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.

Blog 4 (Melina Dabney): Help the Pirates: Mean, Median, and Mode



1) Today I will be teaching you about mean, median, and mode.

2) This information will help you contextualize a distribution of numbers.

The scenario: A group of pirates are shipwrecked on an unknown island. Everyday the temperature changes drastically. Help the pirates organize the data by using mean, median, and mode so that they can be better prepared for the weather while they fix their ship.

Temperatures (in degrees fahrenheit):
60, 55, 76, 77, 78, 78, 79, 80, 80, 90, 80

Step One: Median
To find the median, or "middle point" organize the group of numbers from least to greatest. Then cross off one number from the left, and one number on the right, do this until you reach the middle-most number.

• 55, 60, 76, 77, 78, 78, 79, 80, 80, 80, 90
• median: 78

Step 2: Mode

The mode is the number that occurs the most.

• mode: 80

Step 3: Mean

The mean is the average for the set of numbers. To calculate the mean first add all the numbers and divide the sum by how many numbers are in the set.

• (55+60+76+77+78+78+79+80+80+80+90) / 11 = 75.72

The Point

Now the pirates can anticipate what the weather will be like on a given day. Weather stations will often have the average, highs, and lows of temperatures for a given place so that people can plan what to wear, when to go out, and so fourth, like the pirates!

Work Cited (Image)

"Pirate Island." Blogspot. N.p., 16 May 2013. Web. 10 Dec. 2015. 

     <http://sambaforrats.blogspot.com/2013/05/pirate-island.html>.

Permutations!

In the King's Chessboard it, it showed exponential growth through the story of a wise man and a king.  The King wants to reward the servant for being a good servant but he doesn't want anything in return because he said serving is a reward itself. The king gets mad and wants the wise man to receive an award. After the wise man says, "Very well, I ask only this: tomorrow for the first square of your chessboard, give me one grain of rice; the next day for the second square, two grains of rice...."
The king is embarrassed because he can't figure out how much grain of rice he will be giving the man. The king uses a math genius to figure out if the rate of grain is correct. The final amount that was promised to the wise man was a lot and the king realized that it was impossible and asks if the wise man was happy with it. The wise man was satisfied the whole time but the king wanted to reward him so bad.

Shows exponent ion growth because at first the 64 chessboard starts off with just one grain of rice but by the ninth day the grain of rice grew to 256. Each day represented the growth because it kept doubling every day. This story really represents exponential growth because not one time did anything decrease everything increased.

I think literature in an effective way to teach math because math happens in every day life and there are different things that go on that can describe different concepts. It also makes you thing about what kind of math is going on with situations.

Combinations

Hello My name is Professor Mcroberts and I am going to be teaching you about Combinations today! In class we learned about the difference between a combination and a permutation. A combination would be an equation in which order does not work to have the order specified like the permutation formula. the combination formula is expressed as follows: 300C10= 300!/10!(300-10)!
To quote Professor little's definition of the definition of a combination formula: it is the "# of distinct combinations of "r" items selected without replacements from a pool of "n" items (r<n) denoted by nCr or r!/r!(n-r)!

so say there is a concert at red rocks which has a capacity of 400. only 50 get to sit up front and do not have to sit consecutive order: what is the number of possible lineups:

400C50 = 400!/50!(400-50)! possible lineups.

There are 400 people=n
there are 50 in the front=r
so plug in those values and make the equation= 400!/50!(400-50)!= possible lineups for the concert if order DOES NOT matter.

the purpose of this experiment is to calculate the number of possible lineups or situations in which order does not matter in the experiment.

the math behind this is simple because all it is is plugging in values and solving for the number of lineups. you just plug N and R and know the equation.

the difference between a Combination and a combination is that a permutation requires order.

Thats all for today!

In class we have been learning a lot about exponential growth. An interesting aspect of exponential growth is how it works when dealing with money. Compound interest is a very important function of exponential growth and if used properly can earn a person a whole lot of money. I once read some where that if you have 17,000 dollars invested in a conservative money market account by the time you were 20, that by the time you were 50 you would be a millionaire. However the same is not the case if you invested just a few years later... and that is all because of compound interest. What compound interest is, is interest making money on interest in the most simple terms. When money is put into the stock market or any market where interest is being made then, IF LEFT ALONE, eventually money will begin to be generated from the interest which has already been put into the account. For instance if you invest 1000 dollars into an account with 10% interest annually then one year later there will be 1100 dollars in the account. Interest on this account the next year would gain 110 $ oppose to 100 $ and overtime the increments become much greater.

Say for instance one invests 20,000 by the time they are 20 years old in a 5 % market (is reasonable)

21- 21,000  
22- 22,500
23- 23,625
24- 24,806
25- 26,046
26- 27,348
27- 28,715
28- 30,150
29- 31,657
30- 33,239
31- 34,900
32- 36,645
33- 38,477
34- 40,400
35- 42420
36- 44541
37- 46768
So, within 15 years the money doubled on its own and this is with a low level of interest. With an aggressive market (8-10%) the 100,000 mark would have already been made!

Plotting a Line Graph Lesson by Elatia Wintersquash (Blog 4)

Calculating the Slope of a Line

Hello! My name is Savanna and today we are going to talk about how to calculate the slope of a line, and the different types of functions that we look at when making or analyzing graphs and finding the slope. When we think of linear equations we know that there are three main types of functions: slope intercept, point-slope, and standard.

What is a function? A function relates an input to an output- in a function there is one output for every single input.
Here are three main functions for the equation on a line (linear functions). Within these forms of functions there are different symbols that refer to slope.
To find a slope in the simplest way possible, we can use different methods according to the situation. However, sometimes we have to solve an equation to find the slope mathematically. Here are the linear equations we need to solve to find the slope of our given lines.

An important note: slope always= rise over run, or the height over the width. If you have two points on your graph (see point=slope form below) one can calculate the slop using these two points and rise over run. (y2-y1)/(x2-x1)

-Slope intercept is my personal favorite, and generally easy to remember.
Y=mx +b, where "m" is the slope and "b" is the y intercept. easy enough to decipher.

   Example:
   y=6x -5
   Here, we can clearly see that the slope is given to us as "m" in this case is 6. The slope is 6.

-Standard form is also easy to understand but a little less straight forward.
  ax +by=c, where both "a" and "b" cannot equal zero. In standard form, to find the slope we solve for   x and graph it.

   Example:
   2x + y= 4
   2x=4-y
   x=2-2y
   You find both the x and y intercepts by solving the equation and then through graphing, one can see    find the slope.

-Point-Slope form is less often used but still valid.
   y2-y1=m(x2-x1)
   Here, the slope is given again using the letter "m". We know the slope already, as in slope intercept,    which helps us to further graph the line.

After today we now know the three different types of linear equations and we can now go off and solve these formula in order to find the slope of the line. :) Class dismissed!

Histograms and Mexican Candy - Lorena Aguilera

Hi everyone! My name is professor Aguilera and today we are going to learn about statistics, specifically about how to make a histogram using Mexican candy as an example.

First, we will start with some definitions:

Statistics: the science of collecting, organizing, and interpreting data to describe or summarize something.

Population: the set of people or things being studied.

Sample: subset of the population from which the raw data are obtained.

Frequency table: table showing the number of times that each data point appears.

Histogram: bar graph for quantitative data.

Now that we know those concepts, let’s learn about Mexican candy:

Mexico is a big country with many states and several regions, all of them having specific ways of preparing food, drinks, and candy. Some of the recipes come from before the conquest, and they show different aspects of our culture. In this class I will talk about 5 of the most famous types of Mexican candy, or “dulces Mexicanos” as we call them.

Palanquetas: they are usually made with peanuts and honey or sugar.

Ate: Ate is made with different type of fruits, like strawberry and guava, and they have a gooey consistency.

Glorias: it is a candy made with burnt milk, and the literal translation would be “glory”; they are named like that because people say that’s what you feel when you eat them.

Alegrias: this is a type of candy made with amaranth and honey. Amaranth is an ingredient that was used in religious Aztec ceremonies, so this type of candy has been around for a long time. Alegria means “happiness” in Spanish.

Cocada: cocadas are a very popular type of candy all around Mexico, and it’s made with coconut pulp.

Now, let’s combine statistics and Mexican candy to create a histogram.

It would be hard to ask the entire Mexican population about what type of candy they prefer, which is why researchers use “samples” when collecting data. In this case, I asked 12 of my friends from Mexico about their favorite candy; which will be my sample. The raw data I got is:

Gloria, alegria, palanqueta, Gloria, cocada, ate, ate, alegria, alegria, cocada, Gloria, alegria

With that set of raw data we can then create a frequency table, which include the data, frequency and the relative frequency. We can get the relative frequency by dividing the frequency with the sample, in this case, 12.

Type of candy	Frequency	Relative Frequency
Gloria	3	3/12=0.25=25%
Palanqueta	1	1/12=8.3%
Alegria	4	4/12=33.3%
Cocada	2	2/12=16.6%
Ate	2	2/12=16.6%

Now that we have the frequency table, we can start drawing the histogram. Using graph paper can be helpful, and it is important to know that the frecuency goes in the y axis and the data goes in the x axis. The main idea is to represent how many times a particular candy was chosen. 

When creating a histogram, be sure that the width of each rectangle is equal. Also, the rectangles must be touching (this is the main difference from a bar graph)

The histogram should look like this: 

And that's it! I hope you enjoyed learning about histograms and Mexican candy!

I’m professor Turner, and today we’re going to learn about exponential functions. 

·      A function is a relationship or expression involving one or more variables:

o   One you may already be familiar with is the linear function:

§  Y = mx + b

o   The exponential function typically takes the form of:

§  Q = f(t) (pronounced “f of t”)= ab^t

§  For our purpose, let’s consider “t” as the time step

·      So Q is equal to f at time “t”

§  a is the initial value or y-intercept

·      where the line crosses the y-axis

o   changing the value of a shifts (horizontally) the line along the y-axis

§  b is the growth factor or base

·      when b > 1 – the slope is positive or the line is increasing exponentially

·      when 0 < b < 1 – the slope is negative or the line is decreasing

·      having a larger positive base > 1 will make the slope steeper

o   and bring it closer to the y-axis (horizontal compression)

o   Put it all together:

§  Lets suppose that at every time-step (one day), we double (b) our initial (a) value or amount of songs in our itunes library – what might this look like in the form of an exponential function?

·      Our initial (on day 1 – t = 0) amount of songs is 3 (a= 3)

·      Each time-step (t) is one day

·      We will double (b = 2) our songs everyday for a month (30 days)

·      So: how many songs will we have on day 2, 3, 4, 15 and 30?

o   Our initial equation looks like:

§  No time step has occurred

§  f(0) = 3*2⁰ = 3*1 = 3

o   Our first time step:

§  One day (time-step) of doubling has occurred

§  f(1) = 3*2¹ = 3*2 = 6

o   Second time step:

§  We’ve doubled the amount from the day before

§  f(2) = 3*2²  = 3*(2*2) = 3*4 = 12

o   Third

§  f(3) = 3*2³ = 3 * (2*2*2) = 3*8 = 24

o   Fourth

§  f(4) = 3*2⁴ = 3 * (2*2*2*2) = 3* 16 = 48

·      We can see that the product of the base combined with its exponent doubles at every time-step

o   E.g. 1 , 2, 4, 8, 16