Split-It!

09-05-2011



I had a student ask me recently for some help with an EDC component that I call split it! Actually, I had several students ask on behalf of their parents.

There was a homework problem that asked for students to show strategies to split a number like 7,758.

What I look for is a way to make splitting the number easy by using simple mental calculations. Usually, the first step is to decompose the number into its place values. So, 7,758 becomes

7,000 + 700 + 50 + 8 . Then, I ask that a student rewrite any number that they cannot readily split. Usually, these numbers start with odd numbers. We'll look at 7,000.

7,000 could be rewritten as 6,000 +1,000 (both of which are easy to split). After that, it's all down hill.

The whole number could be rewritten as 6,000 + 1,000 + 600 +100 + 40 + 10 +8, and finding half of these numbers should be EZ! 3,000 +500 +300 + 50 +20 +5 +4 = 3,879!

A Few Thoughts About Operations With Decimals

Lately, our class work has centered on getting kids ready for middle school standards. In doing so, we have started working on multiplying numbers that include decimals.

I have posed many questions like: "How much would it cost to purchase 7.3 lbs. of nails @ $11.29?


I have encouraged students to do a few things to insure that their answers make sense, which roughly translates into getting the decimal located in the correct position. First, I have asked that students make an estimate that uses only whole numbers. In the case of the nails, we would round 7.3 to 7, and we would round $11.29 down to $11. So our estimate would be $77. We know this estimate is a bit low as we rounded both numbers down, but it is plenty good to let us know where to place the decimal. I have also encouraged students to think about the problem as if it was written as a mixed number times another mixed number. If they do so, it is easy to think about the tenths being multiplied by hundredths, and that has to produce a denominator of thousandths. That is what your math teacher did NOT tell you when he/she said to count up the digits to the right of the decimal in the problem and match that number in the answer.


So, our estimate is $77, and the multiplication of 73 X 1129 yields a product of 82417. So it should be pretty obvious that the only place to put the decimal so that you get an answer close to $77 is after the two...$82.417, and since we have no coin worth a thousandth of a dollar, we round to the nearest hundredth and get $82.42 .

Trying to put the math in front of the "
tricks",

T-Cubed

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!