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Algebraic Function Teacher Resources
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Students explore the concept of quadratic equations. In this quadratic equations lesson, students graph parabolas on their calculator and determine the vertex form of the function given the graph. Students examine the vertex of the parabolas and which way the parabola opens.
The skill set for this lesson is to have learners use tables to generate functions and functions to generate graphs. They work through a series of worksheets with the instructor to determine absolute value, domain, x and y intercept and complete transformations. All of the necessary worksheets and a homework assignment is included.
This is a wonderful exercise for learners to apply their critical thinking skills along with their knowledge of quadratic functions and parabolas. Young mathematicians investigate a real-world scenario about the height a baseball reaches when it is thrown. They compare two different representations, a graph and an equation, of the height as a function of time. Answering the three questions the activity poses requires finding the vertex and roots of a quadratic equation using a method of choice and interpreting the solutions within the context of the problem. The exercise can be used for assessment or practice.
After making a correction to the last problem in his previous video, Sal explains how to graph quadratic functions. Those who have a hard time with the concept of graphing algebraic functions will find Sal's instruction and easygoing manner a welcome change from staring at textbooks.
Here is an unexpected resource: chapter 1 of an Algebra textbook. You can use all or some of its contents to teach your Middle Schoolers all about algebraic expression, domain, function notation, linear equations, order of operations, input/output, ordered pairs, and variable expressions. This would be great for a substitute or newer teacher looking for reliable tools.
This is comprehensive lesson that considers many aspects of quadratic functions. It includes using factoring, completing the square and the use of the quadratic formula for finding the zeros of the function (including imaginary roots). It also reverses the whole process by looking at either different graphs of quadratic functions or zeros that are given and challenges the learner to derive the function. This lesson provides an excellent review for the second year algebra student or a multi-lesson unit for the more novice student.
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
Functions are on the move! This lesson plan provides an opportunity for learners to explore transformations of functions. The activity illustrates the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for both positive and negative values of k. Working in small groups, students complete a table of values for a parent function and an assigned transformation of that function. After sketching both graphs on the same coordinate plane, they analyze their results and write a conjecture about how the value of k affects the original function. Each group shares its findings with the class. The results of the activity are reinforced by using graphing calculators to graph the functions and comparing with the sketches done with pencil and paper. The activity concludes with learners applying what they have learned to write equations for functions when given their graphs.
Grab a box of toothpicks and build a model of a dog pen in a lesson that introduces quadratic functions. Students work in groups to investigate how the area of a rectangle with a fixed perimeter varies with different lengths and widths. They record their observations, look for patterns, and build a function to describe the data. Learners make important connections about maximum, minimum, symmetry, and increasing and decreasing intervals when they use a graphing calculator to graph their data points and the corresponding function. Note that the introduction to the lesson task states the dog pen is to be in the shape of a square. The activity is likely to be more productive if the more general term rectangle is used instead. Pupils may question the need to investigate scenarios with different lengths and widths if they are told in the beginning that the pen is to be a square.
Mathematicians study how algebra can tell the stories of linear growth and they develop problem solving skills in relation to linear growth contexts. In this lesson, students organize information to explain growth, they use algebraic equations to make connections between real life and linear change.
Exponential functions are the name of the game. Young mathematicians can work through each of the eight worksheets by evaluating functions, applying logarithms, completing logarithmic functions, and building inverse functions. This would be a great set of worksheets to accompany an entire chapter.
High schoolers are introduced to the techniques associated with interpreting functions. The vocabulary associated with this technique is reviewed, then pupils view a PowerPoint (embedded in the plan), that shows how to interpret functions. Learners then break into four groups and complete the assignments given by the teacher. Fantastic lesson!
Middle and high schoolers complete and solve 12 various types of problems. First, they express the output as a function of the input in each table. Then, pupils evaluate for the given variable when the value is as stated. In addition, they read the information provided and translate as much as they can into mathematical expressions.
This lesson has a number of fun worksheets for a pre-algebra or beginning algebra class. The main emphasis of this lesson is functions, formulas, and looking at square roots. It is the third lesson in a series on solving for unknowns, which you can find if you look first at the "Getting Started" link. This lesson, in particular, focuses on developing an understanding between the inverse relationship of squaring a number and taking its square root, finding probabilities, and creating linear equations and solving problems.
Apply quadratic function graphs to real-life scenarios to develop deeper comprehension through mathematical modeling. This lesson does not provide explicit activities, but rather can be used as a guide. It lists a variety of essential questions, assessment considerations, and instructional strategies that can be adapted to fit the needs of your classroom.
Students explore extraneous roots to radical equations. In this Algebra II lesson, students solve equations which are typically "unanswerable" with paper and pencil. The use of the TI-npire provides a method of solution and moves the focus of the lesson to flexibility in problem solving.