Comparing Fractions

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Objective

Students will be able to compare fractions with unlike denominators.

Big Idea

Given a set of unlike fractions, students will be able to explain and model which fraction is greater.

Anticipatory Set

7 minutes

Since students have been learning several ways to compare fractions. I introduce this lesson by introducing the concept of transitivity.  I write this concept of the board.  If a>b and b>c.  Then I ask students would this same concept apply to letters a and c.  Students should see that a>c.

Then, I ask students if this same rule applies to fractions what would happen to the denominator if we compared them.  (both of the models used have been shown in previous lessons) 

I want the students to channel their thinking towards comparing fractions with unlike denominators.

We will focus on the following the following Mathematical Practices: 

MP.2. Reason abstractly and quantitatively. 

MP.4. Model with mathematics. 

MP.5. Use appropriate tools strategically. 

MP.7. Look for and make use of structure.

Fraction Pad

Modeling

15 minutes

I invite students to the carpet to discuss how to compare fractions with unlike denominators.  I write two fractions on the board that have the same denominator.  I ask students to tell me which fraction is larger.  

1/12      2/12  

 I want them to see that when the denominators are the same the fractions with the largest numerator determines which fraction is larger.  In this case students should say 2/12 is larger than 1/12.  I repeat this task with two fractions with different denominators.  I ask students to compare 3/5 and 3/15 and tell me which fraction is larger.  Students say if two fractions have the same numerator the fraction with the lesser denominator is the greater fraction.

This process is essential for students to understand in order to be successful in comparing fractions with unlike denominators.  (Repeat this process until level of understanding is reached.) 

When a level of understanding is reached and students are able to apply their understanding to compare fractions with unlike denominators, I pair students and give each pair their own dry erase board.  Then, I write Carol read for 5/6 of an hour. Kim read for 1/3 of an hour.  I encourage students to explain and use models to justify their answer.

While students are eagerly working on solving the given problem, I ask them to discuss their answers with their partner…I want to hear what students have learned so far about comparing unlike denominators. Some students rely on visual models to determine which fraction is larger. I encourage them to use models because it will help them progress towards being able to compare on their own.  I also use this time to correct any misconceptions. 

We do this practice for about 15 minutes or so, or until students are able to explain their answers without difficulty.

Student Working

Guided Practice

10 minutes

The goal of this exercise is to let students explore and discuss this concept on their own. Students need time to work with new concepts because it helps them develop their own thinking as to how the problem is structured.

Materials: printable fraction strips.pdf

I ask students to move into their assigned groups. Then, I write the given problems on the board 3/8; 8/10; 1/3; 3/4; 5/8; 2/6.  I tell them to compare each set of fractions using the greater than or less than sign to determine which fraction is larger.  I provide students with fraction strips to help support their learning. Visual models allow students to focus on the actual size of the fraction. 

Student Talk:

 As students are working on their given task, I move into facilitator mode to check students' understanding.  Students are able to explain why two fractions with the same denominator are a part of the same whole. One student determined the fraction with the greater numerator is the greater fraction.  Another student explains that if two fractions have the same denominator, then the fraction with the lesser denominator is the greater fraction.  I also make sure to ask them how and why they solve their given problem.

Independent Practice

20 minutes

Now that students have gained a deeper knowledge of how to compare fractions with unlike denominators, I ask students to transition back to their seats to write what they have learned in their math journals. 

Probing:

Can you explain what you have done so far?

Did the fraction strips help you determine the greater or lessor fraction? Explain?

Can you give me an example?

Student Talk:

  I ask students what do you notice about the relationship between the numerator and denominator of the fractions that are less than ½.  Since they are comparing, some students should be able to explain that the denominator is more than twice the numerator.  It’s ok if students are not able to grasp this concept just yet!  However, it is important for me to understand just how much students have learned so far.  

After that, students are given their independent practice work to assess their level of mastery.  I use the results from their work to see which students needed re-teaching.

Student Sample