Fractions, fractions are everywhere,
We need to know, we really care.
They help us split up things into,
Many parts including two.
Numerator and denominator is where to start,
We love fractions with all our hearts!
“Why and how might you build or use a fraction kit in the classroom?”
Fraction kits can be very useful in classrooms of many grades. Students can start learning about fractions through the concept of splitting things (especially food 🍕🍰🍫🍪) equally before they are supposed to be taught about fractions, to meet the curriculum expectations.
A fraction kit is a tool that students can use to help them visually represent and solve fractions. A fraction kit can be made from paper (easy and inexpensive for a whole class set) and baggies or envelopes for students to keep their pieces in one safe spot. Depending on the grade, you could have the pieces pre-traced with the different fraction lines on the papers (whole, halves, thirds, quarters, etc.) for the students to follow the lines and cut them evenly. For older grades, teachers could give the students the papers (or index cards) and have them measure and cut the pieces themselves into the desired fractions. When I do this with my future students, (when because I will definitely be doing this as I think it is extremely beneficial for students) I will have them create their fractions on different coloured papers (or have them colour their pieces) so that it is easier to identify which papers go together to create a whole and to make them more colourful and fun to use. You can find some directions and activities to do here: EduGains Fraction Kits.
Fraction kits are a useful tool because it visually allows the students to get hands-on and make their own personal kits. Having the students cut up their whole pieces into the desired fraction allows them to see how they can take a whole and break it up into different fractions/size pieces and that a whole requires all of the pieces from that desired fraction. For example, to make a whole out of quarters – you need all four 1/4 pieces and if you want a whole out of eighths – you need all eight 1/8 pieces.
In our Curriculum and Instruction Mathematics course, a couple weeks ago, we made our own fraction kits using index cards. We did it fairly quickly by eyeball measuring the pieces. I thought how great of a resource this was for younger students, specifically the students I tutor on a regular basis. When I got home, I cut out coloured pieces of paper and traced lines on them to cut into different fractions. I traced the lines in a way that would make it easier for students to compare fractional pieces to one another by having all of the lines be cut vertically instead of some horizontal and some vertical. I did this so that my students could easily place the fraction strips on top of each other to compare the sizes. If the fraction pieces are different shapes (some square and some rectangle) it can make it more difficult to compare the sizes.
Fraction kits have helped to improve and deepen my understanding of teaching mathematical concepts using manipulatives. “Manipulatives are physical objects that students and teachers can use to illustrate and discover mathematical concepts, whether made specifically for mathematics, like interlocking cubes, or objects that were created for other purposes.” (Van de Walle, page 25). The word manipulative makes me think of a set of tools that probably cost the teacher a fair bit of money to have enough for a whole class set. Usually, when I think of using manipulatives to teach fractions I think of plastic or foam fraction strips and fraction circles, which can be expensive to provide enough for each student to have their own set. Using a homemade paper fraction kit with students is an amazing and inexpensive way for each student to have their own fraction kit for their reference! Creating our own fraction kits in my university class helped me to see how easy it can be to do with students and that having the fraction strips right in my hands can help visually see how fractions compare to one another. Being able to take my fraction kit home with me that day helped me to realize that a fraction kit like this, that students make can easily be taken home, or be made at home as an additional set. This is beneficial as it can help students to deepen their learning and understanding of fractions at home when completing homework or as additional practice.
When working with fractions, it can be beneficial for students to be able to make connections about the relationships in the problem. Talking about having 12 elephants in your backyard and your neighbour’s backyard is unrealistic and can be harder for students to grasp the concept because they can get stuck on the unrealisticness of the problem. In the article “From Students’ Problem-Solving Strategies to Connections in Fractions” from Teaching Children Mathematics, 2005, it says that “one connection is the relationship between the division of whole numbers and fractions.” (page 454). This is significant because the ideas of both division of whole numbers and fractions go hand in hand. Thinking about dividing 12 elephants in half is dividing the whole number by 2 or thinking about the half as a fraction of 1/2. They are essentially get the same answer but allow students to think about it differently. Students can make fractions by splitting a whole of something into pieces without realizing they are making fractions. Using the fraction kit made from paper allows the students to see that the whole piece of paper is made up of fractional pieces as they physically cut the paper into equal pieces. The fraction kits can be very helpful in answering equal sharing questions as the students can use the set of the denominator number they need and then see how they can split up the pieces according to the question.
Poem from Math Story – Mr. R.’s World of Math
Online Resources for Fractions:
Math Learning Center – digital fractions that you create (online or you can download the app)
Common Sense – a whole list of resources (free or paid)
Teacher LED – interactive teaching resources for fractions, decimals, and percents
Cool Math 4 Kids – steps for helping students with different math questions that deal with fractions
EduGains – resource for teachers to help teach fractions to students
IXL Learning – variety of interactive questions that are great for a Minds On for students
Works Cited:
Van de Walle, John A., et al. Elementary and Middle School Mathematics: Teaching Developmentally. 3rd ed., Pearson, 2011.
Students’ Problem-Solving Strategies to Connections in Fractions. Teaching Children Mathematics, 2005, p. 454.
Goorts' Gearbox 