Intermediate GCSE Course (C/B) GCSE Maths Intermediate Scheme of Work

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1 GCSE Maths Intermediate Scheme of Work Please ensure that you are fully conversant with the details of the new specification. This is our adapted early entry course and avoids students having to repeat foundation material they have mastered in years 7,8,9. It is possible for students to move on to the Higher course after Year 11 mock exams. Others will follow it as a 2-year course, ensuring that they cover all of the Foundation material. General Topic No. of Hours Objectives By the end of the module students should be able to Notes Block 1 Angles 4 Angles recall and use properties of angles at a point, angles on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex distinguish between acute, obtuse, reflex and right angles use parallel lines, alternate angles and corresponding angles understand the consequent properties of parallelograms and proof that the angle sum of a triangle is 180 degrees understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices use angle properties of equilateral, isosceles and right-angled triangles understand congruence explain why the angle sum of a quadrilateral is 360 degrees Solve and justify solutions to multi-step problems Fractions 4 Fractions Calculate a given fraction of a given quantity, expressing the answer as a fraction The key to this topic is ensuring the students are really secure with all the different angle rules, being able to state them. Applying the rules to solve multi-step questions (this was a very common question on the Edexcel papers so there should be a lot of questions for you to use) Calculating exactly with fractions is probably something we will do during other topics not AQA GCSE Maths Intermediate course C/B 1

2 Formulae and Expressions Rearranging Formulae Express a given number as a fraction of another Add and subtract fractions by writing them with a common denominator (Including mixed numbers) Multiply fractions (Including mixed numbers) Divide fractions (Including mixed numbers) Calculate exactly with fractions 4/5 Formulae and expressions Revision of expressions collecting like terms Expanding single brackets Factorising single brackets Use and generate formulae in context Substitute positive and negative numbers into a formula. Understand and use the concepts and vocabulary of expressions, formulae, inequalities, terms and factors Argue mathematically to show algebraic expressions are equivalent. Use algebra to support and construct arguments. 2/3 Rearranging Formulae Change the subject of a formula no longer states where unknown only appears once. necessarily teach it as part of this unit? I have moved expanding and factorising single brackets into this unit as students are going to need to be able to factorise to rearrange formulae. However this should just be a review/starters as this is covered well in the KS3 scheme. It is recommended you revisit negative numbers at the start of formulae (possibly as starters) You can also link this topic nicely into fractions by using giving students them to substitute into a formula. For algebraic reasoning you can link this beautifully to geometric reasoning and revisit angles. Important to note that now we need to cover where the subject appears more than once. AQA GCSE Maths Intermediate course C/B 2

3 Ratio 3 Ratio Understand and use ratios in appropriate contexts (maps, scale diagrams and scale factors) Divide a quantity in a given ratio. Identify and work with fractions in ratio problems Hence why we covered factorising in the previous unit. Can link nicely back to fractions unit when working with fractions in ratio problems Proportion 4 Proportion Solve problems involving direct (teach as Y/X = k mymaths) and inverse proportion, including graphical and algebraic representations Understand that X is inversely proportional to Y is equivalent to Y is proportional to 1/y (teach as XY = k mymaths) Interpret equations that describe direct and inverse proportion Recognise and interpret graphs that illustrate direct and inverse proportion 4 Assessment 1 (Preparation/Review and Follow Up) This is a completely new unit in the Foundation Scheme so make sure you look carefully at the content. Using tables will help support students identifying the multiplier. AQA GCSE Maths Intermediate course C/B 3

4 General Topic No. of Hours Objectives By the end of the module students should be able to Notes Block 2 Decimals 2 Decimals Solve problems involving multiplication and division by decimals with up to two decimal places Work interchangeably with terminating decimals and their corresponding fractions Accuracy, 1/2 Accuracy, Estimation and checking Check solutions to calculations using various methods including Estimating approximating (including answers obtained using technology), using inverse and Checking operations and recognising the effect of multiplying and dividing by numbers less than one and greater than one Estimate answers using appropriate techniques. Round numbers and measures to an appropriate degree of accuracy dp or sig fig. Use inequality notation to specify simple error intervals due to truncation or rounding. Apply and interpret limits of accuracy Transformatio ns Powers 4 Powers 5 Transformations Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation(described as 2D vector) and enlargement including fractional scale factors (not negative) Carry out rotations, reflections and translation and combinations of these description of single equivalent transformation is higher Use positive integer powers and associated real roots (square, cube and Could teach this topic embedded within other topics ensuring students round correctly and check their answers so would not necessary spend a long time on as a unit as you would be constantly revisiting this topic. Remember to highlight key vocab of congruence and similar shape during this topic. Ensure students include all the relevant information when describing transformations. Knowing and using laws of indices including AQA GCSE Maths Intermediate course C/B 4

5 higher), recognise powers of 2,3,4,5 Calculate with roots and with integer indices Use reciprocals in calculations eg, (5 3 +7) (6 2-1). BIDMAS fractional and negative. Practise multiplying and dividing by powers of 10. Calculate with and interpret standard form Ax10 n (B) Primes 2 Primes, HCFs and LCMs Use and understand the terms highest common factor, lowest common multiple, prime number; Find the prime number decomposition of positive integers. Use this to calculate HCF and LCMs Equations 3 Equations Form and solve equations including those with the unknown on both sides of the equation Inequalities 2 Inequalities Form and solve simple linear inequalities in one variable and Represent the solution set on a number line Identify the inequality shown on a number line Percentages 3 Percentages Use percentages to compare proportion Find percentages of amounts Solve percentage problems involving increase and decrease including using a multiplier. Calculate the original amount (reverse percentages) Solve problems involving simple and compound interest (growth and decay) 4 Assessment 2 (Preparation/Review and Follow Up) No change, teach as we always have No change, teach as we always have ensuring they can solve all types of equations. Revisit expanding when solving equations involving brackets. No change, teach as we always have This topic should be well covered in the KS3 scheme, so you might need to spend more/less time depending on your group s prior knowledge. AQA GCSE Maths Intermediate course C/B 5

6 General Topic No. of Hours Objectives By the end of the module students should be able to Notes Block 3 Shapes 6 Shapes (Including Congruency and Similar Shapes) recall the essential properties and definitions of special types of quadrilateral and triangles Calculate the area of a triangle, parallelogram, trapezium and composite shapes. Classify quadrilaterals by their geometric properties Draw tessellations of simple shapes Construct and interpret plans and elevations of shapes Compare lengths area and volumes using ratio notation Use basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Find corresponding lengths in similar shapes Use angle fact, congruence etc to obtain simple proofs Pythagoras 3/4 Pythagoras theorem Recognise the relationship between the sides of a right angled triangle Be able to recall and use Pythagoras theorem to find a missing side of a right angled triangle Apply Pythagoras theorem to solve problems (eg: diagonal of a rectangle) I have put congruency and similar shapes here as I think it fits in nicely and allows us to review transformations, as well as providing the foundations for teaching trig later on. Review of ratio For proving congruency or using it for simple proofs we can link back to angles and revisit angle rules Discovery of the relationship always a nice way to introduce this topic. Where student struggle sometimes is in the applying to a situation where the right angled triangle is not obvious plenty of practise on this style of questions is required (there are plenty of these available on old AQA GCSE Maths Intermediate course C/B 6

7 Trigonometry 6 Trigonometry Know the right angle trig ratios Know exact values for sin and cos for 30 0, 45 0, 60 0, 90 0 and exact value of tan for 30 0, 45 0, 60 0 Be able to use the trig ratios to find missing lengths in right angled triangles Be able to use the trig ratios to find unknown angles in right angled triangles Solve real life problems Sequences 3 Sequences Recognise and use sequences of triangular, square and cube numbers and simple APs including Fibonacci style sequences, quadratic sequences and simple GPs. Deduce expressions to calculate nth term of a linear sequence. Edexcel papers if you need resources) To introduce this topic we need to use the link to similar triangles to introduce the trig ratios. Review of similarity to start and then you could use investigation to show the ratio between the sides of similar triangles is always the same and how this links to the trig ratios. When teaching this topic use this as an opportunity to showing students how to use their calculators correctly. Real life problems in trig often involve bearings so it would be good to review this topic Review of types of numbers. No longer just linear sequences so ensure that you cover finding the term to term rule for quadratic sequences and simple GPs. However from what I can find students will only need to find the nth rule of linear sequences. This is a topic that might not AQA GCSE Maths Intermediate course C/B 7

8 4 Assessment 3 (Preparation/Review and Follow Up) have been covered in year 9 due to the course so could require more time. General Topic No. of Hours Objectives By the end of the module students should be able to Notes Data 3 Describing data Calculate mean from grouped data Comment on and compare data sets. Compare data using appropriate measures of central tendency and spread, including consideration of outliers for discrete, continuous and grouped data. Review of finding averages and range of data needed (Starters) This is covered well at KS3 so should not need too much time spent on it. Block 4 Scatter Graphs Displaying Data 2/3 Scatter Graphs Interpret scatter graphs for discrete and continuous variables, understand the vocabulary of correlation, including positive, negative and no correlation. Be able to draw a scatter diagram from given data Use lines of best fit; make predictions, interpolate and extrapolate apparent trends, whist knowing the dangers of doing so, 1/2 Displaying Data Draw and interpret pictograms, bar charts and pie charts Due to Stem and Leaf and Frequency polygons AQA GCSE Maths Intermediate course C/B 8

9 Circles 4 Circles Compound rates recall the definition of a circle and the meaning of related terms, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment understand that the tangent at any point on a circle is perpendicular to the radius at that point. Solve problems involving area and circumference of circles including composite shapes use pi in exact calculations Calculate arc lengths, angles and areas of sectors of circles 2 Compound rates Understand and use rates and compound measures for speed/distance/time and mass/density/volume Include looking at travel graphs as this is a very common exam topic. 4 Assessment 4 (Preparation/Review and Follow Up) being removed this is left as a very small topic. These are also covered very well in the KS3 course so should not need a lot of time spent on them (depending on your group) Key vocab is important in this topic. Need to ensure we emphasis on leaving answers in exact form as this is new to this topic. Arc lengths and areas of sectors of circles will help revisit fractions. Again application in problem solving questions were common in the edexcel course so if you need resources on these you should be able to find some on the old papers. Mass/density/volume used to only appear on higher but now on foundation. Should be able to link these compound rates to science as students use them in this subject. Formulae triangles work very well for these. AQA GCSE Maths Intermediate course C/B 9

10 General Topic No. of Hours Objectives By the end of the module students should be able to Notes Block 5 Charts and 2 Charts and Tables Tables to use a 2 way table (distance charts or other) to extract information emphasis on constructing a two way table to organise data and solve a problem use of timetables to calculate times of trains etc. Probability 4 Probability Solve probability problems involving theoretical models or relative frequency Understand bigger sample size is closer to theoretical prob Solve problems where probabilities must sum to 1. Enumerate sets and combinations of sets systematically using tables, grids and venn diagrams Calculate the probability of independent and dependent events, including using tree diagrams and other representations and know the underlying assumptions Straight line Graphs 4 Straight lines plotting straight line graphs This topic was covered at the end of KS3 so how long you spend on the first 3 objectives will depend on your group but it should only require a review at the start of the topic. There is a lot on new content in this topic so ensure you are clear on what needs to be covered. Students will need to know the and/or rules when dealing with their tree diagrams. Straight line graphs are covered well in the KS3 AQA GCSE Maths Intermediate course C/B 10

11 Curves 2/3 Curves use the form y=mx+c to identify parallel lines find the equation of the line through two given points, or through one point with given gradient identify and interpret gradients and intercepts of linear functions graphically and algebraically Use graphs to find approximate solutions to real life problems Recognise, sketch and interpret graphs of quadratic, simple cubic and reciprocal function Identify and interpret roots, intercepts and turning points of quadratic functions graphically. Deduce roots algebraically(this is covered in the next topic (Quadratics) Plot graphs of simple cubic functions and the reciprocal function y = 1/x, recognise the characteristic shapes of these functions. Use graphs to find approximate solutions to real life problems Quadratics 3/4 Quadratics Expand double brackets, including those involving surds Factorise quadratics Solve quadratic equations of the form x 2 +bx +c by factorising (no rearrangement), including the difference of two squares. 4 Assessment 5 (Preparation/Review and Follow Up) course so you should not have to spend too much time on drawing. Good way to review coordinates and substitution. A review of expanding and factorising single brackets, collecting like terms and indices could all be revisited through starters during this topic. Link factorising and solving quadratics back to the graph of a quadratic covered in the last topic. AQA GCSE Maths Intermediate course C/B 11

12 General Topic No. of Hours Objectives By the end of the module students should be able to Notes Block 6 3D Shapes Surface Area and Volume Loci and Constructions Simultaneous Equations 4/5 3D Shapes, Surface Area and Volume Be able to name 3D shapes including properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres. construct and interpret plans and elevations of shapes Be able to identify the net of a 3D shape Solve problems involving the surface area and volume of prisms including cylinders Calculate the surface area and volume of spheres, pyramids, cones and composite solids. 3 Loci and constructions Apply loci to spatial problems involving shapes and paths use straight edge and compasses to produce standard constructions including the midpoint and perpendicular bisector of a line segment, the perpendicular from a point to a line, constructing 60 and 30 angles and the bisector of an angle. 4 Derive and solve an equation from a real life situations Derive two simultaneous equations from a real life situation Solve two linear simultaneous equations algebraically Solve two linear equations graphically Students really muddle these two skills up so plenty of practise needed with mixed questions. Also remember to emphasise students using the correct units for their answers. (Can also bring in review of converting between metric measures here) Revision of area of shapes (triangle, circle, parallelogram, trapezium and rectangles) Can use this as an opportunity to revise solving equations (starters) Graphically allows you to revisit straight line AQA GCSE Maths Intermediate course C/B 12

13 Vectors 2 Represent vectors in both column and diagram form Be able to add and subtract vectors Multiply a vector by a scalar 4 Assessment 6 (Preparation/Review and Follow Up) Mock?? graphs Can use this as an opportunity to revise translations by linking back to the topic where they used vectors to describe translations AQA GCSE Maths Intermediate course C/B 13