For the last couple of days, I have been playing around with this geometry puzzle. If you have a student in geometry or higher math, I recommend you print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.
[MathNotations offers many other puzzles for 7-12th grade math students. While you are at his blog, take some time to browse past articles.]
[Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.]
If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?
In general, if n people meet and shake hands all around, how many handshakes will there be?
Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit. You may adjust the script to fit the available number of players.
If you enjoy Raymond Smullyan’s The Lady or the Tiger and similar puzzles, you will probably have fun with this Logic test, posted by JD2718. JD has a wide variety of other math puzzles at his site, so take the time to browse a bit.
Well, I didn’t get any takers with the last story problem challenge. But school is in full session now, and we’re doing story problems in Math Club this Friday, so I thought I’d try again.
Here’s the challenge: Can you and your students make up some original math problems?
In Math Club, we always start by reading part of the book Math by Kids for inspiration. I can’t print those stories here, however, because of copyright rules, so I’ll share some of the stories my past students have made, arranged in roughly increasing order of difficulty. After you solve a couple of these problems with your children, encourage them to try making some of their own.
And please, share their gems with us!
The problems below are now available as a printable handout: Story Problem Challenge.
I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.
Apply logic to that statement. The conclusion simply isn’t valid. …
Update: This post has moved.
[Rescued from my old blog.]
A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.
Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing.
Are your students ready for a challenge?
The Math Forum: 2007 Mathematics Game will be a tricky one:
Use the digits in the year 2007 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100.
- All four digits must be used in the expression.
- Only the digits 2, 0, 0, 7 may be used.
- Multi-digit numbers such as 20, 207, or .02 MAY be used this year.
- The square function may NOT be used.
- The integer function may NOT be used.
[Rescued from my old blog.]
Would you like to introduce your students to negative numbers before they study them in pre-algebra? With a whimsical number line, negative numbers are easy for children to understand.
Get a sheet of poster board, and paint a tree with roots — or a boat on the ocean, with water and fish below and bright sky above. Use big brushes and thick poster paint, so you are not tempted to put in too much detail. A thick, permanent marker works well to draw in your number line, with zero at ground (or sea) level and the negative numbers down below.
The spring semester of homeschool co-op classes starts tomorrow, and I still have a couple of handouts to prepare and several pages of notes to go over in preparation. So naturally, I find myself flitting from here to there on my computer, browsing new links and cleaning out the old.
As the saying goes:
“I used to be an amateur crastinator, but now I’ve turned pro.”
In a dusty pile of long-neglected bookmarks, I rediscovered this treasure:
I love this game!
Have you and your children been struggling to learn the math facts? The game of Math Card War is worth more than a thousand math drill worksheets, letting you build your children’s calculating speed in a no-stress, no-test way.
Math concepts: greater-than/less-than, addition, subtraction, multiplication, division, fractions, negative numbers, absolute value, and multi-step problem solving.
