The Case for Visual Models

The first two models that students focus on are a money model and clock face model. These are helpful when students are working with denominators of 100 and 60, as well as denominators of their factors. If the problem involves fractions with denominators that are not factors of 100 or 60, students are supported by two other models, the double number line and the ratio table. 

Students use these different models in several partner investigations throughout the unit. The different investigations push students to think of how fractions would be combined and compared in different contextual situations, such as placing landmarks along a 30 kilometer trail, or figuring out what the better buy is when shopping for varying quantities of granola bars. In the “River Trail Investigation” students began by identifying fairly easy markings on the trail (1/2, 1/3, etc.) and then used those increments to figure out more challenging fractions (1/12, 1/15, etc.) of the distance, expressing final answers both in fractions and in kilometers. An important step in these investigations is the math forum, where students share their findings and strategies with each other. Fifth graders learn different formats for these forums, either sharing with one other partnership, or sharing in front of the whole class and leading a discussion about their work. The focus during a forum is to hear about strategies and ideas that you didn’t think of. This connects to our STEM throughline: How can understanding and expressing multiple ways to solve problems help me make better sense of my world? Some math goals we focus on throughout the year are to build up our “strategy toolkit” so that we have multiple ways to solve problems, while also learning from each other and having respectful disagreements. 

We often hear from parents that these visual models are different from the way they learned to solve math problems (us too!), but educators and students alike have seen how supportive they can be to all types of learners on a vast spectrum of understanding. We like to think of these visual models as scaffolds that support student understanding until they have a conceptual understanding and are ready for those more abstract algorithms that us adults are more familiar with. We encourage our students’ families to explore these models with their children and see if they reveal a new understanding, perspective, and even joy for investigating mathematical problems.