Data Analysis, Probability, Statistics, and Discrete Math

1. Data Analysis, Probability, Statistics, and Discrete Math You Be the Teacher – Evaluating Answers

2. Directions: • Work independently to solve the problem below. Compare your answers with those of others in your group. Then make any changes needed so that everyone has a correct answer.

3. The Task: Nasser earns $1,000 a month. When Nasser told his boss that he was looking for a new job, his boss told him she would give him a raise but that he must choose from one of two plans. • In Plan A, Nasser would get double his present salary for the year and would be paid in monthly checks of equal amounts over the next 12 months. • In Plan B, Nasser would get paid 15% more than the amount of money he made the previous month for each of the next 12 months. • Nasser made the following table for the first six months to show how much he would make each month.

4. Based on this table, Nasser decided to take Plan A. • Did Nasser choose the plan that would give him the most salary over the year? • If yes, tell why. Make sure to use specific examples and amounts from the problem. • If no, tell why. Make sure to use specific examples and amounts from the problem. • You may want to use your calculator to help solve this problem. • Write your answer in the space provided.

5. Solution • Implement the following steps: • Calculate the remainder of the pay changes for Plan B. • Add up the monthly salary figures to obtain a total Plan B salary for the year. • Compare the total salary for Plan B to the total salary for Plan A.

6. Month Plan A Equal Checks Plan B Salary at 15% increases 1st 2000 1150 2nd 2000 132.50 3rd 2000 1520.88 4th 2000 1749.01 5th 2000 2011.36 6th 2000 2313.06 $12,000 $10,066.81 Ernie: No because he did not chart B for the full 12 months. B’s salary will increase and pass the slary of A. The salery of A will be 24000 and B will be 33,345.92. 2660.02 3059.02 3517.88 4045.56 4652.39 5350.25 23285.12 = 33,345.93 Score of 3 The student states, or it can be clearly deduced, that Plan A does not give Nasser the most money over the year with an explanation that demonstrates an understanding of recursion and presents correct calculations from the problem to support the explanation or conclusion.

7. Score of 3 Rose: Nasser chose the wrong plan. Nasser did not take the right plan because as the amounts total up they equal more then the 24,000 plan A gives you. As you take 15% of the number and then add it on to it, it becomes greater and greater each time. The total go up to over 5,000. Five figures in the second six months equal 9 months of plan A added on to those figure the first 6 months total up to much more than 24,000

8. Score of 2 The student indicates that Plan A does not give Nasser the most money over the year, but there are gaps in the explanation or inferences must be made as to how totals and/or calculations that are shown were determined (for example, there is a total with no evidence of calculations), or there is evidence that indicates some misunderstanding about the recursive process. Elenita: Nasser should have chosen plan B because already at month 5 alone, he is moking more money than month 5 of Plan A. When you add all them up, it will give you a lot more than amount Plan A give you . Each month after month 5 Nasser receive more per month than in Plan A Talib: Plan B is more because over 1 year the 15% add up to 33,352 where plan A only get $24,000 in a year.

9. Score of 2 ORThe student shows basic understanding of recursion and shows calculations, but because of calculation errors, draws either the correct or incorrect conclusion . Christina: Plan B is the best plan. I figured out the amount he would get each month for the rest of the year by multiplying each month by 1.15 and got a total of 14,533.00 added to 10,066.80 is a total of 24,599.80 which is more than in plan A. (Note: The student multiplied everything by 1.15 but uses 1660.03 instead of 2660.03 so the rest of the calculations are off base.) 1660.03 1909.26 2195.65 2525.00 2903.75 3339.31 14533.00

10. Score of 1 The student indicates that Plan B gives Nasser the most money over the year, but the explanation is vague and leaves questions as to the understanding of recursion. Examples are missing or are incomplete and/or contain major errors Libby: I predict that B will gain more money because A is staying at 2000 while b is gaining and I bet will probably get to be more than 30,000 in year.

11. Score of 1 OR: The student indicates Plan A is the correct choice with an explanation that is based on information in the chart that is given or that is based on calculation errors, but shows some understanding of the process. Koki: Yes With Plan A he makes $12,000 per year, but with Plan B he makes 10,066.81 per year. $12,000 10,066.81

12. Score of 0 The student indicates a plan, but has no explanation or the explanation and corresponding examples show no understanding of the concept of recursion. Or the student restates the problem, leaves it blank, or the response has no connection to the problem and makes no sense. Diwane: Plan A: Because in Plan B he makes an average of 1677.80 a month (add the 6 numbers and divide) so 1677.80 rounded to 1800 is only 800 more so he doesn't make the $3600 more he would have made in A. Abel: Plan B This way he makes he makes 2313.06 per month for the rest of the year which is 313.06 more than in Plan A.

13. Sharif’s Response: Sharif's Response: Nasser did not make the right choice. He did not figure the other months in the year. With plan A he made $24,000 with plan B he’d get $33,351.92 obviously you can see the difference. 2660.02 3059.02 3517.88 4045.56 4652.39 5350.25 This response earned a 3 because it shows the salary for each of the remaining months for Plan B and shows how much Nasser would make for the year. In addition, the student clearly states that Nasser did not make the correct choice.

14. Zack’s Response: Zack's Response: No he did not.He didn’t choose the right plan because in plan B the beginning of the months salary started out much lower than 2000 (Plan A) but later on in the year the salary will be much higher than 2000 and it will make up for the difference in the beginning of the year. 2660.19 3059.01 3517.86 4045.54 4652.38 17934.98 +10066.88 28001.86 This response is a 2 because of skipping month 12 when calculating the total for plan B. However, it does show an understanding of the concept and draws the correct conclusion based on the data provided.

15. Mason’s Response: Mason's Response: Wrong, He will make much more w/ plan b. the 2313… will almost double by the 12th month. But with Plan a it will always be $2000 This response is a 1. Even though the student states the correct plan along with a conjecture of why it is more, there is no computational support for the conclusion.

16. Washi’s Response: Washi's Response: No, Nasser choose the wrong plan. In the full year, Nasser would get about 33,352 a year on plan B on plan A he would only get 24,000 a difference of 9350. I think Nasser was a not a good thinker. 2660.19 7 month 3059.01285 8 month 3517.864788 9 month 4045.544495 10 month 4652.376169 11 month 12 month 28,001.58729 per year This response is a 2 because the total in the statement does not correlate to the total in the calculations that are shown. It also contributes to some confusion about how the correct total was determined.

17. Nicole’s Response: Nicole's Response: I figured the rest of the year out for plan B and added them. Its way more than 24,000 This response earns a 3 even though it does not specifically state that Nasser made the wrong choice. The response does show the calculations for the remaining months of plan B with the correct sum. The statement infers that the student does choose B.

18. Lamar's Response: No because he receives double his salary for a year. For plan a he would receive $24,000 a year. But for plan b he would only receive $4168.519. There’s a $19,831.481 difference Lamar’s Response: This response is a 0. The “No” shows that Lamar chose Plan B, but the explanation supports the choice of Plan A. It is evident, however, that the student understands the total salary in Plan A and the need to compare Plans A and B. But there is no rationale for the figure $4,168.519, and its origin is unclear.

19. Lemmas’s Response: Lemmas's Response: No because if you add them all together Plan B is greater. Plan B is greater and greater every month, but Plan A is always the same amount. Plan B will be so great in the end of the year over 29,000. Even though B is little in the beginning but it gets greater and greater each time. This response is a 1 because it indicates Plan B and shows understanding of the concept, but there is no indication of how the $29,000 was determined.

20. Raja’s Response: Raja's Response: Nasser took plan a because he made more money all those six months he made all to gather 12,000 in6 months in plan B he made less every time, except 5 and 6 months he made a little more. This response is a 1 because it makes conclusions based on the information for six months and never indicates examining what happens for the remainder of the year.

21. Eldora's Response: Nasser chose the wrong plan because over time the salary B gains a lot more than the 24,000 of plan A. With 33251 for B. The reason for this is because you start with less money with B but eventually the amount it over 2000 does = more than the money you first lost Plan A = 24000 Plan B = 33,251.91129 2660.019 3059.02185 3517.875128 4045.556397 4652.384857 5350.248353 Eldora’s Response: This is a 3. The student not only computed the total amount of money Nasser should get with Plan B, but also indicated an understanding of the differences between the computations for the beginning months and the ending ones. The response could be improved if rounding were used in the calculations and if the explanations were a little more clear.