Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use what you know about inequalities and absolute values to better understand the game. 1. a) Which player did you select? (1 point)

1. b) What number did the other player pick?
Finding a Relation 2. Should you use an equation or an inequality to represent the ways your player can win? Explain why. (2 points: 1 point for an answer, 1 point for an explanation)

3. If Erik had a 4 and Nita had a 12, would the winner be different if Nita got the 4 and Erik got the 12? (2 points: 1 point for an answer, 1 point for an explanation)
4. Is it appropriate to use
an absolute value function to represent how people win this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)
5. Use your previous answers to write an algebraic statement that represents all the ways your player will win. Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for the correct inequality.)

6. In order to graph your solutions, solve for the variable. Be sure to show your work. (2 points)

7. Sketch a graph of your solutions. (2 points: 1 point for coordinates, 1 point for the correct region) Forming a Strategy and a New Rule
8. What is the range of numbers that will win the game for your player? (Hint: Remember that Erik and Nita can only use numbers from zero to 20.) (2 points)

9. Graph all the possible numbers that your player could pick. Compare this graph to your answer in question 8. Do you think that your student has a good chance of winning the game? Explain your answer. (3 points: 1 point for the correct graph, 2 points for the explanation)