Saturday, December 11, 2010

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!

Sunday, December 5, 2010

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.

Sunday, November 28, 2010

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!

Sunday, November 21, 2010

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!

Saturday, November 13, 2010

A Really Cool Fraction Model

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.

Sunday, November 7, 2010

Math Jobs Anyone?

In a financial way, what can a knowledge of math bring your way? Below is a listing of "math" careers. Can you think of others?
The following were recently were listed as the five "best" jobs.
They were :

software engineer
computer systems analyst
computer programmer

This list was the result of the comparison of two hundred fifty jobs classified according to :
future outlook
physical demands
job security
work environment

A List of Professions:
The following list briefly describes work associated with some mathematics-related professions :
actuary-- assemble and analyze statistics to calculate probabilities of death, sickness, injury, disability, unemployment, retirement, and property loss; design insurance and pension plans and ensure that they are maintained on a sound financial basis

mathematics teacher-- introduce students to the power and beauty of mathematics in elementary, junior high, or high school mathematics courses

operations research analyst-- assist organizations (manufacturers, airlines, military) in developing the most efficient, cost-effective solutions to organizational operations and problems; this includes strategy, forecasting, resource allocation, facilities layout, inventory control, personnel schedules, and distribution systems

statistician-- collect, analyze, and present numerical data resulting from surveys and experiments

physician-- diagnose patient illnesses, prescribe medication, teach classes, mentor interns, and do clinical research; students with a good mathematics background will find themselves being admitted to the best medical schools and discover that mathematics has prepared them well for the discipline, analysis, and problem- solving required in the field of medicine

research scientist-- model atmospheric conditions to gain insight into the effect of changing emissions from cars, trucks, power plants, and factories; apply these models in the development of alternative fuels

computer scientist-- interface the technology of computers with the underlying mathematical principles of such diverse applications as medical diagnoses, graphics animation, interior design, cryptogrraphy, and parallel computers

inventory strategist-- analyze historical sales data, model forecast uncertainty to design contingency plans, and analyze catalog displays to make them more successful; analyze consumer responses

staff systems air traffic control analyst-- apply probability, statistics, and logistsics to air traffic control operations; use simulated aircraft flight to monitor air traffic control computer systems

cryptologist-- design and analyze schemes used to transmit secret information

attorney-- research, comprehend, and apply local, state, and federal laws; a good background in mathematics will help a student get admitted to law school and assist in the understanding of complicated theoretical legal concepts

economist-- interpret and analyze the interrelationships among factors which drive the economics of a particular organization, industry, or country

mathematics professor-- teach mathematics classes, do theoretical research, and advise undergraduate and graduate students at colleges and universities

environmental mathematician-- work as member of interdisciplinary team of scientists and professionals studying problems at specific Superfund sites; communicate effectively across many academic discilplines and be able to summarize work in writing

robotics engineer-- combine mathematics, engineering, and computer science in the study and design of robots

geophysical mathematician -- develop the mathematical basis for seismic imaging tools used in the exploration and production of oil and gas reservoirs

design -- use computer graphics and mathematical modeling in the design and construction of physical prototypes; integrate geometric design with cost-effective manufacturing of resulting products

ecologist -- study the interrelationships of organisms and their environments and the underlying mathematical dynamics

geodesist -- study applied science involving the precise measurement of the size and shape of the earth and its gravity field

photogrammetrist -- study the applied science of multi-spectral image acquisition from terrestrial, aerial and satellite camera platforms, followed up by the image processing, analysis, storage, display, and distribution in various hard-copy and digital format

civil engineer -- plan, design, and manage the construction of land vehicle, aircraft, water, and energy transport systems; analyze and control systems for land vehicular traffic; analyze and control environmental systems for sewage and water treatment; develop sites for industrial, commercial and residential home use; analyze and control systems for storm water drainage and storage; manage construction of foundations, structures and buildings; analyze construction materials ; and surface soils and subterranean material analysis

geomatics engineer -- once known as "surveying engineer", includes geodetic surveying : takes into account the size and shape of the earth, in order to determine the precise horizontal and vertical positions of geodetic reference monuments----ad goes on for 30 lines and make civil engeneering look down right boring!

I know my favorite,and I get to do it each day!

I also know my least favorite, a cryptologist. I hate Soduko!

What about you?

Sunday, October 31, 2010

...Favorite Math Book? Well, uh...let me see...

Well, I am about to ask a rather stupid, or at least risky, question. What is your favorite math book? I fully expect to get a few responses from math teachers, but I hold out little hope that the general populace will have much of an opinion.

As for me, two of the pictures above show my favorite math books, and the other is my least favorite. Can you guess which is which?

Sunday, October 24, 2010

What Kind of a Math-Person are You?

What kind of a math person are you? That's a pretty tough question to answer without some help. So, I will supply some help.

Pick just one of the following problems, and think about how you would go about the math. Would you need tools (paper & pencil, a calculator, just your brain)? If you worked mentally, would you see pictures in your head? If so what would they be? Would you see numbers being carried, borrowed, or traded? Do you see numbers stacked vertically?

Well, here goes...

27 + 53

53 - 27

2,456 divided by 12

27 X 53

Saturday, October 16, 2010

What do you think our kids should be learning in math?

If I were in charge of the math world, I would have classrooms full of calculators, check books, receipts, and bank statements. It seems pretty clear that most "math energy" in our world is spent balancing our assets against our material wishes. It is also clear that many students graduate from high school without these basic skills.
I also think that textbook publishers have a pretty warped view of what real world math is all about. If Bobby, Suzy and Sam have to share any more pizzas, I think that I may become ill (it sounds real world, but it really isn't), ditto for 2n X 48z cubed = the square root of pi.
Having said this, I do deeply value building a deep understanding of basic number sense and mental math abilities. If this ability is developed early, higher math certainly becomes more manageable, and more mundane daily math tasks become less of a mystery.
What do you think?

Sunday, October 10, 2010

I Don't Want to be a Hater, but..........

What is the thing that you most hated about math or a math class?

For me, the thing that I could never understand was teachers assigning 53 similar problems for homework! I can remember sitting at home from the age of about 11 to the age of 17 thinking that the teachers must be quite thick if they did not realize that if I could do two problems, I could do 53 problems. We also never went over more than two problems in the classroom. So, I am still confused and angry. I mean, I could have played a million more minutes of soccer under the street light!



Sunday, October 3, 2010

What Fun is Football Without Math?

How does math improve your life?
Maybe it doesn't, but as I sat and watched the lizards get pummeled by the Tide, I really enjoyed understanding all of the math involved in football. It must really stink not to understand things like, "11 carries for 42 yards" or "allowed two TDs in nine red-zone trips".
Today, as I watch the NASCAR race, thousandths of a second or thousandths of an inch could make all the difference in the world, or Jimmie Johnson could just win like always...
So, I challenge you to answer the question. How does math impact your life daily?

Wednesday, August 18, 2010

For 2010-2011; What math should your kiddo know?

Perhaps the most important, and also the least understood, information that a parent can have relates to the exact information that a student should be learning in their classroom. This is extremely important this year as Florida has adopted new standards in many subjects. For me the New Generation Math Standards should drive my instruction each day. For students and parents, these standards should provide a guide as well.

Really, every parent should expect a teacher to cover all of the concepts listed in these standards, and they should ask questions if they think something is being overlooked. The really cool thing is that these standards are not top-secret. In fact by logging on to anyone on the planet can find out what should be going on in the classroom. Having said that, this does not mean that all children will master all of these standards. Some kids will fly. Some kids will struggle, and most will do both, but at least the standards make the big picture a bit more transparent (not a pun, but it is great for parents). So, please look at these standards often.

Sunday, April 25, 2010

What is a "Normal" Cat?

Please click on the thumbnail images to make them larger.
So, just what is a normal cat? How could a student explain what normal is? Is it easier if you have numbers? Why or why not? What do you do with nonnumerical or categorical data? Can a cat have a mean (average) fur color? If not, how would you describe "normal" fur color. What kinds of charts or graphs would help? Is a sampling of 14 cats enough to represent all of the cats in the world? If not, how many should be sampled?
Is my cat's belly the most disgusting thing that you have ever seen?
Inquiring minds want to know!

Saturday, March 20, 2010

Dude, this is like totally circular!

Please click on the thumbnail image to make it larger.

Use your visual glossary and please identify the following:

All of the radiuses (AKA Radii)

All of the diameters

All of the the chords

The centerpoint

Calculate the circumference (the photo shows the length of the radius).

Sunday, February 21, 2010

Coordinate Grids Using Negative Numbers

Please click on the thumbnail image to see a larger version :-}
In 5th grade coordinate grids go to four quadrants! Please see if you can locate points C and D so that you could create a square by connecting all of the coordinates.

Some hints:

Always start at the origin

Think (left or right, then up or down...plot a point)

Negative numbers on the X axis ask you to move left

Negative numbers on the Y axis ask you to move down

I reached point B by moving right 30 from the origin and then moving down to the -10 on the Y axis. I plotted a point at the intersection of the two line segment found at (30, -10).

Best of luck!

Sunday, February 7, 2010

Guess My Rule....If you know Geometry!

A long time ago, little Tommy was sitting in his classroom, and the teacher asked, "Tommy, can you use the word "geometry" in a sentence?". Tommy said, "Sure! One night an acorn fell asleep, and the next day it wake up and said,'Gee I'm a tree!' ".
All kidding aside, one of the simplest, and yet deepest, ways to explore your knowledge of geometry is to play a game called Guess My Rule. It's simple. You put three or four polygons that follow a certain rule inside a circle and a couple that do not follow the rule outside of the circle. Then, you have someone "Guess My Rule".
So, what do think my rule is? Please don't be cute and say "polygons with less than five sides". While, the shapes inside the circle do have less than five sides (the ones on the outside do as well), my rule is a bit more complex :-}
Oh, a hint you wish? Well, I always investigate polygons by looking at their sides and angles!
Have fun!

Sunday, January 10, 2010

How Do You Read That Decimal?

The picture above tells a thousand stories! Well, actually it might tell a tenth of a story or a hundredth of a story or a thousandth of a story depending on where the decimal point is and what digits follow the decimal point!

I cringe every time that I hear TV reporters read decimals, especially weather forecasters, because they always say things like the barometric pressure is "29 POINT 92 inches", and these guys are scientists? Yikes! I hate to think that scientists are not concerned with things like place value. 29.92 should be read as twenty-nine AND ninety-two hundredths. Maybe students do understand that 29 point 92 is almost 30, but maybe they don't. Anyway, reading decimal values using correct place value is a good place to start.


.7 is seven tenths
.70 is seventy hundreds
.700 is seven hundred thousandths

Simple, say the number like a whole number, and then say the SMALLEST place value. (and thousandths are waaaayyyyy smaller than tenths-don't believe me? ---try cutting your pizza into 1,000 equal pieces versus ten equal pieces:-} )

However, we are not limited to looking at decimal numbers and only reading them as decimals. Huh? Well, .7, .70, .700 are all also 70%, and they can all be written as fractions as well.

So, which way should we read a decimal? In short, in whatever way makes the most sense for the problem. The work above shows three ways to read each decimal, percent or fraction. If I was trying to enter 1/8 on a cheap calculator, I probably would have to use .125. If I wanted to describe the same quantity to a person, I would probably say 12 1/2%, as I have learned that most folks have a pretty good "percent schema". If I was trying to add 1/8 to a simple fraction like 1/4, I'd leave both as fractions (1/8 + 2/8 = 3/8 woohooo).

So, for a fifth grader what is important to know?

.5 or .50 or the decimal way to say 1/2
So, .675 = 67 1/2 hundredths or 67 1/2 % or 67.5 %
.33333333 is the decimal way to say 1/3
.66666666 is the decimal way to say 2/3
1 whole = 100% 2 wholes = 200% .....
So, 3 1/2 = 350% or 3.5

Be flexible, and remember that the word POINT is dead and buried!