Hilda Castillo and Min Sung Ku

 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.

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

 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 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.

 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.

 Create a poster showing your itemized proposal to make a profit.  Share out.

 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)

 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?

 What math was involved in this problem?  What math could be introduced?  How would students be engaged with this problem?

 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

 Begin with a real-world situation.  Identify key factors and simplify.  Create and solve mathematical models.  Analyze the result.  Report and support your results.

 Problem to solve?  Situation to understand  Decision to make  Product or process to create or improve  Question to answer – “I wonder…”

 What are my variables?  What are my constants?  Assumptions?  Features to ignore?

 Create a plan  Use math!  Pictures  Drawings  Graphs  Equations  Tables  Spreadsheets  Maps  Check for reasonableness  Rework if needed

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

 Share your findings  Receive feedback  Accept suggestions  Act! video time!

 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.

 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”

 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.

 Google Henry Pollak  Eric Muller and Hugh Burkhardt’s Application and Modeling for Mathematics   Dan Meyer’s Three Acts Math Tasks   Math modeling task force    Emergentmath.com  Wyrmath.wordpress.com  Other contributors: Bruce Grip and Jenny Hagman  Hilda Castillo  Min Sung Ku-

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