Curriculum Guide: Calculus 1 st Quarter GRADE Algebraic Concepts. Algebraic Concepts

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1 Curriculum Guide: Calculus 1 st Quarter 8/21/ st Quarter, Grade GRADE Unit of Study: Functions & Graphs Resources: Textbook: Calculus of a Single Variable (Larson, Hostetler, Edwards, 2002) pp. 1-40, Graphing calculator Length of Study: Unit of Study: 2 weeks Finding Limits, Continuity & One-sided Limits, Infinite Limits Resources: Textbook: Calculus of a Single Variable (Larson, Hostetler, Edwards, 2002) pp , graphing calculator Length of Study: Unit of Study: 2-3 weeks Finding Derivatives Product & Quotient Rules, Chain Rule Resources: Textbook: Calculus of a Single Variable (Larson, Hostetler, Edwards, 2002) pp. 1-40, graphing calculator Length of Study: 2-3 weeks MA The student will graph and interpret algebraic relations and inequalities. MA The student will solve problems using pattern and functions. 1

2 ASSESSMENT RECOMMENDATIONS 8/21/ st Quarter, Grade Standard: Benchmark MA The student will graph and interpret algebraic relations and inequalities. Skills Skills Skills Skills Sketching all function graphs Analyzing all function graphs Explanation Possible Assessments FOR Learning Essay Identify different types of transformations of functions. Explain differences between all function graphs Suggestion Required Assessments OF Learning Selected Response Short answer Essay Writing out definitions of all types of transformations Assessment Finding domain and range for a given function. Personal Communication 2

3 8/21/ st Quarter, Grade Standard: Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Identify different types of transformations of functions MA The student will graph and interpret algebraic relations and inequalities. Generating and testing hypothesis HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Look at a group name equation giving all transformations that would give you that graph. Skills (): & Explanation Sketching and analyzing all function graphs. Homework & practice AVERAGE PERFORMING STUDENT Activities: Given an equation, sketch what the graph will look like LOW PERFORMING STUDENT Activities: Nonlinguistic representation ELL Activities: Given many graphs, match up graph to equation that gives you that graph. 3

4 ASSESSMENT RECOMMENDATIONS 8/21/ st Quarter, Grade Standard: Benchmark MA The student will solve problems using pattern and functions. Skills Skills Skills Skills Estimating limits algebraically and graphically Determine continuity of one-sided & infinite limits Finding derivative of functions Possible Assessments FOR Learning Develop and use a strategy for finding limits. Use the Intermediate Value Theorem Use Power Rule to find derivative of a composite function Required Assessments OF Learning Selected Response Short answer Essay Writing out definitions of all vocabulary terms Assessment Find derivatives using variety of rules show work Personal Communication 4

5 8/21/ st Quarter, Grade Standard: Benchmark: SUGGESTED INSTRUCTIONAL STRATEGIES WHOLE GROUP Activities: Develop and use a strategy for finding limits MA The student will solve problems using pattern and functions. Cooperative learning HIGH PERFORMING STUDENT Activities: AVERAGE PERFORMING STUDENT Take a graph and find the limit. Discuss the continuity of each graph (groups). Skills (): Estimating limits algebraically and graphically Determine continuity of one-sided & infinite limits Homework & practice AVERAGE PERFORMING STUDENT Activities: Take an equation and find the limit. If it doesn t exist, explain why. LOW PERFORMING STUDENT Activities: Homework & practice ELL Activities: Looking at a graph, find limit. If it doesn t have a limit, explain why. 5

6 8/21/ st Quarter, Grade REQUIRED KEY CONTENT WORDS Function Symmetry Intercepts Slope Ratio Parallel Perpendicular Domain Range Implicit Explicit Transformation Transcendental Even function Odd function Limits Tangent line Secant line Unbounded Oscillating One-sided limit Step function Greatest integer function Continuous Intermediate value theorem Bisection method Infinite limit Asymptote Difference quotient Differentiation Derivatives Power rule Position function Sine function Cosine function Product rule Quotient rule High-order derivative Second derivative Third derivative Chain Rule General Power Rule Implicit function Explicit function Implicit differentiation 6

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a