1. Math Session 2 Mathematical Practices 4 & 5 Modeling with Math PARCC Task Types Lesson Study

2. Modeling with Math 2

3. 3 “Mathematical modeling is the link between mathematics and the rest of the world.” ( Meerschaert, M., Mathematical Modeling, Elsevier Science, 2010 ) The process of beginning with a situation and gaining understanding about that situation is generally referred to as “modeling”. If the understanding comes about through the use of mathematics, the process is known as mathematical modeling. “Mathematical modeling is the link between mathematics and the rest of the world.” ( Meerschaert, M., Mathematical Modeling, Elsevier Science, 2010 ) The process of beginning with a situation and gaining understanding about that situation is generally referred to as “modeling”. If the understanding comes about through the use of mathematics, the process is known as mathematical modeling.

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5. Modeling with Math  GOAL : students pose their own questions about the world and use math to answer those questions  TEACHER’S JOB : construct situations in which students are choosing math to better understand their everyday life 5

6. Modeling with Math 6 Students  Apply prior knowledge to new problems and reflect  Use representations to solve real life problems  Apply formulas and equations where appropriate Teachers  Pose problems connected to previous concepts  Provide a variety of real world contexts  Use intentional representations

7. Modeling Steps 1. Identify a problem situation 2. Make a representation of one or more elements of the situation 3. Create a mathematical expression 4. Compare results or predictions from the mathematical model with the real situation 5. Make revisions to the model if needed 7

8. Modeling with Math Elementary Grades:  Ensure the math students engage in helps them see and interpret the world  Type of thinking required more important than the context 8

9. Modeling with Math 1. Give it context 2. Go deeper 3. Tap into resources 9

10. Modeling with Math Give it Context  Consider applications of the work  To think deeply, math needs to be in context  Spend less time on repetitive problems  More time with real scenarios 10

11. Modeling with Math Go Deeper  Build longer problems with multiple steps and more than one question  Additional questions add depth and rigor – call upon students to demonstrate understanding over multiple skills 11

12. Modeling with Math Tap into Resources  Task prototypes from PARCC  Video Story Problems (The Tech Savvy Educator)  Teaching Channel Problems with real-world implications demonstrate that what students are learning has value. 12

13. Tap into Resources www.theproecenter.info  Math Playground – Thinking Blocks  Watson Math  California Math Project 13

14. Tools to Support Math Modeling Fractions Equations 14