Lesson Plans
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Lessons (with descriptions and correlation)
- Description from originating webpage
- Standards based on ADP Core Algebra II Content
- E1.d: Linear equations and Inequalities; X1.a: Exponential Functions
This task asks students to compare additive and multiplicative growth (represented by linear and exponential models) to make predictions and solve problems within the context of gender-based salary differences. In doing this task, students analyze data sets, create scatter plots, determine the most appropriate mathematical model, and justify their model selection.Uses scatter plots to compare two sets of data.
- P1.d: Quadratic functions, E1 b: Linear equations and inequalities
This task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue. Students may use various methods to determine a quadratic function that fits the mathematical model and helps answer the questions.
P1.a, b, c: Quadratic functions
This is an approach to the quadratic formula based on moving parabolas
Absolute Values of Linear Functions
Students will make predictions, using geometric intuition, about the paths of golf balls, analyze graphs of functions, and determine equations that model the path.
- P1.a, b, c: Quadratic functions
The lesson begins with a review of transformations of quadratic functions—vertical and horizontal shifts, and stretches and shrinks. First, students match the symbolic form of the function to the appropriate graph, then given the graphs, students analyze the various transformations and determine the equation for the functions. This review is followed by an activity where students explore a mathematical pattern that emerges as they build a geometric design with toothpicks. The pattern is quadratic, and the students determine the mathematical model in several different forms.
- P1.a, b, c: Quadratic functions
Students will be able to derive and apply the quadratic formula to various quadratic equations. Students will also be able to interpret when is the best situation to use the quadratic formula or another process to solve a quadratic equation.
- E2.b, e: Non-linear equations; P1.a: Quadratic functions
Students must be able to write and graph the function; give the domain and range for the function; determine an equation and graph quadratic through a given point for a given function.
- E2.b: Non-linear equations, P1.a: Quadratic functions
In the first part of this activity, students graph a quadratic function that models the shape of a bridge trestle. They then solve the related quadratic equation by completing the square, recording each step as they complete it. This list of steps is generalized to deduce the quadratic formula. In the second part of the activity, students store the formula in their graphing calculator, compare its results with those of the Equation Solver, and use it to solve several other quadratic equations.
- E2.b: Quadratic equations and inequalities; P1 d: Quadratic functions
This task allows students to integrate algebra and geometry as they generate a quadratic inequality from a proportional relationship. (Quadratic contextual area problem)
- P1.a, b, c, d: Quadratic Functions
In this activity, students graph quadratic functions and study how the constants in the equations compare to the coordinates of the vertices and the axes of symmetry in the graphs. The first part of the activity focuses on the vertex form, while the second part focuses on the standard form. Both activities include opportunities for students to pair up and play a graphing game to test how well they really understand the equations of quadratic functions.
P1.a, b: Quadratic Functions; E2.b, c: Non-Linear functions
Teacher and student PDF form available
Hands-on activity to simulate biological events. Involves finding maximum of quadratics, starting with ax^2+bx=0 and ending with general quadratics. Method of solution is by symmetry, that is, maximum is half way between two roots. Students then use factoring. Some quadratics factor "easily", others employ quadratic formula if you wish.
- E2.a, b, e: Non-linear equations; P1.a: Quadratic Functions; P2.b: Higher-order Polynomial function
This lesson focuses on having students make connections among different classes of polynomial functions by exploring the graphs of the functions. The questions in the activity sheets allow students to make connections between the x-intercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function. NCTM Publication-Based Lesson Plans are adapted from NCTM's journals. This lesson plan is adapted from an article in the October 2000 edition of Mathematics Teacher Journal.
- PRF.4.AII.2 - Rational Root Theorem
- Students will use the Rational Zero Theorem to find all rational zeros of a polynomial.
Match That Function
- P1.d: Quadratic functions; P2.a: Polynomial functions, X1.a: Exponential functions
This task requires students to analyze a situation, describe the appropriate function for the situation using multiple representations, and make connections among the representations. The task provides an opportunity to compare various types of functions.
- X1.a, b, c : Exponential Functions
Students will be able to:
- use recursive or iterative forms to represent relationships
- approximate and interpret rates of change from numerical data
- draw reasonable conclusions about a situation being modeled
- X1.a, c, d: Exponential functions
In this task, students model a situation with exponential functions in order to make predictions and solve problems.
- X1. a, b, c : Exponential functions
Humorous – check out problem for good problem. Students will model exponential growth and explore graphing exponential functions through transformations
Reading This Could Help You Sleep: Caffeine in Your Body (Teacher & student PDF form)
- X1.b, c, d: Exponential Functions
This unit is an introduction to exponential functions using elimination of coffee from the body. Connects to half-life.
- X1.b, d: Exponential functions (Teacher and student PDF form)
Requires that, "Reading This Could Help You Sleep: Caffeine in Your Body" be covered earlier in the semester. This unit uses logarithms to "undo" exponentiation in solving exponential equations in a study of build-up and elimination of lead from the body. Can serve as an introduction to the need for a logarithm function.
- P1.a, P2 d, X1.a: End behavior – Quadratic, higher-order polynomial, exponential functions
Students will graph polynomial functions and categorize them by their end behavior; analyze how end behavior is affected by the lead coefficient and the exponent of the highest degree in the function.
- P2.d: Key characteristics of rational functions & their graphs
Students will graph polynomial functions and examine their zeros and y-intercepts; analyze how the zeros and y-intercepts of the numerator and denominator affect the graph of a rational function.
- F3.a, b: Piecewise-defined functions
This task allows students to use multiple representations to discover the transformational patterns of a piecewise function.