Respect the Pie!

Circle graphs are used to show how the whole of something can be divided into parts. They can also be described as pie charts and this may be one way to introduce circle graphs first because students can relate this to the real world when they envision a pizza pie as the whole and each piece as the parts. In class today we learned how to make circle graphs with elementary students so that they can visualize and hopefully understand how this type of graph works. The entire class was given a bag of M&M’s and told to count how many of each color they had. We then combined all our data together to find out what the total number of each color M&M’s our class had. Before we began our circle graphs we first put our data into a bar graph so that we could see the different classifications that we were working with, for instance; there were green, brown, red, yellow, orange, and blue M&M’s but, also to visualize the differences between the amounts. We colored our bars the color of the M&M.

We then CUT OUT each bar graph and taped them together to make a circle. To do this correctly, you will need strips of paper that represent a base ten block so that you will have an accurate amount when you’re transferring your data to a circle graph. Remember, a circle graph is considered one whole and all the parts add up to that whole. That is why it is easier for young children to break the information into base ten blocks because each base ten block represents 10 of something or 10%. Using circle graphs in this way can be a great springboard for learning percentages.

Remember, a pie chart is not always the best choice for your data. Here's some simple questions to ask yourself when deciding whether a pie chart is the best choice: Do the parts make up a meaningful whole? Are the parts mutually exclusive? Do you want to compare the parts to the whole? Do you have 7 or fewer different parts? If you answered yes to all of these then a pie chart is for you!
Here's a great website to use with the students to make a circle graph once they have done this lesson.

Probability vs Odds

January 30, 2014

Uh oh, I just realized there is a difference between Probability and Odds! Let's recap probability first:

P(A)=The Number Of Ways Event A Can Occur

        The Total Number of Possible Outcomes

The definition of odds: The odds of an event occurring is the ratio of the number of ways the event can occur(successes) to the number of ways the event cannot occur(failures). For the odds of an event occurring(odds in favor) it can be written as successess:failures or:

The Number of Ways Event A Can Occur(successes)

  The Number of Ways Event A Cannot Occur(failures)

Now if we're talking about the odds of an event not occuring(failures) then it is written as failures:successes or:

The Number of Ways Event A Cannot Occur(failures)

The Number of Ways Event A Can Occur(successes)

 Let's go back to my initial post about choosing sick(green) fish or healthy(not green) fish. Looking back, 10 of our 48 fish were sick and 38 were not . The odds then of choosing a sick fish is 10:38, ten times you will choose a sick fish and 38 times you will choose a healthy fish. Pout away Sheldon!

Probability Using Cards

January 23, 2014

Let's start with the facts. There are 52 cards in a deck, half are red, half are black, there are 12 face cards: four of them are jacks, four of them are queens, and four of them are kings, and there are four different suits. Let's Play!

If a card is selected from this ordinary deck of cards, what is the probability of picking a queen?

There are a total of 4 queens and 52 total cards right? Then 4 times out of 52 times you pick a card, you will draw a queen.

Let's make it a little more interesting!
What's the probability of drawing a queen or an ace?

We already know the probability of drawing a queen is 4 out of 52 and the probability of drawing an ace is also 4/52. These two events are mutually exclusive because they have no elements in common and therefore cannot occur at the same time. In this case we add the probabilities. This gives us 8 out of 52 times we draw a card it will  be either an ace or a queen.

Check out this website! Click here

Experimental Probability

January 21, 2014

Experimental Probability

ROCK, PAPER, SCISSORS:
We all are familiar with the game rock, paper, scissors right?  Although I love Sheldon's version, we will use the original game for our experiment. I partnered with Jamie in our class and we were told to play 45 games. Cool!!! right??? I will assume that you all know how to play this popular game but, have you ever asked yourself if it is a fair game? This is a question I have never thought of. Jamie and I kept score of each game we played. During the first few games Jamie told me that I was playing paper a lot. Well of course I stopped doing that and tried to change it up a bit. Little did I know was that by her telling me this it was changing the probabilities of who would win. Let me explain: If Jamie had not told me this she would have played scissors more often because scissors cuts paper and would have won more games. I think she was just being nice to me because we ended up winning equal amounts of games.

Theoretical Probability:
This is different than Experimental Probability because this is the outcome under IDEAL conditions. Well my experiment WAS ideal because Jamie gave away my playing habits but if she had not it would have ended differently because she would have used the strategy of observation to win.

Probability

January 14, 2014

Probability: This is defined by the measure of how many times an event is likely to occur out of the number of possible outcomes.

Our first task with a partner was to gather an amount of colored goldfish and determine the probability of choosing a certain color.
I'm familiar with probabilities so this task was easy for me.

For our problem there were 48 goldfish and the green ones represented sick fish and the other colors represented healthy fish. We counted 10 green fish so the healthy fish amount is 48-10 which is 38 healthy fish. Now let's compute the probability that a fish in our sample is healthy. If 38 out of 48 fish are healthy, the probability is then 38/48 or when reduced 19/24. This means that for 24 fish that are counted, 19 of them will be healthy. Therefore, the probability of choosing a sick fish is 10/48 or when reduced 5/24. When 24 fish are counted, 5 of them will be sick.

Here's some great games to play with the elementary kids to learn about probability!
Click here