1. MODEL WITH MATHEMATICS

2. 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.

3. Is this mathematical modeling? A switching circuit may be a “model” for a Boolean function. A mathematical object is represented by a real-world object

4. Is this mathematical modeling? A real number may be a “model” for a point on a line, and vice versa. A mathematical object by a different mathematical object

5. Is this mathematical modeling? A logistic function may be a “model” for the growth of a bacterial population. Represents a real-world situation by a mathematical one.

6. 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.

7. “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.

8. Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.comhttp://tandrageemaths.wordpress.com 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

9. 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.

10. 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.

11. To prepare students for the modeling they will do in high 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

12. 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.

13. Dan Meyer

14. 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.

15. Reorder the layers of the problem 1. Begin with the visual only. 2. Immediately ask the question. 3. Throw down the mathematical structure. 4. Students develop sub –steps.

16. 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.