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How Should We Teach Arithmetic?

Posted on by Denise Gaskins

Dave Marain of MathNotations is running a poll about how to teach multiplication, but the question has broader application:

How should we teach the arithmetic algorithms
— or should we teach them at all?

Algorithms are step-by-step methods for doing something. In arithmetic, we have standard algorithms for addition, subtraction, multiplication, and long division. Once the student masters the steps for any particular algorithm, he can follow the steps to a correct answer without ever thinking about what the numbers mean.

Continue reading How Should We Teach Arithmetic?

Euclid’s Game on a Hundred Chart

Posted on by Denise Gaskins

Math concepts: subtraction within 100, number patterns, mental math
Number of players: 2 or 3
Equipment: printed hundred chart (also called a hundred board), and highlighter or translucent disks to mark numbers — or use this online hundred chart

Set Up

Place the hundred chart and highlighter where all players can reach them.

How to Play

  • Allow the youngest player choice of moving first or second; in future games, allow the loser of the last game to choose.
  • The first player chooses a number from 1 to 100 and marks that square on the hundred chart.
  • The second player chooses and marks any other number.
  • On each succeeding turn, the player subtracts any two marked numbers to find and mark a difference that has not yet been taken.
  • Play alternates until no more numbers can be marked.

Continue reading Euclid’s Game on a Hundred Chart

Quotations XIX: How Do We Learn Math?

Posted on by Denise Gaskins

He doesn’t learn algebra
in the algebra course;
he learns it in calculus.

I have been catching up on my Bloglines reading [procrastinating blogger at work — I should be going over the MathCounts lesson for Friday’s homeschool co-op class], and found the following quotation at Mathematics under the Microscope [old blog posts are no longer archived].

Continue reading Quotations XIX: How Do We Learn Math?

That’s Mathematics

Posted on by Denise Gaskins

Things are still hectic, but at least the phone company guy found the problem and got our “extended DSL” service working. “Extended DSL” is what you get when you live out in the boonies. No guarantees that it will be faster than the ancient modem, but at least it doesn’t tie up the phone line anymore.

And it is a bit faster, so I finally get to enjoy You Tube. If the video doesn’t display properly, you can find it at this link:

Funny Math Problems

Continue reading That’s Mathematics

The Game of Algebra

Posted on by Denise Gaskins

NFL football
Photo by velo_city.

My pre-algebra class hit the topic of equations just as the NFL season moved into the playoffs. The result was this series of class notes called “The Game of Algebra.”

We used the Singapore Math NEM 1 textbook, which is full of example problems and quality exercises. These notes simply introduce or review the main concepts and vocabulary in a less-textbooky way.

I hope you find them useful.

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They Grow Up Too Fast!

Posted on by Denise Gaskins

Chickenfoot ready to perform

Even the child in question agrees with that. Chickenfoot is suffering from Peter Pan syndrome: “I don’t want to grow up!” This week, someone asked him, “You’re 17, aren’t you?” Not yet, but 13 has passed into memory…

I got tricky with the hidden present this time. The outside of the envelope changed insignificantly. It read:

I’m your last present.
Can you find me?
I’m hiding some place
That you cannot see…

But the real departure from normal came with the poetry inside. The poem was a success, in that he laughed at all the appropriate spots, but the hiding place turned out to be a little too good. Can you find the two clues in all this mess?

Continue reading They Grow Up Too Fast!

I Need One of These!

Posted on by Denise Gaskins

Funny Pictures

It might really help with the 2008 Game. My morning coffee is not doing the job.

Blogging Notes

I confess: I am a FlyLady drop-out. Housecleaning has never been my strong point. But I read 50 Tips to Unclutter Your Blog, and I thought Skellie had some good points. I hate crowded sidebars, and moving my blogroll to a separate page sounded like a great way to declutter. If you want to browse some great blogs, the link is at the top of this page.

Now, I suppose, I should put my math notebook away and start clearing off the mess on my desk…

2008 Mathematics Game

Posted on by Denise Gaskins

Are you ready for a challenge? Join us for the 2008 Mathematics Game. Here are the rules:

Use the digits in the year 2008 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in each expression.
  • Only the digits 2, 0, 0, 8 may be used.
  • Multi-digit numbers such as 20, 208, or .02 MAY be used this year.
  • The square function may NOT be used.
  • The integer function may NOT be used.

By definition:
0! = 1
[See Dr. Math’s Why does 0 factorial equal 1?]

For this game we will accept the value:
{0}^{0} = 1
[See the Dr. Math FAQ 0 to the 0 power.]

Continue reading 2008 Mathematics Game

Puzzles for the New Year

Posted on by Denise Gaskins
by Koshyk via flickr

As we all head back to school, here are some interesting calendar puzzles:

  • 2008 is a leap year. Why do leap years happen? If we didn’t add a leap day every so often, would January eventually come in the summer?
  • Today is Thursday. What day of the week will it be exactly one year from today?
  • January 1, 2008, came on a Tuesday. When will be the next year that begins on Tuesday?
  • My birthday (in March) lands on a Monday this year. When is the next year my birthday will come on a Monday? How about YOUR birthday — when is the next time it will happen on the same day of the week as this year?
  • Can you find a pattern in the way dates move from one day of the week to another, year after year?

Continue reading Puzzles for the New Year