# Dividing Fractions

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## Objective

SWBAT divide fractions using common denominators.

#### Big Idea

Developing a concrete and conceptual way to divide fractions helps students understand the “why” part of the process.

## DO NOW

10 minutes

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)

## Teacher Model

15 minutes

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)

## Dividing fractions using common denominators

30 minutes

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)