![]() ![]() The lesson is organized to begin with a concept that students already know but is essential for today’s lesson (the basic working of functions). While students are working in groups on the worksheet, identify those who need extra help understanding the concept of composition, and help those students verbalize their questions to their group, to facilitate small-group discussions and ensure understanding. Make sure that colors are available for those who need them. Also, other students in the class get to participate by verbally offering inputs.ĭuring the It Takes Two activity, visual learners will benefit from marking the graphs of the two functions with two different colors. The kinesthetic and social learners in the room will appreciate and remember their turn at the front of the room, being on stage, and doing math with their peers. Much of this lesson relies on kinesthetic learning. Does the student’s answer reflect that s/he has obtained a personal understanding sufficient to make an original representation? Does the explanation of why the order of the composition of functions matters include an example that demonstrates adequate understanding? Is the student able to suggest other questions about the characteristics of composing functions that contribute to more general or specific understanding? Emphasizing the accuracy of speaking and writing the composition is also essential in promoting more complete understanding.Īfter completing the activity It Takes Two, have students reflect on the three questions that examine the core concepts of function composition: What does a function do? What does composition mean? Does the order of composition matter?Ĭonsider each student’s responses to the three questions and the kinds of language used. ![]() Familiar forms of composition-writing prose, making music, drawing a picture-all require bringing certain individual elements as component parts of the thing to be created. The activity reminds students of the familiar process of input/output and the requirement that there is one and only one output for each unique input in order for the relation to be a function.īy directing students’ attention to the language of composition, they can make individual and collective representations of what it means to compose something. The function machine cards will reprise a concept that most students have used in the elementary grades. ![]() In this lesson, students will learn how to represent compositions of functions, how to represent them graphically, and how to make meaningful interpretations of the results of the compositions. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.Īctive Engagement, Modeling, Explicit Instruction W:.Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. Families of functions exhibit properties and behaviors that can be recognized across representations.Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data. ![]()
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