Lesson 12 of 22
Objective: Students will be able to solve division problems that have a remainder as part of the quotient.
Today’s lesson focus is on solving division problems that include a remainder and being able to interpret the remainder. I begin today’s lesson by posing a division riddle to the students. I found Remainder Riddles activity on the Utah Education Network website.
Not only do I want students to understand what a remainder is, I want students to engage their mathematical thinking, applying (and making sense of) guessing and then checking that work. The remainder riddles that we will be doing today require students to guess and check the solution to the problem. This concept of guess and check will aid us in the next two lessons of division when we start to tackle division problems with two-digit divisors.
I display the riddle for the students and explain how we’re going to solve it.
Okay, while searching for some exciting activities to help you guys with division I came across this riddle that someone wrote. I tried solving it on my own but I got stuck so maybe you guys can help me solve it. The only hint the author gave us was that the solution is between 1 and 25. But, we have some clues to help us, so let’s see if we can crack this riddle together.
Students definitely become interested in the puzzle solving activity and we begin going through the clues as a class. I let them get out their whiteboards to help us go through the puzzle. I suggest we set up a list of numbers so we can start eliminating some possibilities as we go. I focus on having the students do the thinking and I just act as a guide. Throughout our discussion I make sure students are using their academic vocabulary. Students also can use their division diagram (place holder link to division diagram) from yesterday to help them.
Once the students and I solve the riddle, I explain that now it’s their turn to write a riddle. The students are given the task to complete a riddle by choosing a number between 1 and 50. They need to write the clues by solving each step of the riddle. I give students a copy of the riddle sheet and allow them to work with a partner while writing their riddle.
Now it’s your turn to write the riddle. You’re going to work with your partner to create a riddle by selecting a number between 1 and 50. Make sure as you’re writing the riddle you are pretty secretive about the number you have chosen. Although you guys are working together, I would like each person to have a copy of the riddle.
I allow students about 20 minutes to work on their riddles. At the end I bring students back to the whole group and ask them for strategies they used while creating their riddles.
What are some things you had to think about while writing your riddles? What does a remainder mean? How did the remainder change throughout your riddle?
My hope is to get students thinking about what a remainder means. I want them to see that a remainder is just what is left over when you divide and that the remainder can change depending on your divisor.
I collect the riddles and save them for a future lesson in which students will solve the riddles.
This is really our fourth lesson reviewing and deepening our understanding of division within this unit. At this point I hope my students have increased their understanding and can apply it to the traditional division equation. In order to check their progress I have created a quick assessment for the students to complete individually. I will use the information from this assessment to plan for further teaching of division or if re-teaching is necessary.
There are six problems on the assessment. The top row of problems is what I would consider low level division problems. The problems do not have remainders and the divisors are “happy” numbers in which students feel comfortable in (2, 3 and 5). The bottom row of the assessment contains problems that do have remainders. When evaluating answers on this assessment I am looking for evidence of the five step process. Small errors may be seen in the product of the multiplication step or the answer in the subtraction portion. But if the student was able to complete the five steps correctly, it demonstrates that the students are fluent in the division process.