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Lesson Plan by Mitchell Zuvela B. Sc., B. Ed.

Mathematical Modeling

This free, printable Pixton lesson plan brings problem solving  to life with comics and storyboards.

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This free, printable Pixton lesson plan brings problem solving  to life with comics and storyboards.
Pixton Lesson Plan on Mathematical Modeling
This free, printable Pixton lesson plan brings problem solving  to life with comics and storyboards.

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Mathematical Modeling

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    Circle
  • Cube
    Cube
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    Hole
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    Line
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    Line
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    Prism
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    Screen
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Teacher Guide

Mathematical Modeling

Step 1Class discussion with students

Note: This section is copied from the Math Common Core State Standards Initiative.

Mathematical modeling links classroom mathematics and statistics to everyday life, work, and decision making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.

A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object like a coin. Even such simple models involve making choices. It is up to us whether to model a coin as a three-dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes. Other situations, e.g. modeling a delivery route, a production schedule, or a comparison of loan amortizations, need more elaborate models that use other tools from the mathematical sciences. Real-world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity.

Some examples of such situations might include:

  • Estimating how much water and food is needed for emergency relief in a devastated city of three million people, and how it might be distributed.
  • Planning a table tennis tournament for seven players at a club with four tables, where each player plays against each other player.
  • Designing the layout of the stalls in a school fair so as to raise as much money as possible.
  • Analyzing stopping distance for a car.
  • Modeling savings account balance, bacterial colony growth, or investment growth.
  • Engaging in critical path analysis, e.g. applied to turnaround of an aircraft at an airport.
  • Analyzing risk in situations such as extreme sports, pandemics, and terrorism.
  • Relating population statistics to individual predictions.

In situations like these, the models devised depend on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time and tools do we have? The range of models that we can create and analyze is also constrained by the limitations of our mathematical, statistical, and technical skills, and our ability to recognize significant variables and relationships among them. Diagrams of various kinds, spreadsheets and other technology, and algebra are powerful tools for understanding and solving problems drawn from different types of real world situations.

Step 2Pixton comic-making activities
  • Make a Comic
    Modeling your Career

    View Activity
  • Make a Comic
    Planning for your Future

    View Activity
  • Extension / Modification
    Poster (Extension / Modification)

    Design a Poster informing students at your school about the risks of various extreme sports.

Step 3Concluding discussion with students

Plan for your survival if a zombie apocalypse were to break out. Determine the amount of water, rations, fuel (for a generator or vehicle), ammunition, and medical supplies that would be required to survive a year. If a friend whom you didn't plan for was to join you, how would your consumption of supplies change? What mathematical skills would be useful during an apocalypse? What tools would be essential?

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Pixton Activity: Mathematical Modeling 1 Modeling your Career

Intro

Mathematical modeling links math and statistics with everyday situations in school, life, and work. Modeling is the process of choosing and using appropriate mathematics and problem solving skills to complete daily tasks. You make important mathematical decisions everyday, however, the majority of the time you may not realize that you are using math. Tasks that involve using math include making change, planning a meeting, measuring fabric, or writing an invoice. By exploring the mathematical skills that you will be required to know in your future job, you will be better prepared to solve the problems that you will face throughout life.

Instructions

Create a Storyboard illustrating the importance of math in your future career.

Research the responsibilities of a job that interests you. In each panel, demonstrate how math plays a role in the daily tasks for a person in that job.

Each panel should include:

  • A title
  • An appropriate illustration
  • A description of how math is used in that job

See the rubric for grading guidelines.

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Pixton Activity: Mathematical Modeling 2 Planning for your Future

Intro

There are three financial milestones that most people will need to plan for during their lifetime:

  • Going to college
  • Buying a house
  • Retiring

These milestones will require years of saving, planning, and careful investing to make them a reality. It is important to be knowledgeable of the costs associated with each of these milestones so that accurate mathematical analysis can be done. In this assignment, you will learn the steps required to properly plan for your future.

Instructions

Research the costs of attending college, buying a house, and saving for retirement in your area.

Create a Timeline explaining how you will prepare for college, buying a house, and retiring.

Each panel should include:

  • An appropriate illustration that matches the narration of your story
  • Calculations that reflect your plans for saving and investing

See the rubric for grading guidelines.

Example Timeline

Planning for your Future by Student
College - 2018My plan is to go to the University of Idaho and become an architect. I hope to complete the degree in four or five years. The cost of tuition and living expenses will be $20,000 per year. I hope to save $5,000 each year with a summer job. I also hope to get $5,000 in scholarships which will cover the costs of my first year. I will also need to apply for student loans or receive help from my parents to cover the costs in the following years.
Wedding - 2025I hope to get married by the time I am 25. I will need to save approximately $20,000 for a wedding. In my first few years of work I hope to save $5,000 to pay for the initial costs. I may need to sell my stocks that I invested in during college before the wedding. A chunk of the cost will need to be paid for with credit card. We will ask for money as wedding gifts which will help cover some of the costs of the wedding.
House - 2030The average price of a house in Seattle is $340,000. My husband and I will need to save $34,000 for a down payment. We will need to put $7,000 per year in savings for five years to have enough for the down payment. About 7% of our gross yearly earnings will go to savings. The mortgage payments will be approximately $1,300 per month.
Retirement - 2065My husband and I will need at least $500,000 saved for retirement. We will invest $100 each week for 35 years into a compound interest account with 3% interest. Over the term, the investment will reach over $321,000. Our pension plans at work should cover $200,000 over the term. Other assets such our house can be sold to make up any shortcomings.

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