She has always loved seeing patterns in math. I remember once, years ago, when she insisted that we change the problems on a worksheet to make the answers come out symmetrical.
feature photo above by Junya Ogura via flickr (CC BY 2.0)
A couple of weeks ago, James Tanton launched a wonderful resource: a free online course devoted to quadratic equations. (And he promises more topics to come.)
Kitten and I have been working through the lessons, and she loves it!
We’re skimming through pre-algebra in our regular lessons, but she has enjoyed playing around with simple algebra since she was in kindergarten. She has a strong track record of thinking her way through math problems, and earlier this year she invented her own method for solving systems of equations with two unknowns. I would guess her background is approximately equal to an above-average algebra 1 student near the end of the first semester.
After few lessons of Tanton’s course, she proved — within the limits of experimental error — that a catenary (the curve formed by a hanging chain) cannot be described by a quadratic equation. Last Friday, she easily solved the following equations:
and (though it took a bit more thought):
We’ve spent less than half an hour a day on the course, as a supplement to our AoPS Pre-Algebra textbook. We watch each video together, pausing occasionally so she can try her hand at an equation before listening to Tanton’s explanation. Then (usually the next day) she reads the lesson and does the exercises on her own. So far, she hasn’t needed the answers in the Companion Guide to Quadratics, but she did use the “Dots on a Circle” activity — and knowing that she has the answers available helps her feel more independent.
After teaching co-op math classes for several years, I’ve become known as the local math maven. Upon meeting one of my children, fellow homeschoolers often say, “Oh, you’re Denise’s son/daughter? You must be really good at math.”
The kids do their best to smile politely — and not to roll their eyes until the other person has turned away.
I hear similar comments after teaching a math workshop: “Wow, your kids must love math!” But my children are individuals, each with his or her own interests. A couple of them enjoy an occasional geometry or logic puzzle, but they never voluntarily sit down to slog through a math workbook page.
In fact, one daughter expressed the depth of her youthful perfectionist angst by scribbling all over the cover of her Miquon math workbook:
- “I hate math! Hate, hate, hate-hate-HATE MATH!!!”
Translation: “If I can’t do it flawlessly the first time, then I don’t want to do it at all.”
Wayne at Home School Book Review just posted a very kind review of my daughter’s book:
Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.
However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!”
I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!
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.
Today’s topic was the Fundamental Counting Principle. It was review, easy-peasy. The problems were too simple, until…
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.]
- Can you figure out the answer?
[Photo by Nestor Galina.]
Our power finally came back on this afternoon after a couple of cold, dark nights.
We heated the house with candles and stove-top burners (propane). We found that if you get enough candles lit in a room, it really can make a difference, and the stove was able to keep the kitchen in the upper-50′s, even above 60 degrees at times, which was pretty comfortable. We dressed in lots of layers and wore gloves, drank a plenty of coffee and hot chocolate, listened to oldies on the battery-powered radio, and went to bed early each night. (Hooray for sleeping bags!)
It’s high time I got back on track with my Alexandria Jones posts, so I’ve been working hard on a short introduction to probability, to go along with The Birthday Surprise. Or, more honestly, I’ve been procrastinating on a short intro … well, anyway, here’s a little of what I’ve been reading around the interwebs lately.
[Photo by dougwoods.]
Today is my daughter Princess Kitten’s blogiversary. Check out her post:
And then take some time to browse her blog. I think you’ll enjoy her stories. She’s even written a few things about math:
- Cops and Robbers *coughcough*
- Negative Subtracting Problems
- Math games for learning Times
- Backwards math
[Update: I just noticed that this is the 500th post to be published on Let's Play Math! blog. Wow! I guess Kitten and I will both be celebrating today...]
[Photo by Arwen Abendstern.]
If a girl and a half
can read a book and a half
in a day and a half,
then how many books can one girl read in the month of June?
Kitten reads voraciously, but she decided to skip our library’s summer reading program this year. The Border’s Double-Dog Dare Program was a lot less hassle and had a better prize: a free book! Of course, it didn’t take her all summer to finish 10 books.
How fast does Kitten read?
[Photo by mape_s.]
I’m afraid that Math Club may have fallen victim to the economy, which is worse in our town than in the nation in general. Homeschooling families have tight budgets even in the best of times, and now they seem to be cutting back all non-essentials. I assumed that last semester’s students would return, but I should have asked for an RSVP.
Still, Kitten and I had a fun time together. We played four rounds of Tens Concentration, since I had spread out cards on the tables in the library meeting room before we realized that no one was coming. Had to pick up the cards one way or another, so we figured we might as well enjoy them! She won the first two rounds, which put her in a good mood for our lesson.
I had written “Prime numbers are like monkeys!” on the whiteboard, and Kitten asked me what that meant. That was all the encouragement I needed to launch into my planned lesson, despite the frustrating dearth of students. The idea is taken from Danica McKellar’s book Math Doesn’t Suck.
[Graphite drawing by Niner.]
Niner (pronounced Neener), who takes the photos for my blog header — which reminds me, we’re about due for a new one of those… — has started a new blog. She calls it 19 & Still Alive, because “the world doesn’t end when you’re 16 if you don’t go to Prom or don’t get your driver’s license. (I never went to Prom, and I didn’t go through Driver’s ED until 17, but I’m alive, amazingly.)”
There won’t be any math there, or at least I don’t expect to see any; the blog will be mostly her rambling thoughts about whatever catches her interest. But she does have a wonderful graphite drawing based on the photo Masarwa man. On her blog, you can click the image to see him up close and personal. Wow!
[I couldn't find a good picture illustrating "division." Niner came to my rescue and took this photo of her breakfast.]
I found an interesting question at Mathematics Education Research Blog. In the spirit of Liping Ma’s Knowing and Teaching Elementary Mathematics, Finnish researchers gave this problem to high school students and pre-service teachers:
- We know that:
How could you use this relationship (without using long-division) to discover the answer to:
[No calculators allowed!]
The Finnish researchers concluded that “division seems not to be fully understood.” No surprise there! Check out the pdf report for detailed analysis.
[Photo by OakleyOriginals.]
Kitten strongly dislikes math when forced to do it on her own, so I am trying to get back into the habit of doing “Buddy Math” with her. We take turns working the problems in her workbook: mine, hers, mine, hers, and so on down the page. We work each problem out loud, explaining how we got the answer and checking each other as we go.
No, it’s not math, but it looks like a great way to kick-start Princess Kitten’s long-neglected blog. She sat down at the computer and browsed the links to other kids’ posts for over an hour last night, occasionally laughing out loud. Then she opened her Dashboard and started to type a response to the green assignment.
I’ll have to let her know there’s a new post up today. Check it out: Homeschool Kids Write
Maybe I can even get her to send something in to the next Homeschool Kids Blog Carnival. It’s worth a try…
Unfortunately, Homeschool Kids Write has disappeared from the web. The Wayback Machine link gives a taste of what the site was like, but It’s just not the same without the Mr. Linky connections to all the children’s writings.
My baby is growing up…
[Photo by jonathansloan.]
One of the best perks of homeschooling is that we can take our snow days when the rest of the world is back in school. Niner and Princess Kitten have the sledding hill to themselves. Meanwhile, I’m brewing up a batch of JD’s Winter Soup while I prepare for co-op classes tomorrow…
[Photo by Niner.]
Thanks to the remnants of Hurricane-turned-Tropical-Depression Ike, our creek has risen well past last spring’s high-water mark. Of course, this is nothing compared to the devastation down south, but it’s enough to keep us trapped at home for the day.
If you’re curious about what’s around that corner of our driveway…
[Photo by *clairity*.]
Have you ever noticed how very different little girls are from little boys, in the way they play and in the way they think about things? Princess Kitten has been playing around with Backwards Math again, and my first thought was, “No boy would ever have done this with numbers.”
Photo by jaycoxfilm.
Math concepts: mental calculations, math vocabulary, and anything else you want to include
Number of players: any number, but I think it works best with two players who alternate asking questions
Equipment: imagination and, if necessary, scratch paper
Many years ago, I read a magazine article by mathematical music critic Edward Rothstein, wherein he described a game he invented for his daughter:
- “What number am I? If you add me to myself, you get four.”
Rather than explaining the rules of the game, let me tell you a story…
Photo by Niner.
My yard, my life! This was our front yard and driveway last weekend, as we rushed through our last-minute preparations for the County Fair. Niner, too old for 4-H, was determined to get her photos entered in the open competition before Saturday afternoon’s deadline. She rolled up her pants legs and waded through the drink, using her feet to feel out the edges of the driveway and marking the path with red-flagged fence posts so the Jeep could make it through.
Just in case you were wondering why there were no new posts this week.
It took 4+ years of practice and one solid hour of sweating — which included punching and kicking his dad as hard as he could (holding the karate pad is no easy job!) and the breaking of two boards — but it was worth it.
Last night, Chickenfoot received his black belt, being presented in the photo by his instructor, Sir John.
[Disclaimer: I gave in to blogger's poetic license for a catchy title. To tell the truth, I am sure Chickenfoot wouldn't consider himself a math geek at all. Math is far from being his favorite subject, even though he is good at it.]
Photo by Niner.
The daughter who supplies my header photos has started a blog to show off her pictures:
[It's pronounced "NEE-ner."]
Update: She no longer posts to that blog, but has been writing and posting photos, recipes, and craft projects to her new blog — College & The Years After.
Her photography skills continue to improve, and her sense of humor comes through in the stories that accompany each photo. I’m sure she’d love to have you stop by and visit!
Photo by Complicated.
Princess Kitten is recovering from her cold and getting some energy back. She came to me and said wistfully, “I wish I could do backwards math.”
I looked up from my keyboard. “Backwards math? What do you mean?”
“Umm. It’s kinda hard to explain, but I can show you.”
Things are still hectic, but at least the phone company guy found the problem and got our “extended DSL” service working. “Extended DSL” is what you get when you live out in the boonies. No guarantees that it will be faster than the ancient modem, but at least it doesn’t tie up the phone line anymore.
And it is a bit faster, so I finally get to enjoy You Tube. If the video doesn’t display properly, you can find it at this link:
Even the child in question agrees with that. Chickenfoot is suffering from Peter Pan syndrome: “I don’t want to grow up!” This week, someone asked him, “You’re 17, aren’t you?” Not yet, but 13 has passed into memory…
I got tricky with the hidden present this time. The outside of the envelope changed insignificantly. It read:
I’m your last present.
Can you find me?
I’m hiding some place
That you cannot see…
But the real departure from normal came with the poetry inside. The poem was a success, in that he laughed at all the appropriate spots, but the hiding place turned out to be a little too good. Can you find the two clues in all this mess?
Our youngest child turns 9 today. Time shoots by at rocket speed, doesn’t it? Every year, the older kids complain that their baby sister isn’t allowed to grow up — they still feel like being nine years old themselves!
I have mentioned before our family tradition of the “hidden present.” [See this post and that.] Every year, one birthday present is hidden somewhere in the house, with the clue placed in an envelope to be opened after all the other gifts are unwrapped.
Farewell to 2007. We have snacks on the table so we can munch the night away, and the little ones are giggling over their Barbies, thrilled at the prospect of more sugar than is good for them.
The teenagers have launched their annual movie marathon. This year, it was the girls’ turn to invite friends over, so the men in my life have all found excuses to run into town.
Meanwhile, I am hiding in my den, indulging myself in a sort of blogger’s nostalgia. Some of the following posts got a lot of attention when they were published, others not so much. Topics range from preschool to high school, from kindergarten games to teaching fractions to Shakespearean insults, so I hope there is something to interest everyone.
[The photos are small so this article won't take forever to load. Click on any picture to view a larger image.]
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.