Do You Like Pyramids or Would You Rather Go to Prism?

In our math classes we are currently working on identifying attributes of three dimensional figures (space figures), and most of that work focuses on pyramids and prisms.

We do need to become familiar with some basic 3DG vocab like: bases, faces, edges, and vertices. We also need to be able to find the surface area of said figures. So, I found a couple of links to basic info that might help.


http://www.math.com/school/subject3/lessons/S3U4L2GL.html#


http://www.mathsisfun.com/geometry/pyramids.html

It's Not Just a Multiple Choice Test!

Years ago, most standardized math tests were using rather low complexity questions. That's not to say that the questions were easy. Some may have been very difficult, but knowing what to do was pretty straight forward.

A test might have asked simply asked for the sum of 3/8 + 1/6, and then given four possible answers.

Today, the state of Florida is putting a heavier emphasis on the cognitive complexity level of questions on tests like the FCAT.

As an example, a test might ask how much pie was eaten if the shaded portion of the first pie represents the pie before dessert, and the shaded portion of the second pie represents the amount after dessert.

This turns a very simple problem into a more cognitively challenging problem.

So, what fraction in its lowest terms represents how much pie was eaten?

A. 4/12 B. 7/12 C. 1/4 D. 1/3

On a scale of one to dumb....

Quite recently, I received a comment on my blog from one of the coolest students that I ever taught. Ferney J. sent me a comment about my posting of the "top math jobs", and in her comment she asked if math was needed for a career in criminal justice.

At that moment, several things popped into my pea-sized brain. First, I really was happy to "hear" form Ferney. I have been wondering how life in Cally had been for her. So Ferney, if you read this, please send an email address (maybe a school email address).

Next, I realized how idiotic the list of top math jobs that I posted was. An actuary was listed as one of the top jobs. Be real. I think that should have been on the list of the "most dreaded" math jobs!

There are millions of careers that require a good math knowledge, and criminal justice is one of them. In fact, the FBI has several special units for folks that have great mathematical abilities. More importantly, everyday quality of life is improved with a good math schema!

So on a scale of one to dumb, my choice to post some random Internet math job statistics was DUMB!

Ferney, thanks for continuing to teach this old dog new tricks!

Fractions, Pizza, Percents, and More

Lately, the class has been involved in answering questions involving the addition and subtraction of fractional amounts.

Some of the typical equations might look like:

2 1/4 + (1 1/3 -5/6) or

4 3/10 - (2 3/5 + 7/10) or

(3 3/4 + 2 1/8) - 2 2/7

While you might expect for me to be interested in the correct answer as my primary goal, I am actually much more concerned that kids are looking at the amounts and using appropriate strategies based on each unique circumstance.

We have studied several models that allow students to quickly create common denominators by thinking of such things as equivalent fractions on a clock, equivalent percents, and/or a good old common denominator. The trick is to know when to use each model.

The first problem is a great opportunity to use a clock model as all of the fractional amounts can be expressed as twelfths. Students should be familiar with clock fractions from the game "Roll around the Clock". 2 3/12 + ( 1 4/12 - 10/12)

The second problem is perfect for using percents as all of the amounts are very easily converted into percents that are easily added and subtracted. 430% - (260% + 70%)

The third problem is probably best solved by finding a common denominator as the fraction 2/7 is not easily represented on a clock, because 12 hours and/or 60 minutes cannot evenly be split into seven whole number pieces. Also, without a calculator, finding and using the percent that is equivalent to 2/7 is not practical. (3 6/8 + 2 1/8) - 2 2/7.... 5 7/8 - 2 2/7... 5 49/56 - 2 16/56...= 3 33/56

Of course, this post leaves out many steps, but the most important step is choosing the best strategy with which to work.

When Does -3 -3 +3 = 12,000,000

Boise State's kicker missed a field goal in regulation to win their game against Nevada this weekend. The same kicker then went on to miss another in overtime. That's the -3 -3 part.

Nevada's kicker made his attempt in overtime for the win.

The loss may mean a loss in $12,000,000 for Boise State as they have no hope in playing in the NCAA Championship game now, and will most like play in the Humanitarian Bowl and receive a much smaller pay check.

See, math is COOL and CRUEL!

Fractions: How Do I Add Thee, Let Me Count the Ways

When it comes to adding fractions, everyone knows that there is only one good way to do it. Right?

So, if I were to ask you to add something simple like 1/2 + 1/4, you would say that we have to find the LCD and change 1/2 into 2/4, add, and get a sum of 3/4. Right?

Or could I change 1/2 into 50% and 1/4 into 25% and then add and get 75% which is equivalent to 3/4? Possibly?

Or could I say that on a clock, 1/2 is the same as 6/12 and 1/4 is the same as 3/12 and then add and get 9/12 which is the same as 3/4? Any chance?

Admittedly, the problem above is very simple. Also, the problem was designed so that three or more methods could be used easily to solve the problem. Not all problems are so friendly! In fact, much of what we do in class centers on finding methods that work for the numbers presented.

Please think about how 1/2 + 1/7 would be different. Do you know both percents? Do you know what 1/7 of a clock face looks like? I don't!

A Really Cool Fraction Model

http://illuminations.nctm.org/ActivityDetail.aspx?ID=11

Please click on this link and tell me what you think about this interactive fraction model. You will have to click on the right hand bottom "length" icon and choose "region" to see the circular model, and the circular model is the best. You also want to choose "Wide Range" on the top tabs to see smaller fractional pieces. Try it. It's cool, even if I am a math geek!

I love to see the regions change size as the denominator is changed. Can you imagine what it would look like if you could show millionths?

I really think that it takes models like these to really "get" fractions. I know that many students would agree that fractions can be frustrating. Perhaps, visual aids like this can help.