Simple Ways to Use Manipulatives to Compare Fractions PART 2

In my previous post, I explained how I used fraction strips to have students explore fraction sizes in order to be able to compare them.  In PART 2, I will show you how I used the same fraction strips to enhance mathematical conversations and support arguments and also, enhance the process with technology.

Fraction Comparison Strategies

By now, the students understood that the larger the denominator number, the smaller the fraction piece.  Fraction strips visually support this.  In this lesson, I used the fraction strips again to review the strategies we had learned while having the students use the following Common Core mathematical practices:

The strategies we had learned were to compare the denominators FIRST.  If they are the same, then we just use the numerator to determine biggest and smallest fraction (greater than or less than).  If the denominators are different, but the numerators were the same, we then use the denominator to reason abstractly about unit fraction size (would you rather have an eighth of a pizza or a half of a pizza?).  The fraction pieces helped support those students who still had a difficult time with reasoning abstractly in their heads.

Fraction Tasks and Partner Work

I gave each student a bag of fraction strips.  They worked with a partner to complete the following task.  As they did this, I went around providing guidance (to those confused about what to do) and to hear their arguments in support of which is largest and how do you know it is the largest.  It was exciting to hear how the students used the mathematical terms of numerator and denominator to support their arguments of which was largest.

We started with the simpler task of just comparing fractions with the same denominator.  Then I upped the ante to Task 2, which ask the students to use the fractions strips to make two fractions with different denominators but same numerators.  Again, it was confusing to some exactly what the task was so I circulated around and helped those students understand the task.

As students were working with their partners, I again circulated to hear arguments.  If there were some good arguments or explanations I took a photo of the fractions made with the fractions strips to share with the entire group.  

Why did I do this?  I want students to use mathematical language and practice those mathematical practices!  By taking photos of different models, other students can listen to and see how to explain your thinking so others can understand as well.

As I had students explain or present their argument for the largest fraction, I also made sure the other students stayed involved using Marilyn Burns Math Talk techniques:

These kinds of questions I use during my math instruction as much as I can to keep the engagement up.  I sometimes even use my pick sticks (popsicle sticks with the student's names on them in a cup) to call on random students.  Keeps them on their toes!

I think if I taught this same lesson again, I would also add another component:  Duo to Duo share.  I would have one set of partners share their explanation to another set of partners.  Then keep rotating around the room for more practice.

I also projected student models for everyone to see and use for practice.

Using Technology to Enhance Understanding

If you're wondering how I was able to project the photos to the entire class, it was done with an iPhone, an AppleTV and a projector.

It is a very quick and simple process to AirPlay over to my projector anytime I want to show something from my MacBook, iPad or iPhone.  I also used student samples for others to come up and explain which fraction was larger or smaller.

Saving the Most Difficult Strategy for Last

The next day I taught using the fraction strips again to teach probably the most difficult strategy for students to grasp:  the missing piece strategy.

It is a strategy that twists your brain least for a third grader!  It requires to think OPPOSITE of what you see.  But with fraction strips, it becomes more understandable and easier to explain.  

I had the students build two fractions:  3/4 and 2/3.  Each fraction is missing just one piece for it to complete a whole.  This is the way I had the students use this strategy.

What is the missing piece in 3/4?  1/4...find a one-fourth fraction strip.

What is the missing piece in 2/3?  1/3...find a one-third fraction strip.

Now put the one-fourth strip above the one-third strip.  Which is bigger? The one-third piece.  

Then using this sentence frame we reasoned it out:

Because the missing piece ____________ is larger than the missing piece ____________, we can say that _______________ is larger than ________________.

Here's how it looks with the example fractions:

As you can see, it can be hard for a student to follow along (especially those students who are English Language Learners).  So by using the fraction strips and the sentence frame, the thinking can be scaffolded until complete understanding is achieved.

Next week, you will see how my students compare and order fractions in Google Slides for digital practice that will prepare them for standardized testing on the SBAC!  Come back for PART 3!

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