Math Calendars for Middle and High School Students

High school math teacher Chris Rime posted three wonderful review calendars for middle and high school students on his blog.

Chris writes:

There are no explicit instructions about process being more important than the answer on these, so you’ll need to stress that in class.

I remind students that everyone already knows the answer to each of the questions, and that one of the things we’re practicing is explaining our reasoning…

Enjoy!

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Infinite Cake: Don Cohen’s Infinite Series for Kids

Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits
Prerequisite: able to identify fractions as part of a whole

This is how I tell the story:

• We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. A 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.

• How big is your piece compared to the whole, original cake?
• But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your piece?
• How much of the whole, original cake do you have now? How can you tell?
• I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?
• Now how much of the whole, original cake do you have? How could we figure it out?
[Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below‌—‌identify how much of the cake is left out.]
• Even for being on a diet, I still don’t feel very hungry…

Happy Birthday, General Relativity

Don’t forget that Pi Day is also Albert Einstein’s birthday! And this year marks the 100th anniversary of his Theory of General Relativity. So Science Magazine has a special Einstein issue online, featuring this interactive comic:

You may also enjoy:

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Pi and Buffon’s Matches

From Numberphile: Dr Tony Padilla’s unique (and low budget) twist on the Buffon’s Needle experiment to learn the true value of Pi.

For a kid-friendly version of this experiment, try throwing food:

Do you have a favorite family activity for celebrating Pi Day? I’d love to hear it!

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The Math Student’s Manifesto

[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]

What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.

(1) I can make sense of problems, and I never give up.

• I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
• I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
• I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
• I like to compare my approach to the problem with other people and hear how they did it differently.

2015 Mathematics Game

[Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both (CC BY 2.0) via Flickr.]

Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!

For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.

Rules of the Game

Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

• You must use all four digits. You may not use any other numbers.
• Solutions that keep the year digits in 2-0-1-5 order are preferred, but not required.
• You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
• You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
• You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

• You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
• You MAY NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.