In this lesson students will be making their posters that were planned in the previous lesson (day 1). You will need glue or tape, markers, and poster paper. It is really important for the teacher to catch any mistakes with division prior to finalizing the poster. The poster may be unusable if mistakes make it hard to see the patterns. Some posters might not get completely finished, but we don't need every single one to do the activity in the next lesson (Poster Patterns). It's a good idea to start looking for posters that will help students see patterns or will raise questions about patterns in the division. I want students to notice that dividing by 3 will result in a repeating decimal, even better if they wonder if all multiples of three will do the same thing. I want students to notice that some decimals terminate in the tenths, hundredths, etc.
The warm up warm up noticing patterns in division.docx gives them four division problems and asks them to share what they notice and wonder when dividing even and odd numbers by 2. Their responses may vary, but they may notice that when dividing odd numbers by two they will result in a decimal number in the tenths place. They may wonder if it will always be point 5. Some may notice or wonder about the remainder being 1. I really just want to focus students on starting to notice similarities and ask questions that will lead to further investigation and testing. This will help them put their posters together as well as to look for patterns in other posters during the next lesson (Poster Patterns)
It's hard for students to "notice" things because they don't always feel that what they see is noteworthy and are hesitant to share. It is really important while circulating to encourage all observations and follow up with "I wonder..." statements. "I wonder if that is just a coincidence or if it always happens", "I wonder what we might do to find out?", "I wonder if we could find one that would do something different?"
This is also a good time to notice who is still struggling with division and check in with their poster during the exploration section. They may have some mistakes that need to be addressed before gluing anything down.
I return their work from the previous lesson (day 1) in which they planned their poster and then tell them to start putting their posters together as soon as they're ready. I don't bring them their supplies. I remind them where the glue and the poster paper are (they know where markers and rulers are) because I want them to get used to figuring out what tools they may need for themselves. If I notice some groups are not starting their poster in a few minutes I let the class know they should begin within the next 5 minutes or they might not finish. Then I go check in with that group.
The teacher's role here is just to facilitate their consensus within their groups and help them make decisions. I circulate and ask how they are organizing the poster and how they are going to make their organization clear to people looking at it. Some groups might be changing their minds about their organization and it is really important to help them by asking why they want to change it and what other ideas they have. If they have trouble coming up with new ideas I ask if any of the decimals have anything in common with each other or if they notice any differences between the decimals. (some repeat some don't, some end in tenths, hundredths, some end in 5, etc.) I ask them to show me what some of those groups might look like.
I am always looking for division remediation needs and students who need to be reincorporated into their group. If a student is taking a break I suggest that they stand up to get a better view of the poster. I tell them they should always be looking for mistakes that need correcting or anything that doesn't look quite right.
Students chose how they wanted to organize the numbers. Some sorted them into categories of odd vs. even, repeating vs. not, more or less than one whole, by denominator. Some students decided to try to put them in order from least to greatest. My first impulse was to reiterate that I wanted them sorted into groups by some unifying characteristic and not allow them to order them, but I thought it would give me valuable insight into their place value sense. I stood by while these groups realized they really had trouble because of their insecurity with place value, but they persevered by converting all the decimals to percents and back again. My whole point was to give them practice with the long division while at the same time having them delve a little deeper into looking for patterns. Some students were still having trouble with the division and I am still considering whether or not to allow calculators for upcoming percent applications.