grocery task

Grocery Task the Question Needed to Be Addressed and Point Distribution for Each Question:

FIRST PART for the SUBMISSION (I have completed the first part, please help with second part. please read my response below and might need revision please feel free to revise)

You all did this but if you want you can revise your prior work in the ilearn. I will grade the final version that include part 1 and part 2.

Please make sure you have given detailed response to the questions 2 and 3 for the first part. Thus, I advise revise your first part. Then, move in the second part.

1. Have you face this situation before? How? (5pts) 2. What is your mathematical suggestion to make the decision? Explain why it is

mathematically meaningful. What information do you need? (15 pts) 3. Which variables may effect the line speed? Explain how? (10pts)

SECOND PART for the SUBMISSION

1. What grade levels/courses do you recommend presenting this problem? Why? Please refer to Common Core Math Standards document available on the ilearn under course materials section. (10pts)

2. Which of the standards for Mathematical Practices can be addressed through using this grocery task? Explain how? (10 pts)

a. What does this practice look like when students are engaging with this task? (Consider your grade level selection) (10pts)

b. What could a teacher do within a lesson to encourage students in this practice while engaging with this practice? (10pts) [Consider mathematical knowledge for teaching]

3. What mathematical content knowledge required for this task as a teacher? (10 pts)

4. What does students need to know as a prior knowledge to engage in this task? (10 pts)

5. What do you hope for your students to learn mathematically as a result of engaging this task? (10 pts) [Think about mathematical concepts, ideas, representations etc.]

My answer to first part:
 First, this is a common issue that happens in my daily life. Second, the mathematical strategy I am going to analyze this problem is called equal probability. However, there is some other information that needs to be clarified. Such as, does these two lines have equally efficient servers? And how long does it take each customer to pay and leave?

In this question, Server efficiency and customer efficiencies are the main factors or the key to analyzing this problem.

If the servers and customers are equally efficient, the critical quantity here is the number of total items in the shopping line, not the number of customers. For example, let the server efficiency be X second/each item. Let the customer efficiency be Y second/each transaction

! (assume customer pay and leave right away). The first line will need at least 11x+4y seconds to complete four transactions. The other queue will need at least 19x+1y seconds to complete one transaction. And to solve the equations lets x= 1sec/item, y=2sec/transaction.

1) the first queue: 11(1)+4(2)=19secs 
 The first queue needs at least 19 seconds to complete all transactions. 
 2) the second queue: 19(1)+1(2)=21secs 
 The second queue needs at least 21 seconds to complete all transactions. 11x+4y<19x+1y 
 I will be joining the shopping line has four customers and with three, five, two, and one

item in four shopping carts. 
 In conclusion, servers efficiency and shoppers efficiency are essential information that

will directly affect our decision. And, do the two queues have the same situations? However, it can be different answers in different cases. If the server and customer efficiency are the same, the numbers of total items will be your number one consideration. If not or the situation even complicated, like different customer pay in various methods, go to the shorter line.