Y13 A level Mathematics 28 Algebra 2 weeks Teaching objectives a Review expanding, collecting, factorisation from AS b Simplify rational expressions using factorising and cancelling c Review algebraic division and factor theorem d Extend algebraic division e Introduce partial fractions f More complicated partial fractions g Review binomial expansion for positive integer h Extend binomial expansion to any rational n and understand validity i Use of partial fractions with binomial expansion j Other Uses of partial fractions eg integration, series Resources for advance preparation: Old edexcel textbook references: Core 3 Chapter 1 (algebraic fractions) and Core 4 Chapter 1 (partial fractions) and 3 (binomial expansion). Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework 1 This starter connects multiplication and factorising with division Review expanding and factorisation from AS (if needed) Follow up starter to highlight any misconceptions or problems Give students mini whiteboards and put up questions to check basic concepts expand two and three brackets expand brackets with more than two terms in them factorise quadratics and simple cubics recognise difference of two squares factorise quadratics with coefficient more than one complete the square Follow up problem areas with consolidation exercises from your old Core 1 textbook. Self marking factorising online tool! Key Question for Plenary: How does factorising and completing the square enable you to sketch the graph of a quadratic function? Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework 2 If you didn’t do lesson 1 then use this starter now: Simplify rational expressions using factorising and cancelling Go through particular techniques which can be helpful when Extend - question on addition and subtraction which require factorising first. Self marking algebra cancellation online tool
This starter connects multiplication and factorising with division Otherwise: Give students mini whiteboards: Put up problems including numerical fractions eg 2/3 * ¾* 4/5*5/6 etc and the classic algebra misconceptions, eg (2+x)/(1+x) Plus some examples which will cancel if they factorise Eg (2x + x2)/(x3 – 3x) Also some with fractions in numerator and/or denominator trying to simplify an algebraic fraction – ie factorising or multiplying through top and bottom by a number or algebra. Give examples for students to practise. Ask students to write down the four operations and how they deal with them with numerical fractions. Then ask them to discuss what is the same or different with algebraic fractions. Give examples of adding, subtracting, multiplying and dividing. This RISP shows how to use Arithmagons to help with doing and undoing algebra. Use figures 9 and 10. Consolidation: Use old Core 3 textbook or MEI integral exercise Level 1 Plenary: Ask students to discuss common errors which they may make when dealing with algebraic fractions and document these as a class. Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework 3 This starter looks at remainders when you divide Review Algebraic Division and Factor Theorem from AS (if needed) Choose a few of the division problems from the starter and ask students to do the division using both the (reverse multiplication) grid method and long division. Extension: Follow up problem areas with consolidation exercises from your old Core 2 textbook or MEI integral exercise Level 1 Plenary: