We continue with our counting lessons — and once again, Kitten proves that she doesn’t think the same way I do. In fact, her solution is so elegant that I think she could have a future as a mathematician. After all, every aspiring novelist needs a day job, right?
If only I could get her to give up the idea that she hates math…
Permutations with Complications
How many of the possible distinct arrangements of 1-6 have 1 to the left of 2?
In a lazy, I-don’t-want-to-do-school mood, Princess Kitten was ready to stop after three math problems. We had gotten two of them correct, but the last one was counting the ways to paint a cube in black and white, and we forgot to count the solid-color options.
For my perfectionist daughter, one mistake was excuse enough to quit. She leaned her head against me as we sat together on the couch and said, “We’re done. Done, done, done.” If she could, she would have started purring — one of the most manipulative noises known to humankind. I’m a soft touch. Who can work on math when there’s a kitten to cuddle?
Still, I managed to squeeze in one more puzzle. I picked up my whiteboard marker and started writing:
Kitten complained that some math programs keep repeating the same kind of problems over and over, with bigger numbers: “They don’t get any harder, they just get longer. It’s boring!”
So we pulled out the Counting lessons in Competition Math for Middle School. [Highly recommended book!] Kitten doesn’t like to compete, but she enjoys learning new ideas, and Batterson’s book gives her plenty of those, well organized and clearly explained.
Pizzas at Mario’s come in three sizes, and you have your choice of 10 toppings to add to the pizza. You may order a pizza with any number of toppings (up to 10), including zero. How many choices of pizza are there at Mario’s?
[The book said 9 toppings, but I was skimming/paraphrasing aloud and misread.]
I know other teachers have done mathquilts, but I’ve never gotten around to trying it in any of my classes. Still, this image caught my eye and practically begged me to make it into a math lesson for my elementary math club.
I thought of at least two ways I could go with this, but I bet that if we put our brains together, we can come up with even more creative ideas. So here’s the question, ala Dan Meyer:
What can you do with this?
How could you use this image as a springboard to doing math? What questions would you ask? What concepts would you try to get across? What would you follow it with? Please comment!
The Art of Problem Solving people recently announced their new Alcumus program, which provides online lessons on assorted math topics, including probability and combinatorics, which most math textbooks do not cover well, if at all.
Update October 2011:
Alcumus currently complements our Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra textbooks, as well as our Algebra 1, Algebra 2, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra 1 online courses. We expect to continue to expand topics in Alcumus.