1.1+Extending+the+Number+Line

21.03.09 MT Example:1) -5+-5=-10 2) -24+-6=-30
 * Big idea:**Negative numbers help us to model many real world situations.
 * Essential Question:** How do i put positive and negative numbers in order?
 * Notes from class:** When you add a negative number to a negative number you get a lower negative number.


 * __1.1 Playing Math mania__**
 * Ms. Bernoski's third-period class is playing Math Mania, a game similar to //jeopardy!// game show. The game board is shown below. The top row gives six match categories. Below each category name are five cards. The front of each card shows a point value, and the back of each card has a question related 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 ||


 * At one point in the game the scores for Ms. Bernoski's class are as follows:**
 * 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 correctly 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 answer is correct.** The Rocket Scientists have the highest score because they are the only team with a score higher then 0 (a positive number score). The Know-It-Alls have the lowest score because they need to win at least 500 points to make their score positive when the superbrains only need to win 300.

Highe st score: 150 lowest score:-500 First you make the lower score positive:-500+500 =0 Next find the difference between the higher score and 0: 150-0=150 Then add the amount needed to make the lower score positive and the difference between the higher score and 0: 500+150=650 650 points seperate the highest score and the lowest score.
 * B.How many points seperate the highest score and the lowest score?**


 * C.The *discussion above describes two possible ways the Rocket Scientists may have reached their score. Describe another possible way. For each of the other two teams, give one possible way the team could have reached their score.**
 * Discussion from above:"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"

The Rocket Scientists may have answered a 250-point question correctly and the missed a 100-point question. The super brains could have missed a 250-point question and then a 50-point question. The know-It-Alls could have missed two 250-point questions.

Here is what happens:** > > **D.What is each team's score?** > __SuperBrains > Starting score__: -300 > -300+200=-100-150=-250-50=-250+50=-150 > __Current score__: -150 > > __Rocket Scientists > Starting score:__150 > 150-50=100-200=-100+100=0-150=-150 > __Current score:__ -150 > > __Know-It-Alls > Starting score:__ -500 > -500-100=-600+200=-400+150=-250-50=-300 > The Super Brains and Rocket Scientists score is -150 and the Know-It-Alls score is -300. > > **E.Which team is in last place? How far behind each of the other two teams is this team?** > The Know-It-Alls are last they are 150 points behind the two other teams.
 * After acheiving the scores shown above, the teams continue to play the game.
 * **The Super Brains answer a 200-point question correctly,a 150-point question incorrectly, a 50-point question correctly, and another 50-point question 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 incorrectly, a 150-point question correctly, and a 50-point question incorrectly.**