The number line is a perfect tool for exploring fractions and giving students a fantastic model for understanding and comparing fractions. Sometimes math instructional materials will direct teachers to use the area model for introducing and working with fractions, then they tack on the number line, almost as an afterthought.
The number line is a powerful tool. It can be used to illustrate equal parts, equivalent fractions, and fractions less than, equal to and greater than 1. True, it can be thought of as a distance model for fractions instead of an area model, but there are so many fraction concepts you can visually illustrate with a number line that it should earn a prominent place in your repertoire of “go to” math tools.
Before we get started with the nitty-gritty teacher talk, if you are working on transforming your math classroom into a space where students actively engage in their learning to practice fluency and math concepts, grab my 10 Free Math Activities. No gimmicks, no sales, no nonsense with this freebie- just one way I can help with making math hour the favorite part of the day for every student!
Two Models for Learning Fractions
Early on in a child’s life they hear certain phrases, and they intuitively know what they mean. “We’re halfway there,” said many a parent. They may not be thinking “I am geographically dead-center between where we started and where we are going,” but they may be thinking “We have to travel the same distance we just did to get there.”
What about sharing something with a sibling? My mother had the perfect hack for when my brother and I had to share a sandwich, or some kind of treat. One of us got to split it, but the other got to pick which half they wanted. Talk about pressure to avoid making one share larger than the other!
Learning about fractional distances as well as fractional areas is important for students since both models will help students gain a deep understanding of how fractions work and why we need them in the first place.
The Number Line as a Structure
The number line is a perfect structure to develop an understanding of equal shares. Students place ½ in the middle of 0 and 1. They can see one of two equal sections. When labeling fourths, they will work to try and space the fractions evenly. Students begin to internalize the idea that each share needs to be the same size, or length. They are also seeing fourths as four equal-length sections between 0 and 1. This is also a great way to understand fractions as part of a whole, or mixed numbers as whole numbers and a part of another whole.
Seeing the fractions in order can help students understand the magnitude of fractions. For example, 2/4 is twice as large as ¼ . Also, they can see a model that illustrates 2/4 is made up of ¼ plus ¼. What a great way to dissect 4/4 and see both the linear progression of fourths and the magnitude of each progressive fraction in the sequence.
Something I completely missed when using the number line for fractions was how it can be used to add fractions with the same denominators. Picture yourself using the number line above with fourths labeled. You start to point out how 2/4 plus another fourth is equivalent to ¾. Each time you move across the number line you add another ¼.
What About Comparing Fractions on the Numberline?
What about comparing fractions with different numerators? The number line perfectly models this. ⅗ is larger than ⅕ because you can see it is farther from 0 and closer to the whole number. But how about comparing fractions with different denominators? Students will need to use some basic fraction concepts to compare fractions with different denominators.
Let’s take ⅔ and 2/4.
A word of caution! If students are going to draw their own number lines to compare two fractions the denominators should be appreciatively different. Like comparing eights to fourths or tenths to thirds. Students can sometimes get the spacing uneven, making it hard to tell which fraction is smaller and which is larger.
Finding Equivalent Fractions on the Numberline
In addition to comparing fractions, the number line is great for visualizing and understanding equivalent fractions. I always start simple. I have students draw two number lines, one below the other. I have students mark one number line with halves. I prefer to always have students write 0/2, ½, and 2/2. This will be a visual reminder that we are working from 0 to 1 and that 2/2 is the same as 1.
Next, I have students partition the other number line into fourths. I have them use the ½ on the number line below (or above) to use as a reference point. Then they go on to label 0/4, ¼, 2/4, ¾ and 4/4. When they see that ½ is at the same point as 2/4 we can have a conversation around equivalence. I tend to always revert back to the area model to reinforce this concept as I divide a rectangle in half, then into fourths in another color to demonstrate the same thing.
Don’t Forget To Let Students Apply What They Have Learned
Once students begin to work with fractions on the numberline, it is time to apply their new learning. Problem solving with distance is a great way for students to make the connection between a linear number line and distance. I’ve created a practice sheet of sample distance problems that will get students started with using fractions on the number line to solve real world problems. Fractions on the Number line Problems
The Long Game
Just a quick reminder that when students are learning about, experimenting with and becoming experts at fractions, we are playing the long game. It takes time, a ton of exposure, practice, AHA moments, a variety of models and examples for students to build a solid foundation with fractions. Wondering how to get the practice in that students need? Check out my popular resource Fractions on the Numberline.As a math teacher of elementary students, I have to remind myself that Rome was not built in a day!
On the flip side, when I think about how critical an excellent understanding of fractions is the math they will be learning in middle, high school and beyond, I keep providing rich experiences that will lay the foundation for what is to come.
More Resources
For more tips on making math fun and engaging, check out Number Line Lyrics on Numberock’s post Fractions on a Number Line.
Twinkle had a video on using the number line to teach fraction. You Tube Video on using the Number Line to Teach Fractions
Wonder how middle school students will continue with fractions on the number line? Check out Illustrative Math’s illustration for a 6th grade math lesson here.
Looking for resources to keep math fun and students engaged? Check out my blog post The Magic Problem to inspire students and to make your math class the best part of the day!
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