Kalkulation Korner

Monday, October 5, 2009

Mistake in Episode #3

There is missing information in Episode #3 - Graphs. The missing information will be recorded and updated later this evening. Do not forget to post comments so Kalkulation Korner can become a better podcast.

Sunday, October 4, 2009

Episode #3 Transcript

Welcome to Kalkulation Korner – Where mathematicians meet.

Greetings fellow mathematicians today is October 3, 2009. I am Mr. Burns and this is episode #3 of Kalkulation Korner. Before we get into this episode I want to tell you about the blog that goes along with this podcast. The title of the blog is also Kalkulation Korner. The web address is kalkulationkorner.blogspot.com or just Google Kalkulation Korner and you will find it. Go visit it to see transcripts, slides or to leave a comment about the podcast.

In this episode we will explain graphs. This topic was chosen by my third hour intervention class and they were essential to the script writing process. We will explore the types, when to use particular graphs, and the parts. Before we go into detail about the graphs we need to go over one vocabulary word and that is graph. By definition a graph is a visual representation of data. First we will discuss all the different types of graphs: line graphs, double line graphs, bar graph, double bar graph, histogram and circle graph. The first visual representation of data, or graph, we will look at is the line graph.

As the name suggests a line graph uses a line to represent the data. Very similar to a line graph is a double line graph. Mathematicians use line graphs to show change over time, also called a trend, and a double line graph is used to compare trends. Bar graphs are used to compare data sets. A bar graph can be used to compare the favorite flavors of ice cream in your class. You would be able to further break down this data into boys and girls to create a double bar graph. One bar would be used to show the girls data and one for the boys. Histograms are next on our list and very similar to a bar graph. In fact a histogram is a type of bar graph. A histogram shows continuous data and the bars must be touching. Histograms can be used to show test scores, number of family members or any other kind of data that can be shown in ranges. The last graph we will discuss is the circle graph. We use a circle graph when we are showing data as a part of a whole.

Now that we know what graphs there are and when they are used we need to discuss the parts of a graph. Graphs we use contain a lot of data and we need away to interpret this data. The first part of a graph is the title. The title tells us what information, or data, the graph contains. Line graphs, bar graphs and histograms, along with the title, also have labels along the axes. These labels help us further develop an understanding of the data being shown. Circle graphs do not have axes to label but they do have labels, usually inside of the circle. A third place you can check for information is the key. The key is helpful in figuring out colors or what lines represent which data.

In this episode we focused on types of graphs: line and double line graphs – which are used to show a change in data over time, bar and double bar graphs – which show or compare two or more data sets, histograms – a special kind of bar graph used to show continuous data, and lastly a circle graph – which is used to show data as part of a whole. We can find important information about a graph form its parts, which could include – the title, the labels of the axes and the key.

That covers all the information we set out to cover in this episode. Make sure to visit the blog at Kalkulationkorner.blogspot.com – I am Mr. Burns and I hope you enjoyed your time here at Kalkulation Korner – where mathematicians meet and I hope you come back soon to explore more mathematical concepts.

Friday, May 1, 2009

Episode #2 Transcript and Pictures

Welcome to Kalkulation Korner – Where mathematicians meet.
Greetings fellow mathematicians today is April 30, 2009. I am Mr. Burns and this is episode #2 of Kalkulation Korner.
In this episode we will focus our attention on finding the area of 2 dimensional figures. Before we get going I would like to suggest you get paper and something to write with so you can do the work with me. If you need to pause the recording, please do, I will be here when you get back.
All right we should all have paper and something to write with now. If you don’t you may be sorry later. Once again we must focus on definitions first. We will first define two-dimensional figure. Remember the strategy we used in episode 1, breaking the word or definition into smaller parts, lets use it again. The first word I came across is two. That is easy enough I will be working with two some things. What are those two some things? Well if I continue reading I read dimensional. Which tells us we will be working with two dimensions. What are dimensions? Well dimensions are, simply put, measurements. The last part of the phrase, two-dimensional figure, is figure. So what is a figure? A figure, for our purposes is a shape. After all the breaking apart and questions we asked we came up with a user-friendly definition for two-dimensional figure. That definition is a shape with 2 measurements. The 2 measurements are called the base and the height. The base of a figure can be described as the part the figure rests on while the height of a figure is how tall it is. There is one more definition we need to learn before we can move on and that is area. Area is the space inside of a shape and that space is measured in square units. Now that we have the definition part done we can move on to the calculations.

To find the area of a square we multiply the base and the height. This is where the pencil and paper may come in handy. You can copy the formula from the screen or just right down A=BxH. Which stands for Area equals base time height. The formula is the same when finding the area of a rectangle. Lets do a few examples before finding the area of a triangle. You may also choose to do the examples with the paper and pencil.

The first example we will try is a square with a base of 4 in. Since all the sides of a square are equal we know the height is also 4 in. The Area Equals Base Times Height or 4 in times 4 in which equals 16 inches squared. Great job on solving the first area problem of the podcast. Lets try a few more examples before we move onto area of a triangle. Lets now try to find the area of a rectangle with a base of 10in and a height of 5in. Again remember to use the formula Area = Base times Height. The area of the rectangle is 50 inches squared. Now time for on last problem involving area of a rectangle. My office is a rectangle with a base of 10ft and a height of 13ft and I want to put in some new carpet. How many square feet of carpet do I need? If you answered 130 square feet then you may have a new profession in carpet sales.

When working with triangles we use a very similar formula. The formula for finding the area of a triangle is Base times Height divided by 2. One of the best ways to learn is to do so lets try a few examples. First we will use a triangle with a base of 10in and a height of 5in. Lets put the numbers into the formula. Area = Base times Height divided by Two. So we have 10in times 5in divided by 2. First we will do the multiplication 10in times 5in is 50 inches squared the same as it was in a previous example but now we must divided it by 2 giving us 25 inches squared. Two more examples and we will be done. Find the area of a triangle with a base of 5in and a height of 14in. This one may take you a little longer to calculate. First we multiply and then we divide to get an answer of 35 inches squared. When will you ever need to know how to find the area of a triangle in real life? I will give you one example then maybe you can come up with more. You are a sailor and your main sail needs to be replaced. It is a triangular sail. The sail has a base of 10ft and a height of 34ft. How many square feet of fabric do you need to replace the old sail? The answer is 170 square feet of material. You are now ready to be a sailor.
We focused our attention on find the area of 2-dimensional figures, specifically rectangles and triangles. In order to find the areas we needed to know two different formulas. The first one was A = B x H for area of a rectangle and the second was A = B x H divided by 2 for triangles. You can use these formulas to find the areas of other shapes as well but we will save that for another time.
I hope you enjoyed your time here at Kalkulation Korner – where mathematicians meet and I hope you come back soon to explore more mathematical concepts.