polynomials Now give a few problems where there is no remainder for them to work through. See if they remember the factor theorem and work through what it means from both directions ie, if f(p) = 0 then (x-p) is a factor, and if (x-p) is a factor, then f(p) = 0 Extend to remainder theorem (not sure if this is still on the syllabus but I would do it anyway) and compare a long division method giving remainder, with using the remainder theorem for an example with a linear denominator. 4 Extend algebraic division Extension: Follow up problem areas with If not used in lesson consolidation exercises from 3, use this starter Ask students to give examples of top heavy fractions, they your old Core 3 textbook or MEI now: will start with numeric examples but get them to think about integral exercise Level 1 or 2 what top heavy means for an algebraic fraction leading to – looking at the highest power (degree) of numerator vs denominator. Plenary: This starter looks at Use division to help sketch a remainders when From the starter form an idea of how the degree of the graph of you divide answer (quotient) and the degree of the remainder relates to y = (2x 5)/(x 3) – – polynomials the relative degree of the numerator and denominator. Answer if a polynomial of degree n is divided by a – polynomial of degree r then the quotient has degree at the most n r and the remainder has degree at most r-1 – Give examples for students to work through with top heavy algebraic division using one or more of three methods: long divison, equating coefficients (ie remainder theorem) or inspection. Starter Main teaching Notes Consolidation/Plenary Including key questions, key teaching points, models and Including Support and Including key questions and resources Extension homework 5 Introduce partial fractions This may throw up Consolidation: MEI Students work in pairs to algebraically show the equivalence problems with using Use exercises in old C4 of the first set of graphs plotted in the starter. common denominators in textbook or MEI exercise level 1 tasks A2 Core Students to demonstrate solutions. algebra so support by 9 Teacher leads students through a method to find coefficients, going through some If you subscribe to MEI there is if this has not come out already or brings together methods. examples of adding an Always, Sometimes, Never
polynomials Now give a few problems where there is no remainder for them to work through. See if they remember the factor theorem and work through what it means from both directions ie, if f(p) = 0 then (x-p) is a factor, and if (x-p) is a factor, then f(p) = 0 Extend to remainder theorem (not sure if this is still on the syllabus but I would do it anyway) and compare a long division method giving remainder, with using the remainder theorem for an example with a linear denominator. 4 If not used in lesson 3, use this starter now: This starter looks at remainders when you divide polynomials Extend algebraic division Ask students to give examples of top heavy fractions, they will start with numeric examples but get them to think about what top heavy means for an algebraic fraction – leading to looking at the highest power (degree) of numerator vs denominator. From the starter form an idea of how the degree of the answer (quotient) and the degree of the remainder relates to the relative degree of the numerator and denominator. Answer – if a polynomial of degree n is divided by a polynomial of degree r then the quotient has degree at the most n – r and the remainder has degree at most r-1 Give examples for students to work through with top heavy algebraic division using one or more of three methods: long divison, equating coefficients (ie remainder theorem) or inspection. Extension: Follow up problem areas with consolidation exercises from your old Core 3 textbook or MEI integral exercise Level 1 or 2 Plenary: Use division to help sketch a graph of y = (2x – 5)/(x – 3) Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework 5 MEI tasks A2 Core 9 Introduce partial fractions Students work in pairs to algebraically show the equivalence of the first set of graphs plotted in the starter. Students to demonstrate solutions. Teacher leads students through a method to find coefficients, if this has not come out already or brings together methods. This may throw up problems with using common denominators in algebra so support by going through some examples of adding Consolidation: Use exercises in old C4 textbook or MEI exercise level 1 If you subscribe to MEI there is an Always, Sometimes, Never