1.1+Extending+the+Number+Line+0910

Thursday April 15, 2010 M.M

__**1.1 Playing Mathmania**__

**Big Idea:**
Negative numbers help us model many real world situations

How do I put positive and negative numbers in order?
 * Essential question:**


 * Mr. Bernoski's third-period class is playing MathMania, a game similar to Jeapordy. The game board is shown below. The top row gives six math categories. Below each category name are five cards. The frong of each card shows a poing value, and the back of each card has a question related to the category. Cards with higher point values have more difficult questions.**
 * **Operations with Fractions** || **Similarity** || **Probability** || **Area and perimeter** || **tiling the plane** || **Factors and multiples** ||
 * **50** || **50** || **50** || **50** || **50** || **50** ||
 * **100** || **100** || **100** || **100** || **100** || **100** ||
 * **150** || **150** || **150** || **150** || **150** || **150** ||
 * **200** || **200** || **200** || **200** || **200** || **200** ||
 * **250** || **250** || **250** || **250** || **250** || **250** ||


 * The game is played by teams. One team starts the game by choosing a category and a point value. The teacher asks the question on the back of the corresponding card. The first team to answer the question correctly gets the point value on the card, and the card is removed from the board. If a team misses the question, the point value is subtracted from their score. The team that answers correctly gets to choose the next category and point value.**


 * At one point in the game, the scores for Ms. Bernoski's class are as follows:**


 * **Super brains** || **Rocket scientists** || **Know-It-Alls** ||
 * **-300** || **150** || **-500** ||


 * There are several ways each team could have reached their score. For example, to earn their 150 points, the Rocket Scientists may have answered a 100 point question and a 50 point question correctly, or they may have answered a 200 point question correctly and then missed a 50 point question.**

__**Problem 1.1 A. Which team has the highest score? Which team has the lowest score? Explain how you know your answers are correct.**__ For Math-Mania, the “Know it Alls” have the least amount of points and the rocket scientists have the most amount of points. 150, (The “Rocket Scientists” score) is the only positive score while the other scores are negative. Any positive number is higher than any negative number. -500, (The “Know it Alls” score) is the smallest number out of the three scores. It is a negative number, so it is less than the “Know it Alls”, and it’s a smaller negative number than the Super-Brains score, -300.


 * __B. How many points separate the highest and lowest scores?__**650 points. If you add 650 to -500 (the “Know it all’s” score) the product with be 150 (the “Rocket Scientists“ score).

__**C. The discussion above describes two possible ways the Rocket Scientists may have reached their score. Describe another possible wa**__**__y__**. For each of the other two teams, give one possible way the team could have reached their score:Super Brains- They could’ve gotten two 150 point questions wrong. (-150 + -150 = -300)Known it Alls- They could’ve gotten two 250 point questions wrong. (-250 + -250 = -500)


 * After achieving the scores shown above, the teams continue to play the game.** **Here is what happens:****The SuperBrains answer a 200 point question correctly, a 150 point question incorrectly, and two 50 point questions correctly.****The Rocket Scientists answer a 50 point question incorrectly, a 200 point question incorrectly, a 100 point question correctly, and a 150 point question incorrectly.****The Know It Alls answer a 100 point question incorrectly, a 200 point question correctly, a 150 point question correctly, and a 50 point question incorrectly**


 * __D. What is each team’s score now?__**Super Brains: 0. (-300 + 200 + 50 + 50)Rocket Scientists: -150. (150 + -50 + -200 + 100 + -150)Know it alls: -300. (-500 + -100 + 200 +150 + -50)


 * __E. Which team is in last place? How far behind each of the other two teams is this team?__**The Know it alls are still in last place. Super Brains is ahead 300 and the Rocket Scientists are ahead 150.
 * __Follow Up:__****In Mr. Bernoski’s fifth period class, the Smarties have -300 points, and the Brain Surgeons have -150 points. After answering the next four questions, the Smarties are tied with the Brain Surgeons. Give two possible ways the Smarties could’ve done this:**The smarties could’ve gotten four 100 point questions wrong and the Brain surgeons could’ve gotten 3 100 point questions right and one 50 point question wrong.ORThe smarties could’ve gotten four 100’s right and the brain surgeons could’ve gotten three 50 point questions right and one 100 point question right.