Fractions can be challenging. There is no doubt about it. And in my years in elementary school classrooms, teaching and coaching, I've heard the struggles of teachers and students.
But there's good news! Fractions do not have to be abstract. When you teach multi-digit multiplication, it is hard to represent the numbers with pictures because they are so big. The concrete models are really used in the early stages of multiplication. But with fractions in elementary school, we spend the whole time in the early stages. You can represent everything with fraction bars, making it concrete and accessible to every child.
Fractions are by far my favorite math unit to teach. With any fraction standard, I first introduce it with fraction bars (also known as fraction tiles and fraction strips). This hands-on, visual way to learn about fractions means that every student can grasp the concepts and experience success with fractions.
Yes, fraction circles are visual, but can you line them up next to each other and see how they compare or if they are equivalent? Not easily!
Using Fraction Bars
Introducing Fractions
Introduce fractions with a printable fraction bars. Cut and laminate a set for every student. It is helpful to use the printed, premade fraction bars at first, rather than having students draw them on their own because students need to see what accurate fractions look like. Once they are familiar with the fraction bars you've provided, you can begin to work on drawing accurate representations of fraction bars. Spend some quality time on this. If students cannot accurately draw fraction bars on their page, it is not so helpful.
Also, some examples in math books will have only the part of the fraction drawn as a bar. Always draw the whole bar and shade in the fraction. You need the whole there to compare fractions, to see which are equivalent, etc. If there is only part of the bar represented, the visual ends up not being accurate.
Fractions on a Number Line
I don't know what it is about number lines, but I must say every year I have a group of students who are utterly perplexed and overwhelmed by this awesome mathematical tool. Well overwhelm be gone! I teach students to first draw their fraction bars and then use the fraction bar as the guide for the number line. Just draw the number line under the bar. The ends of the bar are 0 and 1. Each dividing line in the bar is a tick on the number line. Easy as that.
Equivalent Fractions
Love fraction bars for equivalent fractions. Before introducing students to the "multiplying/dividing the numerator and denominator by the same number" strategy for equivalent fractions, have them make equivalent fractions with their fraction bars. This lays a solid foundation so that when they do the more abstract work of multiplying the numerator and denominator by a number to generate equivalent fractions, they will understand what is really happening.
I have seen math problems that ask students to identify equivalent fractions with different shapes (circle fractions) or groups of objects shaded (1/5 of the hearts are colored). Some students tackle these just fine. And others need additional help. Teach students to redraw the pictures as fraction bars lined up under each other. Then identify the equivalent ones.
Comparing and Ordering Fractions
Again, comparing and ordering fraction problems are presented in different ways. For those who are not struggling with fractions, introduce this concept with fraction bars and then let them move on to other strategies and visuals. For those who fractions present a challenge, teach them to draw whole, shaded fraction bars for each problem, each time.
Adding and Subtracting Fractions
I love fraction bars for adding and subtracting.
I want to add 3/4 and 1/4. Draw a fraction bar. Divide it into 4ths. Shade 3/4. Shade 1/4. Oh look, the whole is shaded so it equals 1!
I want to add 5/8 and 7/8. Draw a fraction bar. Divide it into 8ths. Shade in 5/8. Start to shade in 7/8. Uh oh! I ran out of spaces to shade. Draw another whole bar and divide it in 8ths. Continue shading the 7/8s. Oh look, I shaded 12 of the pieces, 12/8. And it's so easy to make that into a mixed number because I can see I shaded 1 whole bar and 4 pieces of the next, so it's 1 4/8. And because I used these bars with equivalent fractions and now have such a strong fraction foundation, I know that I can reduce this number and it is now 1 1/2.
Easy as pie.
The same strategy works for subtracting, except you shade in the spaces and then cross out the ones you are subtracting. When you teach students this strategy they start reminiscing about kindergarten math, when everything was tallies and pictures. It is really that simple.
Unlike Denominators
I'm not saying that you should never teach your students how to find common denominators using the multiplication trick. But I am saying that you may find yourself with students who struggle to remember these strategies because they seem like abstract steps that you have to memorize. And if that is the case, then letting them rely on the concrete fraction bars is a wonderful option that gives every student mathematical success.
You are adding 2/3 and 5/6. Well we did so much work with fraction bars and equivalent fractions that students know how to use their fraction bars to find an equivalent fraction for 2/3 that shares a denominator with 5/6. Now they can use the steps from the section above to add.
But what if it is denominators like 1/4 and 1/6? Not as easy to find a common denominator here! I tell students to start each assessment of fraction worksheet by drawing out their full fraction bar set. From the 1 whole bar down to 12ths. They can look for a fraction that is equivalent to both 4ths and 6ths on their drawing and go from there!
Multiply Fractions by a Whole Number
You want to multiply a fraction by a whole number? Fraction bars got your back! Multiple 3/4 by 3. Draw 3/4 fraction bars 3 times. Count how many shaded squares there are. Ta-da! 9/4. You want to write that as a mixed number, but have trouble remembering the steps for changing that to a mixed number? Just redraw the picture! Continue to draw and shade 4ths until you have 9 spaces shaded. You shaded in 2 whole bars and have 1/4 in the third bar. So, it is also 2 1/4.
I think you get the idea now! Teaching students strategies beyond fraction bars is great, but having students that rely on them until the end is fine too if that means they can access the work and successfully complete a wide range of fraction problems. Good luck!