entirelysonja: (Default)
This morning Erika was doing some schoolwork by herself so I could pack a picnic lunch. After about 10 minutes, she came to me and said, "Mama, I don't understand what I'm supposed to do in the math problem."

So I began to explain. "Imagine you're in a car. The car has a gas tank that holds 20 gallons of gas. After you've been driving for a while, you only have twelve gallons left. How many gallons of gas do you need to add to the tank to fill it back up?"

"But Mama, you wrote that the car's tank held 10 gallons!"

"I did? Oh. I'm so sorry, I meant 20 gallons. Please change it to 20 gallons. Now does it make sense?"

"Yes."

She then proceeded to correctly solve the problem, which involved filling out a chart showing how much gas you would need to put into the tank based on different values of how much was already there. I got this problem from MEP 2a, which I've been finding very useful for Erika's "Math Warmup." now if only I could copy the problems correctly!

Oops. At least she was in a good mood, so I think it was probably a positive experience involving asking for help before being totally frustrated, and hearing me apologize for a mistake. If it had happened in the afternoon when she was tired, it might have turned out differently...
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We had another great day today, featuring lesson 98 in the Ordinary Parent's Guide to Teaching Reading (the "oa" in words like "boat" and "float") and various math stuff, including lessons 35 and 36 in MEP.

We did have a bit of a conflict over the use of a balance scale -- I had found some checkers that were part of my old Connect Four set and happened to all weigh exactly the same amount, and had intended to use them to expand on some balancing equations exercises we'd been doing. Unfortunately, she balked at the use of the checkers, wanting to use the metal weights that came with the scale instead. Since there were only two 1-gram weights, we ran into trouble, but she wouldn't consider using the checkers instead. I do think that this evening, when we experimented with many other objects around the house and found that nothing else we found was actually sufficiently uniform, she may have gotten over it. We'll see.

Anyway, other than that, we had a fantastic time. The highlight for me was when I tried a new approach to even and odd numbers. We've only touched on them briefly before, and she clearly didn't get it then. This time, I took out some of Erika's glass "math stones", in groups of 2, 3, 4, and 5. I asked her to divide each group into two equal parts, and then explained that the groups she could divide into two equal parts were even numbers of stones, and the ones she couldn't divide into two equal parts were odd numbers of stones. We then took this further into 6, 7, 8, 9, and 10. The cool part was when she started saying things like, "I don't really need to divide these into two parts, because I know that 8 is equal to 4 plus 4." and "I don't really need to divide these into two parts, because I know that 9 is equal to 4 plus 5, so it's an odd number."

I was also impressed that she was able, after only one reading, to answer the question, "Mary has one more Red hat than she has Blue hats. How many Red and how many Blue hats can she have if she has not more than three hats of either colour?"

The only problem she didn't quite get today was a pattern that began:

|00|||0000|

She completed it:

|00|||0000||||00000|||||000000

Which isn't quite right -- she correctly identified that the number of lines and the number of 0's increased each time, but she didn't figure out exactly how.

Then this evening before bed, she read a Bob book called "Joe's Toe" quite successfully -- there were only a few words she needed help with, and she figured out some long words she'd never read before, like "doctor," without any help. I was very impressed!
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This afternoon Erika and I did lesson 97 in the Ordinary Parent's Guide to Teaching Reading, and lesson 34 in the Mathematics Enhancement Programme.

Earlier in the day, we'd reviewed the exercise at the end of lesson 33 using a new teaching method and some Cuisenaire rods -- the exercise was to color every second ball in a series one color, and every third ball another color. Erika didn't really understand what "every second ball" and "every third ball" meant, so I got out some Cuisenaire rods and showed her how to count 'one-two, one-two, one-two" for every second block, and "one-two-three, one-two-three, one-two-three" for every third block. Then I laid out a row of white Cuisenaire blocks, and had her put a red one next to every second block, and a green one next to every third block. That seems to have worked for her, so hopefully this idea will be less confusing in the future.

Anyway, our lessons this afternoon were just lovely. The reading lesson was short and easy, and the math lesson was exactly right in terms of challenge. Erika was really receptive to my suggestions on how she might think about the problems, and it was just a totally pleasant experience.

Here's hoping our "official" school days next year go mostly this way!
entirelysonja: (Default)
Today we did our second day of Domino Math. Yesterday's was pretty much straight out of MEP Year 1 lesson plan 21 (though we used bigger numbers), while today's was inspired by MEP lesson plan 22 with some Miquon thrown in. I had Erika pick out dominoes of her choice, write an addition problem with them, and show the same thing with Cuisenaire rods.

A photo )

One thing I'm noticing is that there are areas where I need to start jumping over some of the MEP lesson segments. There's stuff Erika has thoroughly mastered, and just doesn't need more practice on. So I may need to start putting more energy into figuring out which parts of each lesson would be worthwhile, and which ones I should never even put out there.

Oh, and the best math moment from yesterday was when I asked her if she was done writing 6 dots, and she said something like, "no, I haven't done two threes yet." :-)
entirelysonja: (Default)
I had always planned to do Miquon math with Erika, I just got caught a little short when she suddenly decided she wanted to do math lessons this year. I had the main teacher's guide (the "Lab Sheet Annotations") and the First Grade Diary, which explains how math was actually implemented in the Miquon school. I'd even read the First Grade Diary and parts of the Lab Sheet Annotations. What I didn't have was any of the actual Lab Sheets!

After Erika's math obsession had gone on for a couple of weeks, I ordered the Miquon "Orange Book," and today we did the first two sheets. It was easy material for her, and I think I'm going to omit a few pages to get to something with a little more challenge. I'll be interested to see what she thinks of Miquon as we move on with it. I also introduced the concept of putting your name and the date onto the lab sheets today.

We also did more MEP today, wrapping up the end of Lesson Plan 19 and moving on into Lesson Plan 21. (Every tenth lesson doesn't really exist, it's intended for consolidation and review in the classroom.) A few pictures )

M & M Math

Dec. 29th, 2009 04:13 pm
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Erika was not really "getting" the less than or equals sign and the greater than or equals sign, plus she was unenthused about subtraction, so I decided today to make it more fun with some M & M's.

I put M & M's on each side of a symbol, and asked her to take away M & M's (eating the ones that were taken away) in ways that preserved the correctness of th mathematical expression. Well, what I actually said was more like, "Ok, now where can you take away an M & M and still have it be right?"

Picture of M & M lesson )

By the end of several exercises like this, I think she had a pretty good grasp of the "greater than or equals" and "less than or equals" signs.

We also did a bunch of subtraction problems, which was indeed made considerably more fun by being allowed to eat the M & M's that were subtracted.

After we spent some time on M & M math, we did a bunch of other stuff, including having her complete patterns like "1, 3, 5, ..." and "10, 8, 6, ..." orally, without me telling her what the pattern was. All in all, a very good day of math.
entirelysonja: (Default)
This morning the kids decided to "play school" and told us they were "math kids." Karl even had to put his backpack on to go to school. Aww...

Later, we worked on lesson plan 6 from MEP Year 1. I involved both of the kids in an exercise where we threw balls back and forth and shouted out opposites (tall/short, left/right, up/down, etc.). Then when Karl was napping, Erika and I did most of the rest of the lesson. It took a really long time because we went off on some tangents, which I thought was fine. After all, part of what drew me to homeschooling in the first place was the idea that it would be possible to spend more time on whatever interested the kids, instead of being constrained by predefined time blocks.

One of the exercises involved drawing a figure like this:

            *
         *
      *     *
   *     *
*     *     *
   *     *
      *     *
         *
            *

The idea was to then count the number of dots in each column. Which was all well and good, but then, at my suggestion, we spent some time drawing lines between the dots to make triangles. Erika then also drew a second collection of dots for us to make triangles out of.

Another activity involved drawing a ladder and labeling each rung with a numeral from 1-10, so we could count up, count down, and count by 2's. Erika decided to augment the ladder by adding 11 and 12 to the top of it, and putting the corresponding number of dots next to each numeral.

Snowed in

Dec. 19th, 2009 06:49 pm
entirelysonja: (Default)
We're snowed in, so in addition to baking bread and making mushroom soup, we did some math today, something I've previously avoided doing with any kind of formal curricular approach.

I printed out the first 10 pages from Year 1 of the Centre for Innovation in Mathematics Teaching's Mathematics Enhancement Programme, decided to skip the actual lesson plans for the first few pages (since I was pretty sure Erika already got the concepts involved), and worked on the worksheets with Erika.

The only thing she had trouble with was an exercise on permutations at the bottom of page 4 )

She really didn't seem to understand the idea, so a couple of hours later I got out the Cuisenaire rods so we could practice. It made total sense to her with concrete objects )

I'm impressed so far with the Mathematics Enhancement Programme, and am looking forward to trying out some of their lesson plans soon.

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