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You absolutely MUST start with hands-on activities for fractions. It’s an abstract concept that can easily be made concrete for your learners. But keep in mind that all math manipulatives are NOT created equally! Various tools offer varying levels of support to your students.
While you certainly don’t need every hands-on gadget out there that claims it will help your students to learn fractions, it can be helpful to have a small variety of hands-on tools.
A teacher addressing the topic of place value would likely keep linking cubes (a groupable model), base ten blocks (a pre-grouped proportional model), and place value disks (a pre-grouped non-proportional model) nearby. A teacher addressing fractions can keep these same types (groupable vs. pre-grouped) on hand!
Groupable Models
Groupable models allow students to put unit fractions together to create non-unit fractions. Whether your students are simply building and naming fractions, comparing fractions or adding and subtracting fractions, these tools will provide your students the opportunity to physically combine and take apart unit fractions.
Fraction Cubes are a tool that can be likened to linking cubes for whole numbers. They allow your students to put together and take apart unit fraction pieces. These are useful in the initial stages of fraction learning as your students are learning that fractions are composed of unit fractions but are also incredibly useful when it comes to comparing, adding, subtraction, multiplying and dividing fractions.
Pattern blocks are another groupable model. This tool is slightly more abstract than the fraction cubes listed above because each individual piece does not have the fraction written on it.
Although, that’s something to keep in mind– you don’t need to be too dear with your manipulatives. You absolutely could have a set of pattern blocks that you use exclusively for teaching fractions and you can write the unit fractions directly on the pieces. As your students become more comfortable, you can move to pattern blocks without the scaffold of written unit fractions.
So many other groupable models exist including fraction circles, fraction bars and even these very unnecessary but also very fun and engaging fruit fractions! It is not necessary to have each and every one of these tools, however, having a few on hand will allow your students to test out their fraction understandings in a variety of contexts.
Pre-Grouped Models
Pre-grouped models generally come in two types, proportional and non-proportional. In terms of fractions, this distinction is a bit skewed because the size of the whole changes the size of the parts. So even a proportional tool can get a bit dicey in terms of what each piece represents. For example, a manipulative one inch long is 1/2 when it is compared the a whole that is 2 inches long. That same manipulative can also represent 1/4 when compared to a whole that is 4 inches long.
Pre-grouped models can be excellent for conveying the importance of the size of the whole when discussing fractions.
You can make your own fraction manipulatives to use by asking your students to color in a given part of a fraction bar. Students can then cut and compare this pre-grouped manipulative.
Cuisenaire rods are a classic pre-grouped fraction tool. Each of the pieces can represent a variety of different fractions depending on the size of the whole. This tool lends itself to really interesting investigations.
Segmented rods are another option. Much like Cuisenaire rods, the size of the whole dictates the label for each piece. I like this tool because the segments allow students to start thinking about denominators.
For example, a green piece with 3 segmented parts would be a third of a rod with 9 segments but would be a half of a rod with 6 segments. Seeing the segments allows your students to start connecting the manipulatives to written fractions.
