Today, I gave the 4th graders four questions to get a glimpse into how they think about multiplication and division before starting their multiplication and division unit. Michael Pershan had given the array question to his 4th graders last week and shared the work with me. As we chatted about next steps with his students, I became curious if the students think about multiplication differently depending on the type or setup of the problem.
Here were the questions:
After sorting 35 student responses I found the following:
- 17 students got the area question wrong but the two multiplication problems on the back correct. Not only correct, but with great strategies based on place value.
- 8 students got all of the problems correct, however the area was found in many ways, some not so efficient with lots of addition.
- 10 got more than two of them incorrect. Some were small calculation errors on the back.
So, what makes almost half of the students not get the area?
Here is the perfect example of what I saw on the majority of those 17 papers:
Then I did a Number String with them to hear how they shared their mental strategies. I wanted to get more insight into some of their thinking because a few students had used the algorithm on the back two problems.
They did great. They used the 10 and 20 to help them solve the problems and talked about adding and removing groups of one of the factors. I was surprised on the final problem of 7 x 18 that no one used the 7 x 20 but instead broke the 18 apart to find partial products.
This makes me think there is something about that rectangle that makes them not use the 10s to help them decompose for partial products. I would love others thoughts and ideas!
After reading the comments about area and perimeter, I wanted to throw another typical example of what I saw to see what others think of this (when I asked her she could easily explain partial products on the second and third problem)