2007 Mathematics Game

Posted on by Denise Gaskins

Are your students ready for a challenge?
The Math Forum: 2007 Mathematics Game will be a tricky one:

Use the digits in the year 2007 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in the expression.
  • Only the digits 2, 0, 0, 7 may be used.
  • Multi-digit numbers such as 20, 207, or .02 MAY be used this year.
  • The square function may NOT be used.
  • The integer function may NOT be used.

Continue reading 2007 Mathematics Game

Order of Operations

Posted on by Denise Gaskins

[Rescued from my old blog.]

Marjorie in AZ asked a terrific question on the (now defunct) AHFH Math forum:

“…I have always been taught that the order of operations (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) means that you work a problem in that order. All parenthesis first, then all exponents, then all multiplication from left to right, then all division from left to right, etc. …”

Many people are confused with order of operations, and it is often poorly taught. I’m afraid that Marjorie has fallen victim to a poor teacher — or at least, to a teacher who didn’t fully understand math. Rather than thinking of a strict “PEMDAS” progression, think of a series of stair steps, with the inverse operations being on the same level.

Continue reading Order of Operations

Fraction Division — A Poem

Posted on by Denise Gaskins

[Rescued from my old blog.]

Division of fractions is surely one of the most difficult topic in elementary arithmetic. Very few students (or teachers) actually understand how and why it works. Most of us get by with memorized rules, such as:

Ours is not to reason why;
just invert and multiply!

Continue reading Fraction Division — A Poem

Math Quotes III: Five out of Four People

Posted on by Denise Gaskins

[Rescued from my old blog.]

I’ve been procrastinating my preparations for co-op classes this week, but I think I’m ready. I almost forgot the scissors, but now I have them in my bag, so we will be able to cut the “infinite pizza” pieces. And I have two fun quotes for the blackboard:

Continue reading Math Quotes III: Five out of Four People

Math Quotes II: The Ultimate Goal of Mathematics

Posted on by Denise Gaskins

[Rescued from my old blog.]

I thought you might enjoy the quote I’m going to use on the blackboard in math class:

The clearer the teacher makes it, the worse it is for you. You must work things out for yourself and make the ideas your own.

—William F. Osgood, quoted in
Out of the Mouths of Mathematicians
by Rosemary Schmalz

Continue reading Math Quotes II: The Ultimate Goal of Mathematics