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Directions

Directions. Complete the handout that you were given at the door. Do NOT put your name on it. Crumple the handout into a ball. Stand at the designated line and shoot your paper ball into the basket; shoot ONE time. One person shoots at a time. Form a line as needed.

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Directions

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  1. Directions • Complete the handout that you were given at the door. Do NOT put your name on it. • Crumple the handout into a ball. • Stand at the designated line and shoot your paper ball into the basket; shoot ONE time. • One person shoots at a time. Form a line as needed. • Return to your seat as soon as you shoot your paper ball.

  2. Directions for Activity 1 • With your team factor the quadratic expressions on the handout. • Once finished (or as you go) copy each problem onto a sticky note. • x2 + 3x + 2 • (x + 1)(x+ 2) • 5 minutes to complete activity x2+ 3x + 2 (x + 1)(x+ 2)

  3. x2+ 3x + 2 (x + 1)(x+ 2) Sticky Notes (1 minute) x2 + bx + c x2 - bx + c x2 + bx - c x2 - bx - c x2 -3x + 2 x2 + 4x - 8 • What is the factored expression? x2 - 4x - 8

  4. Rotations (20 minutes) • As a team, you will go to one of the 4 posters. • 4 Rotations • Write your name on the front page of packet. • Under each question is a space to answer the question for each poster. • Fill out table at the bottom of the page as you go. • Repeat for each poster. • You will get 5 minutes at each poster.

  5. Handouts for Posters • Look at the factored expressions on each sticky note. What do you notice about the signs in the factored expressions? Are they both positive, both negative, or is one positive and one negative? x2+ 3x + 2 (x + 1)(x + 2) One POSITIVE and one NEGATIVE! x2 + 8x – 9 (x + 9)(x – 1) Both POSITIVE!

  6. Handouts for Posters • If one sign is negative and the other sign is positive (in the factored expressions), answer the following questions: • What is the bigger number in the factored expression? Is it with the positive or negative? • 9, positive • What is the smaller number in the factored expression? Is it with the positive or the negative? • 1, negative • Pass out clip boards. x2 + 8x – 9 (x + 9)(x – 1)

  7. Tables Same Same Positive Negative Different Different Positive Negative

  8. Teach Me How To Factor! • http://www.youtube.com/watch?v=OFSrINhfNsQ

  9. Factor: x2 + 5x - 6 • Will our signs in the factored expression be the same or different? • Different • (x + _)(x - _) • What are factors of 6 that combine to get 5? • 6 and 1 • Which sign in the factored expression needs to go with the larger number, in this case 6? • The positive or plus • (x + 6)(x – 1) • Check • x*x = x2 • x*-1 = -1x = -x • 6*x = 6x • 6*-1 = -6 • x2 – x + 6x – 6 = x2 + 5x – 6 • Remember: 6*-1 = 6 and 6 + (-1) = 6 -1 = 5

  10. More Examples • x2 + 18x – 40 = (x __ 2)(x __ 20) • x2 – 6x + 8 = (x __ 2)(x __ 4) • x2 – 3x – 18 = (x __ 3)(x __ 6)

  11. Day 2: Dude Perfect! • http://www.youtube.com/watch?v=PD6eQY7yCfw

  12. Dude Perfect! • What did you think about the video? • Do you think the basketball shots made in the video were simply luck? • If we looked at the video through our math lenses, how can we apply math to what occurred in the video?

  13. Discussion • What does it mean to factor a quadratic? • What are the steps you can use to factor? • What did we do yesterday? • When we factored, how did our final answer look? • What is an equation? When have you seen equations in the past?

  14. Fill in the Gap Activity Directions: Below are quadratic equations at different stages. You must either solve or create the quadratic equation from the given information. Problem 1 Equation: x2 - 4x + 3=0 Process: Answer: x = -3 and x = -1 Problem 2 Equation: Process: Answer: x = 2 and x = -5

  15. Fill in the Gap Discussion • What did you think of the activity? • Were there any problems that you found difficult to solve? Was there anything that you did not expect? • Will a group that understood how to solve the requested problem(s) volunteer to present how you solved the problem(s)?

  16. Fill in the Gap Discussion • What information did you need to fill-in for this problem? • How did you go about completing the problem? • What was different from what we did yesterday with quadratics to what we did today? • What is another term we use to describe the two solutions?

  17. Do the Quad Solve! • http://www.youtube.com/watch?v=jGJrH49Z2ZA • Exit Slip

  18. Basketball Problem • There are twenty seconds left in the basketball championship. John takes a basketball shot from a horizontal distance of 5m from the hoop. The height of the ball can be modeled by the relation h=-7.3t^2+8.25t+2.1, where h is the height, in meters, and t is the time, in seconds, since the ball was released. • a) From what height was the ball released?b) What was the maximum height reached by the ball?c) If the ball reached the hoop in 1 s, what was the height of the hoop?

  19. Basketball Problem Answer Key • a) From what height was the ball released?Released when t = 0, therefore -7.3(0^2) + 8.25(0) + 2.1 = 2.1 meters

  20. Basketball Problem Answer Key • b) What was the maximum height reached by the ball?Max height occurs at the axis of symmetry, x = -b/(2a; in this equation we have:t = t = .565 secMax height = -7.3(.565^2) + 8.25(.565) + 2.1,h = -2.33 + 4.66 + 2.1h = 4.43 meters max height

  21. Basketball Problem Answer Key c) If the ball reached the hoop in 1 s, what was the height of the hoop?Substitute 1 for t, find hh =-7.3(1^2) + 8.25(1) + 2.1h =-7.3 + 8.25 + 2.1h = 3.05 meters

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