Christmas in July Math Problem

[Photo by Reenie-Just Reenie.]

In honor of my Google searchers, to demonstrate the power of bar diagrams to model ratio problems, and just because math is fun…

Eccentric Aunt Ethel leaves her Christmas tree up year ’round, but she changes the decorations for each passing season. This July, Ethel wanted a patriotic theme of flowers, ribbons, and colored lights.

When she stretched out her three light strings (100 lights each) to check the bulbs, she discovered that several were broken or burned-out. Of the lights that still worked, the ratio of red bulbs to white ones was 7:3. She had half as many good blue bulbs as red ones. But overall, she had to throw away one out of every 10 bulbs.

How many of each color light bulb did Ethel have?

Before reading further, pull out some scratch paper. How would you solve this problem? How would you teach it to a middle school student?

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What’s Wrong with “Repeated Addition”?

[Photo by Alejandra Mavroski.]

Myrtle called it The article that launched a thousand posts…, and counting comments on this and several other blogs, that may not be too much of an exaggeration. Yet the discussion feels incomplete — I have not been able to put into words all that I want to say. Thus, at the risk of once again revealing my mathematical ignorance, I am going to try another response to Keith Devlin’s multiplication articles.

Let me state up front that I speak as a teacher, not as a mathematician. I am not qualified, nor do I intend, to argue about the implications of Peano’s Axioms. My experience lies primarily in teaching K-10, from elementary arithmetic through basic algebra and geometry. I remember only snippets of my college math classes, back in the days when we worried more about nuclear winter than global warming.

I will start with a few things we can all agree on…

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Christmas in July?


[Photo by krisdecurtis.]

Being moderately tech-illiterate, I don’t pay much attention to SEO (Search Engine Optimization, the magic art of convincing Google to fetch me more readers). Even so, I enjoy browsing through the list of search terms that have brought visitors to my blog. Sometimes I find ideas to write about, or motivation to move an old draft off the back burner, or simply a chuckle at the funny things people look for on the Web.

This month, however, the most popular search term seems strangely out of season — more than 300 people have come to this site wanting “Christmas” or “Christmas tree.”

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Answers: Euclid’s Geometric Algebra

Alexandria JonesRemember 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

Continue reading Answers: Euclid’s Geometric Algebra

Free Multiplication Bingo Game

Math concepts: multiplication, mental calculation, times table
Number of players: one leader (teacher) and two or more players
Equipment: free MINGO number cards and boards; bingo chips, pennies, or other tokens to cover numbers

Continue reading Free Multiplication Bingo Game

Crazy 4 Math Contest

I heard of this contest in an e-mail from ClickSchooling:

Kids, share your creative math ideas! Describe how you use math in any activity you love to do — a sport, game, craft, hobby, or anything else.

Send in a description of the activity and how it uses math, as well as any drawing(s) or diagram(s). There are many great prizes to be won. Please ensure you’ve read and understand our contest’s rules and regulations before entering.

Sounds like fun! If you want to enter, act quickly. Entries must be submitted online by July 30th. Visit Crazy4Math.com for more information and to check out the winners from previous years.


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