Statistics

Graphs!

Where you scared to look at this blog because it had the word "statistics" on it? Come on tell the truth you jerked and almost left my blog. It's okay, I did the same thing in class, I almost walked straight out of class because I thought "this is it, this is were I fail." No worries though I am going to talk about the use of a variety of graphs to display data and explore relationships among data.

Our class was given each a sample bag of m&m's to construct about four graphs which were a real graph, pictograph, dot plot, and a bar graph. Each one was about the m&m's but each one showed data differently.

First, we made a real graph were we put the actual m&m's on a graph were the horizontal axis was labeled with the colors brown, green, orange, red, blue, and yellow. The vertical axis was labeled with the frequencies of zero through ten and the title of the graph was Graph 1: Frequencies of m&m's. A real graph is were you use actual items and put them on a graph to show how many of each there are. Next, we made a pictograph by coloring in where each m&m was and removing them from the graph. A pictograph uses pictures or symbols to show the value of the data. Later, several small dot plots were needed to be made to record how many m&m's of each color each student received and calculate the average for each color by using the dot plots. Using the dot plot we constructed the last two graphs which were another pictograph and a bar graph. They both showed the same data but the bar graph was easier to read and calculate the exact numbers for each color.

At the end of the lesson I understood that graphs are used to show different types of data in different ways but some also carry a relationship between each other. My favorite types of graphs are pie graphs because they show data as a whole so you can see which subject is most effective. How about you what is your favorite type of graph.

Fun with Graphs!

Odds??

What are odds? Odds are the  number of ways something can occur to the number of ways it can't occur. Probability is the best way to get to the point of finding odds. Probability shows you the number of ways something can occur to the overall total. Now your wondering how its possible to find odds by using probability. Well that is exactly what our class was wondering when we were given an activity where our class figures out the probability of dice and later the odds of dice.The first step was to fill out a table where we calculated the sum of two dice. Then we calculated how many sums of 1, 2, 3, 4, 5, 6 were calculated. Next we filled out another table that contained three categories. The first being the sum of dice, next the number of outcomes for each sum, and lastly the probability of each outcome, reduced down. Lastly after finding their probability we found the odds.

Now let me explain, as you can see in the example above we have one out of the total of eight chances of winning. So you have seven chances of losing and one chance of winning.In this example we are finding the ways something can't occur to the ways it can occur. This happens because eight subtracted by the one chance of winning gives you seven chances of losing while you still have one chance of winning. That is what odds is!

To me this was the easiest of all our lessons to understand because we used probability to define and show what odds are. Hopefully I didn't confuse you and you found this helpful. Have a great and wonderful day.

Simple definition of Odds!

Simulations

Cards, dice, coins, spinners, and random number generators are different ways you can run a simulation. A simulation models what could happen in a given situation.

Our class was asked to predict how many boxes of cereal we would need to buy in order to get at least 6 toys.

My guess was 36 boxes of cereal because in a real life situation you repeat toys a lot. To test the situation the class was asked to use a random number generator and to use a graph to tally how many times we got each toy. Each toy had to happen at least once on the graph.

My results were that I had to buy 16 toys to get at least one of each. Then we were asked if each box cost $3.99 each how much money did we spent all together? The total amount of money I spent was $63.84.

Anbviously no one in the class had the same answer. So next we were asked if it was worth it just to get all six toys and the answer went both ways. For me personally it's not worth it because I could spend money on other healthier food choices other than cereal. One student on the other hand did think it was worth it because they didn't have to spend much and received close to six toys.

Lastly, this activity seemed very simple and easy to me to understand. In my test though I read a question wrong and got it wrong. I think I might need some more practice what do you think?All in all, this activity was fun and I hope I helped you to understand what this concept means and that you liked my blog. Have a great day!

Random Number Generator!

Colors Spinner!

Fun dice games for kids!

Coin flipper!

Rock, Paper, Scissors!

We all have had the pleasure of playing rock, paper, scissors.If not, it is a really fun game that gives you three chances to win. However, it is not only a game but it also shows us experimental and theoretical probability. Experimental probability means that you actually do an activity to figure out how many ways you can win out of the combined percentage. Theoretical probability means having the perfect atmosphere where your probabilities of winning and losing are equal, in other words, fair. Our class played this game both ways and even though we all collected different data from the experimental game, we all concluded that the theoretical part of this game would always be fair because everyone would have a fair chance of winning.

The reason behind experimental probability in this game never being fair is humans. We cheat, play strategically, or read the other persons expressions to win. In theoretical probability its only numbers involved and numbers can't cheat, play strategically, or read other peoples faces because its opponent is also numbers and they both have an equal chance of winning. So now you know the mathematical reason of why your always winning or losing.

Although these two ways of finding probability are different they have something in common. They are both trying to find what will happen in a certain situation. This activity was not very hard but I had some problems with the theoretical part because I couldn't grasp the concept of not actually having a situation happen in order to get an outcome. Now I understand that numbers help you figure out the most probably correct answer to a situation. Thank you so much for reading my blog and I hope you have an awesome day!

More Math Fun!!!

Pom Poms and Cards

Multistage experiments help your chances of winning or losing get higher. In this post I will inform you about our classes encounter with this term and a few others in our class activity. What our class used to work through this activity were a standard deck of cards, and two different sets of colored pom poms. The words that relate to the activity are multistage experiments, probability, replacement, and tree diagrams.

First we started the activity with the deck of cards and groups of two to four to answer a few questions about probability. The first part of this activity included two separate sets of questions. The first consisted of eight questions asking for example to "Find the probability of a red card" or "Find the probability of not getting a face card and not a club." Next we found probability by placing the card back in the deck, which is called replacement. This part of the activity only had five questions asking for example "What is the probability that the first card is an ace and the second card is black?" or "What is the probability that the first card is an ace or the second card is black?" When the first side of the activity was concluded the concepts of  probability and replacement were covered. To conclude this part we all agreed that probability is the likelihood of a certain event happening and replacement means to put an object back after drawing it which makes the results independent. The other side of our activity covered the concepts of tree diagrams and multistage experiments.

For this part of the activity we worked with pom poms and made tree diagrams. The tree diagrams help children visualize how multistage experiments work and show how replacement and no replacement affect your outcomes. With replacement you have a fair chance of getting either color. No replacement means that there are more chances for another color to get drawn more. When we made our tree diagrams they showed what a multistage experiment is and what your chances of getting one color rather than the other is.

In writing all this information might seem boring but once you do the activities yourself you'll have as much fun as we did and your students or children will think more critically of what they are trying to solve.

Probability Game with replacement!

Probability Goldfish

Probability is a hard concept for small children to grasp unless you give them an activity to work through. That is exactly what we did on March 24 of 2015, we played with goldfish! The material you would need to replicate this activity would be: edible goldfish of at least two different colors to represent healthy and sick goldfish, a zip-lock bag, and a probability worksheet. Next you have the children record how many sick fish, healthy fish, and the combined total of all the goldfish that were in each of their bags. Now they are ready to calculate the probabilities, like the probability that a fish in their sample is healthy or the probability that a fish in their sample is sick. They decide whether they compute these probabilities in percentages, fractions, or decimal form. This way they learn the different ways they can show probabilities. Going on to the next step they add together the probability of getting a sick fish plus the probability of getting a healthy fish. When they add them up they will see that the total comes to one because these events are mutually exclusive. This means that the fish cannot be both sick and healthy at the same time. Continuing forward they will compute the probability of not getting a healthy/sick fish. This step introduces them to complements. No, I do not mean admiration I mean the opposite of something. For example the opposite of a healthy fish is a sick fish. Lastly, they will be learning proportion. Proportions means that two ratios are equal which will show them how to figure out a missing part of a problem. For example, 7/43 = x/300 this can be solved by cross multiplying which gives you an approximation of 48.

We as a class discussed and went over these concepts to agree and discuss over how and why this is important for children to know. Of course, math is always a wonderful thing to know and teach to everyone. For me this was a very easy thing to understand but reminded me of complements, proportions, and mutually exclusive problems. Every time I think of this activity and do it with my future classroom I will remember of the fun times we had in class :)

Click here for more!