerical expressions involving powers, e.g.33 35 = 38, (23 25) 24, (4a3 b2c)/2a2 bc, 40, (2a2)3, etc Grade Notes C (Note – there may not be a table given in the exam, so students must be able to do this themselves) Understand the standard form convention Convert large and small numbers to, and from, standard form Calculate with numbers given in standard form with, and without, a calculator. Solve word problems involving standard index form Round numbers given in standard form to a given number of significant figures B B B C Suggested Enrichment / FM Use Autograph to investigate straight line graphs. B Link gradient of line as being average speed or velocity in speed or velocity graphs – used commonly in science. D/C B B Mock Exams First week of December XMAS BREAK GCSE Mathematics - Medium Term Plan Link to use in science. Ensure students can read standard form answers from calculators, as some give 4-5 as answer – candidate needs to know this means 4 x 10-5 FM: Oil crisis and teacher notes GCSE EDEXCEL Linear Higher Tier SOW for W1 General Topic No. of lesson Statistics: Representing and interpreting data – cumulative frequency & box plots 5–7 Algebra: drawing quadratic, cubic graphs 4-5 Spring term Geometry: Similar shapes 4-5 Algebra: Inequalities & regions 6 Algebra: Quadratic functions 4 Geometry: Sine, cosine and tangent 6 Objectives Students should be able to … Draw a cumulative frequency table for grouped data (using the upper class boundary) and understand the rationale for using one. Draw a cumulative frequency curve for grouped data Use a cumulative frequency diagram to find estimates for the median, quartiles and interquartile ranges of a distribution Use a cumulative frequency diagram to solve problems, e.g. how many greater than a particular value. Draw a box plot from a cumulative frequency diagram Be able to draw a box plot directly from given data. Compare dual box lots to make inferences about distributions Know and recognise the general shapes of quadratic, cubic graphs. Accurately draw quadratic, cubic curves. Know the points where the quadratic curve crosses the axis are the solutions. Given an x or y value – be able to find the other co-ordinate by reading from the quadratic graph. Use integer and non-integer scale factors to find the length of a missing side in each of two similar shapes, given the lengths of a pair of corresponding sides including similar triangles Communicate clearly whether two 2D shapes are mathematically similar or not. Know when two triangles are congruent Identify the solution set on a number line for linear inequalities. Write down the integer solutions that satisfy a linear inequality. Rearrange and solve linear inequalities in one variable. Draw the graphs of linear inequalities in two variables and interpret the solution sets given by regions in the coordinate plane, or to identify all the integer coordinates with crosses Expand and simplify expressions involving two pairs of brackets Solve quadratic equations by factorising a = 1 Use trigonometric ratios (sin, cos and tan) to calculate angles in rightangled triangles Use the trigonometric ratios to calculate unknown lengths in rightangled triangles Calculate the angle of elevation and depression using the trigonometric ratios. Grade Notes C B Use of ICT for drawing graphs. B B When comparing: Emphasise that actual statistics must be given in answers, e.g. boys had bigger median – 0 marks. Boys had larger median at 23 to girls 19 – 1 mark. B B B Often lose a mark as curve has a “flat” or “pointed” bottom C Suggested Enrichment / FM Algebra: Simultaneous equations; drawing quadratic, cubic and reciprocal graphs FM: Scale models and teacher notes B C B NRICH Marbles – how many of each in the bag? Uses inequalities to set up the problem. C B B Trig beginnings – worksheet investigating RA triangles in circles. (1) B GCSE Mathematics - Medium Term Plan Make a clinometer – then take them outside (1) GCSE EDEXCEL Linear Higher Tier SOW for W1 Optional Target teaching topics from mock examination analysis here. Following targeting teaching from Mock results – either begin Note: Teacher’s must ensure 4 weeks available for GCSE revision OR use Teacher discretion for teaching the revision before examinations begin. following topics: Algebra: Simultaneous equations Geometry: Circle theorems Number: Limits of accuracy 3-4 4-6 3 Solve algebraically two simultaneous equations Use circle theorems to find unknown angles and explain their methodquoting the appropriate theorem Students need to be able to find and explain: The angle subtended at the centre of the circle is double that subtended at the circumference, when from the same arc. Angles subtended at the circumference from the same arc are equal. Angles subtended at the circumference from a diameter are 90˚ Opposite angles in a cyclic quadrilateral add up to 180˚ Tangents from an external point are equal in length. Understand and calculate the limit of accuracy, knowing it is +/half a unit. Find when numbers are given to a specific degree of accuracy, the upper and lower bounds of perimeters and areas of shapes. B B B In exam – candidates often lose marks for inappropriate explanations. They cannot say “arrowhead”, “bow” to explain their answers– they must be specific. NRICH Partly Circles Triangles in Circles Subtended Angles Right Angles B Ensure they are familiar with the “sneaky” arrowhead – it is an examiners favourite. B Mainly knowing +/- half a unit at this level B/A Summer Term – Examination revision. GCSE Exams begin mid-may so many students will not be in lessons. The mathematics examinations are usually the first week after half term. GCSE Mathematics - Medium Term Plan