Objective

Warm-Up

Multiple Representations Assessment

Closing

Multiple Representations Fixed Perimeter Problems

Objective

SWBAT identify patterns and describe relationships in fixed perimeter problems that are shown in multiple representations.

Big Idea

Dig deeper into these relationships with a lesson that promotes rigorous thinking and understanding the same problem from multiple perspectives.

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

quadratic functions

Algebra

modeling

Quadratic Equations

Standards

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.C.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF-IF.C.8a

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Warm-Up

30 minutes

There is a lot for students to think about on this warm-up. To frame their work time, I tell them: "The big idea here is to think about multiple representations of the same information and equivalent expressions that show the same formula." When students get stuck with computations or algebra, I redirect them back to this big idea and ask them to try to figure out the details using these connections. The more they think about the big ideas to develop their methods for solving the problems, the more sense their methods will make to them.

Students can work on this warm-up for 30-40 minutes, with you circulating to ask them questions and trying to understand how their are thinking about the problems.

Multiple Representations Assessment

40 minutes

Math Practice Standards 2, 7 and 8

Multiple Representations Reflection.pdf

Closing

10 minutes

The end-of-week check out gives students the chance to reflect on all of the big ideas of the week. I tend to rush the check-outs towards the end of class, but I find check-outs like these to be more worthwhile if students have a bit more time to think. This check-out, for instance, is best done with 5-7 completely silent minutes. This gives students a chance to think, and helps them know if they are learning the big ideas.

There is no need for a share-out with this one, because we as teachers can read and process the information on our own time to decide which of these big ideas need more emphasis for the upcoming week.

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