using limits legacy resources) to confirm use of rule. (ensure that includes some Extension example where students have to Combining product and chain rules Finding a repeated root, use chain rule in conjunction Ask students to work in pairs to differentiate . Emphasise opportunity for proof with the product rule) the importance of setting work out very clearly; complete the chain rule part as a side calculation then link in Or MyMaths/Y2/Product Rule clearly to the main part of the working. (but includes some e and ln) Practice: There are lots of legacy resources in textbooks etc on this to practice the techniques, or integral subscribers can use the product rule questions from integral exercise level 1 Starter Main teaching Notes Consolidation/Plenary Including key questions, key teaching points, models and Including Support and Including key questions and resources Extension homework 6 LO: Differentiate using the quotient rule (and Support Plenary Students to choosing appropriate rule) Khan academy , includes “Mark my homework” style differentiate y = derivation of quotient rule from problem. Teacher prepared 2x/(x+1) by writing it Students to establish quotient rule by writing u/v as uv-1 product and chain rules. solution to a quotient rule as 2x(x+1)-1 and and using the product rule (note, this will require a very problem containing deliberate using the product careful application of the chain rule in the general case Pair strong with weak for errors for students to identify – rule. weaker students will need support with this) support and correct. Could give a Once the quotient rule has been established, students to problem with harder to spot check their answer to the starter. Extension errors to stronger students. NB Students may ask why they just always use the Combines with curve can’t product rule by writing a quotient as uv-1. Emphasise sketching and problem solving Or that subsequent algebraic manipulation and simplification is often made much easier by using the quotient rule. The from Kangaroo Maths! Types of Differentiation. (not a free resource) Students Home Learning to sort expressions into a 3 way Venn re how they would Questions from legacy differentiate; product vs quotient vs chain and then resources or integral exercise differentiate as many as they can (will need to leave out level 2 differentiating expressions involving e and ln etc for now but can still sort into Venn diagram) Or MyMaths/Y2/Quotient Rule Or
using limits legacy resources) to confirm use of rule. Combining product and chain rules Ask students to work in pairs to differentiate . Emphasise the importance of setting work out very clearly; complete the chain rule part as a side calculation then link in clearly to the main part of the working. Practice: There are lots of legacy resources in textbooks etc on this to practice the techniques, or integral subscribers can use the product rule questions from integral exercise level 1 Extension Finding a repeated root, opportunity for proof (ensure that includes some example where students have to use chain rule in conjunction with the product rule) Or MyMaths/Y2/Product Rule (but includes some e and ln) Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework 6 Students to differentiate y = 2x/(x+1) by writing it as 2x(x+1)-1 and using the product rule. LO: Differentiate using the quotient rule (and choosing appropriate rule) Students to establish quotient rule by writing u/v as uv-1 and using the product rule (note, this will require a very careful application of the chain rule in the general case – weaker students will need support with this) Once the quotient rule has been established, students to check their answer to the starter. NB Students may ask why they can’t just always use the product rule by writing a quotient as uv-1. Emphasise that subsequent algebraic manipulation and simplification is often made much easier by using the quotient rule. Types of Differentiation. (not a free resource) Students to sort expressions into a 3 way Venn re how they would differentiate; product vs quotient vs chain and then differentiate as many as they can (will need to leave out differentiating expressions involving e and ln etc for now but can still sort into Venn diagram) Or Support Khan academy , includes derivation of quotient rule from product and chain rules. Pair strong with weak for support Extension Combines with curve sketching and problem solving Plenary “Mark my homework” style problem. Teacher prepared solution to a quotient rule problem containing deliberate errors for students to identify and correct. Could give a problem with harder to spot errors to stronger students. Or The from Kangaroo Maths! Home Learning Questions from legacy resources or integral exercise level 2 Or MyMaths/Y2/Quotient Rule
26_differentiation_a2_bom_sow.docx