Working with Functions I

Working with Functions I
Working with Functions I
Working with Functions I
Working with Functions I
Working with Functions I
Working with Functions I
Working with Functions I
Working with Functions I
Created ByBarbara Smith
Grade Levels
File Type
Presentation (Powerpoint) File (3 MB|24 pages)
Standards
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  • Product Description
  • Standards
The unit on functions is one of the most challenging for math students to master. Finding domain and range of functions, determining inverses and real roots and using function notation are all included in this package.

Working with Functions I is designed to be used as an introduction of functions for Algebra I and as a strong review for Algebra II and Advanced Math classes.

The included material includes study pages with keys for each level, two quizzes and five student help pages for class bulletin board. These help pages include definitions and worked examples similar to problems on the study pages and quizzes.

Log in to see state-specific standards (only available in the US).
Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (𝑦 – 2)/(π‘₯ – 1) = 3. Noticing the regularity in the way terms cancel when expanding (π‘₯ – 1)(π‘₯ + 1), (π‘₯ – 1)(π‘₯Β² + π‘₯ + 1), and (π‘₯ – 1)(π‘₯Β³ + π‘₯Β² + π‘₯ + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 Γ— 8 equals the well remembered 7 Γ— 5 + 7 Γ— 3, in preparation for learning about the distributive property. In the expression π‘₯Β² + 9π‘₯ + 14, older students can see the 14 as 2 Γ— 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(π‘₯ – 𝑦)Β² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers π‘₯ and 𝑦.
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
Produce an invertible function from a non-invertible function by restricting the domain.
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Total Pages
24 pages
Answer Key
Included
Teaching Duration
3 days
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