Fractions of a circle

How can I represent a fraction with a picture?

Our math focus question for day 2 ended up being quite simple for my students to answer. That energized me and allowed me to alter the lesson on the spot and add a few challenges to the circle geoboard lesson, like finding and representing 1/12 of a circle.

I thought that students would have the most difficult time creating 1/3 of a circle, but I was pleasantly surprised when this came easily to the majority of the groups.  Getting students to use the Geoboard before simply drawing out the different fractions proved to be the largest problem. Oh the math practices and the heartache that can sometimes come with them!

Students had easy transitions into their groups and partnerships today, which was wonderful to hear and see. I have a voice level chart in my room anyway, which helps to monitor such events in the classroom.  I think that the numbering around the room is also helping in these transitions. Label everything you can to make math workshop run smoothly!

Partner Math Parallel Questions

How do you know that 1/2 is larger than 1/3?

How do you know that 1/2 is larger than 1/4?

How do you know that one whole is larger than 1/2?

Take Aways from Day 2

One aha! moment for me was actually during the independent math portion of the workshop. At least 3 different students let me know that they had forgotten what each comparing symbols meant (<,>).  Yikes!  I need to print off Comparing Symbols bookmarks for my students so that those symbols are easily remembered.

            Re-engagement for whole fractions
Yesterday I had three students that circled either 1/3 or 2/3 to represent one whole, which obviously concerned me.  So today during our independent math portion of class I invited them to my work table to talk about this concept. Turns out that one of these students knows an infinite amount of fractions that equal one...so I am thinking that he just rushed through the problem because it was the end of class. That's another issue to tackle, but I'm happy to know that his answer was not because of a misunderstanding.

The other two students who circled fractions besides the whole took a little longer to come around and I am only convinced that one of them now understands and would be able to recognize fractions that represent the number one independently. 

I wrote a variety of fractions on their white boards and asked them to circle the fraction that meant the same as one whole. Both were able to complete this task with success, but only one was able to create different examples of fractions that equal one whole.   

I will provide another re-engagement the next time we meet, but this time it will be with some different manipulatives...maybe some of that lovely Dollar Tree clay I found last week! 


Loving this math unit but we have an assembly tomorrow, which means no math...no school Friday...I have a meeting on Monday...

So no math until next Tuesday?? What am I going to do with myself...sigh.

Yummy Fractions!

So I started my fractions unit today by being a true risk-taker. And I'm so glad I was! We had fun with fractions while making Trail-Mix....Yum!

Pulling this off with 30 students took some planning and thinking about the proper set-up, but it was so worth it! I have five groups in my math workshops, but further dividing them into partnerships A,B,C, was a great plan. Since this was the first day of the new unit, the students belonging to partnership A were the captains. This proved to be clear for the students and quick for me when passing out materials. (Click here for more info about my math workshop organization.)
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I used some basic trail mix ingredients (minus the peanuts) for this intro fraction activity:

- One box of honey nut toasted oats cereal

-3 bags of mini-marshmallows

-one container of raisins

-one bag of mini-pretzels (that I crushed up even more)

-two bags mini semi-sweet chocolate chip pieces

The quantity you need will vary depending on how many students you have in your classroom and on how much of the mix you would like for your students to take home. 

We ended up with 1/2 cup of trail mix for each student, which I thought was just enough for them to enjoy while remembering that the true purpose of the trail mix was to think about and work with fractions.
-----------------------------------------------------------------          The Math Workshop Parts for Day 1


Math Talk
As students enter the room, they are to head to the "Math Talk" tray to grab the warm-up for the day. I used a simple and quick fractions worksheet to get brains flowing while not taking up too much precious time from the main activity.

Mini-Lesson

I started the mini-lesson with an anticipatory set. I had already asked students to wash their hands before entering the room (we had recess directly before this lesson) and they used that fact as a clue to help them infer what I was hiding inside my box. I also had some clues around the box (measuring cups and large zip-top bags) to help with the inferring. Look at that...math and reading strategies together in harmony.

Once I gave students a minute to talk about the clues with their partners, the work began. I passed out the jumbo zip-top bags and measuring cups to groups and then asked students "what do you notice?" about the measuring cups themselves.

Thinking quickly moved toward the fractions on the handles of the measuring cups (yes!) and then a student mentioned cooking...then the excited whispers started..."Food is in the box!"

Once students made the connections, I opened the box to reveal the zip-top bags filled with the ingredients for making the trail-mix.

Teaching Point: "Today I want to teach you that we can use fractions in everyday life. I also want you to think about how many ways we can represent one whole today."

Partner Math
The mini-lesson and the partner math then meshed together, as the class stayed whole group on the carpet while creating their trail mix with their groups. Each person had a turn scooping out a certain fraction of an ingredient to add to the trail mix bag. I altered the portions so that in total we had about three cups of food in the trail mix bag. When trying this with your own class, you might want to play around with the proportions to make sure the total can be divided evenly.

            Possible questions to pose during the activity:

"How do you know that you have more/less of _______ than _______.?"

"If we add 1/4 of a cup to the bag, how many total cups will we have?"

"If we need a total of 1/2 of a cup of pretzels, how many times should we scoop using the 1/4 measuring cup?"


Before each scoop, we talked about the fraction and if that fraction was less than, equal to, or greater than 1/2 of a cup.

Summary of Learning
At the end of the mixing, students had to figure out how much each person could scoop to make sure that they were being fair with the mix. 

I first proposed dividing the contents of the bag in half so that two out of the six students could take home trail mix, which was quickly shot down..."That's not fair!" one student protested, "unless I'm getting one of the halves!" She joked. Ahhh, I love when students forget that they are doing math and just decide to be present in the moment!

With students knowing that simply taking 1/2 of the bag would not be fair to everyone, I shifted the conversation into thoughts about what fraction would be fair.

I was blown away by how quickly students grasped the concept of using the measuring cups to be precise about their fairness...which then led to the discussion of precision of language...which cup? why? 

We soon found the correct language and vocabulary and students were using the 1/2 of a cup to make sure that the divisions were fair. Students then began scooping our their share into smaller zip-top bags for them to keep. Students were engaged the whole time and excited to see the connections that can be made between food and fractions. This real-world application really worked well!

Independent Math
In math workshop, I usually have the independent math portion come before the summary of learning, but the layout of this lesson did not lend itself to that tradition very well. I had another type of exit slip already planned for students, but due to how the lesson played out and time constraints, I simply used the Little Baker's Recipe Card as student's independent math.

                            I used the Little Baker sheet below as an exit slip...

                              Click on the picture for a free download!

Students simply filled out the questions and I paid close attention to which fraction was circled as I stapled this sheet onto their plastic bags. Out of 30, there were 3 that had something other than 3/3 circled...I will be meeting with them in a small group tomorrow to reinforce whole fractions!

Fractions are Numbers too!

Well it's the end of Spring Break for my district. It's been absolutely wonderful having a few days off to regroup and plan out our next units. And now its really grinding time---only 9 weeks left for the school year!

We are ready for our next unit on Fractions, so my time this week included a few hours at Panera thinking about fractions and reading the Common Core standards while sipping my coffee in the sunshine. (love the Hazelnut flavor!)

I am really trying to embrace math workshop with an overarching inquiry question for students and I started with this question for me: 

    How can teachers help students reach a quantitative understanding of fractions?

Students more often than not seem to place fractions in a completely different category from other numbers. My goal for this unit is to help students understand that fractions are numbers too...very important numbers.

                  I have 5 methods to reaching this quantitative understanding:

1. Use the Math Workshop model for differentiated learning

2. Use a variety of manipulatives (to illustrate the number line, the part-to-whole model of fractions, and the part of a set model of fractions)

3. Have students develop a math dictionary of fraction-related terms

4. Embrace formative assessments with specific and timely feedback

5. Use cooking and games to entice students into the world of fractions

I'm trying to narrow down a student-friendly inquiry question. I could really use your help blogging world!

Here are the options:

1. Is taking 1/2 always fair?

2. How can we be fair to our friends when sharing?
3. When is taking 1/2 not fair?

Vote on your favorite or add one that you think works well for fractions!