MODEL WITH MATHEMATICS

STANDARDS FOR MATHEMATICAL PRACTICE

#4

Is this mathematical modeling?

An engineer may make a mechanical model,” with

weights and springs, of an electrical circuit with

capacitances and resistances.

One real-world object is represented by another.

What do we mean by mathematical modeling?

Is this mathematical modeling?

A switching circuit may be a “model” for aBoolean function.

A mathematical object is represented by a real-world object

What do we mean by mathematical modeling?

Is this mathematical modeling?

A real number may be a “model” for a pointon a line, and vice versa.

A mathematical object by a different mathematical object

What do we mean by mathematical modeling?

Is this mathematical modeling?

A logistic function may be a “model” for thegrowth of a bacterial population.

Represents a real-world situation by a mathematical one.

What do we mean by mathematical modeling?

The first three all represent meanings of a model in a scientific or mathematical setting. However, we are concerned with the forth and last meaning, is a mathematical model, which represents a real-world situation by a mathematical one.

What do we mean by 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 and mathematical modeling.

Our Definition

SMP 4: Model with mathematics

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Problems in everyday life…

Mathematically proficient students• make assumptions and approximations to simplify a situation, realizing these may need revision later

• interpret mathematical results in the context of the situation and reflect on whether they make sense

…reasoned using mathematical methods

© Institute for Mathematics & Education 2011

Identify important quantities in practical situations and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.

Analyze those relationships mathematically to draw conclusions.

Routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Students who are Proficient at Modeling can:

The CaCCSS expects mathematically proficient students to be able to apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

Students who are Proficient at Modeling can:

To prepare students for the modeling they will do inhigh school, students must have practice in:

Translating from real world context to mathematics (“mathematizing”)

Selecting and using multiple representations and manipulatives

Using academic language for the purpose of communication

Checking the validity of solutions and adjusting or changing representations when necessary

Model with MathematicsK-8

Talk given by Dan Meyer on March 6, 2010 where he blends real-life modeling with tips on how to take a textbook problem and create a problem more suitable for modeling.

He teaches high school math outside of Santa Cruz, CA. He received his Masters of Arts from the UC Davis in 2005 and Cable in Classroom’s Leader in Learning award in 2008.

How do we create math modeling problems?

Dan Meyer

You Tube

1. Lack of initiative.2. Lack of perseverance.3. Lack of retention.4. Aversion to word problems.5. Eagerness for a formula.6. Jeff Linder picks his nose.

5 Sympt0ms you are Doing Math Reasoning Wrong

Reorder the layers of the problem1. Begin with the visual only.2. Immediately ask the question.3. Throw down the mathematical structure.4. Students develop sub –steps.

Developing Patience Problem Solving

1. Use multimedia.2. Encourage student intuition. “How long will

it take to fill the water tank?”3. Ask the shortest question you can.4. Let students build the problem.5. Be less helpful.

Develop Math Reasoning