Learning Objectives
Students will demonstrate an understanding of mathematical modeling and its components by engaging in real-world problem solving involving choosing the best dog food brand based on quality and price.
Note: This lesson may take multiple days to complete.
Grade Levels
9-12
Common Core Mathematics Standards (Modeling)
CCSS.MATH.CONTENT.HSN.Q.A.1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.
CCSS.MATH.CONTENT.HSN.Q.A.3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Materials Needed
Computer, laptop, or personal device with internet capabilities (one per student pair)
Mathematical Modeling Activity Packet: HERE
Graph paper
Colored Pencils
Rulers
Calculators (one per student)
Lesson
Introduction
- Explain to students that they will be researching and applying various mathematical approaches to make important decisions about a real-world problem through mathematical modeling. First, discuss and define the important components of mathematical modeling below with students before instruction begins (they will need to write these in notebooks to reference):
Identify the Problem: Devise a question that relates to the real world and can be solved.
Make Assumptions and Identify Variables: Determine various factors or variables that are the most important and will help solve the problem.
Perform Mathematical Operations: Complete the math model by using mathematical terms and operations that best represent how to solve the problem and gain results.
Analyze and Assess the Solution: Do the results address the problem accurately and do they make sense?
Review: Repeat the process if necessary and make changes to the model.
Implement: Report the results to others and implement the solution.
Instruction
- Start the lesson by posing the question/problem to students: What dog food brand should you choose for your dog based on quality and price?
- Group the students into pairs and tell them that they will work together to solve the dog food problem using the mathematical modeling components to guide them. The teacher will be facilitating the process and circulating to assist students complete their modeling packet.
- When complete, each student group will present their findings to the class.
Group Project (Teacher-Facilitated)
- Pass out the Mathematical Modeling Activity Packet, graph paper, calculators, colored pencils, and rulers to student groups. Ensure students have access to a computer, tablet, or personal device with internet service.
- Work through each component step by step with the students and help to facilitate their thinking while completing the activity. Students must cite their sources. Assist when necessary.
Review and Closing
- Students will present their findings to the class in an oral or visual presentation of their choosing.
References
Dog Breeds. (n.d.). Retrieved from www.akc.org/dog-breeds.
Felton-Koestler, Mathew; Hernández, Maria L; Levy, Rachel; & Zbiek, Rose Mary. “Mathematical Modeling in the High School Curriculum.” Mathematics Teacher. National Council of Teachers of Mathematics, December 2016. Retrieved from https://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue5/Mathematical-Modeling-in-the-High-School-Curriculum/.