Fraction strips are rectangular pieces of paper, cardboard, or digital shapes that represent fractions as parts of a whole. Each strip is the same length as every other strip in the set, but divided into a different number of equal sections. A strip split into two equal parts represents halves, one split into three equal parts represents thirds, and so on. Teachers use them heavily in elementary math because they turn abstract fraction concepts into something students can see, touch, and physically line up.
What a Set of Fraction Strips Includes
A standard set starts with one uncut strip that represents “1 whole.” The remaining strips are the same length but divided into progressively smaller equal sections: halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths. Each individual section within a strip is called a unit fraction, meaning it has 1 as its numerator (1/2, 1/3, 1/4, and so on). The pieces are typically color-coded so that all the fourths are one color, all the sixths are another, and students can quickly tell which denominator they’re working with.
You can buy pre-printed sets, print them from a template, or make them by hand with paper and a ruler. Digital versions are also widely available. Some interactive tools let you drag individual fraction pieces into a workspace and arrange them in a line (sometimes called a “fraction train”) to explore how different pieces relate to each other. Many digital tools also let you include or exclude certain denominators and customize colors, which is helpful when you want students to focus on specific fractions.
Comparing Fractions by Lining Strips Up
The simplest use of fraction strips is figuring out which of two fractions is larger. Because every strip starts at the same length, you place two strips next to each other and compare how much of each one is shaded. If you shade 3 out of 8 equal sections on one strip and 1 out of 2 on another, you can see immediately that the shaded portion of the 3/8 strip is smaller. That makes it visually obvious that 3/8 is less than 1/2, even though the raw numbers might confuse a student who hasn’t learned cross-multiplication yet.
This side-by-side approach works because the key rule is always the same: start with rectangles of the exact same size, split each one into the number of equal sections indicated by the denominator, and shade the number of sections indicated by the numerator. When students follow that process for two different fractions and hold the results next to each other, the comparison becomes a simple question of “which one has more shaded area?”
Finding Equivalent Fractions
Fraction strips make equivalent fractions concrete instead of abstract. Take a strip divided into halves and shade one section. Now take a strip divided into fourths and shade two sections. Line them up and the shaded areas cover the same length, which shows that 1/2 equals 2/4. You can extend this further: shade four sections on an eighths strip, and it still matches. Students can see that 1/2, 2/4, and 4/8 are all the same amount.
The underlying idea is that you’re taking each existing equal section and subdividing it into smaller equal sections. When you cut each half into two pieces, you get fourths. When you cut each half into four pieces, you get eighths. The shaded area doesn’t change, but the number of pieces does. This is the visual version of the rule that multiplying both the numerator and denominator by the same number produces an equivalent fraction.
Adding and Subtracting With Strips
Fraction strips also help students understand addition and subtraction of fractions, especially when the denominators are different. To add 1/3 and 1/4, a student places a 1/3 piece and a 1/4 piece end to end in a line. The combined length represents the sum, but it’s not immediately clear what fraction that sum equals. This is where the student tries other strips underneath the combined pieces to find a match. Laying twelfths strips below the line reveals that the combined length of 1/3 and 1/4 equals 7/12.
This process mirrors what happens mathematically when you find a common denominator, but students discover it through physical exploration rather than memorizing a rule. They can see why a common denominator is necessary: you need pieces of the same size to count them up into a single fraction. Subtraction works the same way in reverse. Place the larger fraction’s pieces in a line, then see how many of the smaller fraction’s pieces fit within that length. The leftover space is the difference.
Multiplication and Division
Strips can model multiplication and division as well, though these operations require a slightly different approach. To multiply 1/2 by 1/3, a student takes a 1/2 strip and then divides that shaded portion into thirds. The result is one piece out of six total sections, showing that 1/2 times 1/3 equals 1/6. This reinforces the idea that multiplying fractions by fractions produces a smaller result, which often surprises students who associate multiplication with “getting bigger.”
For division, the question becomes “how many times does this piece fit into that piece?” To divide 1/2 by 1/6, a student lines up 1/6 pieces along the 1/2 strip and counts how many fit. Three 1/6 pieces match the length of 1/2, so the answer is 3. This gives students an intuitive understanding of why dividing by a fraction yields a larger number.
Why They Work as a Teaching Tool
Fractions are one of the most difficult concepts in elementary math because they break the pattern students have learned with whole numbers. A bigger denominator doesn’t mean a bigger number, and multiplying can make things smaller. Fraction strips address this confusion by grounding everything in a visual, physical comparison. Students don’t have to take the teacher’s word that 1/3 is bigger than 1/4. They can hold the two pieces side by side and see it.
Strips also build a bridge to more advanced work. Once students are comfortable comparing and combining strips, the transition to number lines, common denominators, and algebraic fraction rules feels like formalizing something they already understand rather than learning a brand-new concept. Many curricula introduce strips in third grade and continue using them through fifth or sixth grade as the operations become more complex.
Making Your Own Fraction Strips
All you need is paper, a ruler, scissors, and markers. Cut several strips of equal length, typically around 8 to 12 inches. Leave the first strip whole. Fold the second in half and mark the crease. Fold the third into three equal parts, the fourth into four, and so on. Color each set of strips a different color so they’re easy to identify. Laminating the strips or using cardstock helps them last through repeated use.
If folding precisely into odd numbers like fifths or sevenths is difficult, measuring with a ruler works well. For a 10-inch strip, each fifth is exactly 2 inches. Label each piece with its fraction (1/5, for example) so students can connect the visual length to the written notation. Store each set in a separate bag or envelope, and students can pull them out whenever a fraction problem comes up.