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Then that would be 600 books given away.” T-Could you give each teacher 50 books a third time? S-“Yes.
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It wouldn’t take as long to give the books away as 10 at a time would.” T-Could you give each teacher 50 books again? S-“Yes. 50 would be a good number because the teachers can carry them more easily. We could give 10 to each teacher a bunch of times, but I think 10 would take a long time.”ĥ0 to each teacher- S- “50 x 6 is 300. I ask students what they think about that and comment that it would take a long time, and wouldn’t be very efficient.Īfter students have had a chance to jot down a number for an idea, I have them show me their whiteboards and I write down 5-10 of their ideas on the whiteboard.ġ00 to each teacher- S- “100 is a big portion of the books we have to give away ” T- How do you know you won’t run out of books? “6 x 100 is 600.”ġ0 to each teacher- S- “10 x 6 is 60.” T-And then, could you give away 10 to each teacher again? What do you think about using 10? S “Yes. I also usually make a big “to do” about how we could totally give the teachers one book at a time until we run out (I kind of run around the room pretending to give out one book at a time from the box). We just want to deliver some books to each classroom without running out. I tell them we don’t have to figure out the EXACT number the teachers will get.
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I prompt students to jot down a number of books that they think we can give 6 teachers without running out. Individual whiteboards are a great addition to this lesson because you can get ideas from each student and see what they are thinking. It’s our job to figure out how many books each teacher will get! How would you start to “divide out” these books? Won’t the teachers be so excited to get their hands on these new books?! Pretend they all fit in this box (holding up the Scholastic box). We just received a huge shipment of books for 6 teachers to share. Let’s use 989 books shared among 6 teachers as our example. On the colored copy paper, I write a 3 digit dividend and “books.” (If you are teaching 5th grade, you can be brave and use a number in the 1,000s). In my first lesson to introduce the area model for division to students, I grab a Scholastic Book Order box and a sheet of colored copy paper. My Introduction Lesson for the Area/Rectangular Array Model for Division (When solving example problems in whole group or small groups, I ask students who have “solved” the division problem if they can solve it another way using the same method.) Students can be encouraged to solve the problem “another way” to develop their understanding of the model and become more efficient. Students can check their work using the same exact division method, but beginning with a different starting number. (In my teaching, the rectangles serve as a symbolic representation of an actual box or group of something.) Using and explaining the “boxes” for the area/rectangular division model allows students to connect division to “taking away” from what we have to create as many “equal groups” as possible. The Area Model for Division provides entry points for all students to begin solving larger division problems, regardless of their multiplication fact knowledge (when taught the “open-ended” way). Four Benefits of Teaching with the Area Model/Rectangular Array Model for Division I do, however, encourage students to find more efficient ways to divide (use larger partial quotients/multiples of the divisor) as we move through our unit, so that they do not have to go through as many subtraction steps to get to the answer AND so that they learn to be thoughtful in the partial quotients that they choose.Įfficiency with the area model is something I think students can develop with encouragement and experience, but not something that I think needs to be required in teaching this method for division right at the beginning of students’ learning. Having a method for division that allows for multiple entry points for students is why I love this method so much and one of the main ways it differs from the rigidity of the standard algorithm for division. This approach is more “open-ended” and this is the way that I teach the area/rectangular array model to my students.
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In the second approach, students can begin with any number that makes sense to them and they are not required to always take the largest amount possible from the dividend. I’ve found that the area model for division is usually taught one of two ways-in one approach, students are taught that they MUST use the largest partial quotient for each place of the dividend.