Representing Fractions on a Number Line

I love teaching fractions! There are so many things you can use to teach fractions like Play-Doh to cut equal parts, using real foods like fruit, waffles, or tortillas to partition, and all the different fraction manipulatives you can buy.

My intervention students generally have a hard time understanding how fractions can be represented on a number line. They are unsure how to divide the number line into equal parts or label the hash marks with the correct fractions. Over the years, I have found that when my students make and cut their own fraction bars it has a huge impact on their understanding. When they color and physically cut the fractional parts and put the fractions parts together to make a whole, they really start to see how fractions work for themselves. 

Here is an example of one of the intervention lessons I created to help my students. In this lesson, students colored their own fraction bars and cut them out. They separated them by color. They also practiced counting the fractional parts to 1 whole using their own fraction bars. They placed the parts on the number line as they counted with me. Between every two fractional parts, they marked the number line with a hash mark. Then, students wrote the fractional names under each hash mark. This also allowed us to discuss equivalent fractions like 3/6 is equivalent to 1/2, as well as vocabulary words (numerator, denominator, and whole).

Here is a picture of the students placing the fractional parts on the number line and counting the parts aloud with me.

Now, students are marking the number line and labeling the hash marks. We even examined composing and decomposing fractions. For example, 1/4 + 1/4 + 1/4 +1/4 = 4/4 or 1 whole. Also, 1 = 1/3 + 1/3 + 1/3 or 1 = 1/3 + 2/3.

Check out a finished example of fourths to 1. Then, we kept going to the the twelfths! My students keep the fraction bars in their math folders. I plan to send them home later in the year as a spiral practice. If you need to send home the fraction bars, simply print another copy and have parents work with their child to reinforce their fractions understanding.

You can find this entire Fractions Intervention here. There are 8 different fractions intervention lessons plus the progress monitor for each lesson. Just download, print, and you're ready to teach fractions!