Math Teachers at Play #2

[Photo by Sister72.]

Welcome to the second Math Teachers At Play blog carnival! Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few of my favorite quotations.

Let the mathematical fun begin…

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Happy Square Root Day!

square-roots-by-arsheffield
[Photo by arsheffield.]

Check it out:

And coming soon: Pi Day.

Edited to add: Jonathan‘s class enjoyed extending the concept to include other products. Using the m/d/yy format (not the 4-digit year), how many times in your life has it been true that month \times day = year ?

Quotations XXIII: The Poetry of Logical Ideas

distinctively-red-by-pshutterbug
[Photo by pshutterbug.]

It’s been ages since I posted any blackboard quotes, so here are a few gems from last semester. [Hat tip: I found most of the quotes in this list at The Quote Garden’s Quotations about Math page.]

Pure mathematics is, in its way, the poetry of logical ideas.

Albert Einstein

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Math Teachers at Play #1

[Photo by StuSeeger.]

Welcome to the inaugural edition of the Math Teachers At Play blog carnival! I hope you enjoy this collection of tips, tidbits, games, and activities for students and teachers of preschool-12th grade mathematics.

For this first carnival, I’ve drawn several recent posts from my blog reader as examples of the types of posts I’d love to include in future editions of Math Teachers at Play. I tried to find something for everyone, from multiplication drill for elementary students to advice for understanding high school math equations.

Let the mathematical fun begin…

Continue reading Math Teachers at Play #1

MathNotations Contest for Middle-High School

math-team-edit
[Photo by ccarlstead.]

Can you can put together a team of 2-6 middle or high school students for an afternoon of mathematical play? If so, then Dave at MathNotations is running a math competition you just have to check out.

Teachers register by email on or before Thursday, January 29, and will receive the six thought-provoking contest problems and official answer form by return email. Hold the contest at your convenience on Tuesday, February 3, allowing your team up to 90 minutes to complete and electronically submit their answers.

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A Mathematician for President

In 1876, a politician made mathematical history. James Abram Garfield, the honorable Congressman from Ohio, published a brand new proof of the Pythagorean Theorem in The New England Journal of Education. He concluded, “We think it something on which the members of both houses can unite without distinction of party.”

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Online Game: Math Caching

In the treasure-hunting game of Geocaching (pronounced “geo-cashing”), players use GPS systems to locate boxes hidden at different geographical locations across the country.

Now, the creative people at Mathbits.com have come up with an online treasure-hunting activity for junior high and high school students, called MathCaching. Students solve mathematical problems to find hidden “boxes” on the Internet. Each box reveals clues to the location of the next one.

The MathCaching game covers pre-algebra through trigonometry topics, with calculus levels under development. For more information, visit the MathCaching site, or read the post on my Frugal Homeschooling blog.

Answers: Euclid’s Geometric Algebra

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.

Euclid’s Geometric Algebra

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Euclid’s Geometric Algebra

Picture from MacTutor Archives.

After the Pythagorean crisis with the square root of two, Greek mathematicians tried to avoid working with numbers. Instead, the Greeks used geometry to demonstrate mathematical concepts. A line can be drawn any length, so straight lines became a sort of non-algebraic variable.

You can see an example of this in The Pythagorean Proof, where Alexandria Jones represented the sides of her triangle by the letters a and b. These sides may be any length. The sizes of the squares will change with the triangle sides, but the relationship a^2 + b^2 = c^2 is always true for every right triangle.

Continue reading Euclid’s Geometric Algebra