Year 11 Scheme of work Autumn Term Half term 1 Foundation level

Transcription

1 Year 11 Scheme of work Autumn Term Half term 1 Foundation level

2 Topic Title: Transformations 5 lessons Routemap: 3 Year Foundation Pre requisite knowledge: From the Key stage 3, students will already have some experience of carrying out transformations of shapes in two-dimensions. The new Key Stage 3 Programme of Study states that pupils should be taught to: identify properties of, and describe the results of, translations, rotations and reflections applied to given figures identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids Keywords: congruent, similar, co-ordinates, co-ordinate axes, -axis, -axis, line, line, rotation, reflection, translation, enlargement, scale factor, centre of rotation, centre of enlargement, vector, column vector, horizontally, vertically, origin, angle of rotation, mirror line, line of reflection, ratio, direction of rotation, clockwise, anticlockwise, reverse transformation. Candidates should be able to: Basic Foundation Content: identify, describe and construct congruent and similar shapes, including on co-ordinate axes, by considering rotation, reflection, translation and enlargement (G7) describe translations as 2D vectors (G24) Number of lessons required: 5 lessons. Additional Foundation Content: including fractional scale factors (G7) Topic commentary: In the current GCSE specification, students are required to recognise reflection and rotation symmetry of 2D shapes (G1.6) and understand and use congruence and similarity (G1.8). They also are required to describe and transform 2D shapes using single or combined rotations, reflections, translations or enlargements by a positive scale factor and determine properties that are preserved under particular transformations (G1.7). The specification also indicated that vectors would be used to represent translations. Therefore much of the content of the new Foundation GCSE is the same as for the previous specification. However, there are some new aspects which are included in the Foundation tier content which were previously on the Higher tier only:

3 Fractional scale factors, which is listed in the new additional Foundation content. Combinations of transformations are technically Higher tier content, however it could be covered as extension activities/questions. It is worth noting that negative scale factors are still Higher tier only. Congruence and similarity were covered at the end of year 10. Therefore, the terms congruent and similar will be mentioned here. Lesson Plans available Notes AQA 8 lesson plans available Pearsons 6 lessons available ( ) Lesson Assessment Problem Solving activity

4 Topic Title: Sequences 3 lessons (Revision from end of year 9) Pre requisite knowledge: Algebraic notation Substitution Candidates should be able to: Basic Foundation Content: Generate terms of a sequence from either a term-to-term or a position-to-term rule including from patterns and diagrams (A23) Recognise and use: sequences of triangular, square and cube numbers(a24) simple arithmetic progression,(a24) other recursive sequences as defined in the question (A24) Deduce expressions to calculate the nth term of a linear sequence (A25) Route Map; 3 Year Foundation Keywords: Sequence, Pattern, Rule, Term, Term-to-term rule Position-to-term rule, n th term Number of lessons required: 3 lessons Additional Foundation Content: Recognise and use: Fibonacci sequences,(a24) quadratic sequences, (A24) and simple geometric progressions (r n where n is an integer and r is a rational number > 0) (A24) Topic commentary: This topic should have been taught at Key Stage 3 and at the end of year 9 so it will be revision. Lesson Plans available Notes AQA 4 lesson plans available Pearsons 2 lessons available (5.7,5.8) Lesson Assessment Problem Solving activity

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6 Topic Title: Algebra: Quadratics, Rearranging Formulae and Identities 8 lessons Route Map: 3 Year Foundation Pre requisite knowledge: What a surd is. This can be covered in the intro lesson if not. How to multiply a single term over a bracket. How to factorise a linear expression. How to collect like terms. How to calculate area and perimeter of rectangles or compound shapes made up of rectangles. Students will hopefully have seen the skill of substitution before but might need a recap. How to and why you can simplify a fraction. Candidates should be able to: Basic Foundation Content: Keywords: Simplify, expand, bracket, factorise, like terms, expression, surd, square root, irrational number, quadratic, area, perimeter, coefficient, binomial, FOIL, difference of two squares/dots, sum, product, index, indices, power, substitute, formulae, formula, variable, positive, negative, rearrange, the subject, operation, inverse, equation, identity, function, input, output, equivalence, equal. Number of lessons required: 8 lessons simplify and manipulate algebraic expressions by: collecting like terms (A4) multiplying a single term over a bracket (A4) taking out common factors (A4) simplifying expressions involving sums, products and powers, including the laws of indices (A4) understand and use standard mathematical formulae (A5) rearrange formulae to change the subject (A5) where appropriate, interpret simple expressions as functions with inputs and outputs (A7) Additional Foundation Content: simplify and manipulate algebraic expressions (including those involving surds) by: expanding products of two binomials (A4) factorising quadratic expressions of the form, including the difference of two squares (A4)

7 know the difference between an equation and an identity (A6) argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments (A6) Topic commentary: Equations, Expressions and Identities content from A6 was previously on the Higher Tier and this is expected to be found challenging by a majority of Foundation Tier students. Students will also find it hard to rearrange formulae when the unknown is on both sides or is under a square root. Students also now need to be able to expand a product of binomials. Common misconceptions in this unit are: expanding the product of two binomials incorrectly either due to: o adding values to get the last term incorrectly, o adding coefficients of the first x values (rather than multiplying), o incorrectly applying addition with negative numbers to get the incorrect middle term, o incorrectly applying the negative multiply by negative equals a positive rule to get the incorrect final term, expanding a squared bracket by just squaring each term and summing together, factorising a quadratic expression by just writing the two numbers seen in brackets, simplifying algebraic expressions by collecting everything together rather than only like terms, incorrectly remembering the laws of indices e.g. multiplying powers instead of adding etc. An intro lesson will help remind students of the basics of what a surd is, how to multiply a term over a bracket and factorise a linear expression into a bracket and how to simplify an expression by collecting like terms. FOIL (First Outer, Inner, Last) is a good way of remembering a correct order of expanding a product of two binomials. Students are often taught the grid method at primary school and this can be used to help expand brackets correctly. Encouraging students to check their work on factorising a quadratic by expanding the brackets again is a good way of reinforcing the link between the two operations; this can also be re-applied to how to check they have expanded correctly (does their resulting expression factorise back into the brackets they started with). Factorising the difference of two squares is not particularly difficult once the skill has been learnt but is difficult in that it uses a different method to that of factorising other quadratic expressions. Lesson Plans available Notes AQA 8 lesson plans available Pearsons 2 lessons available (16.1, 16.4) Lesson Assessment Problem Solving activity

8 Topic Title: Inequalities 3 lessons Route Map: 3 Year Foundation Pre requisite knowledge: Identify numbers that satisfy an inequality. Candidates should be able to: Basic Foundation Content: Keywords: Integer, inequality Number of lessons required: 3 lessons Solve linear inequalities in one variable (A22) Represent the solution set on a number line (A22) Additional Foundation Content: This lesson does not contain content that is new to the Foundation tier. Topic commentary: Some students may forget what is meant by the term integer, or forget that 0 is an integer value. Remind students that an integer is a whole number. Display an integer number line to help them. Using inequality signs incorrectly. Discuss ways of remembering the meaning of inequality signs. For example, the larger number is on the wider side of the sign. Some students may forget to do the same thing to all three parts of a two-sided or double inequality. Suggest students split the inequality into two separate inequalities and remind them that they will still need to do the same to both sides when solving them. Students may forget to change the direction of the inequality sign when multiplying or dividing by a negative number. Encourage students to check their answers using substitution. Remind them that when there is just one inequality sign, they can remove a negative unknown by adding it to both sides of the inequality. Lesson Plans available Notes Pearsons 2 lessons available (5.4, 5.5) Lesson Assessment Problem Solving activity

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10 Year 11 Scheme of work Autumn Term Half term 2 Foundation level Topic Title: Algebra and graphs 6 lessons ( (A17) Revisit from year 9 ) Route Map: 3 Year Foundation Pre requisite knowledge: Candidates should be able to: Basic Foundation Content: Keywords: Number of lessons required: 6 lessons Solve linear equations in one unknown algebraically Including those with the unknown on both sides of the equation Find approximate solutions using a graph (A17) Translate simple situations or procedures into algebraic expressions or formulae derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution (A21) Additional Foundation Content: including those with the unknown on both sides of the equation Lesson Plans available Notes Pearsons (3 lessons available) Lesson Assessment Problem Solving activity

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12 Topic Title: Solving Quadratic Equations 6 lessons Routemap: 3 Year Foundation Pre requisite knowledge: Expanding products of two binomials Factorising quadratic expressions of the form x 2 + bx + c, including the difference of two squares. Solve linear equations in one unknown algebraically Substitute numerical values into formulae and expressions Calculate with roots, and with integer indices Work with coordinates in all four quadrants Plot and interpret graphs Candidates should be able to Additional Foundation Content: Solve Quadratic equations algebraically by factorising (A18) Find approximate solutions using a graph (A18) Keywords: Quadratic Factorise Substitution Rearrange Number of lessons required: 6 lessons Topic commentary: This topic is new to the Foundation tier and will be quite challenging for Foundation students. Ensure lots of practice factorising quadratics containing only positive values so students can become confident with the concept before introducing any negative terms. Encourage students to write the factor pairs down individually, and then look at each pair to see if they add to make the coefficient of x, this will ensure that they have a logical approach for the more complicated quadratics which have one or more negative term. Factorising quadratics with negatives requires a good understanding of directed numbers so attempt to develop these skills throughout the topic. Students should be checking their solutions whenever possible, by expanding and simplifying their double brackets when practising factorising and by substituting their solution(s) back into the equation when solving quadratics. Although drawing quadratic curves is not covered in this topic, it is worth ensuring that students are clear that by substituting different x values, coordinate points are generated which can be plotted and joined together with a smooth curve to create the graph. Lesson Plans available Notes AQA 6 lessons available Pearsons 3 lessons available (16.1,16.4,16.5) Lesson Assessment Problem Solving activity

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14 Topic Title: Quadratic graphs 3 lessons Route Map: 3 Year Foundation Pre requisite knowledge: Be able to square terms. Candidates should be able to: Basic Foundation Content: Keywords: line of symmetry, parabola Number of lessons required: 3 lessons A12 Recognise, sketch and interpret graphs of quadratic functions A11 Identify and interpret roots, intercepts and turning points of quadratic functions graphically Deduce roots algebraically including the symmetrical property of a quadratic Additional Foundation Content: Identifying and interpreting roots, intercepts, turning points of quadratic functions graphically, and deducing roots algebraically are all new to the Foundation tier.

15 Topic Commentary Objectives Plot graphs of quadratic functions. Recognise a quadratic function. Use quadratic graphs to solve problems Common errors and misconceptions Drawing lines y = (a number) incorrectly as x = (a number). Check if the line crosses through the x-axis (so, the line will be x = ) or the y-axis (so, the line will be y = ). Drawing a parabola with feathered, double or dot to dot lines. Students should aim to draw a single smooth curve. This takes practise, but drawing from the inside of the curve and moving the paper round can help to improve the outcome Lesson Plans available AQA Notes 0 lesson plans available yet Pearsons 2 lessons available (16.2, 16.3) Lesson Assessment Problem Solving activity

16 Mock exams and revision. 2 weeks Year 11 Scheme of work Spring Term Half term 1 Foundation level Topic Title: Sketching graphs 3 lessons Route Map: 3 Year Foundation Pre requisite knowledge: Recognise the shape of linear and quadratic graphs. Candidates should be able to: Basic Foundation Content: Keywords: Cubic function, asymptotes Number of lessons required: 3 lessons Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions and the reciprocal function with (A12) Additional Foundation Content: All the content in this lesson is new to the Foundation tier. Students often find drawing curved graphs tricky, but they will already have drawn quadratic graphs Topic commentary: Common errors and misconceptions

17 Calculating y values inaccurately in table of values and then plotting them as part of the graph, not realising they are incorrect. Encourage students to sketch the shape of the graph they expect before they begin. If any of their plotted points do not fit the expected shape, they should go back and check their calculations. Lesson Plans available AQA Pearsons Notes 0 lesson plans yet 1 lesson plan (20.1) Lesson Assessment Problem Solving activity

18 Topic Title: Direct and Inverse Proportion 3 lessons (Ratio and proportion was covered at the end of year 9) Routemap: 3 Year Foundation Pre requisite knowledge: Apply the four operations, including formal written methods, to decimals Understand and use place value (e.g. when calculating with decimals) Plot and interpret graphs Substitute numerical values into formulae and expressions Solve linear equations in one unknown algebraically Candidates should be able to: Basic Foundation Content: Solve problems involving direct and inverse proportion, including graphical and algebraic representations (R10) Keywords: Proportion, Direct, Unitary, Inverse, Constant of proportionality, Variables Number of lessons required: 3 lessons. Additional Foundation Content: Understand that is inversely proportional to is equivalent to is proportional to (R13) Interpret equations that describe direct and inverse proportion (R13) Recognise and interpret graphs that illustrate direct and inverse proportion (R14) Topic commentary: This is a new topic to the Foundation Tier and some aspects (particularly inverse proportion) will quite challenging for some students. Ensure lots of repetition with constant review of what is happening and why. This is a topic which can easily be learned by repeating a process but this will not help the Foundation students in the long term with their broader understanding, so asking students to explain what is happening to each other and the class teacher throughout will help their understanding and application for later lessons in the topic. To extend each lesson, students should be encouraged to devise their own examples; this is a great way to assess understand and highlight misconceptions. The approach to this series of lessons is to fully grasp direct proportion before introducing inverse proportion; it could be equally effective to mix up the lessons to teach both concurrently if the class are able. Lesson Plans available Notes AQA 8 lesson plans available Pearsons 1 lesson available (14.5) Lesson Assessment

19 Problem Solving activity

20 Topic Title: Trigonometry 6 lessons Routemap: 3 Year Foundation Pre requisite knowledge: Simplifying fractions. Candidates should be able to: Basic Foundation Content: Keywords: Hypotenuse, opposite, adjacent Number of lessons required: lessons. Additional Foundation Content: G20 Know and use the trigonometric ratios Apply them to find angles and lengths in right-angled triangles in two dimensional figures R12 Compare lengths using ratio notation

21 Topic commentary: Trigonometry was not previously covered in the Foundation tier. It is relatively difficult conceptually and so care is needed to provide adequate support to students. Lesson Plans available Notes AQA 0 lessons available Pearsons 5 lessons available ( ) Lesson Assessment Problem Solving activity

22 Topic Title: Growth and decay 4 lessons Routemap: 3 Year Foundation Pre requisite knowledge: Writing numbers in index form Calculating percentages of amounts Increasing and decreasing amounts by a given percentage Using multipliers Candidates should be able to: Basic Foundation Content: Keywords: Index form indices growth decay appreciates appreciation depreciates depreciation increase decrease set up solve interpret exponential growth exponential decay compound interest Number of lessons required: 4 lessons. Additional Foundation Content: Set up, solve and interpret the answers in growth and decay problems, including compound interest. (R16) Topic commentary: This topic is new to Foundation Tier and some of the work will be quite challenging for some of the Foundation students so a steady and personalised learning approach would be beneficial. It is worth reviewing the use of indices and solving linear equations as an introduction to the topic so students are familiar with the concept of indices and how they affect the value of numbers. It will also help to eradicate the main misconception that 5 2 = 5 2 and therefore students give the answer 10 instead of calculating 5 5 to give 25. Students at Foundation Tier often find solving equations difficult. It often helps to use flow diagrams to solve linear equations or the cover up approach. Students will need reminding that when drawing the graphs, the points should be joined using a smooth curve. Lesson Plans available Notes AQA 4 lessons available Pearsons Only 1 lesson found (20.2) Lesson Assessment Problem Solving activity

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24 Topic Title: Vectors 4 lessons Routemap: 3 Year Foundation Pre requisite knowledge: Students need to know how to add and subtract negative numbers and work with co-ordinates in four quadrants. They should also know properties of plane shapes such as parallelograms. Candidates should be able to: Basic Foundation Content: Keywords: Number of lessons required: 4 lessons. Additional Foundation Content: Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors (G25). Topic commentary: This topic is new at foundation level. Students may confuse column vectors with co-ordinate pairs and may struggle with the addition and subtraction of negative numbers. It would be helpful to make links with the topic of transformations as this is a context in which students will have come across vectors earlier in the GCSE course (start of year 11). Throughout the topic, the correct use of notation should be emphasized, such as vectors being expressed in bold font in printed documents and with an arrow of the form. Lesson Plans available Notes AQA 8 lessons available Pearsons 2 lessons ( ) Lesson Assessment Problem Solving activity

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29 Year 9 and 10 Overviews

30 Year 11 Overview