Let’s Play Math!

Photo by peigianlong.

Here is a puzzle from Just a Substitute Teacher:

Lesson plan entry: “Hand out worksheet packets and have students staple before starting. They know what to do.”

Sounds simple enough! Four numbered sheets, eight total pages, printed front and back. What could go wrong?

Do you know how many possible combinations four pieces of paper can be arranged for stapling?

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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 afterwards. 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.

Puzzle: Figuring out figurate numbers

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Photo by frumbert.

Alexandria Jones’s parents decided that the family needed to relax after the excitement of tracking Simon Skulk, so they spent the next day at a beach on the Mediterranean coast. Leon collected pebbles and tried to build up figurate numbers — numbers that make a figure, or shape — the way Dr. Theano had shown them.

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Photo by RBerteig.

Take a break from “serious” math and have a little fun today with some classics of recreational mathematics. Do you have a favorite math or logic fallacy? Please share it in the Comments below.

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Photo by gotplaid?.

While checking out the book table after a homeschool group meeting, Maria Jones glanced up to see her children laughing with some kids she did not recognize. Driving home, she asked about the new family, but Alex and Leon had been too busy exchanging silly stories to even ask the strangers’ names.

“Well,” Leon said, “the boy told me he has twice as many sisters as brothers.”

No way!” said Alex. “The girl told me that she has the same number of brothers and sisters.”

How can that be?

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Leonhard Jones is Alexandria Jones’s younger brother. He enjoys woodworking, and he cut a wooden cube into 8 smaller blocks to make himself a puzzle.

Puzzle #1

Leon painted the 8 blocks with his two favorite colors: red and forest green. When he was finished, Leon could put the blocks together into a red cube, or he could switch them around to make a green cube.

How did Leon paint his blocks?

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Photo by Behdad Esfahbod.

I have been busy with the end of Math Olympiad season and getting ready for the MathCounts state test this weekend, but I wanted to post this link before it’s too late. You have until Sunday evening to send in your answer to the first…

Monday Math Madness puzzle

Combinatorics is my weak area, but I gave it a try. How about you?

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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:

[See Dr. Math's Why does 0 factorial equal 1?]

For this game we will accept the value:

[See the Dr. Math FAQ 0 to the 0 power.]

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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?

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Here is the simplest puzzle from the November/December 1998 issue of Alexandria Jones stories. The answer (and more puzzles) will follow.

Christmas gift for Leon (pdf, 68KB)

Edited to add

More puzzles are now here:

Magic square puzzles

Answers are also posted:

Christmas puzzle answers

:: :: :: :: :: :: :: :: :: :: :: ::

• The golden Christmas tree
• A-hunting they will go
• Alexandria Jones and the Christmas present quandary
• more mathematical adventures of Alexandria Jones

Maria at Homeschool Math Blog has posted a fun set of worksheets:
Pan balance problems to teach algebraic reasoning.

Princess Kitten, at nearly 9yo, keeps telling me, “I hate math, but I like algebra.” So I printed all four pages for her to try. These get pretty complicated, and the 2-variable problems had her flummoxed for awhile. But after an explanation and bit of pouting (I think she hates math because she’s such a perfectionist that she can’t bear to get something wrong, even the first time), she came back and conquered the toughest ones.

• Pre-Algebra Problem Solving: The Tools
• Negative Numbers for Young Students
• The Game of Algebra
• How to Solve Math Problems
• Math Contest Tip Sheets

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 afterwards. 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 posts. Figure them out for yourself—and then check the answers just to prove that you got them right.

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