1. Ditch the butterflies.
Students need opportunities to develop deep conceptual understanding of fractions. Using things like “the butterfly method” pigeon hole students into an algorithm base for solving the problem. They understand they do this method because “the teacher told me so”, rather than having a deep understanding why this trick works. Using manipulatives and models give students the understanding they need to tackle more complex problems.
2. Use ALL the manipulatives & models.
Providing students a variety of models and manipulatives gives various entry points at solving problems. Students are able to explore which models and manipulatives serve them best at problem solving. Using one model or manipulatives acts as an algorithm. Students again, use the model because “the teacher told me so”. By giving students manipulatives like two color counters, number lines, and fraction tiles, they learn a variety of strategies at solving fraction problems. This also deepens their understanding about why certain “tips and tricks'' work. This better prepares them for high level math content like algebra.
3. Ensure students understand the WHOLE.
Fractions are grounded in the size of the unit or whole. Sharing a large pizza and sharing a medium pizza does not represent the same fractional size, because the whole is not considered the same. Students must understand what part of the WHOLE the fraction is referring to. Give students lots of opportunities to make sense of the whole. Identify this in number talks and lesson openers. The deeper understanding they have of the whole, the better understanding they have to manipulate the fractional pieces of the whole.
4. Scrap the terminology “# on the top, # on the bottom”.
Students need exact exposure to math terminology. By reframing the words “numerator” and “denominator” students may lose track of their true meaning. Students should have explicit instruction that the numerator accounts for the total number of fractional pieces in the fraction. While the denominator is the total number of fractional pieces in the fraction. The more explicit this connection is through models and manipulatives, the deeper understanding students will have of fractional parts.
5. Make real-life connections.
Whether through cooking or building something exquisite or small, students will interact with fractions throughout their life. This is the perfect opportunity to activate schema and begin building new connections with fractions to real-life. Fractions can be scary for some students, integrating student literature helps create a safe-environment for fraction understanding. Students need to know, while fractions may seem scary, with the right tools and explicit instruction, they can have success in understanding how to solve fraction problems.
