Misconception+Analysis

Drew, Kenzie, and Kimberly sit at the same table in math. Their math teacher Mrs. Summers told them to work together to solve the following problem, **23 + 57** but they didn't listen. Instead, each of them solved the problem on their own, and now they have three different solutions. The problem is, all of them are wrong.

Analyze each problem below to find where the misconception was made, and write a sentence or two to explain how where the student went wrong.

Drew 2 + 5 = 7 3 + 7 = 10 7 + 10 = 17
 * Grades (1-3)**
 * 23 + 57**

Kenzie 20 + 3 = 23 5 + 7 = 12 23 + 12 = 35

Kimberly 23 + 5= 28 23 + 7 = 30 28 + 30 = 58

Drew 20 x 3 = 60 5 x 7 - 35 60 + 35 = 95
 * Grades (4-5)**
 * 23 x 57**

Kenzie 20 x 5 = 100 20 x 7 = 140 3 x 5 = 15 3 x 7 = 21 100 + 140 + 15 + 21 = 276

Kimberly 23 x 5 = 115 23 x 7 = 161 115 + 161 = 276

Solve the problem yourself, and explain your thinking. Drew Student explains that Drew did not break his tens into tens and ones into ones Student does not explain that Drew did not break his tens into tens and ones into ones Student explains that all of Drew's digits were treated like ones Student does not explain that all of Drew's digits were treated like ones Student provides a clear explanation of how and where Drew went wrong. Student does not provide a clear explanation of how and where Drew went wrong
 * Grades (1-3)**
 * 23 + 57**

Kenzie Student explains that Kenzie broke 23 into 20 and 3 Student explains that Kenzie broke 57 into 5 and 7 incorrectly, and explain why Student explains that Kenzie broke 57 into 5 and 7 incorrectly, and does not explain why Student provides a clear explanation of how and where Kenzie went wrong. Student does not provide a clear explanation of how and where Kenzie went wrong

Kimberly Student explains that Kimberly broke 57 into 5 and 7 incorrectly, and explain why Student explains that Kimberly broke 57 into 5 and 7 incorrectly, and does not explain why Student provides a clear explanation of how and where Kimberly went wrong. Student does not provide a clear explanation of how and where Kimberly went wrong

23 x 57 Drew Student explains that Drew broke 23 into 20 and 3 correctly Student does not explain that Drew broke 23 into 20 and 3 correctly Student explains that Drew broke 57 into 5 + 7 incorrectly Student does not explain that Drew broke 57 into 5 + 7 incorrectly Student explains that Drew treated 50 like a 5 Student does not explain that Drew treated 50 like a 5 Student added sub-products correctly Student provides a clear explanation of how and where Drew went wrong Student does not provide a clear explanation of how and where Drew went wrong
 * Grades (4-5)

Kenzie Student explains that Kenzie broke 23 into 20 and 3 correctly Student does not explain that Kenzie broke 23 into 20 and 3 correctly Student explains that Kenzie broke 57 into 5 + 7 incorrectly Student does not explain that Kenzie broke 57 into 5 + 7 incorrectly Student explains that Kenzie multiplied 20 x 7 correctly Student does not explain that Kenzie multiplied 20 x 7 correctly Student explains that Kenzie multiplied 3 x 7 correctly Student does not explain that Kenzie multiplied 3 x 7 correctly Student explains that Kenzie multiplied 20 x 5 incorrectly and that it should be 20 x 50 Student does not explain that Kenzie multiplied 20 x 5 incorrectly and that it should be 20 x 50 Student explains that Kenzie multiplied 3 x 5 incorrectly and that it should be 3 x 50 Student does not explain that Kenzie multiplied 3 x 5 incorrectly and that it should be 3 x 50 Student provides a clear explanation of how and where Kenzie went wrong Student does not provide a clear explanation of how and where Kenzie went wrong

Kimberly Student explains that Kimberly broke 57 into 5 incorrectly, and explain why Student does not explain that Kimberly broke 57 into 5 incorrectly, and explain why Student explains that Kimberly multiplied 23 x 7 correctly Student does not explain that Kimberly multiplied 23 x 7 correctly Student explains that Kimberly added the sub-products correctly Student provides a clear explanation of how and where Kimberly went wrong. Student does not provide a clear explanation of how and where Kimberly went wrong **