“Please Mrs. Reed, can we do just one more division problem?”
Pre common core
The first time I heard one of my students ask this question I was stunned. I thought that maybe I misunderstood what he asked. In fact 10 years ago I would usually hear groans, and painful cries of despair, not joyful cries of excitement with please for just one more problem. In the past it was painful to teach my 5th grade students the long division algorithm. It brought my students frustration, anxiety and a dislike (to put it lightly) of mathematics.
What changed all that? Several years before Common Core was unveiled, I was desperately looking for resources in my division teaching, I came across division strategies illustrated that I had never thought of nor knew existed. Partial quotients became my “go to strategy”. I found that my students grasped it quickly. Students differentiated this strategy on their own. Some students would have 12 steps to finding their quotient, others three. Every student in my class (yes everyone and I have had many categories of students) could feel success with this strategy. This has brought me to a happy place in my division-teaching career, with students enjoying mathematics again.
Common Core strategies
Next came the long division strategies that are incorporated into common core mathematics. The Progressions list the strategies that our 4th and 5th graders need to know, but I didn’t actually know how to teach them. I have come across a few lessons that I have found to be priceless for my students’ understanding and knowledge of the strategies needed for Common Core Mathematics.
- To introduce the partial quotient strategy my first go to lesson is from Placa-Schwartz Mash Up. https://gfletchy.files.wordpress.com/2014/09/scaffolding-division-through-strip-model-diagramming.pdf. This is a terrific scaffolding lesson. It starts with a tape model, fair sharing out the dividend. The students “fair share” their dividend using friendly numbers and they “discover” the partial quotient strategy. Students are engaged and they understand the math using conceptual understanding. What more could a teacher want?
2.I incorporate the distributive property strategy in my classroom through Number Talks. Because the distributive property strategy was used practically daily in our discussions on multiplication it was a natural step to use it with division problems. This has not been an easy strategy for my students to “own”, but though our number talks using easy division problems and the area model they are catching on.
Area Model Division
- I recently found this last lesson on area model for division. I have tried to “figure out” how to teach this strategy on my own for a few years with not much success until I found this lesson at http://ioer.ilsharedlearning.org/ContentDocs/bc2cc184-41bf-464b-a363-11a554da4126/303/G5_U1_L2_S4a_Area_Model_Division.pdf. This lesson also has great scaffolding to it. There is a gradual release for the students. Students are engaged and understand the strategy the way it is presented.
So there you have it- three division strategies that 4th and 5th graders need to know. Once taught I incorporate the attached game in my center rotation. I have my students “play” this game about once a week to keep up their strategies throughout the year.
This is what I love-teaching, engaging, and enlightening my students’ lives. And when they ask me for just one more division problem, I relent, with a sigh and great joy in my heart.