Wednesday, March 10, 2010

Week 20, day 3

Wednesday: Math. While I had my shower, I let the kids play with pattern blocks and the pegboard. Then we did all our review. I did this week's SSGMR activity with E, which involved doing a given activity a set number of times (clap your hands 3 times, hop on 2 feet 5 times, wiggle like a snake until I say "stop"). He loved this - I'll bear it in mind for when he's antsy. P struggled with the subtraction on her 5-a-day. I asked her to solve 16-9, and when she set it up she tried to solve 6-9 and instead solved 9-6, so I hauled out the manipulatives (pennies). I had her count out 16 pennies and remove 9 of them, so she saw that that was 7 pennies, and wrote 7 down as her answer, but then wanted to write a 1 in the tens place because 1-0=1. So I showed her how the 1 had already been used in getting the answer in the ones place: we started with 6 pennies, and I asked her to take 9 pennies away from those 6 pennies. She couldn't, of course, so I brought in a dime. I showed her that the dime was the 1 in the tens place, and the 6 pennies were the 6 in the ones place. We traded in the dime for 2 nickels, and I asked her to take away 9 cents from the 2 nickels and 6 pennies we had. She successfully removed a nickel and 4 pennies, leaving a nickel and 2 pennies: 7 cents. Using the dime first and transforming it into nickels and seeing it incorporated into the answer helped her see that it had been used up. I'm going to move subtraction onto more frequent review, since she struggled with it last time I asked her about it on her 5-a-day as well. I think I'll ask her to show the process with manipulatives, as well - she does fine when she can count on her fingers, but with numbers greater than 10 she runs into problems.

(Aside: here is a benefit of homeschooling! If she were in a class of 30 kids, and answered that 16-9 was 13, or 17, it would just be marked wrong, and the source of her confusion wouldn't be addressed, and like many people she might start to think math doesn't make sense or is too hard).

Another problem involved making 75 cents using the fewest possible coins. P has internalized that 2 quarters makes 50 cents, but not that 3 quarters makes 75 cents, so she started with 50 cents, added 2 dimes and a nickel, and traded the dimes and nickel in for a quarter. We then talked about how a dollar is made up of 100 cents, and half a dollar is 50 cents, and half of a half dollar is a quarter dollar, which is why the 25-cent coin is called a quarter. This turned out to be useful for the next activity.

I bought a book, Primary Grade Challenge Math, which just arrived from Amazon yesterday. It contains a variety of types of problems, each with a chapter of its own which gives an explanation and then contains 4 levels of problems. This means that, while P is ready for some of the Level 1 problems now, we'll be able to keep coming back to the book for the next several years at least. Today we looked at the first chapter, on sequences. It started with a story about a girl whose mother gave her the choice between having her $2 weekly allowance increase by $4 at each birthday or double at each birthday. Looking at just the first 3 numbers in each sequence ($2, $6, $10 vs. $2, $4, $8), the girl was about to choose the first option, but she made a chart of how the numbers increased over the next 8 years and discovered, of course, that exponential increase is awesome. Another example was given of a boy with 100 jelly beans in a jar, who decided to eat half of them every day. We took out coins and let them represent jelly beans - first, 100 cents in quarters, then half of that (2 quarters), then 1 quarter. When we needed to break it in half, P and E both laughed at my efforts to fold the quarter coin in two. I then showed them how to trade down to 2 dimes and 5 pennies. We divided them into a dime, 2 pennies, but I was still incapable of breaking the final penny in half (I really tried, and was deemed quite amusing by my offspring). I then had the idea of tracing the penny on a piece of paper with a crayon and cutting it in half, so we saw that half of 25 cents was 12 1/2 cents (so Jimmy, or whatever his name was, ate 12 and a half jelly beans). P was so entertained by this that we had to go on dividing, and she was able to figure out that the sequence was 6 1/4 and 3 1/8 jelly beans (I had to cut up the whole penny into 8ths, and have her count all of them, to get the final result). At that point, although P was still having a great time, I could foresee that 1 9/16 was going to be much too complicated to keep track of (all those tiny bits of paper!), so we moved on to the first problem in Level 1, which was continuing a sequence of even numbers. P was able to do it with a bit of help. I think she'll enjoy re-reading the chapter intro each week until we've done all the Level 1 problems for the chapter.

I also introduced the concept of adding 3 numbers together. Since P has a solid grasp of what addition is, it wasn't at all difficult for her. The key difficulty for her, I think, will be getting the numbers correctly lined up in vertical format. She was easily able to solve the problems I set up for her, so I'm going to start putting them on her 5-a-days.

This afternoon was my final midwife checkup (6 weeks postpartum) - everything is fine, and B is now 12 lb 6 oz (almost 3 pounds above his already large birth weight - he's gained an average of half a pound a week, which explains why I feel like he's always nursing). On the way home, we discussed the concept of exponential decay some more, but P didn't seem to have grasped it quite as well as I thought. It might be an idea to make it even more concrete with actual jelly beans. We might start with 32 or 16, though, so as not to have to deal with half jelly beans the first time. Also I don't think letting my kid eat 50 jelly beans in a day is a good plan. I did that for my glucose test when 28 weeks pregnant with B, and no longer like jelly beans. But my kids do, and they may as well have a solid grasp of the idea that math is delicious.

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