Quadratics-Style
Red Bird, Yellow Bird, Blue Bird and Black Bird are angry with the pigs!!! The pigs stole the birds' eggs! The birds want their eggs and will stop at nothing to get them back. The flight path of the birds can be modeled with a parabola using distance as the independent variable and the height as the dependent variable. So, x is the ______and y is the ______.1.Red Bird starts his flight from point (10, 0). His flight path reaches a maximum height of 18 yards and lands at point (38,0). Graph Red Bird’s flight. Make sure you label all parts of the graph. What is the maximum height the bird flew? What is the distance the bird traveled?
The Red Bird’s maximum height is also called the ______. Describe how you determined the distance traveled?
2. Yellow Bird’s flight path can be modeled by the quadratic equation y = -x² +14x – 24 . What information do you need to find from the equation in order to make the graph? Show all work needed to find the necessary information and graph.
3.Blue Bird’s flight is represented by the graph below. Describe the information that the graph tells you.
4.The table below contains partial data points of Black Bird’s trajectory. Graph the data. Determine the distance traveled and the height of the bird.
Mathematical Conclusions:
1.If you were playing Angry Birds and had to pick a bird to use that could go the furthest, which would you choose and why? Answer in a complete sentences.
2.If you were playing Angry Birds and had to pick a bird to use that went the highest, which would you choose and why? Answer in a complete sentences.
3.After looking at the distance traveled and height, if you had to choose only 1 bird, which would it be and why? Answer in complete sentences.
4.Which representation did you find it easier to determine the distance traveled and maximum height? Why?
Just for Fun… Let’s see who hits the pigs!!! Graph and label King Pig and Moustache Pig on each graph. Which birds hit the pigs?
King Pig is located at point (21, 19.5). Moustache Pig is located at point (9, 21)
Other ways to do an Angry Bird parabola activity:
Angry Birds Parabolic Edition: http://dpsmsmath.wikispaces.com/file/view/Angry-Birds-2.pdf/448250002/Angry-Birds-2.pdf
Angry Birds Project: http://teachers.stjohns.k12.fl.us/brailsford-d/wp-content/blogs.dir/320/files/2014/03/angry-birds.pdf
You tube video: https://www.youtube.com/watch?v=bsYLPlXl7VQ
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices.1. Distribute copies of the article “Frustrated with Math? Try Angry Birds!” by Tim Chartier from http://www.huffingtonpost.com/tim-chartier/frustrated-with-math-try-_b_1581042.html. Have students read independently and then debrief about article.
2. Assign students into groups of 2-3. Distribute a copy of Angry Bird resource sheet for groups to complete. (Students should graph quadratics on calculators and sketch on their paper.)
3. Discuss answers with students and lead a discussion with a series of questions.
· What is similar between linear and quadratic graphs? What is different?
· What relationship does the maximum/vertex have in relation to the time it takes the bird to hit the ground? What happens to the direction of the bird at this point?
· Do any equations in your resource sheet have a minimum? Does this make sense?
· Where in the equation indicates which way the parabola opens?
· Would it make sense to graph below the y-axis or to the left of the y-axis? Why or why not?
· When the bird hits the ground, what will also be the value of y? Do you think that’s the case for all quadratics? What will be the value of x?
4. As an extension, have students go to the website http://www.geogebratube.org/student/m2713. Students need to move sliders so that the parabola will match the path of the birds. Have students record the equation, vertex, and where the bird will land. Have them also record any connections they see with the equation in vertex form and any points they just listed. Equation: y = -0.09(x – 10.15)² + 11.6, vertex: (10.15, 11.6), will land at 21.5.
Evidence of Success: What, exactly, do I expect students to be able to do by the end of the lesson, and how will I measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding.
Students are able to accurately graph the quadratic and able to identify the maximum and zero of the graph. Through observations of student produced graphs and answers to questions on their handouts and in class discussion, it should be clear students have grasped the concept.