Y13 A level Mathematics 35 Numerical Methods 1.5 weeks Teaching objectives a Understand that some roots cannot be found using analytic d Solve equations using the Newton-Raphson method and methods; understand the importance of numerical methods represent the process graphically b Locate roots of functions by considering changes of sign, e Establish how iterative methods can fail to find a particular understanding how a change of sign method can fail root c Be able to carry out a fixed point iteration after rearranging an f Understand how to use numerical methods (specifically the equation into the form x=g(x) and represent the process trapezium rule) to find the approximate area under a curve graphically (staircase and cobweb diagrams) and the limits that it must lie between g Use numerical methods to solve problems in context Resources for advance preparation: – - 1 sheet per pair Starter Main teaching Notes Consolidation/Plenary Including key questions, key teaching points, models and Including Support and Including key questions and resources Extension homework 1 in pairs (this could be Discussion of the starter should lead to: Extension: Use plenary to discuss in more preceded by some depth the failure of the change The bisection method (change of sign) becoming equations for which of sign method to locate roots secure (through sharing/demonstration) students have analytic Discussion and understanding of the of phrase ‘change methods) initial values should you choose? Why? sign’ (What During the starter, you may How do you know if your initial values will be want to share (perhaps successful in finding a root?) using one of the pairs’ work) Understanding of an error bound and ensuring that the initial ideas of the these are being stated (How accurate is your solution? bisection method for those What does it mean to state a value to a specified pairs found a who haven’t number of decimal places?) way to begin. Students can then continue with: Could add additional practice questions here to ensure students can perform the method correctly.
Y13 A level Mathematics 35 Numerical Methods 1.5 weeks Teaching objectives a Understand that some roots cannot be found using analytic methods; understand the importance of numerical methods b Locate roots of functions by considering changes of sign, understanding how a change of sign method can fail c Be able to carry out a fixed point iteration after rearranging an equation into the form x=g(x) and represent the process graphically (staircase and cobweb diagrams) d Solve equations using the Newton-Raphson method and represent the process graphically e Establish how iterative methods can fail to find a particular root f Understand how to use numerical methods (specifically the trapezium rule) to find the approximate area under a curve and the limits that it must lie between g Use numerical methods to solve problems in context Resources for advance preparation: – - 1 sheet per pair 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 in pairs (this could be preceded by some equations for which students have analytic methods) During the starter, you may want to share (perhaps using one of the pairs’ work) the initial ideas of the bisection method for those pairs who haven’t found a way to begin. Discussion of the starter should lead to: The bisection method (change of sign) becoming secure (through sharing/demonstration) Discussion and understanding of the phrase ‘change of sign’ (What initial values should you choose? Why? How do you know if your initial values will be successful in finding a root?) Understanding of an error bound and ensuring that these are being stated (How accurate is your solution? What does it mean to state a value to a specified number of decimal places?) Students can then continue with: Could add additional practice questions here to ensure students can perform the method correctly. Extension: Use plenary to discuss in more depth the failure of the change of sign method to locate roots
35_numerical_methods_a2_bom_sow.docx