In order to understand division of fractions, I’m taking them back to think about whole number division. Essentially, division asks “how many”. It’s important to verbalize that no matter what units we have(as long as they are same units) , the answer is still the same. Therefore, when working with division of fractions, we can utilize common denominators to get our same units and be able to divide just the numerators. (SMP 7). Students can use athink-pair-share to discuss their thoughts on each statement.(SMP 3)
For each problem, I want the students to say “ how many _________ go into _______”. The reason I do this is because it gets them thinking about the action in the problem. If we have same units(common denominators) then we will model the division by dividing the numerators (remember, the units don’t matter if they are the same). I want the students to model the division to get a conceptual understanding of how division works. Once they have modeled it, we will find our answer by dividing the numerators. If we have different units, we will need to find equivalent fractions. Each time we need to find equivalent fractions, I’m going to create the model and the number sentence to go along with the model.(SMP 4) It’s good for students to see the visual and symbolic representations to continually make connections between the two.(SMP 2) Since this is a new topic for the students, I will be modeling along with them. I’ve put together an example that is already done for them. I want them to watch and listen as I explain the problem. I do not want them taking notes at this time.
I will say,
The problem is asking us how many 2/3 are in ¼?
The model shows this and I will write the symbolic notation next to it.
Then, I will say if we can get the fractions to have common units (denominators), we can divide the numerators to find the answer.
To find common denominators, we can use the LCM or any common denominator. We will use 12 as our common denominator.
So, ¼ = 3/12 and 2/3 = 8/12
Now our problem becomes how many 8/12 in 3/12. Since the units are the same, we can divide the numerators.
3÷8 (it is modeled so they can see the answer is a fraction) = 3/8
Our answer is ¼ ÷ 2/3 = 3/8.
You can take this one step further and let them know they can check this answer by multiplying the quotient by the divisor 3/8 x 2/3 to see if it equals ¼. This method is used in regular division and applies to fractions as well. (SMP 6)
Now, it’s time for the students to interact with the math. Work through each problem together and have the students explain the process. Each slide on the power point and in their notes is outlined with say, re-write, model, and answer. To start, the students will be working with common units. I still want them to model to get a visual understanding of what it looks like. Next, I have them finding common denominators and finally I have them working with whole number by fraction division. My role during this time will be to facilitate the instruction. Asking questions such as, is our problem ready for division by having common units? What is the problem asking us to find? When we have common units what can we eliminate?
Before students move on to the next activity, I’m going to have them reflect on the solution to their division problems. I want them to go back and look at their problem and see if they notice that each time they divide, their quotient becomes larger. (SMP 7)
The NHT is located in the power point. I did this because I wasn’t sure how much time would be needed for instruction, but I wanted to get the students working independently too. So, I will use some or all of the NHT depending on time. Each problem in the NHT asks the students to write a division problem and model their thinking. I liked how the problems start out by asking them How many _____? This is what we have been learning about today, but instead of starting out with the number sentence, they have to find the number sentence using the “how many” question. This will also help them when we start to look at division word problems. (SMP 1, 2,4)
As students are working independently, I will be targeting the students that seem to be struggling. These students will not know how to start on their own. They will forget to find their common denominator or they may not be able to read the model. I will be reminding students to use their notes for a resource to assist with any difficulties.
I’m going to do a think-pair-share activity for the closure. I want students to make the connection between division and addition of fractions by saying that they both need to have common denominators. The difference being that division asks us about equal parts or how many whereas addition asks us about total. This understanding will help the students work through word problems and it gives me a good idea who understands the meaning of division with fractions.