Making Sense of Remainders Day 3

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SWBAT investigate real world problems in which remainders are shared, dropped and rounded.

Big Idea

Students develop an understanding of remainders in real life situations.

Warm Up

10 minutes

I display the problem 44 / 7 on the board.  I ask students to evaluate and analyze my thinking when I record the quotient as 42 R 2.

The reason I chose this as a warm up is because this is a very common error among fourth grade students. Many fourth grade students confuse or mix up their multiplication product from a related multiplication fact, as the quotient of the division problem. 

This warm up allows students to self reflect on whether or not they also do this.

Then, I ask students to list the three ways remainders are used in division. Students respond with, "drop it, share it, and round it."  Then I have students solve 26 / 5 in their notebooks as I pass out the supplies needed for today. 


Concept Development

50 minutes

It often takes a jump in understanding for students to apply the procedural algorithm of division with remainders to real-world situations where remainders are encountered. A child who can easily calculate 40 divided by 6 = 6R4 will too often state 6R4 as the answer to the number of cars necessary to transport 40 children to a baseball game if 6 children can fit in each car.

The problems in this lesson will first review the concept of division as proportional reasoning involving equal shares and then they will lead children to discover the three usual ways of dealing with remainders in real life: they are either used to round up to the next whole number, they are dropped and discarded, or they are split evenly among the participants.

For this lesson, students sit with their learning partner in a circle on the floor.  I direct students to solve the first problem on page two of the division problem worksheet with their learning partner.  Students use Math Practice Standard 1 as they make sense of each problem and make sense of the situation involving remainders. As students talk with their learning partner, I am observing and listening to their conversations.  After about most pairs have finished, I direct students to freeze and put their pencils down. I then ask students to show a thumbs up if they found a quotient for the problem.  I don't always call on students that have answers, which my students have grown accustom to. I might call on a student with a thumb up, or I might ask a student that doesn't have a thumb up to discuss the problem and confusing aspects about the problem. Then, I can guide students' responses in order to help the students that did not get an answer. I have found that this strategy takes the emphasis off of the "right answer" or "the answer" to how did you get your answer and why did you do what you did.  

I continue with this strategy as students work to finish all problems on the page. I don't get bothered by the quantity that we (as a class) get through, this lesson is more focused on the why and how to solve division questions. 

In the second half of this video, a student questions his learning partner about why they drop a remainder.


You can watch this video and hear a partner discuss dropping the remainder for the flower problem on the division problem set worksheet.

Student debrief - Wrap Up

10 minutes

For this student debrief, I wanted to give my students a review task and assessment of multiplication with a two step word problem.  I think this is especially important because so often, students assume that once they begin a new unit or new chapter, every word problem they get, must be using the new skill. I did have several students say, "but it doesn't make sense to divide" after seeing the problem. It was a good way for me to remind students that math isn't about just practicing skills in isolation for large amounts of time, but rather using the skills learned to solve all kinds of problems.

Click here to see an incorrect student's assessment and to hear my thoughts.

Click hereto see another student's assessment and my thoughts.