This week my students and I embarked on the journey of learning the concept of division. When I began the teaching the division concept I did not realize that it would involve teaching students to interpret the meaning of division before they actually divide. This idea may sound strange but it made sense to me when I was reviewing 2 warm up problems with my students. The first problem was 18 divided by 3 and the second problem was find the missing number 36 divided by blank equals 6. I was amazed when my students struggled with the first problem because I had done activities with them that required them to divide a total into different groups.
Well, what I didn’t realize is that before the students could answer these two problems proficiently they have to interpret the meaning of the two problems. One of the 3rd grade standards for division is to determine the unknown number in a multiplication and division equation. This one standard can prove to be very challenging for students and teachers because if the students do not understand that each number in the division equation has a meaning then solving these kinds of problems will become a rote process that relies solely on the students memory. 
When a student encounters these two types of problems they should first determine which number is missing. If the size is missing in the problem then the students will have to draw the number of groups and then decide how many are in each group. If the the groups are missing then the students will place an equal amount in each group and then skip count to the total. These two problems required two different thought processes and requires the higher order thinking process comparing and contrast. Using a double bubble map, Venn diagram or a T-chart to show the similarities and the differences between the two process will help struggling students see that the two problems are alike but different.
Interpreting the Meaning of Division
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6 thoughts on “Interpreting the Meaning of Division”
If we remember that division is actually repeated subtraction, and we approach both of these problems with that concept in mind, we’ll have more success:
(a) how many times can we “take away” 3 from 18 ?
(b) how many do we need to take away each time from 36 to take away six times ?
You can improve my patter, but do you like the approach ?
Ned McMillan
It’s a good approach when introducing student to division. This method gives division value because it shows why long division is necessary.
Nicole Schuler I think it’s important for the students to understands the two types of division- in kids terms- repeated subtraction and fair-share division. If they learn that it’s not just repeated subtraction, and they learn the difference between the two- then they do better with word problems. I have given my kids the same word problem, but one asked for the number of groups, and the other asked for how many in each group. We used manipulatives to model it to see if it was fair share or repeated subtraction. Then I made them turn that same scenario into a multiplication problem. This was 5th grade, and they didn’t realize that there was more than one type of division problem. I think this is why so many students don’t know what operation to use for word problems.
I sometimes think that the teachers don’t realize that there 2 kinds of division problems because many of them only teach it one way.
Do you teach both meanings on the same day?
No not for students who are learning these for the first time. For students who are intervention I introduce them at the same time so that they can see the similarities and differences as well as make connections to clear up misconceptions.