Blog 4: The Counting Principle

Blog 4: The Counting Principle

My name is Professor Wilson and today I will be explaining the counting principle and how it works.  The fundamental counting principle is an easier way to find out how many options or combinations you have when you have selections to choose from.  So this means that when there are B ways to do one thing, and C ways to do another, then there are BxC ways of doing both.  This works whether you have 5 different choices, or maybe just 2.  Here is an example:

How many options of cars do you have?

a) Sedan/Hatchback                        2

b) Red/Black/Blue/White/Green     5

c) Standard/Luxury/Sport               3

2 x 5 x 3 = 30

Because you have 2 style options, 5 color options, and 3 model options, there are 30 total combinations of cars that are available to you.

Blog 4-Linear Growth

My name is Professor Brownsword and today I will be going over Linear growth! Linear growth is all about rise over run which is essentially slope. The way you find slope is by taking two points on the graph or table and putting the numbers in an equation as y2-Y1 OVER X2-X1. Your x is the independent variable and your y is dependent on the x. Lets put this into some real world context! Say you go candle shopping and every candle is five dollars. The amount of money you spend depends on how many candles you buy… making the amount of candles you buy the X value and the money you spend the Y value. If you get 1 candle you spend 5 dollars which can be represented as 1,5. If you get two candles you spend 10 dollars which can be represented as 2,10. The slope is easy to find if you plug the numbers into the equation. 10-5 over 2-1 is 5. 5 is the slope! Whenever you have a constant relationship between two variables you are able to find linear growth! 

Blog 4: Be the Professor

Hi! I'm Professor Sisk and today I will be teaching y'all about everybody's favorite..... Fractions!!!  It is really important to study fractions because they are the foundation of a lot of different math techniques that you will be expected to acquire knowledge of at some point in your life.  For example, algebra.  Algebra would be incredibly difficult to learn without basic knowledge of the addition, subtraction, multiplication, and division of fractions.

First, we will cover the addition and subtraction of fractions.  It's easy!  If the denominators for the fractions you are adding or subtracting are the same, then just add your numerators together.  If there is not a common denominator, you just need to find a common denominator by using cross multiplication and the addition of your uncommon denominators.  Here is an example of simple addition and subtraction of fractions and a variable example to help you understand how to find the common denominator.
ex: a/b + c/b = a+c/b
ex: a/b + c/d = ad+cb/bd

Next, I'll explain multiplication of fractions.  All you need to do to multiply straight across!
Here is a variable example and a numerical example that will show you the exact process.
ex: a/b x c/d = ac/bd
ex: 3/4 x 2/3 + 6/12 or 1/2 !!!

A little jingle to help you remember how to multiply fractions is...
Multiplying fractions ain't no problem.. top times top and bottom...

Finally, the division of fractions!  Dividing fractions is easy too!  You keep the first fractions exactly how it is, and multiply it by the opposite of the second fraction.  Check out these examples.
ex: a/b ÷ c/d = a/b x d/c = ad/bc
ex: 1/2 ÷ 3/2 = 1/2 x 2/3 = 2/6 or 1/3

To remember how to divide fractions sing...
Dividing fractions don't know why.. Flip the second number and multiply!

Together, your jingle should sound like-
Multiplying fractions ain't no problem, top times top and bottom times bottom.  Dividing fractions, don't know why, flip the second number and multiply ! ( but fiiiiiiirst, cross cancel)

You guys should be set!
Thanks
-Professor Sisk

Blog 1: Getting to know you

1.) Madeleine Stegman

2.) Maddy

3.) 66'

4.) 21 years old

5.) About 9 am during the school week

6.) Chocolate

7.) Popcorn

8.) Hang out with friends, run, listen to music

9.) I can't choose a favorite but I love Led Zeppelin and the Rolling Stones; like rap and other music too

10.) Alg 2

11.) uncomfortable

12.) Uncomfortable

13.) Uncomfortable for most except graphs, mean, median, and mode, Venn Diagrams

14.) no

15.) All

16.) texting, facebook, instagram, snapchat

17.) Psychology, business minor

18.) I thought it was a requirement

19.) Yes, I have to take calc

20.) Gain some general math skills

Blog 4: Be the Professor

Hello class! My name is Ms. Stegman.
Today I will be teaching about how to find the mean, median, mode, and range of a set of given numbers. And explaining how these are relevant to everyday life.

The mean is the average of the set of numbers or the calculated central value of the set.

The median is the middle number of the set when the numbers are set up from least to greatest. If there is two numbers in the middle, you find the mean of those two numbers and that is now your median.

The mode is the number that is most frequently repeated in the set.

The range is the difference between the highest and lowest values in the set of data. To find the range, set up the data from least to greatest and then subtract the smallest value from the highest value in the set.

Example:
A survey of women's shoe sizes is taken in a classroom that contains 20 girls.
Here is the data set:

5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 11

To find the mean of this set, you would add up all of the numbers and get 150. You then divide 150 by 20 (which is the number of values in the set). The mean is then 7.5.

To find the median of this set, you have to organize the set from least to greatest value (which is already done in this case). The number in the middle is your median. In this case it is two 8s, which would just made the median 8.

To find the mode, simply count to see which number is most frequently repeated. In this set, the mode is 8 because there are 7 of them.

To find the range, identify the lowest and highest values in the set. In this case, 5 is the lowest and 11 is the highest. Now simply subtract 5 from 11 and the range is 6.

Hopefully that made sense to everyone, they are pretty simple concepts that can not only be applied mathematically, but in everyday life as well. Throughout life the ability to understand how to find these numbers is needed more then you think and is useful even for everyday activities. For example, teachers have to analyze the test scores from their class and see what the class average, or the mean, is. As well as the most common test score, or the mode.
Even everyday when you check the weather outside. There is a high and low temperature and the estimated temperature for the day is the average or mean of the daily temperature.
In Baseball, you see a player's batting average, which is his total number of hits divided by the number of times at bat and this number is the mean. I could go on and on with everyday examples of the median, mean, mode, and range.

Hopefully now you all better understand how to find the mean, median, mode, and range of a set of given numbers and in everyday life. And understand the importance of this!


Ms. Stegman, out.
Have a good day!!

Blog 3: Mathematics in a story

I chose the book The Very Hungry Caterpillar. In this book, it begins with a little egg where a little (and hungry) caterpillar is born. The first day, he ate 1 apple. The next day he ate 2 pears, but was still hungry. And the next day, 3 plums. Then 4 strawberries, then 5 oranges. He was still hungry and ate many things on Saturday, then he felt sick. On Sunday he ate 1 green leaf and felt better. He was no longer a little caterpillar and was now a large one. After eating so much, he formed a cocoon and became a beautiful butterfly.

The first day he ate 1 thing, then 2, then 3, and so on. Everyday he eats an amount of something, then the next day it is one more, then one more. This is a great example of linear growth; the growing of the same amount in each step. If this was in graph form, the line would be straight but gradually increasing upwards by the same amount. If this pattern were in linear function form it would be shown as y=1x + 1. The first day is the Y intercept and the slope is 1 because the amount he is eating increases by 1 each day. The book makes understanding the concept of liner growth extremely easy and simplifies it.

I think that literature is an effective way to teach or learn a mathematical concept because it turns something that is thought of as math into easy, fun reading. Most people learn much better (especially visual learners) when they have a visual to refer to and help them better understand the concept. By applying math into a story, it also helps people see how math is applied and used in real life. Literature helps turn complicated concepts into much simpler, everyday ideas.

Blog 2: Believe it or not?

1.) Weight Watchers- makes you lose weight

2.)
Major premise: If you use weight watchers, then you will lose weight.
Minor premise: Mary does not use weight watchers
Conclusion: Mary will not lose weight.

3.)



4.)
It's valid because p --> q and if q is not true, p is not true (valid). It can be argued whether it is true or not. You could use weight watchers and it could work and help you lose weight. Or you could use weight watchers but your weight could be effected by other factors as well (eating healthy, exercising, following the program exactly or not). If you do not use weight watchers, that doesn't necessarily mean you won't lose weight (you can lose weight other ways) or you could not use Weight Watchers and not lose weight because you aren't changing
anything.

5.) If you use weight watchers, you will lose weight

6.)

 

a. It is a tautology and has a solution mathematically. It also makes sense in real life, if you use Weight Watchers, you could lose weight. But you might not lose weight (other factors).

b. Truth tables are useful because you can tell if it's valid or not through a mathematical way of finding out.

7.)

Consider the source: The source of information is pretty clear and has credibility to a certain extent because Weight Watchers is a very popular and trusted program. But, whether or not you lose weight depends on other factors going along with the program (exercise, sleep, how closely one is sticking to the program, etc.). The source does have crediability on the issue though because Weight Watchers is a pretty well-known program.
Check the date: It is still relevant because Weight Watchers is a long on-going program.
Validate accuracy: Looking at other websites, forums, and reviews of the program, people claim that Weight Watchers really does work and there's a large support group. One forum says that "Weight Watchers is one of the most successful weight loss programs of all time".
Hidden agendas: It doesn't seem to have any hidden agendas; it's a company and all companies want to make money but it also seems like they're a reliable company who actually wants to help people lose weight. When the make the statement that you'll lose weight, that's not necessarily true but if you follow the program exactly then you most likely would.
Don't miss the big picture: I think that it doesn't conflict with things that are true. The Weight Watchers plan makes sense and you could lose weight from it. But you can't not lose weight if you don't use weight watchers.

8.)
With the conclusion of Mary will not lose weight (because she doesn't use Weight Watchers), it is a fallacy. It is a fallacy of hasty generalization because you can't generalize that since Weight Watchers claims that you will lose weight and Mary doesn't use Weight Watchers, then she won't lose weight. That's assuming that because the program helps people lose weight, that without the program you can't lose weight.

9.) 

I think that this activity did help me be more critical about media in a different way. Looking at an add in a mathematical way rather then a typical way is a different way to view it. I find media criticism  to be very important because we're fed so much information on a daily basis that we just take it without any criticism, but it's important to not listen and buy into everything that's thrown at you.