Productive Failure III

Corrected Solution:

In my first solution the mistake I made was counting groups size 1/16th big and accounting for each group that was size 1/16th big as being one whole group. Reading the division problem however, it states that we are looking for the number of groups size 9/16th big in 3/8. The mistake that I made is a mistake that could commonly be seen among students first learning this method as well because it is much easier for us to account for groups size 1/16th big instead of a group size 9/16ths big. After finding where I went wrong with this problem and reattempting it, I came across another tricky part that could very easily lead students to the wrong answer. Once coming to the conclusion that there are 6/16ths in 3/8, a simple mistake one may make would be to put 6/16ths as the answer, relating to the 48/128 rectangles filled within 3/8 out of the whole unit (128/128). When solving for our answer however, we do not put the 48 over 128 because we are not looking for a group size 16/16 (or 128/128), we are looking for a group size 9/16 (so 72/72). Since 48 rectangles make up our 3/8, to find the number of groups size 9/16 48/128 is, we solve for 48/72. Once reducing 48/72, we come to the correct answer of 2/3. 6/16ths is 2/3 of a group size 9/16ths big, therefore there is 2/3 of a group size 9/16 in 3/8.

From this mistake I learned to pay close attention to what the problem is asking and make sure that the answer I arrive at makes sense logically. If I had looked at the problem closely and really thought about it, I would have realized that 9/16 is actually greater than 3/8, resulting in my inital answer of 5 3/128 making absolutely no sense. From this mistake I also learned to really take my time and make sure I am correctly accounting for what the problem is asking for. This problem had a couple tricky steps to it where one could very easily get confused, therefore, it is extremely important to take your time and really understand what each part of the question is asking of you.