How can math be used in sports?

Targeted Content Standards and Benchmarks

• 19.0 Students know the quadratic formula and are familiar with its proof by completing the square. 21.0 Students graph quadratic functions and know that their roots are the x-intercepts. 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements: 25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.

Student Objectives/Learning Outcomes

• Students will improve their skills in critical thinking and problem solving. They will analyze the problem and synthesize information in order to solve problems and answer questions.

• Students will know the quadratic formula and recognize when it is to be used. They will learn how to prove the formula by completing the square. Students will gather data and represent the findings through graphs and charts. Students will relate the graphs to physical problems such as finding the year when the net sales of a company will reach a certain amount, or how long it will take a ball to reach the ground after it was hit with a bat. Students will also use properties of the number system to validate results, explain and justify procedure, and to determine if the statements are true or false.

Curriculum-Framing Questions

• Essential Question: Can math make you a better athlete?

• Unit Question: How can math improve performance in baseball?

• Content Questions: What type of equation can be used to determine the amount of time it would take for a ball to hit the ground after it was hit with a bat? How do I gather data and graph it? What is the solution: In what year will a baseball player reach a certain salary if the salary trend continues?

Assessment Timeline

• Before project work begins: Pre-test about quadratic equations, Questioning and KWL chart, Handouts given with strategies to solve quadratic equations, Discussion in groups about quadratic formulas: i.e. what they are, where they are seen in our everyday life

• Students work on projects and complete tasks: Summaries about findings, Self and group assessments, Questioning, Conferences, Discussion in groups, Quiz, Feedback about project

• After project work is completed:Presentation, Exam, Conferences, Questioning, KWL chart, Students write about the importance of quadratic equations

Assessment Summary

• In order to gauge student needs the unit will include independent and group work. It will have several ways in which students will participate. Students will be given checklists they need to follow, and charts they need to fill out in order to view the progress. There will be discussions and conferences to make sure each student understand the material. Students will present in front of the class, and be able to express their opinion about the topic and experience with the project at the end of the unit.

Gauging Student Needs Assessment: Quadratic Equation

• Students will respond to the following questions independently, and then discuss the responses in a small group.

• Give an example of a quadratic equation. ax² + bx + c = 0 .• What is the quadratic formula? • What shape does the graph of the quadratic equation have? U-

shape . • Where are quadratic equations used in our everyday life? • Used to find the stopping distance of a car traveling at a given

velocity .• Used by engineers to build bridges.• Used in baseball statistics.

Designing an Effective Visual Aid

Important Elements • quadratic equation• quadratic formula• example of equation and graphOrganized into a meaningful pattern In order: equation, formula, shape the graph makes, and example with

points to plot and graphIntegrate with existing knowledge • Students already know how to solve linear equations and are now

learning how to solve and graph quadratic equations. Best type of visual? • An example so that students become familiar with the formulas and

how the graph should look.

Quadratic Equation ax² + bx + c = 0 , a ≠ 0 .

The Quadratic Formula gives the solutions of any quadratic equation

Visual Aid

What shape does the graph of the quadratic equation have? U-shape .

Visual Aid cont’d

ExampleA slow pitch softball is pitched to a batter. The ball follows a path in which the height, h, is given by h = -2t2 + 8t + 3, where t is the time in seconds elapsed since the ball was pitched.

•(a) Draw a sketch of the graph. Be sure to label your axes and scale.

•(b) At what height was the ball released from the pitcher's hand? 3 feet

•(c) What is the maximum height reached by the ball? 11 feet

•(d) The batter hit the ball at the same height in which the pitcher released the ball. How much time elapsed until the ball was hit? 4 seconds

Example from : “Algebra 1, Unit #5 – Quadratic Functions – L6.” The Arlington Algebra Project. LaGrangeville, NY 12540. 26 Sept 2009

<http://www.teacherweb.com/ny/arlington/algebraproject/U5L6ApplicationsofQuadraticFunctionsDay1.pdf>.

Visual aid cont’d

t h

0

1

2

3

4

3

9

11

9

3