##
* *Reflection: Rigor
Dividing Fractions within word problems - Section 3: Word Problems Independent Practice

As I've been teaching the concept of dividing fractions, many of my colleagues ask me why I don't use the standard algorithm of multiplying by the reciprocal. My response is this. As a teacher, I want my students to understand the "why" component of their learning. Far too long we have been shoveling information in to our children and not developing a deeper understanding. I tell them that I learned to multiply by the recipricol and only until recently could I explain the "why" part. With that said, I tell them that the students are increasing their mathematical rigor by providing multiple representations to one problem. They are also implementing **practice 3 **by proving their solution is correct. They must provide support to their solution with an understanding of "why" along with their visual representation which is justifying their answer. The students are also modeling the mathematics which is **SMP 4.**

Video Explanations (Dividing fractions word problems) of the problems used in this lesson. I skipped the bucket filling question. After more practice and a better understanding, I will bring this question back to see how they do with it.

*Rigor: Word problems explained*

# Dividing Fractions within word problems

Lesson 15 of 26

## Objective: SWBAT divide fractions within word problems using multiple representations.

#### Do NOW

*10 min*

This problem sets them up for the learning for the day. It’s easy enough to rationalize to get to the answer, but I want the students to set up a visual and a number sentence to solve. This is the first of 3 problems used to demonstrate how to get information from the word problem into a visual and then to a solution. **(SMP 1,2,4)**

Students should recognize that they could make 3 recipes with the amount of sugar needed and given. **(SMP 6) **1 ½ ÷ ½. Students may need a reminder to change the mixed number into a improper fraction. Once there, they should be able to model it out.

*expand content*

#### Word Problems

*20 min*

The next two word problems build on each other. The second word problem (new recipe) uses 1/3 of a cup. Students will use the same thought process as the DO NOW problem. They will visually represent and write the number sentence to solve. Some students will be able to do this mentally. Encourage them to create the visual representation to support their answer. They can also check their answer with multiplication **(SMP 6)**

The third problem has the same set up as the last two, but cannot be solved using mental math. The students will have to use the strategies used in the other problems to apply them to this problem.

I like the way these problems build on each other to show the relationship but still get the students to think about the how and why.

*expand content*

There are 3 word problems I’m using from **illustrative mathematics **that support the objective for today’s lesson. The problems will be in their notes. They can use notes or extra paper to work on the following problems.

Before each problem, I’m going to have the students read the problem, think about their strategy and then share with a partner **(think-pair-share**). I want to do this because some students have difficulty getting started on a problem and this will help give them a little push in the right direction. **(SMP 1 and 3).** Then after each problem, have students partner up again to share/explore solution.

Side note: my students are sitting in mixed ability groups where the High student and the low student are diagonally across from each other and do not pair up at any time.

Once the students have completed the think-pair-share, I’m going to have them start working on the 1^{st} problem. We will complete each problem together. Students that finish early can check their answers and write out their how and why for the current problem.

Problem 1: Tiffany’s moist cake recipe

Time: 20

This problem is the easiest of the three. I’m starting out with it because the students will feel some success right away. Our goal is to get them to stretch, not give up. As students are working on the problem, remind them to visually represent what is going on by using tape diagrams or area models. Remind them to use common denominators to make the division easier. If students finish this problem early, have them explore the connection between multiplication and division. Ask them if they notice anything about the number sentences that appears to be the same. **(SMP 7) **This type of thinking should be used for students that are ready to make that connection.

Cooking is a real life skill.

Problem 2: Filling the bucket

Time: 20

This problem has the students working on a variety if differently worded fraction division problems. I chose this problem because students need to use a visual and then they are making connections to the equation that represents the situation. Students typically have difficulty deciding what order the fractions should be in when dividing. This problem allows students to figure out the order and making sense of what they are being asked to do.**(SMP 1,6)**

Measuring is a real life skill.

Problem 3: Travel Times

Time 20

Finding a fraction of an hour is key here. Students can use their knowledge of division of fraction using common denominators, a tape diagram, or a double number line. All of these tools are in their tool box and they should be encouraged to use them. **(SMP 4,5)**

Students may have difficulty working on this problem because they may not realize what the division will look like. In all of the other problems, the expression has been given and they can work through the problem. So for students that are struggling, you can ask them the "how many" question. Are we finding how many miles travelled in an hour or how much time it will take to travel in miles. By asking the how many question, students should remember that it becomes what we are dividing by.

#### Resources

*expand content*

#### Closure

*5 min*

Since this is the 3^{rd} day of working on dividing fractions, I want to do a quick assessment of the students understanding of this concept. I’m going to use a comprehension menu. The comprehension menu assesses understanding and learning style. Students should work through all four sections: mastery, understanding, interpersonal, and self expressive. They should place a mark on the box that felt the most comfortable for them to solve. Each section pertains to the topic of dividing fractions. **(SMP 1,2,5)**

#### Resources

*expand content*

*Responding to Kim Haber*

Hi Kim,

When I teach dividing fractions with common denominators, I use the model along with the approach. I start by modeling the scenario for the students and then get them to see that when you have common units all they have to do is divide the numerators. I model every problem for them because some of the students don't see the connection and you are correct, they need to be able to understand how to model the division.

| one year ago | Reply

Hi Michelle, First of all I want to thank you for your amazing lessons. I used two of your complete units last year and my kids enjoyed the lessons and developed a solid conceptual understanding of the material. I also picked up some great teaching strategies. I love your closures especially the comprehension menu and the three way tie. I am writing because I am curious why you decided not to do much modeling of fraction division (unless I am missing something). I like the understanding kids will build from the common denominator approach but I am a bit nervous when I read 6.NS.A.1 that I should be modeling more and relating division to multiplication. I spent a ton of time on this last year. What do you think? Thanks, Kim H

| one year ago | Reply

This sheets are perfect to give to students. The clarity is very good. Thank you for your assistance in creating something that relates to real life that students can understand fractions better.

Jeff M. in Massachusetts

| 3 years ago | Reply*expand comments*

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###### Fractions Review: Simplifying Fractions

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- LESSON 1: Divisibility Rules
- LESSON 2: Finding the Greatest Common Factor
- LESSON 3: Distributive Property
- LESSON 4: What's really going on with division?
- LESSON 5: Division of multi-digit numbers
- LESSON 6: Checking your quotient
- LESSON 7: Finding the Least Common Multiple (LCM)
- LESSON 8: LCM stations activity
- LESSON 9: Finding Equivalent Fractions
- LESSON 10: Benchmark Fractions and more
- LESSON 11: Adding and Subtracting with Fractions
- LESSON 12: Multiplying with Fractions
- LESSON 13: Dividing Fractions
- LESSON 14: Dividing Fractions - Stations
- LESSON 15: Dividing Fractions within word problems
- LESSON 16: Review & Assessment 6.NS.A.1 and 6.NS.B.4
- LESSON 17: Dealing with Decimal Models
- LESSON 18: Reading and Writing with decimals
- LESSON 19: Dewey Decimal system for ordering decimals
- LESSON 20: Adding and Subtracting with decimals
- LESSON 21: Multiplying Decimals by Whole Numbers
- LESSON 22: Multiplying Decimals by Decimals
- LESSON 23: Dividing Decimals by Whole Numbers
- LESSON 24: Dividing Decimals by Decimals
- LESSON 25: Prepping for the Exam!
- LESSON 26: Final Assessment 6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4