I open with the essential question: Do the signs of decimal quotients follow the same rules as integer quotients? I'll then ask students to take a minute to fill in the sign of quotients for a dividend and quotient with the same sign and with a different sign.
Next, I want to remind students that the rules for signs are not arbitrary or magical; they are based on mathematical properties. I say remind because this work was done with integer quotients. Students take a two multiplication facts and write related division facts. Of course, we have already explored the signs of products. The resulting division facts confirm that division of decimals is just like the division of integers in terms of the resulting sign. This exercise speaks to MP3, as students take some of the math they already know and related it to a new task.
Now that we have confirmed the signs of quotients, I want to go to a more fundamental check. The remainder of the lesson focuses on fluency of decimal long division. Therefore, I present students with 8 various division problems and ask them to set up the long division problem without actually solving for the quotient. I want to make sure students know how to handle decimals in both the divisor and the dividend.
Students will now solve 6 problems with my guidance and the help of their partners. Some students may be more successful with long division if they are given graph or grid paper. In this case, they must be instructed to write only 1 digit per square. This grid paper makes it much easier for students to correctly place and align values. So many of the mistakes in long division come simply from misaligned work!
Throughout this section (and in the later sections) I have tried to include problems that are not overly tedious. I believe only 1 of the problems requires students to complete values beyond the thousandths place. There is also one answer that has a repeating decimal value.
Now students work along. The first 6 problems mirror the guided practice problems. The last 4 problems are rate problems. Students are asked to find the unit rate. Two of these four problems use very friendly numbers just to remind students that unit rates can be found through division. I include these problems as a subtle way to review and perhaps extend some of their unit rate work from a previous grade, while getting them prepared for the next unit on ratios and proportional reasoning.
The extension consists of several one-step rational number multiplication equations. Consequently students now get to practice solving equations using division. This too is a way to prepare the students for a later unit on expressions and equations while practice rational number division.
Note: I have not given a lot of room to show work in the resource. I may have my students do the work on whiteboards or notebook paper.
The exit ticket has 4 problems that (again) are similar to problems students have just finished completing. I may consider given two points per problem: 1 for the correct sign for the quotient; 1 for the correct value. This way I assess that students understand that when dividing values with the same sign the quotient is positive, otherwise the quotient is negative. Yet I also just assess their ability to do long division calculations.