Feb 6 2014

hi

Test Anxiety!

Our first test is on Wednesday and I am scared to death! Some problems seem to trick me still even though I understand most of it. I have a hard time describing how to solve a problem or what certain things are called. I am glad we have a vocab list that I can refer to. Sadly, I can't refer to it during the test though! I will be practicing my math skills this weekend and part of next week and reviewing my homework! I always get so nervous for test and I don't understand why?! I really don't like essay questions, but what can you do?! I just keep telling myself that I am going to ACE this test! (I guess I am trying to be like the Little Engine that Could and tell myself over and over "I think I can"!)

Rock, Paper, Scissors!

I absolutely loved playing rock, paper, scissors in elementary school so when Roxanne (our college professor) told us yesterday that we were going to play it in class, I was so excited. I thought to myself, "oh I got this." We had to play 45 times in a row with a partner. I was awful at first! I couldn't concentrate on what to pick because I was keeping track of each round and counting 1, 2, 3 for when we would reveal our sign. So I blame my failure on the distractions. But as we kept playing, I got better! Over all, I won by 4 rounds! Woo Hoo! I am still a champion. On a side note, I actually played my dad later that day (winner got the cookies) I schooled him because of all of the extra practice! haha. Anyway, you are probably thinking "what does this have to do with math?" and it has everything to do with math! In this case, probability! We used this activity to find experimental probabilities and to make a tree diagram to calculate theoretical probabilities. Through experimental probability, we found that our game was very close to fair, but not perfectly fair because we almost had equal probabilities for the chances that I win, my partner wins, and a tie. (To be fair means that all the outcomes probabilities are equal). Through making a theoretical probability matrix, we found that this game is a fair game because the outcomes all have the same likelihood of happening. It was really fun to see that you can use probability for almost any game or activity!

I win!!

Homework Fun...

Do you ever get sick of doing homework? That's how I felt today! I was having a hard time focusing on my homework and I kept getting distracted! Some of the problems took a long time which made it worse! haha. I even had to watch videos to help me. I didn't even know there were videos! 
One problem that I didn't know how to start asked to estimate the total amount of deer in a game preserve. It said that a forest ranger caught 250 deer, tagged them, and released them. Later 105 deer were caught and only 36 of those were tagged. Estimate how many deer there are total in the preserve. Well I was stumped! I had to watch a video, but I figured it out! 
You have to set up a proportion. On one side of the equal sign you take the total number of marked deer caught over the total number of marked deer which was (36/250). For the other side of the proportion, you take the number of deer caught over the number of total deer in the reserve which was (105/x).  So the problem now looks like:
36/250=105/x

Then you have to solve for 'x' by cross multiplying. So you get:
36x=26250

Then you divide by 36 on both sides to find 'x'. 
x=729.166667  which rounds to about 729 total deer in the preserve.

So the problem stumped me at first, but once I knew how to set up the problem, it was a piece of cake! Most of the problems are like that, I just need to figure out the first step!


This LINK will help you understand better by walking you through a 'fish pond' example step by step! Or click HERE for an experiment to go with it (More interactive and fun looking) (It is a PDF download).

Rewind back to class

I want to talk about another activity we did in class last week (the day we used face cards for probability). Not only did we use the cards, but we also used Pom Poms to make tree diagrams. Pom Poms are like little fluffy balls- almost like a cotton ball. We used white and black ones. Man was that tricky! I am still a little confused with it, but I think I got it now?! Here is an example we had...

A box contains three white balls and two colored balls. A ball is drawn at random from the box and not replaced. Then a second ball is drawn from the box. Draw a tree diagram for this experiment and all possible outcomes. Find the probability that the two balls are different colors.

So above the problem is the diagram I drew. On the first draw you either get a black or white ball. Then on the second draw, it is the same outcome since you replaced the balls so you add that outcome to the first one (look at picture).  The cool thing I learned about tree-diagrams is that you can check your work! On each "<" sign, the probability of drawing each object on either side of it must equal one. For example, if you look at the first "<", the probability to get a white ball (3/5) and the probability to get a black ball (2/5) add to one when put together so you know you did it right! Now that we drew the tree-diagram, we have to find the probability that the two balls are different colors. On the side of the diagram, I drew all of the outcomes. So we find the outcomes that have one of each color. Then you have to multiply the probability of getting the first color to the second color to find the probability of getting both (follow the lines on the diagram to know what numbers to multiply). Then you add those two probabilities together! See it sounds really tricky right?! So HERE is a link in case you need more practice, like me! ;)

Homework: Piece of cake (for now)

Today I tackled my first homework assignment on probability. It surprisingly was really easy! It wasn't as hard as I thought it was going to be. Most of it was basic probability. For example, one problem stated, "A marble is selected at random from a jar containing 3 red marbles, 6 yellow marbles, and 4 green marbles. What is the probability that the marble is either red or green?" So to solve this you take the probability of getting a red marble (3/13) and add it to the probability of getting a green marble (4/13). The answer is 7/13! Most of the homework was as easy as this one. There were some harder problems, but I figured them out. The tricky part was learning how to decide if you add or multiply probabilities. When the question is asking for an "or" you should add and when it asks for an "and" you should multiply. Sometime you have to do both, but that is in the next homework section/chapter! More fun ahead!

I was searching the internet for ways to teach probability to my students and I came across this website full of worksheets I could give to my students to practice. It has answer sheets to all of the worksheets and it has different scenarios using probability, including using marbles and spinners! Click HERE to view!

Pick a card, any card!

Todays math lesson on probability was a little more challenging than last time. We used a deck of playing cards to practice probability. Some questions were easier like finding the probability of drawing a red card. Half of the deck is red so the probability of choosing a red  card was 26 over 52 which reduced to one half. 
Other questions were harder. One I had a hard time with asked to find the probability of drawing a red card or a 10. I solved it by finding the probability of each and adding them together. 
So I took the probability of getting a red, P(r)=26/52 and added it to the probability of getting a ten, P(10)=4/52 to get 30/52, but I forgot a step. 
My answer included the cards that were both red and 10. The question only asked for the chances of getting one or the other, not both. So you have to subtract the intersection: which is 2/52 because there are two cards that are both red and 10. So the real answer is 7/13 after you simplify. 
There were a couple questions that were similar to this question that confused me. I learned that when the question has 'or' in it, you need to subtract the intersection of both items. Also, I learned that to find the probability with an 'and' in the question you have to multiply the two item's probability to find the answer. For example; if you were to draw a card then return it to the deck and then draw again, what would be the probability that the first card is an ace and the second card is black? First, find the probability of drawing an ace: 4/52. Then find the probability of drawing a black card: 1/2. Now you add the two together and the the probability is 1/26!

This might sound a little confusing so here is an article about how to use a deck of cards for probability and examples to try. Click HERE to read it and try it out!