Mathematical Modeling Cycle
Mathematical modeling (MM) helps students make sense of real-world situations through problem-posing and decision-making.
It is a powerful equity and empathy lever in K-12 mathematics.
MM is a cyclical process where students engage in:
(1) making sense of the situation and posing a modeling problem;
(2) listing quantities and assumptions;
(3) representing, exploring and creating a solution/model
(4) interpreting and revising the model and
(5) reporting out. (Scroll down to learn more about each phase of the modeling cycle)
This cycle can be posted in the classroom and referenced when students are engaged in the modeling process. It is cyclical and students will naturally go back to different phases as they refine their model.
Download the Mathematical Modeling Cycle
Unpacking the Mathematical Modeling Cycle
Connect to Context and Student Experience
Select a context for modeling. Use images, videos, stories or real world artifacts that reflect the context. Ask students to share their experiences and understandings about the context.
Make Sense of a Situation
Discuss important aspects of the situation. Ask students to share what they notice and wonder about the situation. Ask students to share connections to the context.
Pose a Modeling Problem
Ask students to pose mathematical questions related to the situation. Draw on students’ ideas and questions to pose a modeling problem for the lesson.
List Quantities and Assumptions
Identify and describe quantities, decisions and assumptions relevant to the situation. Ask students to share what they know, need to know, need to decide, or need to assume about the situation to answer the problem posed. Ask students to explain the reasonableness of their assumptions.
Represent and Explore
Mathematically explore possible models using various representations (equations, pictures, written descriptions, tables, graphs). Ask students to explain the different components of their models, including how quantities are related.
Create Modeling Solutions
Reach a solution related to the problem posed. Ask students to use their models to operate on quantities and to explain their solutions.
Interpret and Revise
Interpret and revise models in relation to the real-world context. Ask students to compare and contrast models and solutions and to explain how their solutions answer the problem posed. Ask students to revise and refine models and solutions if necessary.
Report Out
Communicate models and solutions to others, and use solutions to inform decisions or actions. Ask students to explain how their model works to solve the problem, and how their model could help others in a similar situation.
Mathematical Modeling Lesson Analysis Tool
We can develop students’ mathematical modeling competencies through routines and modeling tasks and use these look fors.
For each phase of the modeling cycle, the MM Lesson Analysis Tool offers teachers some skills to develop and look for.