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NATIONAL MATH + SCIENCE INITIATIVE Mathematics Charades LEVEL High school math courses in a unit on transformations of functions MODULE/CONNECTION TO AP* Analysis of s: s *Advanced Placement and AP

1 NATIONAL MATH + SCIENCE INITIATIVE Mathematics Charades LEVEL High school math courses in a unit on transformations of functions MODULE/CONNECTION TO AP* Analysis of s: s *Advanced Placement and AP are registered trademarks of the College Entrance Examination Board. The College Board was not involved in the production of this product. MODALITY NMSI emphasizes using multiple representations to connect various approaches to a situation in order to increase student understanding. The lesson provides multiple strategies and models for using those representations indicated by the darkened points of the star to introduce, explore, and reinforce mathematical concepts and to enhance conceptual understanding. ABOUT THIS LESSON This lesson actively engages students in demonstrating their understanding of s and of interpreting the transformations described with function notation. Students select a card and a card and then, in the style of a Charades game, act out the information on their cards so that teammates can correctly identify their function and its transformation. In addition, students can match a card with its function notation to a card containing the appropriate vocabulary for the transformation. OBJECTIVES Students will act out the shape of s. act out the effect of transformations, stated in function notation. connect function notation to a verbal description of a transformation. T E A C H E R P A G E S G N P A V P Physical V A Analytical N Numerical G Graphical i

2 Mathematics Charades T E A C H E R P A G E S COMMON CORE STATE STANDARDS FOR MATHEMATICAL CONTENT This lesson addresses the following Common Core Standards for Mathematical Content. The lesson requires that students recall and apply each of these standards rather than providing the initial introduction to the specific skill. The star symbol ( ) at the end of a specific standard indicates that the high school standard is connected to modeling. Targeted Standards F-BF.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. COMMON CORE STATE STANDARDS FOR MATHEMATICAL PRACTICE These standards describe a variety of instructional practices based on processes and proficiencies that are critical for mathematics instruction. NMSI incorporates these important processes and proficiencies to help students develop knowledge and understanding and to assist them in making important connections across grade levels. This lesson allows teachers to address the following Common Core State Standards for Mathematical Practice. MP.7: Look for and make use of structure. Students develop fluency connecting the parent graph, the verbal description, the function notation describing the transformation, and the physical enactment of the transformation. ii

3 Mathematics Charades FOUNDATIONAL SKILLS The following skills lay the foundation for concepts included in this lesson: Graph s Translate function notation into a transformation of f(x) ASSESSMENTS The following additional assessments are located on our website: Analysis of s: s Algebra 1 Free Response Questions Analysis of s: s Algebra 1 Multiple Choice Questions Analysis of s: s Geometry Free Response Questions Analysis of s: s Geometry Multiple Choice Questions Analysis of s: s Algebra 2 Free Response Questions Analysis of s: s Algebra 2 Multiple Choice Questions Analysis of s: s Pre- Calculus Free Response Questions Analysis of s: s Pre- Calculus Multiple Choice Questions T E A C H E R P A G E S MATERIALS AND RESOURCES Charades cards Interactive applet which demonstrates transformational changes in functions of the form : GeoGebra-Worksheets/graphing-transformations.html iii

4 Mathematics Charades T E A C H E R P A G E S TEACHING SUGGESTIONS This activity can be done in teams or with the entire class. Teachers may customize the game for any particular class by omitting any of the cards that are not yet in the students repertoire. If students need to review the meanings of the various function notations for transformations, consider having the students match the appropriate and cards first before playing the charades game. To play the game: Decide which team (student) will go first. Set a maximum time limit for each turn. Choose a person to: a. Draw one card each from the and stacks. b. Act out the. c. Act out the transformation(s). (When multiple transformations are required, player should act out changes separately.) Player s turn ends when the team correctly identifies the transformed equation or the time limit expires. Teachers who wish to assess student mastery of the concepts addressed in this activity might consider one or more of the following ideas: Hand out the and cards, one to each student and instruct them to find their matching card and then report in to the teacher. When everyone has reported, shuffle the cards and repeat as time permits. This could also be done in a race format. Select n cards and n cards (make an answer key for use in scoring), have students number their papers 1 to n, ask n students to act out a and a transformation while the remaining students write their answers on the appropriate lines on their own paper. Give students a short matching quiz, where they match a list of s to a list of s. Suggested modifications for additional scaffolding include the following: All Provide a list of s with graphs. All Provide the written description of the transformation to the student acting out the transformation. iv

5 Mathematics Charades NMSI CONTENT PROGRESSION CHART In the spirit of NMSI s goal to connect mathematics across grade levels, a Content Progression Chart for each module demonstrates how specific skills build and develop from sixth grade through pre-calculus in an accelerated program that enables students to take college-level courses in high school, using a faster pace to compress content. In this sequence, Grades 6, 7, 8, and Algebra 1 are compacted into three courses. Grade 6 includes all of the Grade 6 content and some of the content from Grade 7, Grade 7 contains the remainder of the Grade 7 content and some of the content from Grade 8, and Algebra 1 includes the remainder of the content from Grade 8 and all of the Algebra 1 content. The complete Content Progression Chart for this module is provided on our website and at the beginning of the training manual. This portion of the chart illustrates how the skills included in this particular lesson develop as students advance through this accelerated course sequence. 6th Grade Skills/Objectives 7th Grade Skills/Objectives Algebra 1 Skills/Objectives Geometry Skills/Objectives Algebra 2 Skills/Objectives Pre-Calculus Skills/Objectives Apply transformations to tessellations as well as to points, segments, and figures on the coordinate plane. Apply transformations to tessellations as well as to points, segments, and figures on the coordinate plane. Recognize and identify equations for parent functions including constant, linear, quadratic, and absolute value functions. Apply transformations including af( x c) + d to linear, quadratic, exponential, piecewise, and generic functions. Recognize and identify equations for parent functions including constant, linear, quadratic, and absolute value functions. Apply transformations to circles and apply transformations including af( x c) + d to linear, quadratic, exponential, piecewise, and generic functions. Recognize and identify equations for parent functions including constant, linear, absolute value, power, reciprocal, root, exponential, and logarithmic functions. Apply transformations to conic sections and apply transformations including af( x c) + d and compositions with absolute value including f ( x ) and f (x) to parent, piecewise, and generic functions. Recognize and identify equations for parent functions including constant, linear, absolute value, power, reciprocal, root, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Apply transformations to conic sections and apply transformations including af( x c) + d and compositions with absolute value including f ( x ) and f (x) to linear, polynomial, exponential, logarithmic, trigonometric, piecewise, and generic functions. T E A C H E R P A G E S v

6 Mathematics Charades T E A C H E R P A G E S vi

7 NATIONAL MATH + SCIENCE INITIATIVE Mathematics Charades Answers Answers will vary with cards drawn. T E A C H E R P A G E S vii

8 Mathematics Charades T E A C H E R P A G E S viii

9 NATIONAL MATH + SCIENCE INITIATIVE Mathematics Charades The following pages are templates for making cards for the charades activity. They are formatted so they can be copied on colored card stock and cut apart. The,, and pages should be copied on the backs of the playing cards to differentiate the three types of cards. 1

10 Mathematics Charades 2

11 Mathematics Charades 3

12 Mathematics Charades constant linear absolute value quadratic square root cubic reciprocal of x reciprocal of x² exponential growth exponential decay 4

13 Mathematics Charades 5

14 Mathematics Charades logarithmic natural logarithmic sine cosine tangent cotangent secant cosecant arccosine arcsine 6

15 Mathematics Charades 7

16 Mathematics Charades f( x) f( x) f( x) 4 f( x ) + 2 f( x 1) f( x+ 3) f( x+ 2) f( x) 2 f( x+ 1) + 2 f( x 3) + 1 8

17 Mathematics Charades 9

18 Mathematics Charades 1 ( ) 2 f x 2 f( x) 2 f( x ) ( ) 2 2 f x + f( x 2) 2 f( x 1) f( x 3) f( x) + 1 f( x 1) + 3 f( x 2) 1 10

19 Mathematics Charades 11

20 Mathematics Charades Reflect across the x axis Reflect across the y axis Translate down 4 Translate up 2 Translate right 1 Translate left 3 Translate left 2 then reflect across the x axis Reflect across the y axis then translate down 2 Translate left 1 then translate up 2 Translate right 3 then translate up 1 12

21 Mathematics Charades 13

22 Mathematics Charades Halve the y-values (vertical scale change) and reflect across x-axis Reflect across the y-axis then double the y-values (vertical scale change) Double the y-values (vertical scale change) then translate up 1 Halve the y-values (vertical scale change); Reflect across the x-axis then translate up 2 Translate right 2 Translate right 1 then double y-values (vertical scale change) Translate right 3 then reflect across the x-axis Reflect across the y-axis then translate up 1 Translate right 1 then translate up 3 Translate right 2 then translate down 1 14

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.