Fraction circles have been used for ages to assist students in learning fraction concepts. This is mainly because a circle can be divided into any number of equal size pie slices. Try slicing a rectangle into seven equal sized sections and you'll see why circles are so convenient.
Not only did we improve on the old fraction circles, we added a new choice: the multi-color fraction circles.
|First page of the multi-color fraction circles. These fraction circles continue up to twelfths.|
In these fraction circles, we've kept the pie slices with the same numerators the same color. For example, every fraction slice with a 4 as a numerator (4/4, 4/5, 4/6, 4/7, etc.) is colored pink. This might be useful for comparing fractions with the same numerators in a question such as, "Which is greater: 7/8 or 7/11?" Of course, there are certainly other imaginative uses for these fraction circles.
Ideas for Using Fraction Circles
Here are ten teaching ideas you can employ with fraction circles.
- If you use fraction circles as manipulatives, try to get them printed on transparencies/overhead slides. Not only will they be more durable, they will be translucent to allow overlapped items to be partially visible.
- Use fraction circles for comparing and ordering fractions. If necessary, cut the fraction circles up into separate circles or even into separate fractions. With separated pieces, it should be easy enough to see which fraction of two given fractions is greater in size. Giving students this visual memory will encourage them to remember the relative sizes of various fractions. They will also start to recognize equivalent fractions.
- Using the black and white fraction circles, you can easily compare fractions if you make a paper and a transparent version. Color the paper copy with pencil and the transparent version with a non-permanent marker, compare, rinse/erase, and repeat.
- Operations with fractions usually require the the fraction circles be separated. To add two fractions together, continue the circle started by the first fraction with the second fraction. If the sum is less than a full circle, then find a section that is the same size using the remaining fraction circles. For example, adding 1/3 and 1/2 together makes a partial circle and should compare quite nicely with 5/6. To subtract using paper black and white versions, overlap the two numbers to be subtracted with the subtrahend on top and with one edge (radius) lined up. Draw a line at the end of the subtrahend's other edge and find another fraction circle section that is the same size as the remainder of the section not overlapped. This assumes that the difference is positive. For negative differences, you might have to flip the circles over.
- Use the multi-colored fraction circles in simple probability experiments. A paper clip bent out and a pencil or compass point turns the fraction circle into a simple spinner. Just hold the pencil or compass point on the center of the circle, hook the paperclip over the point and flick the other end of the paper clip to spin it.
- If you print multiple copies of the fraction circles, multiplying fractions with whole numbers can be accomplished through repeated addition and consolidating the fraction circle pieces into wholes (if you have a multiplication question that gets that high, e.g. 1/7 x 5 won't but 3/4 x 9 will).
- Thinking about simpler skills, modeling fractions is easily accomplished with the black and white versions. Start with the segmented ones that are labeled, then the unlabeled ones, then try to see if the student can model fractions on the 1/1 whole circle (i.e. without guidelines to help). They can check how close they were by holding a segmented circle and their answer up to a light, or by using a transparent answer sheet.
- Use the unlabeled versions for recognition. Have students identify fractions either still intact as full circles or sections of those circles cut out. The more visual information they have, the better they will understand what fractions are later on.
- For students who breeze through everything else, give them some challenges like, how many different ways can you add three fractions together to get one whole. Have them show their work and/or make a poster showing the different ways they made one whole.
- Use the fraction circles in games. This is limited by your imagination, but here is one idea. Give each team a full set of fraction circles cut into segments and with magnets on the back (to attach to a magnetic chalk or white board). Give students a question, such as, "This fraction is greater than 5/6 but less than 7/8." Either give each team a turn or make it a race. Keep score, and of course, try to make it a tie so everyone feels good at the end :-)
We thought of ten ideas to use our fraction circles, do you have any other ideas? Comment on this post to share them if you do.