Angelo Ditta Math PD Activity

Fall Math PD


Math Equation: 
Part One: (Find the mean, median, and mode of the following set of numbers. (2, 34, 5, 16, 37, 45, 5).
Part Two: (Construct a set of 10 numbers with a mean of 7, a median of 6 and a mode of 3). Is there more than one way to do it?                                                                                                                      This equation was presented in the Math GED class on Monday, December 2, 2013.


Planning: I chose this equation because students enjoy working on mean, median and mode. They tell me it is very easy for them to solve these equations because it allows them to apply a formula and solve for the correct answer. Most students solve correctly and they feel they have accomplished a math task. The second part of the question invites the student to delve deeper into the knowledge and complexities of the concept by applying already learned skills and to allow students to integrate cognitively deeper strategies by examining various methods and structures to solve the equation. There is a higher level of thinking and analysis that occurs when solving for part two. I believe this helps to prepare them to tackle higher levels of math equations particularly those that may appear on the GED Exam. This equation meets our criteria because it requires some out of the box thinking. In addition, the equation helps students to consider more than one mathematical concept, encourages students to build off of previous knowledge, asks students to think backwards, and it requires students to come up with their own way of solving the equation. I believe some challenges will include a longer amount of time to solve the equation, some confusion on how to start, how to arrive at the given numbers (the median and mode) in the equation, and remaining with the equation after some helpful prompts from the teacher or other students.

My Work: I solved the problem by identifying what number divided by 10 would give you 7. I then proceeded to find a configuration of 10 numbers that added up to 70 keeping in mind the median of 6 and a mode of 3. 2, 3, 3, 4, 5, 7, 9, 10, 11, 16 = 70 /10 = 7 Mean 7 + 5 = 12/2 = 6 Median 3 is the most occurring = Mode I added the 10 numbers to check if they added up to 70. I then divided by 10 to check to see if the mean was 7. I then checked to see if my median and mode was correct. After verifying these check points, I was satisfied that I completed the task successfully.


Student Work: The students tried to find out what configuration of the ten numbers would give them 7 when divided by ten. Some students picked up on this immediately and others took some time after promptings to begin working on the median. I helped them to draw similarities between finding the mean in part one and now for part two. After that, the students began to set up a series of numbers that would add up to 70 and then divide by 10 to prove that 7 would be the median. Most students set up a series of three or four sets and added them. However, they also had to cognitively arrange the mode and the median to meet the given numbers set forth in the equation. The student busily arranged lines of numbers adding and inserting numbers to create their set to answer the equation correctly. After the allotted time, I asked five students to place their sets on the board and to explain their method and reasoning to the class. As they explained their process, the class began to realize how those students arrived at their answers and that there were several ways to solve the equation. One surprise response was, “No one person has the same numbers.” Also, students were able to identify one set that was not in sequential order and how it had to be rearranged since the median was now going to be incorrect. I thought this was a great insight for the class particularly the students whose set was not sequential order. Two students in particular, Tracy and Yeshi had some difficulty in beginning. They realized on their own that they needed 10 numbers that added up to 70. After this they progressed at a good pace and came up with the correct solutions. Tracy had some difficulty in arranging the 10 numbers. Yeshi had difficulty locating the median. It took Tracy three times to complete the equation and Yeshi two times to solve correctly.

Student Reflection: I asked the students what they found difficult at first sight. The said finding the numbers that added up to 70 and grouping the numbers in sequence to find the median and mode. I then asked the students to identify the moment they began to find the equation make sense. They responded that when they found the number 70, everything was clearer. In addition, some of the prompts from the teacher assisted them in their persistence. When asked what they learned, they said persistence was essential to solving the equation, there was more than one way to answer the equation, and that sequencing was an important element to this equation. They also indicated that this equation helped them to really think and apply more knowledge to a math equation. Some students who had previously taken the GED test indicated that it reminded them of some of the equations they saw on the GED test.