## Mr. Felix K. Colon

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## Tips and Facts for PPT

Potential Math Portfolio Defense Questions:

Normal Distribution:

1. If a set of data is normally distributed, what do the normal curve percentages tell us about that data? The middle 68% of the data is within 1 standard deviation, the middle 95% of the data is within 2 standard deviation and the middle 99.7% of the data is within 3 standard deviation.

2. What does standard deviation mean? What is something with a high/low standard deviation? Standard deviation tells us how spread out the data is and how far away a value is from the mean.  Weights and heights in a nursery, temperature in the month of January, salaries of working high school students can all have low standard deviation.  Weights and heights on a basketball team, temperature on a distant planet or moon, salaries in Wall Street, NYC can have high standard deviations.

3. What kinds of things fall in a normal distribution? The life span of man made products, IQ's, weights, heights, salaries.

5. Any basic normal distribution question, given a mean and S.D.

6. How do the 8 elements of thought apply to your presentation?

7. PPT:  A basic example to demonstrate the curve should involve a problem with the mean and standard deviation.

TIPS FOR ALL THREE POWERPOINT PRESENTATIONS

8. PPT:  Fully understand your problems and how you were able to get a solution.

9. PPT:  Make sure you can connect an element of thought to the problem.

10.PPT: Make sure you are prepared to discuss how you learned to use the element of thoughts to complete your assignments.

Binomial Probability:

1. In what situations can binomial probability be used? When you want to know the probability of the same outcome occurring after a fix number of trials.

2. How do you know what is the probability of success and what is the probability of failure? probability of success, p and the probability of failure, q = 1.  Therefore, if p + q = 100%, then p = 1-q and q = 1 - p.

3. Why is a combination used in the binomial probability formula? nCr in the binomial formula represents the number of arrangements of the outcome happening after a fixed number of trials. For example, 2 wins out of 3 games could look like this: win win lost, win lost win,  or lost win win. Each arrangement represents the same outcomes, 2 wins out of 3.

5. Any basic binomial probability question.

6. How do the 8 elements of thought apply to your presentation?

7. If you cannot create a histogram with excel, google "probability distribution of throwing two dice".

Mathematical Modeling – Exponential Functions:

1. Explain the concept of exponential functions. What do the various values of the exponential function tell us?Exponential functions are functions in the form of y = ab^x, where y = value over time, "a" = the beginning value, "b" = the growth factor, and "x" = the amount of time.  With an exponential function the slope s constantly changing.  For growth, the rate of change is slow and with time becomes faster.  With decay the rate of change is fast then slows down over time.

2. How can exponential functions be used to make predictions and why is this important? To make plans based on your prediction or estimate.

3. How are exponential functions different from linear functions? For linear functions, the rate of change is constant. This is called the slope.

5. Given two variables, a start value, and a rate of growth/decay, write a function.

6. IMPORTANT: YOU MUST HAVE ONE SLIDE THAT STATES: "Exponential models are functions in the form of y = ab^x, where "y" is the value over time,  "a" is the initial value, "b" is the growth factor,  and "x" is the amount of time AND another slide that states "Linear models are functions that are in the form of y = ax + b, where "a" is the slope (constant change) and "b" is the y-intercept. ("x" is the independent variable, "y" is the dependent variable)

7. Know how to sketch a linear model, growth model (such as compound interest),  and decay model (such as depreciation, half-life).

8. If you use the 1/2 life of an isotope as an example, remember the "t/h" tells you how many times the isotope decays by 50%.

8. You may use an image for your graphs but if you can create one that would be more impressive.  If you use an image from google, make sure you can discuss that particular graph.  The problems do not have to relate to the graphic examples but again if you do that it would be more impressive.

MATHEMATICAL MODELING (SLIDES):

POWERPOINT PRESENTATION – MATHEMATICAL MODELING

1. Mathematical Modeling  Felix K. Colon             01/19/12

2. Linear Models

What are linear models?

Linear models are models that are in the form y = ax + b where “a” is the slope, “b” is the y-intercept, “x” is the independent variable, and “y” is the dependent variable.

3. Slide 3 I had a graph from the essay, graph “Poverty Income level”. You can use any image that shows a linear relationship. Keep it simple. Find one you can describe if you had to. Most important point to state is that the rate of change with a linear model is constant.

4. From the essay, the table and scenario for the poverty income level problem.

5. In this slide, the title “Exponential Models”

What are exponential models?

Exponential models are functions that are in the form of y = ab^x. Explain what the variables stand for, it’s in the website.

6.Next slide I had a graph of the “compound interest over time” problem. You can use an image from google. Easy to explain. Remember to mention that the rate of change for growth starts slow and accelerates, for decay starts fast and slows down.

7. Slide 7 I gave the problem and the solution (similar to essay, see essay model on website).

8. Slide 8, Demand vs Price of Laptop graph (inverse variation, similar to decay, but it’s actually a graph of the reciprocal, i.e. as one variable increases, the other decreases proportionally) ex: when x increases by 2, y decreases by ½

9. Gave a scenario and question

10. explained steps to the solution for this problem

11. table of data that relates to problem, if you can show tables with your graphs that ‘s even better. If you can not produce a graph for any reason, use a table. In this slide I mention that a mathematical model is used to predict. Remember, based on your prediction, you can make plans for the future.

12. slide 12, graph of depreciation “car”

13. scenario, question, solution

14. same graph (not necessary)

15. same as 13, ignore

16.  Essential question

17. State concepts and examples “Mathematical Modeling….. linear growth, variation, etc.

18. and 19. EOT…..learn to ……. (similar to other slides)

20. Extensions (same as other examples):

half-life of isotopes, population growth of bacteria or species, use of cellphones, processing speed of computers

21. THANK YOU!