Tools and Resources

Teacher Resources: Planning Tools and Routines

The files on this page will help teachers and teacher educators learn about what mathematical modeling can look like in a classroom and plan their own modeling routines.

There are Word documents linked below, as well as images and slides for creating modeling routines.

  1. Types of Mathematical Modeling Tasks
  2. Planning a Modeling Task starting with Community
  3. Planning a Modeling Task starting with Curriculum
  4. Planning a Mathematizing the World Routine (with examples)
  5. Planning an Assumption-building Routine (with examples)
  6. Lesson Planning Template
  7. Modeling Cycle and Lesson Outline

Descriptions for each of these resources are given below.

Descriptions of Planning Tools and Resources

We discuss four types of modeling tasks: Descriptive Modeling, Predictive Modeling, Optimization Modeling, and Rating and Ranking Modeling. This quick reference sheet describes each modeling type and includes questions and prompts to help structure the task. Use this sheet to design modeling tasks.

To jump start connections with local community settings of your students, go on a community math walk to see your students’ communities from students’ perspectives. This planning tool supports teachers to identify community settings to visit and to consider what activities and practices might occur there. Teachers are invited to make lists of things they are wondering about or information they want to know about these settings including people they might interact with. After the community math walk, teachers can use planning prompts to design modeling tasks that draw on the information gathered. The types of modeling tasks planning sheet is also attached to this tool.

This tool helps teachers adapt mathematics curriculum activities to be more modeling friendly. There are three main ways to open up curriculum to support modeling: 1) Change the way the problem is defined; 2) Expand the range of possible solutions; and 3) Adapt the context. Examples are provided to help teachers make these modifications.

Mathematizing the world routines (MWR) build students’ observation and problem-posing skills. The key to planning a MWR is to find an image, video, or object that includes both mathematical and contextual features that will hook student curiosities or connect to their lives. In this routine, teachers pose three questions to students: What do you notice?, What do you wonder?, and What questions can be answered using mathematics? The MWR can be used as a stand-alone routine or as part of a launch to answer a question posed by students. Use the planning sheet and example images to help plan your MWR.

Assumption-building routines develop students’ critical thinking skills and abilities to make inferences about a given situation. In these routines, students are asked to make assumptions about a situation when not all the necessary information is provided or available. The key to planning an assumption-building routine is to find an image, video, or object that includes both mathematical and contextual features that connect to students’ experiences. Then, teachers pose where-when-what prompts to help students use what they know about the context to make reasonable assumptions. For example: Where was this photo taken? When do you think these events happened? What is happening in this video? In another version of the assumption building routine, students identify reasonable or unreasonable assumptions about a given situation, question, or quantity. Assumption building routines can stand alone, follow a mathematizing the world routine, or be part of a launch of a complete mathematical modeling task. Use the planning sheet and example images to help plan your assumption-building routine.

This lesson planning template provides important prompts to plan modeling lessons. It includes sections for standards alignment, connections to previous math knowledge and students’ experiences and cultural/community funds of knowledge, as well as language considerations to support access and engagement of students, especially multilingual learners. There is also a section called “task variation” that invites ways to adjust the cognitive demand and access points of the task for diverse learners. Teachers can use the template to anticipate student strategies. The final section provides a brief lesson outline with space for describing the activities and focus questions in the lesson launch, explore and summary.

This diagram shows the modeling cycle in relation to the Lesson outline format: Lesson Launch, Explore, and Summarize. It highlights instructional moves teachers can use throughout the lesson to support students’ engagement in the modeling process.