1

Transformation 2013 Design Challenge 5E Lesson

Title: Authored by: Additional content and revisions by: Subject: Grade Level: Challenge Abstract:

Super Water Slide Julie Rohan Transformation 2013 Algebra 2 High School In this Design Challenge, students will take on the role of engineers who design waterslides for a water theme park. The students will investigate, generate, and solve systems of equations and use the solutions to solve real world problem

Meeting the Needs of STEM Education through Design Challenge

2

Design Challenge Title: Super Water Slide TEKS addressed: Targeted: 2A.1B; 2A.3A, B; 2A.4A, B, C; 2A.6 B, C; 2A. 8D ~ Quadratics TEKS Anticipated: slope, angles (building ramp), measurement .

Engage Activity Approximate time: 20 min The teacher demonstrates the trajectory of various sized balls as they travel down different slide surfaces. After the demonstration, the teacher will guide the students in a discussion about parabolic paths. As the students discuss the topic, the teacher will ask the students to complete a KWL chart. The teacher will then show the following clip… http://www.makingthemodernworld.org.uk/learning_modules/maths/04.TU.02/?section=3 Ask the students: “Where have you seen parabolic paths occur in the real world?” Have the students record their responses as a journal entry. Show the following clip… http://www.makingthemodernworld.org.uk/learning_modules/maths/04.TU.02/?section=1 Introduce students to the design challenge, stating that the final product will provide the students with a real-world problem that will need to be solved after acquiring additional knowledge with regards to quadratics: The owner of the new local water theme park has offered free life-time passes for the engineer who can design a popular, yet safe, waterslide that will attract people of all ages. The slide must encompass (but is not limited to) a straight away and a parabolic projectile of a person landing in a pool of water. Are you up to the challenge?

3

Engage Activity Products/Artifacts

The students will produce the following artifacts: – KWL chart – Journal entry regarding where they have seen parabolic paths occur in the real world

Materials/Equipment: – Pencil – Journal – KWL chart Resources: http://www.makingthemodernworld.org.uk/learning_modules/maths/04.TU.02/?section=3 http://www.makingthemodernworld.org.uk/learning_modules/maths/04.TU.02/?section=1

4

Explore Activity 1 Approximate time: .35 min The students will explore the graphs of quadratic functions through the use of a computer. Each student/pair of students should have Internet access to a computer and should use the following web page to answer the questions below… http://orion.math.iastate.edu/algebra/sp/xcurrent/applets/quadraticfunction.html What is the parent function of a quadratic equation? What is the general (standard) form of a quadratic equation? What happens when “a” is positive? What happens when “a” is negative? What happens when the absolute value of “a” is between 0 and 1? What happens when the absolute value of “a” is greater than 1? What happens when “c” is greater than 0? What happens when “c” is less than 0? What is the role of “b”? What is the vertex form of a quadratic equation? What happens when “a” is positive? What happens when “a” is negative? What happens when “h” is positive? What happens when “h” is negative? What happens when “k” is positive? What happens when “k” is negative? Have students graph examples of each transformation. Also, have students create their own equations that have several different transformations present and graph those equations. Explore I Activity The students will produce the following artifacts: Products/Artifacts – Completed assignment – Journal entry regarding the results of the explore activity

Materials/Equipment: – worksheet with questions and graphs – journal – pencil – computers with Internet access Resources: http://orion.math.iastate.edu/algebra/sp/xcurrent/applets/quadraticfunction.html

5

Explain Activity Approximate time:25 min The students will discuss their observations from the Explore activity and share equations that they derived that reveal several different transformations. The teacher should introduce the correct vocabulary associated with quadratic functions during the discussion: vertex form, general (standard) form, transformation, vertical shift, horizontal shift, vertical stretch, vertical compression, vertex (minimum/maximum), axis of symmetry, y-intercept, x-intercept(s)/root(s)/zero(s)/solution(s), domain/range. The teacher should show students how to graph quadratic functions using their graphing calculators. Use the examples that the students offer during the discussion. Have the students try to identify what types of transformations will occur prior to graphing the equations. Also, ask the students to find the roots and y-intercepts of each function, and show them how to calculate the roots of the function using the graphing calculator. Demonstrate how to find the minimum/maximum of a quadratic function using the graphing calculator. Ask the students to add to their KWL charts. Explain Activity Products/Artifacts

Materials/Equipment: â€“ pencil â€“ KWL chart Resources: None

The students will produce the following artifacts: KWL chart

6

Elaborate Activity Approximate time: 2-3 hours Students will work in groups to complete the “Flying Off the Handle” Activity (from the tmt3 Region XIII Conference offered by Jo Peters) to finalize the Design Challenge. ***View the attachment using the following link: Please note that advanced preparation is imperative. The ramps must be constructed before prior to the activity. The teacher will serve as a facilitator for the activity, following the Facilitation Questions as outlined in the link.

Elaborate Activity Products/Artifacts

The students will produce the following artifacts: – tmt3 worksheet

Materials/Equipment: – 1 ramp per group (see the link to the activity for supplies for the ramp) – 1 marble per group – tape measures – desk or chair – carbon paper or NCR form – copy paper – hard flat plastic surface (for carpeted rooms only) – tape – cups – textbooks – graphing calculator – activity sheets – tmt3 worksheet – pencils Resources: link to tmt3 activity:

7

Explain Activity Approximate time:25 min The students will discuss the results of their Elaborate activity. Guide the students in a discussion of how the projectile path of a water slide is similar to that of a car driving off a cliff. Introduce the students to the concept of using matrices to develop a function rule based off of the data that they collected. (See pages 39-41 of the tmt3 materials). Have the students document (in their own words) how to derive function rules using matrices.

Explain Activity Products/Artifacts

Materials/Equipment: – Pencil – Journal

Resources: None

The students will produce the following artifacts: – Journal entry

8

Evaluate Approximate time: 2 hours After completing the tmt3 activity, have the students read a printout from the following link: http://entertainment.howstuffworks.com/water-slide.htm Ask the students to come up with their own design modifying the current ramp so that it will become a “popular, safe water slide”. Provide the students with additional materials that they can use to modify the design (PVC pipe, additional molding, tape, etc.). Remind the students that the design must have a straight away that will produce a parabolic projectile as per the original design challenge. Have the students demonstrate their final products for the class.

Evaluate Activity Products/Artifacts

The students will produce the following artifacts: – Modified, working ramp – 1-page paper highlighting their design process, resources they used, materials that were necessary to complete the design – Completed KWL Chart

Materials/Equipment: – Ramp – Additional supplies (PVC pipe, molding, tape, etc.) – Pencil – Paper Resources: How water slides work link http://entertainment.howstuffworks.com/water-slide.htm