Equivalent Fractions – Educational Aspirations

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My third grade students have been exploring fractions. For the past month, students have been delving deeper and constructing a better understanding of fractions. Last week, students cut out fraction area circles and matched them to find equivalent fraction pairs.

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For the most part, students were able to match the fractions to observe equivalency. Afterwards, students discussed how to find equivalent fractions through different means. Some students made the connection between doubling the numerator and denominator, while others noticed that they could divide to find an equivalent fraction.

Early this week, students started to place fractions on number lines. They used the whiteboard and a Nearpod activity to become more accurate when identifying and labeling fractions on a line.

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It was interesting to see how students showcased their understanding as the number line increased from 0-1 to 0-2, and beyond. Giving an option for students to decide which number to use seemed to encourage them to take a risk with showing their understanding.

On Wednesday, students started a fraction task related to computation. Students were asked to color each fraction bar, cut them out and organize the fraction pieces to complete given number sentences. Students had to rearrange the fraction pieces and found that there were leftover pieces, which makes this a more challenging task. You can find more information about this activity here.

This task took around a day to complete. Students struggled at first and they used a lot of trial-and-error. Students compared the fractions bars and switch the pieces around quite a bit before taping down the sum. A few students needed a second attempt to complete this.

On Friday, students used polygon blocks to show their understanding of fractions. Using polygon blocks, students were asked to take one block and label that as 1/4, 1/2, 1/8, or 1/12. They then combined at least three different blocks to find a sum of 3 1/2.

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Students used whiteboards and geometry blocks to combine the fraction pieces. I observed students using different strategies to combine and then take away blocks to find the sum of 3 1/2.

Next week, students will investigate the relationship between fractions and decimals.

A few days ago I started gathering resources to supplement a math unit on fractions. The classroom was studying equivalent fractions and I thought there might be a variety of resources available on a few of the blogs that I regularly visit. I generally follow the #mathchat hashtag and find/share ideas that relate to mathematics. While reading a few math blogs on fractions, I came across John Golden’s site that has some amazing ideas that can be used in math classroom. His triangle pattern template sparked my interest.

John provided a template that’s available on his site. I printed out the template and began filling out each triangle with fractions. I ended up with a sheet that looked like this.

So what happened?

First a lot of brainstorming and error checking. Then I decided to have students cut out the triangles and compile equivalent fractions. This is what happened …

Students in fourth grade cut out each triangle and combined them to make equivalent fraction squares. Students worked in collaborative pairs during the project. I observed students using math vocabulary and having constructive conversations with each other to finish the assignment.

Before giving the assignment to a fifth grade class I decided to eliminate two triangles on the sheet above. It was the job of the student to find what triangles were missing and create equivalent fractions to complete the squares. The students were engaged in this activity from start to finish. Some students even wrote the equivalent decimal next to each square.

Overall this project took approximately 45 minutes to complete and it was worth every minute. Students used the terms fraction, improper fraction, mixed number, numerator, denominator, multiplication, division, and pattern throughout the project.

Just as I did, feel free to tweak this project to best meet the needs of your students.