# Fractions Day 9: Comparing and Sequencing Fractions

Today was a “test” day in fourth grade–a test for me to see where my students are with fractions. I started by giving them an “entrance” slip that just asked them a few basics, and then asked them to respond to the following prompt in their math journals:

“Can a fraction ever have more than one name? Explain your thinking.”

In my head, I needed the following activity to “take the temperature” of my class to see how they could apply some of the things we have explored–and to see what misconceptions have continued. I learned a lot about where to head next! Here’s how Day 9 unfolded. . .

### Comparing Fractions

I divided the class into 3 groups (if I did it again, I would do 4 groups) and provided each group with a stack of fraction cards. I simply asked them to work with their team to put the fractions in order from largest to smallest. NO–we haven’t worked on this yet. NO–we haven’t worked with equivalent fractions yet (although many students have made some discoveries about both of these along the way).

As the students worked, I walked around and recorded interesting things that students said. A few students came up to ask clarifying questions, and–as they are now used to–I simply shrugged and suggested they check with their team. The students worked for TWENTY MINUTES and I heard some of the most interesting logic (LACK of logic!) and great discussions. . . and even heard some great teamwork with compliments, suggestions, and “Oh–THAT makes sense”-type comments.

Debating what a fraction with the same numerator and denominator means…

A student trying to “prove'” her idea with a picture — but her group didn’t listen!

Eventually, all the groups realized that they would need to “stack” some fractions that they determined to be the same size.

I was intrigued to see how much shifting there was back and forth with certain fractions. The “3/10” card seemed to be a HUGE issue for all three groups! I heard everything from

“It’s almost the same as 1/3.” to

“It’s a long way from 3 to 10 so it’s a small fraction.” to

“3 is way more than 1 so it has to be bigger than 1/3.”

I frantically wrote down interesting things I heard . . .

After it seemed like the groups were fairly set in their sequence, I gave the 2 minute warning and then asked them to stand by their “number line”. I then asked them to rotate to each of the other groups’ work and compare it to their own–to see if they could notice similarities and differences.

They walked around and had some really nifty conversations . . . “I wonder why they put the 3/10 there?” and “Everything above 1 whole is just like ours.” and “They did it like ours but switched the smallest ones.”

We came back as a whole group and studied the list I had put on the board a little more . . . students explained their thinking–and then begged to know if they “did it right”. I smiled and told them that NONE of the groups put all the cards in the correct sequence–but that all were close.

I told them that we would be studying some of the concepts needed to do this well–and I promised I would let them try this again later–and I guaranteed their groups could do it correctly and far more quickly!

### Fraction Understanding:  Making Math Observations

What did I learn? I learned a few new tidbits about my students’ understanding:

1. They have not yet all discovered that larger denominators mean smaller pieces.

2. They have not discovered that fractions that have the same “gap” between numerator and denominator are not equal (ex. 2/3 and 9/10 both have a “gap” of 1 but are not equal)

3. They have not all developed a fluent or accurate way to determine if fractions are equivalent.

I noticed a few more things for individual students, but I know now where to head tomorrow! We are going to start some more paper folding to try to “discover” some things about equivalent fractions. It was a great learning experience for the students AND for me today!

I have had several of you ask about whether or not I was going to write all these lessons up and make a product for my store. The answer is YES–but it probably won’t be ready for a while because I want to go all the way through the unit first.

That being said, I DID create the sequencing cards I used today and put this activity with two other ones in my store. I have used these activities in the past with GREAT success, and I have those ready for any of you who wish to try. I have similar activities for decimals and larger numbers. I also created a bundle of all three “number sense” sets at a reduced price. If you think they would help you, check them out! Just click the image below.

***UPDATE***

This blog post and sequencing activity is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions!