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Assessing Conceptual Understanding Chris Chung & Adam Lavallee Episcopal Academy [email protected] [email protected] Resources Available: adamlavallee.com Assessing Conceptual Understanding Please start by working on these two examples: 1) Find the inverse of f (x) = 23 x- 6 2) Find the inverse of g(x) = - x- 3 Assessing Conceptual Understanding Chris Chung & Adam Lavallee Episcopal Academy [email protected] [email protected] Resources Available: adamlavallee.com Assessing Conceptual Understanding Please start by working on these two examples: 1) Find the inverse of f (x) = 23 x- 6 y = 23 x - 6 x = 23 y - 6 x + 6 = 23 y 3 2 (x + 6) = y f -1 (x) = 23 x + 9 2) Find the inverse of g(x) = - x- 3 Assessing Conceptual Understanding 2) Find the inverse of g(x) = - x- 3 What might a student do? y= - x-3 Correct Solution y = - x - 3, x = - y- 3 x2 = y - 3 x2 + 3 = y g-1 (x) = x2 + 3 x = - y- 3, x³3 y£ 0 x£0 y³3 g-1 (x) = x2 + 3, x £ 0 Calculus: Limits Graph a function such that the following are true Evaluate x -4 lim x®2 x - 2 2 x- 5 lim x®¥ 2 - x g(3) = 0 g(1) = dne lim g(x) = 3 x®1 lim g(x) = dne x®-1 Calculus Limits Calculus Limits Calculus Limits Why Assess Conceptual Understanding? • Does not replace standard procedural problems • Math is more than memorizing steps • “How do you know they know?” How to Implement? • No surprises • Should not be the majority of an assessment • Relevant to the topic, but stretching their understanding How to Implement? • No surprises • Should not be the majority of an assessment • Relevant to the topic, but stretching their understanding Example: The following is a graph of the function y = x2 - 4x- 3. Draw the solution to y < x2 - 4x - 3. How to Create • Consider a rational function x - 4x - 5 (x - 5)(x +1) f (x) = = 2 x -4 (x - 2)(x + 2) 2 • Find intercepts • Find asymptotes • Graph How to Create • Re-Create: work backwards Write a possible function for the graph to the right How to Create • Re-Create: work backwards • Multiple Choice How to Create • Re-Create: work backwards • Multiple Choice • True/False or if-then If lim f (x) exists, then f (a) is continuous. x®a If f (a) is continuous, then lim f (x) exists. x®a (a+ b)2 = a2 + b2 How to Create • Re-Create: work backwards • Multiple Choice • True/False or if-then • Explain to another student • Explain to another student Are these two numbers equal? 6 8 3 4 Are these two functions equal? (x + 2)(x - 3) f (x) = (x - 3)(x+ 5) x+ 2 g(x) = x+ 5 The monthly cost of a prepaid cell phone plan is given by the equation C = 0.5m+ 25 where C represents the total cost in dollars and m represents the number of minutes used. State the y-intercept as an ordered pair, and interpret the meaning of this point in the context of the problem. The Vertical Line Test helps us determine whether or not a graph of a relation is a function. Explain why a graph that fails the Vertical Line Test is not a function. How to Create • • • • Re-Create: work backwards Multiple Choice True/False or if-then Explain to another student Use this time to create a conceptual problem share it via email: [email protected]
