Division

Updated 2/24/15

I have to brag on my kiddos they are really doing GREAT with division!

We begin by creating a multiplication t-chart. This is helpful for all students, but especially for those students who do not fluently know their multiplication facts. (see t-chart example in picture below)

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At this point in the year my kiddos have had a lot of practice with multiples of 10 and 100. After modeling and many examples, most of my kiddos understand 30 x 6 is a ten times bigger than 3x6 and 300 x 6 is a hundred times bigger than 3x6. Some students are able to justify this by repeated addition.

We use the partial quotients method or repeated subtraction method to teach division. (see examples in picture below) I LOVE this method of division for 4^th graders because it helps them retain their place value understanding. In a short amount of time, they are even completing some division problems mentally.

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When I introduce division, I put into a story. I tell them I baked 298 cookies for the bake sale. I tell them I want to buy some fancy boxes in which to put the cookies. I explain to them that these boxes are really expensive so I just want to buy enough boxes for the cookies. I tell them I am going to put 5 cookies in each box. At the fancy box store, they sell boxes, in packs of multiples of 100, multiples of 10, and 1-9.

I ask the students if I need 100 boxes. They discuss this at their groups. This question usually has a good discussion the first couple of times. Once they decide that I do not need 100 boxes, I ask them if I need 10 boxes. They decide I do need 10 boxes. I tell them that the fancy box store sell packs of boxes in multiples of 10. (10, 20, 30, 40, 50, 60, 70, 70, 90) Next, we figured out what size pack we should buy from the store. We used our 5s t-chart for visual reference. We decide to put the 50 pack of boxes in our shopping cart.  I ask them how many cookies will I be able to box if I buy 50 boxes. They tell me 250.

I baked 286 cookies and I have enough boxes for 250 cookies. How can we figure out how many cookies I still need to get boxes for? (Subtraction)  We have 36 cookies that do not have a box. If we buy a box of 10, I will have left over boxes. So we look at buying a 1-9 pack. Using the t-chart again, they decided that a 7 pack would get us the closest without going over. Boxing 35 of my cookies. 

We put 285 cookies into the 57 boxes. There was one cookie remaining. 

A friend of mine introduced me to this partial quotient website, The Quotient Cafe. My kiddos loved it! 

I also have a division set of practice problems. These problems increase with difficulty as you progress through the set. This makes differentiating easy. The problems are on a "Big 7" as I call it, so that students' work can be neat and organize when they are first learning. Select a page from this set and you have a quick assessment. Answer keys are completely worked out, so you can quickly see in which step your students made their errors. Click here to checkout this set!