I always invite conversation around how we teach fractions because there are so many ways to help students make sense of them. As I walk through our work, I try to share photos, student examples, and the reasoning behind each step. I do this partly to keep myself honest about my choices, and partly because I love hearing what has worked well in other classrooms, too. If you have ideas or resources that have been successful for you, I’m always eager to learn from them.
Teaching fractions throughout the year
One thing our district math team emphasized when we built our pacing was the importance of giving fractions more than a single stretch of instructional time. We built in two units. We do one one now to develop foundational understanding. Then we built in a later one that connects fractions, decimals, and the more sophisticated ideas students will need. That structure has really shaped how I approach the beginning of this work.
Today I started by asking students to reflect on what they already know about fractions and to rate their overall confidence (using our 4 3 2 1 ) scale (Click here to revisit earlier blog post about this!) and the results were quite amazing! In a ten minute writing time, I got to witness a number of misconceptions, poorly explained reasoning, and a bunch of “3’s” and “4’s” in confidence!
Good thing I had planned on starting slowly! Today we started our new math notebooks, and I explained to the students that we are “raising the rigor” one level more. The poor things have heard this all year! I told them we are going to work hard to use our new notebooks to both record our thinking, our practicing, and our new learning.
I’ll blog more about this later as it unfolds! For today, we started the section we called “Fraction Concepts” and even talked about what the word “concept” means. Fascinating! I told the students that our job through this unit would be to determine some things we could determine to be “true” about fractions and that we would be working our way through a number of these “truths” during the unit.
Today’s fraction “truth”
Today’s “truth” involved ensuring that students understand that fractions represent equal parts of something. (I didn’t really want to use the term “whole” yet–I don’t really like to treat fractions of “objects” and “sets” differently until I have to!) I also told them that we would be spending some time creating equal parts.
Then, I put the students into pairs (I love popsicle stick picking!) and gave them each 3 minutes to find a classroom object that was either a square, rectangle, or circle. The item needed to be bigger than a deck of cards and smaller than a book. Each team was then assigned a color of paper and we got started.
The Task
With your partner, trace and cut out your shape. You will need many of these as the investigation unfolds. Your job is to find ways to divide your shape into equal parts. . . first in two equal parts, then three, and so on.
I made sure that we had plenty of objects accessible in a variety of sizes. You could also have cardboard tracers if that is more appropriate for your learners.
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I then showed the students the following charts–each is labeled “halves”, “thirds”, “fourths”, and so on. I used pieces of bulletin board paper, but you could use construction paper or even just set your shapes on the floor by the headers. As they discovered a way to fold their shape, they were asked to put it on the correct chart. I was on the prowl for work that was not accurate and precise.
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| Voila! Posters are taped to the ground with deliberate “aisles” so they don’t get trampled on! |
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| Each poster is labeled with the word for the fractional part–I will use the words and different symbols interchangeably throughout the unit. NOTE: The chart does NOT say “1/3” because we were not identifying 1 out of 3 parts. |
FRACTION MISCONCEPTION ALERT! Make sure students are aware of the difference between drawing “thirds” and drawing 1/3. Watch for this and help students see the difference.
Digging In
Students dug into their work and did need some frequent reminders about using straight edges, working carefully, and so on. (I know–shocking!) That being said, they were very engaged and thoughtful. I heard some pretty nifty stuff like:
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| Tracing… |
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| Using a straightedge for precision… |
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| Circles are the toughest as this team found! |
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| The charts started to fill…first halves and thirds, then fourths and eighths…we’ll see how it “unfolds” tomorrow! Got to love a little math humor, right? |
What’s next?
This is the difference between asking students to REPRESENT and MODEL fractions rather than just identifying fractions on a piece of paper. This activity deepens understanding, gets students noticing and talking, and helps you as the teacher to notice misconceptions and to better understand where things might be going wrong.
One more thing…
The terms “numerator” and “denominator” did come up in our lesson today. I made a poster to represent this and hung it on our math board. You may need to introduce the terms over the next days if your students do not bring them up!
UPDATE!
