IMPLEMENTING MATHEMATICAL MODELING IN THE COMMON

CORE CLASSROOM

Hilda Castillo and Min Sung Ku

ABOUT US Over 30 years combined teaching

experience in 4-8th grade in Ontario Montclair School District.

Active participants of Algebraic Concepts for Elementary Students (ACES) since summer of 2010 facilitated by California State University of San Bernardino.

This work was supported by ACES - sponsored by the National Science Foundation, Ontario-Montclair School District, and the Center for Enhancement of Mathematics Education at CSU San Bernardino.

WHICH FLIGHT IS THE BETTER VALUE? WHY?

WHAT IS MODELING WITH MATHEMATICS?

Describe “Modeling with Mathematics” and what that looks like in a classroom.

WHAT IS NOT MODELING WITH MATHEMATICS?

It is NOT showing students how to do a procedure.

It is NOT using manipulatives to teach a mathematical concept.

It is NOT modeling just because the word “model” is there.

It is MORE THAN using mathematical models such as tables, graphs, equations, drawings, etc.

TRADITIONAL APPROACH VS

MODELING APPROACH Traditional Approach to Teaching Math

Math Math Math Possible Application

o Mathematics is learned in a logical, pre-determined order. Application problems are usually contrived, overly guided or often skipped.

Modeling Approach to Teaching Math

Life Math Life Extend to Other Contexts

o Models and mathematics applied to one context may be adapted to other contexts. Original context may need to be simplified to apply useful mathematics. New mathematics may need to be learned.

VALENTINE’S DAY DANCE PTA would like us to plan and host a

Valentine's Day dance as our next fundraiser.

What would we need to prepare for the dance?

Dance is set for Friday, 02/12/16 from 4:00 pm – 6:00 pm

The goal is to make a profit.

WORK ON THE TASK!

Create a poster showing your itemized proposal to make a profit.

Share out.

THINK TIME!

Write out “I notice/I wonder” on Post-it. Write “I notice” on one Post-it and “I wonder” on a separate Post-it. Place responses on board.(2 minutes)

Share your “I notice/I wonder” with your group (3 minutes)

EXTENSIONS What happens if we doubled the

number of ticket sales, how would it impact the amount of food we need to provide?

How would the pricing vary if we buy food for 20 people versus 200 people?

What if only 20 people came to the dance, how would that impact the profit?

DEBRIEF

What math was involved in this problem?

What math could be introduced?

How would students be engaged with this problem?

MATHEMATICAL MODELING Henry Pollak

“Mathematical modeling…begins in the “unedited” real world, requires problem formulating before problem solving, and once the problem is solved, moves back into the real world where the results are considered in their original context.”

“(The real world) usually has so many facets that you can’t take everything into account, so you decide which aspects are most important and keep those. At this point, you have an idealized version of the real-world situation, which you can then translate into mathematical terms. What do you have now? A mathematical model of the idealized question.”

Remember: Life Math Life Extensions

THE MATH MODELING PROCESS

Begin with a real-world situation.

Identify key factors and simplify.

Create and solve mathematical models.

Analyze the result.

Report and support your results.

BEGIN WITH A REAL-WORLD SITUATION

Problem to solve?

Situation to understand

Decision to make

Product or process to create or improve

Question to answer – “I wonder…”

IDENTIFY KEY FACTORS AND SIMPLIFY

What are my variables?

What are my constants?

Assumptions?

Features to ignore?

CREATE AND SOLVE MATHEMATICAL MODELS Create a plan Use math!

Pictures Drawings Graphs Equations Tables Spreadsheets Maps

Check for reasonableness Rework if needed

ANALYZE THE RESULT Will it work? Is it doable? Do we need to simplify? Add back complexity? Change the question? Change assumptions? Change the model?

REPORT AND SUPPORTYOUR RESULTS

Share your findings

Receive feedback

Accept suggestions

Act!

video time!

MODELING WITH MATHEMATICS IN THE

CLASSROOM Modeling problems can be completed in

one class period or over several periods.

Simple to complex

Modeling problems can be used to

Introduce new math skills

Reinforce recently learned math skills

Authentic Engagement

Modeling problems can be adapted to your students’ skills and grade level.

POTENTIAL REAL WORLD IDEAS TO USE FOR

MATHEMATICAL MODELING

Planning a party or event Examples: Quinceñera, birthday party,

wedding Baking brownies for fundraiser How much to charge for a cup of

lemonade to fundraise for a field trip? Determine the better buy Comparing smart phone plans Direct TV vs. Dish Network

Validating claims McDonalds: “Over 247 billion served”

IN CLOSING Reflection: How has your

thinking about modeling with mathematics changed?

How will modeling with mathematics increase problem solving skills with your students?

Modeling with Mathematics, like many things worth doing, is not built in a day.

RESOURCES Google Henry Pollak Eric Muller and Hugh Burkhardt’s Application and Modeling

for Mathematics http://www.mathshell.com/papers/pdf/hb_2007b_icmi_14_intro.pdf

Dan Meyer’s Three Acts Math Tasks www.threeacts.mrmeyer.com

Math modeling task force

http://caccssm.cmpso.org/k-8-modeling-task-force

http://caccssm.cmpso.org/high-school-modeling-task-force

Emergentmath.com

Wyrmath.wordpress.com

Other contributors: Bruce Grip and Jenny Hagman

Hilda Castillo hilda.castillo@omsd.net

Min Sung Ku- minsung.ku@omsd.net

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