Tag Archives: Geometry

A Simple Geometry Poem

One of my students came up with this poem to help remember the difference between acute, obtuse, and right angles.

Acute angles are small and cute below 90. 

Obtuse angles are big and obtrusive and mighty,
they stand tall over that perfect 90,
but right in the middle none can compare
the 90 degree angle holds a perfect square!

Scotch Tape and Gas Prices Dilemma

So, my whole recent obsession with Scotch Tape sort of began a few weeks ago when the following problem popped into my mind…

Suppose your boss wants you to buy six 1/2 in x 450 in rolls of Scotch tape at the dollar store (remember the 6% Michigan sales tax).  Your boss wants you to use the tape to enclose an area of 3,225.8 square cm, but has only given you a budget of $7.00 to do so, including the amount of gas to drive back and forth to the dollar store, which is exactly 1.5 miles away from work.  Your car gets 0.0735 liters per kilometer city (you will not be taking the highway), gas is $4.09 per gallon, and your boss does not care about the gas that it takes to actually start your car.  Do you have enough tape to enclose the area that your boss asked to have enclosed?  If you do have enough tape, explain why.  If you do not have enough tape, do you at least have enough money to buy another roll of tape?  If you need to buy another roll of tape, but cannot afford to, how much short would you be?  If this is the case, would it be worth it to pay the amount out of your own pocket, or would you rather call your boss and explain the situation?

Tape

Free Open Reference Interactive Geometry Book

Check out this website I found at mathopenref.com

I will definitely be using some of the applets here the next time that I teach geometry as part of a pre-algebra course. In fact, maybe I’ll have the students read through this and play with all of the applets as part of their homework (before) coming to class.

New Application Problems from the Classroom

Here are few more problems that I came up with during today’s class:

1.  Clyde owed 8 different people $4 each for some doughnuts that he bought to eat on his birthday. Then when he wasn’t looking, Hellman’s stole $4 from Clyde’s wallet.  In order to reclaim his debt, Clyde needed to split up his total losses over a period of nine months.  How much debt will he recover over each of the nine months?

2.  Clyde went to the store and he bought seven nuclear weapons, but he doesn’t know the price of them yet.  He had to return four of the weapons because they were defective.  Then Clyde had to pay $9 in order to bribe a government official into letting him keep the weapons.  Finally, when buying the weapons, Clyde had a $4 off coupon.  How much did Clyde pay since he did not yet know the price per weapon?

3.  The hypotenuse of a right triangle is the median of {0.52, 0.69, 0.71, 0.34, 0.54} and one of the legs is the median of {0.26, 0.12, 0.35, 0.43, 0.28}.  Find the length of the missing side.

4.  The length of a boat is the mean of {11, 32, 21, 74, 32, 25, 29} ft.  Convert the length of the boat to meters.

5.  The diameter of a doughnut is the average of {3.6, 7.4, 3.9, 6.2, 7.6} cm.  Convert the diameter to millimeters.

Interactive Demonstration Tools

Here are a few highlights of some of the Interactive Demonstration Tools that I have come across in the past few weeks:

1.  All Interactive Whiteboard Resources – Although the applets on this website are designed to be friendly for those classrooms with Smartboards and the like, I see no reason why these applets can't be used in any classroom.  In fact, I plan on use this Angle Measure resource when teaching my classes about angles in the upcoming weeks.  Other great resources on this website include this Translation Plotter, which helps students to visualize translating a shape in the Rectangular Coordinate System.

2.  Interactive Slope Applet – Although I ran out of time to actually use this with my own class, this is a wonderful resource that lets students click and drag points such that when the line between the point changes, the calculation of the slope of the line also changes on the screen as well.  Very useful!

3.  Slope-Intercept Equation Applet – This appears to be the exact same applet I introduced to you a few weeks ago in the Geogebra Tutorial video.  It's a very simple resource that allows students to visualize the slope-intercept equation of a line by using sliders to change the slope and y-intercept.

Mathematics Origami

This morning with a stack of blank, unused paper sitting right next to me, I was thinking about some new projects that I might be able to assign my students for next semester.  Then it popped into my mind… Origami!  I think an assignment on origami would be especially interesting to my students in art and design.  I am looking forward to seeing what students will create in the semesters to come.  By the way, below is a link to a related TED talk by Robert Lang.  It could serve as a good way to introduce an entire unit on this topic (to the right group of students).
 

Pre-Algebra and Algebra Resources

A few months ago I had students in my Basic College Math class create a game about fractions.  One student created “Fraction Bingo”.  I decided to search the web to see if there were printable bingo sheets available.  Well, there were, along with some other activities that I found on the same website from Holt, Rinehart, and Winston.  And below is a list of a few of my favorite ones, appropriate for college-level basic math classes (organized by topic):

Operations on Numbers

Dimensional Analysis Problem

The other day in my Pre-Algebra class at HFCC we were talking about geometry, but I wanted to link it to the dimensional analysis that we had just done in the previous chapter since I knew that some of the students were struggling with the concept and could probably use the review.  So, when the opportunity arose, I came up with a problem off the top of my head.  This isn’t something that I usually do because I have a hard time being creative under the pressure of standing in front of a room full of students.  However, I think that this problem just became an instant classic in my book, and that I will probably use the problem as an example again in the future.  Take a look for yourself.