Including key questions, key teaching points, models and Including Support and Including key questions and resources Extension homework 3 Recap finding the Project a graph of y=x2. working more quickly can Worksheet/Exercise to gain equation of a line Find the equation of the line through the points with work with even finer intervals routine practice from old between two points. coordinates: (3.001 etc.) resources or integral. (3, 9) and (3.5, 12.25)? (3,9) and (3.1,9.61)? (3,9) and (3.01,9.0601)? Students then repeat this for another point of their choosing (e.g. 2.5, 2.1, 2.01). Make sure as many different points as possible are chosen. Class discussion to find that all points end up with y=2x. Repeat the process as a class using x, x+h to derive differentiation formula. Use the formula to compare with answers from the ‘new’ previous lesson’s homework, and identify that this works for different initial functions. 4 Students recap Using calculus to find speed from displacement/time, and Complete the sketched graphs. understanding from acceleration from velocity/time graphs. GCSE that gradients of distance-time graphs give speed, Students use this activity to match up displacement-time and gradients of and velocity-time graphs (assuming that students know speed-time graphs the difference between distance and displacement - if not give acceleration - then ) use old GCSE Qs, such as parts of Students then work on , their understanding of the Some students may be able to questions found relationships between work back from the later displacement/velocity/acceleration, to generate graphs of questions. the other two given one. Starter Main teaching Notes Consolidation/Plenary Including key questions, key teaching points, models and Including Support and Including key questions and resources Extension homework
Including key questions, key teaching points, models and resources Including Support and Extension Including key questions and homework 3 Recap finding the equation of a line between two points. Project a graph of y=x2. Find the equation of the line through the points with coordinates: (3, 9) and (3.5, 12.25)? (3,9) and (3.1,9.61)? (3,9) and (3.01,9.0601)? Students then repeat this for another point of their choosing (e.g. 2.5, 2.1, 2.01). Make sure as many different points as possible are chosen. Class discussion to find that all points end up with y=2x. Repeat the process as a class using x, x+h to derive differentiation formula. Use the ‘new’ formula to compare with answers from the previous lesson’s homework, and identify that this works for different initial functions. working more quickly can work with even finer intervals (3.001 etc.) Worksheet/Exercise to gain routine practice from old resources or integral. 4 Students recap understanding from GCSE that gradients of distance-time graphs give speed, and gradients of speed-time graphs give acceleration - use old GCSE Qs, such as parts of questions found Using calculus to find speed from displacement/time, and acceleration from velocity/time graphs. Students use this activity to match up displacement-time and velocity-time graphs (assuming that students know the difference between distance and displacement - if not then ) Students then work on , their understanding of the relationships between displacement/velocity/acceleration, to generate graphs of the other two given one. Some students may be able to work back from the later questions. Complete the sketched graphs. Starter Main teaching Including key questions, key teaching points, models and resources Notes Including Support and Extension Consolidation/Plenary Including key questions and homework
10___21_differentiation_and_variable_acceleration_as_bom_sow.docx