Grade 6 Statistics and Probability Coin Combinations

Transcription

1 Grade 6 Statistics and Probability Coin Combinations Margarita wants to buy a drink that costs $0.60 from a vending machine. The machine takes correct change using only quarters, dimes and nickels. At least one of the coins Margarita uses to buy her drink is a quarter. Show all the different combinations of coins that Margarita could use.

2

3 1 Statistics and Probability Coin combinations Margarita wants to buy a drink that costs $0.60 from a vending machine. The machine takes correct change using only quarters, dimes and nickels. At least one of the coins Margarita uses to buy her drink is a quarter. Show all the different combinations of coins that Margarita could use CU 5 The translation of the key concepts (the value of each coin, combinations, using at least one quarter) is complete in the original solution and made thoroughly developed in the check where more details are recorded. PS 5 The process of creating a chart to show each of the different combinations followed by a listing indicating each sum of the values of the coins would be 60 is completed in the original solution and made thoroughly developed in the check where more details are recorded. V 4 The check includes the translation of the key concepts, revisiting each combination, detailing each sum to be 60, and finally, identifying that there are 6 combinations. The verification is a complete review of each part of the solution. C 4 The mathematical symbols and the use of tables communicates the path between the translation of the task, the process of listing the combinations and indicating each sum to be 60, and the check using a more detailed table, towards the identified solution. Although few words are used, the path is complete. Acc. 5 6 different combinations is a mathematically justifiable solution to the task. This is an excellent example of how a lack of grammar should not detract from the overall effectiveness of the student s work, especially when it comes to the communication score. All of the key concepts were addressed and the process showing the combinations was effective. The paper might have been enhanced if s/he had addressed the issues of maximum coins to arrive at the 60 total.

4

5 1 Statistics and Probability Coin combinations Margarita wants to buy a drink that costs $0.60 from a vending machine. The machine takes correct change using only quarters, dimes and nickels. At least one of the coins Margarita uses to buy her drink is a quarter. Show all the different combinations of coins that Margarita could use CU 5 The translation of the key concepts (the value of each coin, combinations, using at least one quarter) is thoroughly developed in the use of an organized table (allowing the student and reader to know all possible combinations had been found). PS 4 The process of creating the key, then creating an organized table of the possible combinations that total 60 is complete. V 4 The second look includes the second creation of an organized table of the combinations (also showing the translation again). This is followed by the calculations verifying the sum of each combination is 60, making the review complete. C 5 The path connecting the translation of the task into the details of the table, the organization within the table as the process used to solve the task, and the verification is thoroughly developed with the prose explaining the connection between the values in the tables and the calculations. Acc. 5 6 different combinations is a mathematically justifiable solution to the task.

6

7 1 Statistics and Probability Coin combinations Margarita wants to buy a drink that costs $0.60 from a vending machine. The machine takes correct change using only quarters, dimes and nickels. At least one of the coins Margarita uses to buy her drink is a quarter. Show all the different combinations of coins that Margarita could use CU 4 The translation of the key concepts (the value of each coin, combinations, using at least one quarter) is completed in the use of a table of combinations with a sum of 60. PS 3 The process of creating a table of combinations using quarters, dimes, and nickels and then showing each combination has a sum of 60 is only partially useful when the table is not organized to help him/her know if all combinations have been found. V 3 This verification could not stand on its own as a solution to the task, it relies on the work done in the original solution and would not catch an error beyond one where the sum was not actually 60, making the review only partially effective. C 4 The path connecting the translation of the key concepts to the process of completing the table and showing each combination has a sum of 60, to the check and to the solution of I got 4 is complete. The gap (where did the 4 come from?) would be filled the same by the majority of readers familiar with the task that it came from the combinations not crossed out in the original table making it not a significant gap. Acc. 4 There is sufficient evidence the student understands the key concepts of the task and has a strategy that could work to solve it. The further instruction would be in carrying out a better organized table to assure all combinations had been found. Another perspective on this paper would be that the student really doesn t have a process for finding all possible combinations and would need further instruction in that process. If the reader believes this perspective, the score for CU goes down to a 3 and the accuracy score becomes a 1. This is a good example of when talking with a student would be very helpful!