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Functions Teacher Resources
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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.
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.
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.
In this algebraic functions worksheet, learners write a function to determine the relationship between people and barrels of oil used. They research the population of the 10 largest cities in their state and use this functional relationship to calculate the number of barrels and gallons of oil used by each city.
Students solve formulas by using substitution. In this algebra lesson, students utilize formulas introduced in the lesson which apply to science as well as volume and area. The lesson gives detailed instruction for solving each type of problem. Detailed answers to all practice problems are provided with step by step solutions to assist.
Examine multiple ways to solve algebraic equations. Pupils will generate a problem solving strategy that addresses the prompt given by the teacher. They will then share their problem solving strategy with the class. Graphic organizers, problem solving prompts, and tables are included.
Elementary schoolers use a function machine in order to help them look at the relationship between input and output, and to look at the rule for the change. The machine is actually a cardboard box, and it serves quite well for the lesson! One student takes the input numbers and creates an output number. After enough have been done, learners try to figure out the rule that is being used. A good teaching idea!