1 / 17

Math Challenge: Conjectures, Proofs & Logic

Engage in a fun team game where you solve math problems related to inductive reasoning, conjectures, proofs, and logic. Test your skills in algebraic and geometric proofs while exploring conditional statements and more!

emery-marsh
Download Presentation

Math Challenge: Conjectures, Proofs & Logic

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2 Review “Family Feud” Mr. Shelly-style

  2. Instructions • By now, you should be in teams of 4. • Each team should have one sheet of paper on which to record their answers • Write all team member names on the paper • For each category (concept) there will be five separate questions • As a team, these are your responsibilities • In the time provided, solve all the problems in each category you can • Write your answers on your paper • Check your answers when covered after the category. • Receive a point for each problem correctly solved.

  3. Example Round • Solve: • 2 + 6 • 22 – 7 • 54 – 23 • 4 + 39 • 81 - 63 • So in the real game, if you answered the first 4 correct but didn’t get to the last one, you would get 4 points…

  4. ROUND 1 Inductive Reasoning and Conjecture

  5. Round 1 • Make a conjecture and find the next term (if needed) • -5, 10, -20, 40, … • 1, 1.2, 1.4, 1.6, … • 1 and 2 form a right angle • ABC and DBE are vertical angles • Point P is the midpoint of

  6. ROUND 2 Conjecture: T or F (+counterexample)

  7. Round 2 • Determine if the conjectures below are true or false. If false, give a counterexample. • If points A, B, and C are collinear, then AB + BC = AC • If A D, then mA=mD • If 1 is complementary to 2 and 1 is complementary to 3, then 2 3 • If ABC and CBD form a linear pair, then ABC CBD • X and Y form a linear pair, then X and Y are supplementary

  8. ROUND 3 IF you’re ready, THEN we’ll go on…

  9. Round 3 • Take the statement below and follow the directions listed as problems. “If you live in San Diego, then you live in California” • Write the converse • Write the inverse • Write the contrapositive • Determine if the conditional is true/false • Determine if the converse is true/false

  10. Round 4 Inductive/Deductive (and the laws)

  11. Round 4 • Conclusion or no conclusion? What Law? • If a dog eats Super Dog food, then it will be happy. Rover is happy. • If you study for the test, you will receive a good grade. You study for the test. • If mA is less than 90°, then A is acute. If A is acute, then A B • Inductive or Deductive? • You must be 5’2” to ride the roller coaster, and Timmy is 5’0” tall. Timmy concludes he cannot ride. • Mr. Shelly watched “The Big Bang Theory” on Monday, Tuesday, Wednesday, and Thursday. His friend concludes he will watch it again on Friday.

  12. ROUND 5 Algebraic Proof: Properties

  13. Round 5 • Name the property that justifies each statement below. • If m1 = m2, then m2 = m1 • If 7x = 28, then x = 4 • If VR + TY = EN + TY, then VR = EN • RS = RS • If AB = CD, then 2AB = 2CD

  14. ROUND 6 Geometric Proof: Properties/Definitions

  15. Round 6 • Name the property or definition that justifies each statement below. Or explain how you know (justify your own answer!) • If X Y, then Y X • If S and T are complementary, then mS + mT = 90° • If 1 2 and 2 3, then 1 3 • If bisects XYZ, then XYW WYZ

  16. ROUND 7 Grab Bag

  17. Round 7 • Write the conditional and converse of the biconditional statement below “Water boils if and only if its temperature is 100°C” • Fill in the proof below.

More Related