How do you use Virtual Manipulatives to meet Standards for Mathematical Practice?

MP4: Model with Mathematics

This series of posts cover the use of virtual manipulatives to meet the Standards for Mathematical Practice (SMP) of the Common Core State Standards for Math (CCSSM) that carry across all grade levels and describe habits of mind of a mathematically expert student. The rigor actually can be applied to any content area and the real world: problem solving, critical thinking skills, and students’ ability to articulate how they are solving problems. Virtual manipulatives in the elementary classroom , like concrete manipulatives, help students understand abstract concepts and link to prior knowledge. The advantage of online virtual manipulatives is that they are dynamic representations that can be altered, adapted, and allow students to direct their own learning.

Should I move to a hybrid car or stick with trips to the gas station? Is it truly cheaper to purchase groceries in bulk? How can I set up a tournament so each team has a fair amount of home and away games and similar schedules? What will the score be in next week’s game? Virtual manipulatives can provide meaningful context and tools to help students solve these everyday problems, and achieve math literacy as required by the Common Core State Standards for Math and Standards for Mathematical Practice.

Real world questions

Each day, we come across situations requiring mathematical modeling. We encounter questions about our world, and setting up models to work through these situations empowers us to answer them. We must prepare students to not only work through directed problems such as 43 x 68 but also modeling problems like finding the true MPG of a hybrid car.

Students shaping their own problem solving models

The Common Core State Standards, in the Standards for Mathematical Practice, list “Model with mathematics” (CCSS.math.Practice.MP4) as an important piece of math literacy. Specially, students must be empowered to “solve problems arising in everyday life, society, and the workplace.” What this means for educators is that we must put forth content that forces students to shape their own models and design their own pathways to finding answers. It is no longer acceptable to direct students to problems with step one, step two, and so forth to obtain an answer. We must present work that honors student’s individual strategies to find an answer.

Virtual manipulatives provide context

One such example of mathematical models is a virtual manipulative of the open number line to solve contextual problems. Again, we could have simply prompted students to “Solve 403-119” and to provide multiple choice options for a student to select the answer. Doing so robs students of the opportunity to model and make sense of the problem for themselves. Here, the virtual manipulative wraps this problem in a context; in this case it is a pirate ship sailing to find treasure.

 Empowering students to find their own ‘treasure’

For this example, let’s say a student wants to get to a friendly number to subtract, and recognizes 119 = 100 + 19. The student can enter their own equation seen below, and model their work by sailing the ship toward the treasure. The advantage here of modeling on an open number line is to empower students to think through the problem in their own way and not be bound by predetermined choices and constraints.


From this point, solving the problem is simple. The student subtracts the remaining 100 and digs to find the buried treasure. The importance of setting up a problem requiring students to model their work is that it forces interpretation; it forces a child to analyze, to plan their steps accordingly, and to think about their work.


Mathematical thinking is a beautiful thing

The beauty of mathematics is not simply straight lines to computed answers; it is the variety of pathways work can take and the abundance of models one can use to solve problems. Whether you are deciding whether or not to purchase a hybrid car, or searching for buried treasure, modeling mathematical work is essential to success. In the same Standard for Mathematical Practice, students “reflect on whether the results make sense” after utilizing a given model. It is essential that our students engage in reflection and feedback with their mathematics, and empowers students to create and adapt models over time as tools to solve everyday problems.

How do you teach your students to model with mathematics? Let us know!

Tag: common core state standards for math, virtual manipulatives, model with mathematics


Neal Manegold

Producer, DreamBox Learning | MBA, Technology Management | NBCT, Middle Childhood