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# Mathematical Modeling

### Description

The Mathematical Modeling Performance Task Guide introduces the steps to developing a mathematical model that presents real world, empirical data to support understanding and analysis, and to justifying the use of this model as appropriate within the problem context.

Creating and using models is fundamental to the study of mathematics. While mathematical models are often simple, the process of developing even basic models requires a great deal of thought and understanding, calling on both algorithms and hueristics. Mathematical modeling is a powerful performance task because it has applications not only in math, but across all the STEM subjects.

### Opportunities for Student Choice

Student choice can be encouraged in a number of ways. Students can choose real-world phenomena to model, find or generate data, and choose to argue a specific position their model elucidates. If students are given the problem context and/or data, they can determine which model is appropriate to represent this data and discuss the affordances and limitations of their model. In some instances, they can also choose the resources they review, the data they will present, and/or the audience for their model.​

Creating and using models is fundamental to the study of mathematics. Models are used in almost all professions, including medicine, business, legal services, educational tools and services, engineering, news, and politics.  They are used within these fields in various ways, including sales presentations, advertising, visual arguments, website design, presentations, and reporting. ​

### Opportunities for Exhibition to an Audience

There are many possible audiences for mathematical models: simple graphs and charts can be created to help others understand complex data; Excel and CADD can be used to create virtual models of prototypes too costly to create; complex systems can be translated to mathematics to make predictions about likely outcomes of decisions. ​

### Grade Level Exemplars/Models

3-4 Levels below High School:

2 Levels below High School:

High School:

3-4 Levels below High School:

Student learning might focus on how to represent mathematical data in three samples charts, including a bar chart, a line chart, or a pie chart; and drawing out a position on their topic based on the data available.​

2 Levels below High School:

Students will potentially be able to choose from a wide range of visual representations of data and be able to defend their visual choices based on the nature of the data and the point they are trying to portray.  Students will also potentially focus learning on creating the most memorable and attractive representation of data towards furthering their main position.​

High School:

Students might focus their learning on using larger data sets and more than one visual to display their data and support their position.  Students will also potentially learn to adjust the visual representation of their data and position to engage and attract different audiences, as well as choose the most memorable visual representation.

### Teacher Resources

General Information about Characteristics of Mathematical Models

A set of videos that explore traditional approaches to teaching mathematical modeling

Dan Meyer, creator of Three Act Math, presents his remarks to the NCTM in 2014: “Fake-World Math—When Mathematical Modeling Goes Wrong and How to Get It Right”

In this video, Conrad Wolfram proposes approaching math as a four step process: posing the right questions; turning the real world into a math problem; computing; and turning the solution back to the real world to verify the formulation.

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## Explore Mathematical Modeling

What is the Mathematical Modeling?

Develop a clear enough understanding of the characteristics of mathematical modeling to be able to explain your understanding to others.

• CCSS.MP.4

1-3 Hours

## Choose A Topic (Mathematical Modeling)

What makes for an effective topic?

Identify a topic that you either feel strongly about or wonder about.

• CCSS.MP.5
• CCSS.MP.4

### Time To Complete

1-2 Hours

What questions will guide my work?

Learn to uncover your authentic guiding questions.

• CCSS.MP.4

1-3 hours

## Research The Issue (Mathematical Modeling)

What do people know, say, and believe about this issue?

Find and analyze resources that will help you grasp the topic’s key concepts, in addition to deepening your understanding of the range of perspectives about the issue.

• CCSS.MP.5
• CCSS.MP.4

2-3 Hours

## Find or Gather Numerical Data (Mathematical Modeling)

What data can I find or gather about my topic?

Find or gather data that will help you grasp the topic’s key concepts.​

In some cases, the relevant data for this task will be supplied to students. If the data is not supplied, students will locate numerical data that they can use to address the research topic. The...

• CCSS.MP.5
• CCSS.MP.4
• CCSS.MP.2

1-2 Hours

## Analyze The Numerical Data (Mathematical Modeling)

What does the numerical data reveal about my topic?

Think about the story the data has to tell.

• CCSS.MP.5
• CCSS.MP.6
• CCSS.MP.2

3-4 Hours

## Work With Numerical Data In A Spreadsheet (Mathematical Modeling)

How do I use a spreadsheet to manipulate, analyze, and represent numerical data?

Develop a clear enough understanding of a spreadsheet program to enter data, perform basic calculations using functions, sort data, and create pictorial representations to export into another document.

• CCSS.MP.5
• CCSS.MP.6
• CCSS.MP.2

1-3 Hours

## Model The Data Using Mathematical Representations

What are various ways to represent numerical data?

Develop a clear enough understanding of numerical data and how it is presented to be able to identify and explain various ways sets of numbers are presented visually and how visual representations are used to tell a story about the numbers.

• CCSS.MP.5
• CCSS.MP.6
• CCSS.MP.4
• CCSS.MP.2

3-4 Hours

## Articulate Why The Mathematical Model Is Effective (Mathematical Modeling)

What makes my mathematical model effective?

Provide evidence and reasoning to convince others that your model is effective.

• CCSS.MP.4
• CCSS.MP.2
• CCSS.MP.3

1-2 Hours

## Take A Position (Mathematical Modeling)

What do I have to say about my topic?

Consider the research you have undertaken and the data you gathered, using it to inform the crafting of a main idea, a thesis, or an evidence-based position to focus your work.

• CCSS.MP.4
• CCSS.MP.3

1 Hour

## Give And Receive Feedback (Mathematical Modeling)

How can I improve my work?

Strengthen your work by giving and receiving feedback from a peer or teacher.

• CCSS.MP.6
• CCSS.MP.3

1 Hour

## Revise (Mathematical Modeling)

How can I improve my draft?

Using feedback from a peer and/or teacher, strengthen your draft by ensuring your facts and details are relevant, your organization is clear, and your use of voice is strong and appropriate to the audience.

• CCSS.MP.5
• CCSS.MP.6

2-3 Hours

## Edit (Mathematical Modeling)

How can I improve my draft?

Using feedback from a peer and/or teacher, strengthen your writing with a focus on conventions such as grammar and professional language.

• CCSS.MP.5
• CCSS.MP.6

1-2 Hours