Thursday, June 21, 2007

The Mathmatics of Sharing

I wanted to post this before it sank into my mental oblivion. This was school, and we've been all about summer for almost 3 weeks, so it seems terribly old, but it was a "good idea," and worth sharing.

Like the Ark Family, our path to Waldorf-inspired learning has been full of detours. We too tried the Well Trained Mind approach for a time. Falcon loved the stories, and we read loads of myths and beautiful "living books," however, the bit about reading "early, fast and well" just wasn't happening for us. Glad we moved on. One of the few things that hasn't changed for us is our math curriculum. We started with RightStart, and we like it (for the approach, the manipulatives and the games - I'll post a review at some point). RightStart is different from the recommended Waldorf approach in quite a few ways, noteably in that the functions are introduced much more gradually. That is why, at the end of his 3rd grade year, Falcon had not yet been formally introduced to Division.

So we had a Sharing week.

At breakfast on the first day, I felt Falcon out by asking him a simple sharing question, "If you and The Skater were walking and you both saw a $5.00 bill at exactly the same time, how would you share it equally?" Falcon paused over his oatmeal and answered, "We'd take it up to Marcs, and get change and we'd both get $2.50. I'd spend the 50 cents on a Yu-Gi-Oh card from Marcs' vending machine"

I thought he would understand the concept without much difficulty. We proceeded by going out to our front walk to create a number line. Falcon has been working with his times tables, so we re-introduced math (we'd had a breather) by playing number line games. We spaced the number line so that a jump of ten was the maximum distance that Falcon could jump, and he went leaping all the way through his tables. Next I brought out a bean bag and threw it so that it landed on 15. I told Falcon and Charlotte that this was a new way of playing hopscotch, and that you had to jump on multiples that would get you to the bean bag, counting how many jumps you made. This went over pretty well, although I hadn't though out how to keep score, or what to do when the bean bag landed on a prime. Despite my lack of planning, we played until it started to rain (goodbye number line!). The rest of the day we took many opportunities to share - cookies, grapes, cherries, both within our family, and as fictional problems with lots of friend. Falcon noted that some things, like cookies, were easily split in half, whereas giving three kids 2 out of 3 pieces of a marble wasn't really a possibility. At the end of the day we read 17 Kings and 42 Elephants by Magaret Mahy. Falcon noticed right away that every elephant had a king on its back, and that there was no way that this could be the case. Charlotte loved the poetry of the book and immediately decided to create a Twinkling Tunester.

The next morning I asked Falcon what sort of a picture he wanted to make in his ML book for 17 Kings and 42 Elephants. He whined. This is not unusual for Falcon. He loves to be read to and the do fun things, but coloring and writing are not a strong point. However, this was an unusual whine. "I already know the answer, and I don't want to do a whole page for that baby book!" Fair point. This book was recomended in "Math and Literature (K-3)" by Marilyn Burns for a third grade lesson, but it was mostly just a bouncy poem. Charlotte asked me to read it again (and again), and then Falcon and I moved on. We visited several problems from the previous day (including 42 divided by 17), and I introduced the division symbol, and the concept of a remainder. Falcon wrote math problems on the chalkboard, and he discovered that he needed to think of the problems as "42 shared between 17" to get the numbers in the right order. He accidentaly reversed the order of one of the problems, and realized that this matters with division.

Latter I read from "The Man Who Counted" by Malba Tahan (Thanks Sara for this great idea - read her lesson here: Falcon was entirely entralled by the story in which a herd of 35 camels is divided between three brothers: the eldest was to receive 1/2 the herd, the middle 1/3 of the herd, and the youngest 1/9. When Beremiz (The Man who Counted) arrives and adds his camel to the herd, suddenly not one, but 2 extra camels are available. "How did he do that?" Falcon asked repeatedly. The ML page for the next day was Not Whined About.

Sharing Week was briefly interrupted at this point when Falcon got a nasty gash on his writing hand/wrist. He had to have 4 stitches and couldn't possibly write or draw or color for quite a while. But he still wanted to hear more from "The Man who Counted." Our last lesson was also a story of division. Beremiz and the Narrator find a man left for dead by bandits in the middle of the desert. The man is famished and asks to share whatever food Beremiz and the Narrator have, offering to pay a gold piece each for the 8 loaves that they have between them. Beremiz had 5 of these loaves and the Narrator had 3, so when the man was returned to his home, he offered Beremiz 5 gold pieces and the Narrator 3. Beremiz quietly tells the man that this division is incorrect; he should receive 7 pieces of gold and the Narrator only 1. Each loaf is shared between three men, so the narrator eats 8/9 of the bread that he provided, whereas Beremiz only eats 8/15 of what he originally had. In the end, however, Beremiz splits the money evenly, explaining that this is Divine Division.

Oh how Falcon loves this story! Beremiz is So Cool! He has been practicing telling it (often it's a Star Wars version, with Yoda for Beremiz), using props. When he gets it perfect, he'll tell the story to his Grandpa, who loves tricks and subtlety.


Sara said...

Oh, this is great! I'm glad you all enjoy The Man Who Counted as much as we do! --And I love the hopscotch multiples! We'll definitely be trying that with our number line this Fall. Thanks!

Aleisha said...

Thanks for this post. I really love reading about math ideas that involve physicality - like the hoping and bag throwing etc. We'll try that for math next fall.

GailV said...

What fun!

We also use RightStart, but I find that I veer off the script and use other approaches, particularly movement games and stories. I think RightStart plus Waldorf ideas is the perfect combination for our family.

shukr said...


My children have just told me they want to do more maths, more sums.

I am not inclined to maths at all, so these resources and direction are just what I need to work on right now.


Site Meter