Prove or Disprove: 1/2 +1/3 = 2/5

Prove or Disprove: 1/2 + 1/3 = 2/5

This prompt was handed to my classes last week. They were told that they could use words, numbers, pictures, charts, pieces of paper....in order to prove or disprove the above. They could not just say "yes" or "no". It was quite fun watching the wheels turn! Try it at home.

Word Problem Blues

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One of these things is not like the other. Both were answers on a recent HW sheet, and both have similarities. However, only one really answers the question asked. I think that you will be able to tell which is which!

When I see a student answer a word problem with only a number, I often remind students that teachers and test graders are among the least intelligent life forms on the planet. Are we talking 21 9/25 tons of elephant poo? 21 9/25 pounds of cheese? Is 21 9/25 even a legitimate answer to the question that was asked? Without a sentence, I simply do not know.

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