Dividing Fractions within word problems

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SWBAT divide fractions within word problems using multiple representations.

Big Idea

: This lesson completes the conceptual understanding of dividing with fractions by using it with real life problems.


10 minutes

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.

Word Problems

20 minutes

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.  

Word Problems Independent Practice

60 minutes

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 1st 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. 



5 minutes

Since this is the 3rd 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)