Visual Fraction Models

fractionmodelstitle

Today students explored fractions using number and visual models. Students have been practicing how to add and subtract numbers for the past few weeks. Most of the students have an understanding of how to find common denominators and add or subtract problems.  Yesterday students answered word problems involving fraction computation.

What I’m noticing is that students are understanding and compiling their number models but aren’t as comfortable with visual representations. Being able to model fractions is important and a key ingredient in understanding fractional parts. As the class progressed I felt like there was a disconnect between fraction representation and computation. Eventually, the lack of conceptual math understanding impacts a student. I’ve found this to be especially clear with fractions.  So today’s class focused on showing both, the number model and visual representation. Students worked in groups on the page below.

Visual Fraction Models
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Students worked together on the two problems. There was a lot of struggle, especially with the visual model portion of problem two. I was tempted to lean in and help the students but I wanted them to use strategies and their partner to find a solution. I let the students work and even debate strategies with each other. Near the end of the class students presented their final number models and visual representations.

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This student turned a pentagon into 5 triangles. Each triangle represents 18 miles.

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I gave them feedback and asked questions in return. Two of the better examples are above. Tomorrow the class will be exploring visual fraction models via Thinking Blocks. Overall, I felt the productive struggle was worth their time and I hope that another layer of conceptual understanding is starting to cement.

Exploring Fractions

Exploring Fractions

Fourth grade students explored fraction computation last week. Since the beginning of the year they’ve been periodically reviewing how to add and subtract simple fractions. About a month ago this same group of students used fraction pieces of a pie to show a visual model of adding/subtracting different fraction less than one. Last week students identified and compared fractions and mixed numbers. They started to convert mixed numbers into fractions and vice versa. I’m finding that as the students became more comfortable with converting fractions they’re becoming better at fraction computation. Not all the students are at this level, but many are ready to add/subtract mixed numbers.

Over the past few years I’ve used a fraction computation activity that I often refer back to throughout the year. Every year I tweak it a bit more to fit better with my students. This year I felt my students were ready for the challenge. The students cut out the fraction pieces below. Students are then given time to explore how different fraction pieces are equivalent.

Fraction Blocks

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I asked the students to model different types of fractions with their pieces. The class came to a few different conclusions on how fraction sums were calculated. I didn’t really hear students talk about finding common denominators; instead I heard students saying the words “equivalent” “matches” “is the same as” throughout the conversation.

Students were then asked to combine their fraction pieces to find certain sums. For example, students were asked to show 1 1/2 using 7 pieces.  Students wrote the number model below their visual representation.  I was encouraged to see that some of the students showed fraction multiplication in their number model eg. (5 x 1/6) + 1/3 + 1/3 = 1  1/2 .

fraction pieces

Through trial and error students started gaining traction in finding the sums. Students had to place all the questions out on their desk and match the fraction pieces to find the sum. After all the fractions were found students taped/glued them to their paper. The class then discussed how this activity could be completed in a variety of ways. Next week students will reflect on this activity in their math journals. The activity described in this post can be found here.