Understanding What Mathematical Modelling Really Is

Mathematical modelling is not simply using a graph, chart, equation or physical model to represent a concept, but rather the process of engaging in a multistep, iterative process in which students use mathematics to make sense of a real-world context.  It's a creative process, involving making assumptions and decisions, in order to understand something new and relevant and make informed choices based on that learning.

The chart and articles below can help to clarify and support your understanding of mathematical modelling.

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Curriculum

Depending on the real-life situation, coding may be a tool in mathematical modelling.

Grade 7:

C3.1  solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves events influenced by a defined count and/or sub-program and other control structures 

C3.2  read and alter existing code, including code that involves events influenced by a defined count and/or sub-program and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code 

Grade 8:

C3.1  solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions 

C3.2  read and alter existing code involving the analysis of data in order to inform and communicate decisions and describe how changes to the code affect the outcomes and the efficiency of the code 

Pedagogy

Grade 7 - Handwashing Policy  Students will create a model then collect and organize data in order to determine the impact of a school board's handwashing policy. Students will use their model to make predictions, then test those predictions by playing out the handwashing scenario in real life. In the end, students will present their opinion on the policy, using mathematical arguments based on information provided by their models.

Grade 7 - Forests in Crisis   Students will apply the process of mathematical modelling to analyse data about the current rates of deforestation in Canada. Students will create a model that can be used to predict the point at which we will no longer have enough forestry products to meet our needs.

Grade 7 - Top 10 Players   Students will create a model, then collect and organize data in order to predict the 10 best pro-athletes in a given sport. Students will use their model to make and test predictions about which hockey players should be chosen for a fantasy hockey league.

Grade 8 - Let's Plan a School Trip   Students will put their financial literacy and research skills to work as they move through the process of determining the perfect outing for their year-end Grade 8 trip. Students will explore the financial implications, supervision ratios, distance regulations as well as research the hidden attractions within their community.

Grade 8 - Predicting the Next YouTube Stars   Students will try to discover what it takes to become a Youtube superstar. Students are task with determining the factors required to become one of the most famous YouTuber on the planet. Using those factors, students will then try to create a model that will predict and rank the future stars of the video platform.

Grade 8 - How Water Rich is Canada?   Math and science meet to form an open and engaging learning opportunity. Students are tasked with examining Canada's water richness to determine at what point will the tables be turned. As students sift through the various factors that contribute to Canada's water richness, supply and use they will begin to reflect on the assumptions they are making to formulate a mathematical model.

Modelling Pedagogical Resources

Some Sample Modelling Task Resources

3-Act Math Tasks can introduce the process of mathematical modelling with a shorter task that can potentially be done in one math block.  Using these tasks on a semi-regular basis can help students become familiar with the modelling process.  Then when they tackle a larger, more complex problem, they are less likely to feel overwhelmed. 

Dan Meyer: The Three Acts of a Mathematical Story (blog post) and 3-Act Math Tasks

Andrew Stadel: 3-Act Math Tasks

Jon Orr: MrOrr-IsAGeek.com

Kyle Pearce: TapIntoTeenMinds.com

Graham Fletcher: FGletchy.com

The 2021 Census Teacher's Kit has been developed for use in elementary, intermediate and secondary classes across the country. The kit includes four activities that are appropriate for many subjects, including mathematics, social studies, and English or French language studies. These activities also include "next steps" ideas to help connect the subjects with concepts in the sciences and creative arts.

All activities are classroom-ready and have been reviewed to meet curriculum requirements. Through these exercises, students will gain an understanding of what the census is used for, how it is conducted, and the role it has played in shaping present-day Canada.

Assessing and Supporting Mathematical Modelling

The following rubric was created based on criteria adapted from Guidelines for Assessment & Instruction in Mathematical Modeling Education (Bliss, Karen, et al).  The accompanying student guide mirrors the criteria in the rubric.  The guide is intended to support students through a larger modelling task but as student become more comfortable with the process of mathematical modelling, they will likely require this support less and less.   Both documents can be copied and edited to suit your needs.

technology

Using Nearpod and Desmos Activities are useful tools for facilitating a smaller modelling task (like a 3-act math activity) or launching a more involved task.  Below are some templates to help get you started.

Connecting Tables of Values, Equations and Graphs

The Desmos graphing calculator app is a great way for students to quickly see graphs from data they've collected or equations they've generated from observing patterns. It's easy to use and available as an iPad app or at desmos.com.