Real World Mathematics in Images
Mathematics in Visuals
Activities and Tasks
Navigate to the Math Modeling Intro page for a summary of the modeling process: Life --> Math --> Life
Some contexts are more "real" than others. Some are more relevant to your students or at least to the world they understand. Some sources introduce engaging real-world contexts only to ask a question that no ordinary person would think to ask (usually because the goal of the not-so-real problem is to dig into particular math rather than understand and solve a real-world problem).
Use activities/tasks/contexts within the resources listed below or modify as needed to make your activities more real and relevant for your students. Perhaps these will inspire you to capture pictures and artifacts for your teaching to bring life to mathematics and mathematics to life. Choose culturally-relevant contexts for you and your students to explore mathematics as a powerful tool to understand and impact social justice and equity.
Enjoy, along with your students, (1) applying math to something real and meaningful and (2) learning new math in order to solve a real problem.
MMC^3 - Julia Aguirre
Lessons for grades 3 - 5. Ideas may be adapted to other grades.
Mathematical Modeling With Cultural and Community Contexts (M2C3) https://m2c3.coe.arizona.edu/Advancing Equity and Strengthening Teaching with Elementary Math Modeling https://www.eqstemm.org/
EQ STEMM Math Modeling Tasks
Disruptive Numbers: The Chaos Numbers Bring to Uncover HIdden Stories - Ma Bernadette Andres-Salgarino
Links for activities, lessons and resources to implement social justice and culturally-relevant contexts for mathematical modeling in classrooms.
Engaging Real-World Activities
Citizen Math (Mathalicious)
Real-world lessons (Member Cost/Free Sample Lessons)
- 3-Act Math Tasks K-12
- Kristen Acosta K-6
- Dan Meyer
- Graham Fletcher K-5
Interesting lesson starters or modeling activities.
Achieve the Core/Student Achievement Partners Jason Zimba
Consortium for Mathematics and Its Applications
Activities and articles related to real-world applications of mathematics.
Emergent Math: Problem Based Learning
Study: Culturally Relevant Math UConn
Creating Balance In An Unjust World
Conference resources intended for educators integrating issues of social and economic justice into their math classes and curriculum.
Chapter 10: Forensic Science
Introduction to Criminal Investigation:
Processes, Practices and Thinking
Make Math Moments
Problem-based tasks and units for grades 3 - 10.
Connecting Industry to Math Instruction
NSF ATE Award #1954291
NCTM Presentation 09/29/2022
Learning and Teaching
Mathematics Teacher PK-12
The following articles can be found in this NCTM publication offered to members.
Real Math Explorations
Empowering Latinx Families to Help Children With Mathematics
Volume 114_Issue 10_October_2021, p. 777
“Big, Medium, Small: This three-minute bilingual video features a parent and child engaged in the routine activity of sorting laundry, while playfully talking about comparisons and measurement.”
GPS: Diving into Dolphin Data
Volume 114_Issue 11_November_2021, p. 886
Questions that arise while investigating data about dolphins and questions for which data should be captured.
Bridging Modeling and Environmental Issues
Volume 114_Issue 11_November_2021, p. 845.
“Have you ever noticed trash collecting in streams or waterways? How does trash influence our environment, and what can be done to enact change?”
Exploring Playground Access with Mathematics
Volume 113_Issue 11_November_2020, p. 887.
“Four-year-old children used mathematics to examine the location of and access to public playgrounds in their community. They collected and recorded data, using the information to advocate for a social justice issue.”
Mathematizing Multilevel Marketing
Volume 113_Issue 05_May_2020, p. 416
“This article dives into the importance of engaging students in investigating the mathematics behind businesses that pressure their employees to recruit new members as a basis for success,…”
Let’s Hit the Target
Volume 113_Issue 05_May_2020, p. 368
Projectile motion explorations.
Productive Struggle in Action
Volume 113_Issue 05_May_2020, p. 361
Fair division of pizza problem.
Volume 113_Issue 06_June_2020, p. 497
“Inspired by the Batman Equation of 2011, the author presents a challenging and engaging process for graphing complicated designs from just a single parametric equation pair.”
A Wonder-Full Task Leads to a Wonder-Full Intervention
Volume 113_Issue 06_June_2020, p. 474
Described task to determine draft order for professional baseball organization. Uses player performance statistics.
Giving Birth to Inferential Reasoning
Volume 113_Issue 04_April_2020, p. 287
“What is the probability a newborn baby is a boy?”
Beyond Hooks: Real-World Contexts as Anchors for Instruction
Volume 113_Issue 10_October_2020, p. 821
Financial problems including Date Night, Net Worth, Worst Client
Not-So-Real Math Explorations
Filling Bottles With Water
Volume 114_Issue 10_October_2021, p. 803
“If you gradually fill a bottle with water, how does the water level change as you pour in the water? If you graph the height of the water level in the bottle versus the volume of water in the bottle, how does the shape of the bottle affect the shape of the graph?” A context from the real world is used to explore math relationships. Perhaps ask instead, "How do you know when you have used half of a bottle?"
Productive Technology Use in Mathematics Explorations
Volume 113_Issue 11_November_2020, p. 925.
“This interactive diagram of the Skateboarder ID is designed to explore time and position graphs.” What if we explored connection between rates and safety?
Mathematical Modeling Handbooks
Mathematical Modeling Handbooks
- Getting Started and Getting Solutions
- Computing and Communicating
Mathematical Modeling and Modeling Mathematics, Annual Perspectives in Mathematics Education, NCTM 2016
SIAM Math Modeling Resources
Guidelines for Mathematical Modeling
Guidelines for Assessment and Instruction in Mathematical Modeling
Guidelines for Statistics Education
Guidelines for Assessment and Instruction in Statistics Education
Math Modeling Appendix:
CA 2013 Math Framework Appendix B
Modeling Our World With Mathematics
Modular structured curriculum: Health & Fitness, Environmental Science, Civic Readiness, Finances for Life, Digital World, The Arts
"...career-connected thematic units where students use high school mathematics to analyze everyday life and work." From Washington
Becoming a Teacher of Mathematical Modeling, Grades K-5, Grades 6-12
Arnold, Burroughs, Carlson, Fulton, Wickstrom
These books, published by NCTM, identify modeling by Four Big Ideas rather than a cycle
1. Modeling begins and ends outside the mathematical world.
2. Modeling deals with situations that are open and complex.
3. When investigating problems, modelers exercise judgment that stems from a set of values that may or may not be fully articulated but are always present.
4. Modelers decide when a solution is good enough.
Levy et. al
Data Activities and Resources
The following sites are excellent resources for data-driven lessons around topics of relevance to students and adults.
What's Going On In This Graph? - NY Times
Our World in Data
Excellent sources of graphs to promote discussion and sense-making.
Data Talks on Youcubed
Office of Civil Rights Data on Schools
Information is Beautiful