Last Unit!

I can't believe we are almost finished with the semester!  It seems like just yesterday we were assigning projects and groups to work with.  I have really learned a lot this semester, not just in math, but about myself.  I realized I have a much easier time doing homework that I can relate to my own life.  After posting comments on other blogs, I was able to revisit some of my favorite activities this semester.  It was cool to see which activities I remembered, and which ones I had blocked from memory. 

I really enjoyed this class.  My professor was wonderful and could easily get a group of college students engaged in activities made for children half their age.  I learned how to use new technological resources in the course of each project.  My math skills were refreshed, and I feel like I could conquer the world of elementary mathematics!

Thanks for a great semester everyone!

My favorite website discovered during the course of this project is: Math Play!

Translations!

I really enjoyed doing this worksheet about translations.  I realize I'm a total math nerd, but I thought it was really interesting.  This is an example of the problems on the assignment. 

Having the graph paper made translations easy to understand, but it's pretty easy to do them without a graph.  If you are given the original coordinates of a shape, you can use the information given to find the new location of each coordinate.  I will use the information provided in the example above to explain.

Original coordinates:  H (4,3) W (4,0) and G (2,1)
Since the translation is along the line (x-2, y-3) you can perform each operation to the original coordinates to find the new coordinates.

H (4,3) and (x-2, y-3)

(4-2, 3-3)

H' (2,0)

Perform the operation for each coordinate provided to find the new coordinates of the translated figure.  New coordinates are labeled as prime and that's why there are apostrophes in all of them. 

H' (2,0) W' (2, -3) G' (0,-2)

The guy narrating the video looks like he'd be a cool person to hang out with.  Enjoy!

Painting Problems

I have been obsessed with painting walls since I was a kid.  Growing up, I changed the paint on my bedroom walls nine times.  My dad always talked about how much paint I would need, and square footage, but I never really paid attention until I had to start paying for the paint.  We received a word project in math class related to this, and I actually liked working on it. 

The problem is to find the surface area of the walls and doors of a garage you need to paint.  There was a diagram provided with the dimensions for the garage.  The three doors would be white and the rest of the garage would be blue.  The windows would not need to be painted. 

This is the diagram provided on the worksheet...

I labeled the windows and doors of the garage by numbers, so it would be easy to identify which windows and doors correlate to the table.  I drew my own diagram with colors, so it would be easier to solve.

The areas colored blue were to be painted blue, the areas colored pink were to be painted white, and the orange areas are not to be painted at all.  I made a chart to easily see the measurements and compute the total surface area to be painted.

I enjoy doing math homework that relates to real life situations!

I found this website with puzzles and games for math class.  I had a fun time messing around on here, and I can only imagine what a great time students would have! Math is fun .com

How much wrapping paper will I need...?

I have always loved wrapping presents. Birthdays, Mother's Day, Father's Day, and any other day I could wrap a gift, I would.  My mom even used to pay me to help her wrap gifts before Christmas and to keep my mouth shut about what my brothers were getting!  Even though I loved wrapping, sometimes I failed.  Some gifts looked like this...

And others turned out like this...

But every once in a while, a package turned out looking great.  Similar to this...

When I remembered the properties of surface area, I made a nicer looking gift.  Surface area is the sum of the areas of the surfaces of three-dimensional objects.  Let's estimate the right prism above measures 4in x 4in x 1in if the measurements are l x w x h.  The formula for surface area (SA) = 2B + ph, where B is the area of the base, p is the perimeter of the base and h is the height of the prism. 

SA = 2B + ph

SA = 2 (4in x 4 in) + (16in x 1in)

SA = 32 squared in + 16 squared in

SA = 48 squared in

To wrap the gift in the picture above, you would need 48 squared inches of wrapping paper.  But you might want to add a couple of extra inches, to make sure it overlaps.

Here's a fun website to encourage you to practice your surface area skills!  Gift Wrapping Ideas

Discovering Pi

My math class did a fun experiment to explain the numerical value of pi.  I thought this would be a great way to have students learn about pi without having to do a boring worksheet! 

The class divided into groups and measured the circumference of different circles.  We used a piece of string to measure the diameter and circumference of each circle.  Since the circumference of a circle is the distance around a circle, we wrapped the piece of string around the outside of the circle, then laid it flat on a meter stick to get the circumference.  It's similar to the way Ashley is measuring the circumference of my bicep in this picture from class that day. 

Then we wrote the measurements in a chart to help organize the data.  This is a picture of the worksheet we used and some of the things we measured.

After measuring five different things, we were required to divide the circumference by the diameter.  For instance, the circumference of the orange pumpkin lid was 47 cm and the diameter of the same lid was 15 cm.  Dividing 47 cm by 15 cm gave a quotient of 3.1.  The relationship discovered by this problem was circumference = diameter times 3.1 (C=3.1d).  The circumference formula I learned in school was circumference = diameter times pi.  Through this experiment I was able to figure out what pi was for myself.  This would be a great way to have students learn about pi without telling them what it equals!

I also found this video a great refresher of the information we learned about circumference in class. 

I also found this video a great refresher of the information we learned about circumference in class.

Pythagorean Theorem

I remember learning the Pythagorean Theorem in high school.  I was in freshman geometry.  My class learned the formula a² + b² = c² where a and b are the lengths of the sides of the triangle and c is the length of the hypotenuse.  We were required to memorize it and use the theorem when necessary throughout the rest of the class.  I never really learned why this is a math formula, just the letters and how to use it. 

Since my current math class is revisiting the Pythagorean Theorem, I decided to do a little research into the discovery of this mathematical rule.  I found an article about the theorem.  It was written by Stephanie Morris from the University of Georgia.  She wrote that the Babylonians were the first civilization to discover a special relationship between the measurements of a right triangle.  (I found this same belief in other articles though, so I'm going to consider it accurate.)  Although we all learn the Pythagorean Theorem with letter substitutes, the original theorem was stated "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides".  I'm so glad they condensed it to the formula used today!

Here is the article I found: The Pythagorean Theorem by Stephanie Morris