entirelysonja

Erika has been using Math Mammoth Blue Series for quite some time, and is perhaps halfway through Add & Subtract 3. I gave her the placement test for Beast Academy 3a, to see if she was ready for that, and based on the results, decided to let her try it.

The first chapter is on geometry, and contains some really interesting and difficult problems. Our approach has been for her to try them herself, and then if she doesn't quite see everything, I let her know that she needs to try again and offer her hints and suggestions if she wants them. I'm very happy with the level of thinking required thus far -- and was amused that I encouraged her to play Tetris in order to deepen her understanding of one of the lessons.

I'm looking forward to seeing how it goes from here, and I'm pleased that she's been willing to accept help; unwillingness to actually be taught has been an ongoing issue for us.

This has definitely been the spring of reading for her -- she just finished the entire Harry Potter series, and has now started reading the Percy Jackson series.

I didn't really expect her to read the entire first Harry Potter book, let alone the whole series! But she just kept wanting to keep going, and I don't believe in censoring kids' reading, so...

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...

Over lunch, we were discussing the number of days in each month, which led to a discussion of different methods of remembering which months had which number of days. Naturally, we wound up talking about the number of days in February, during which John pointed out that the leap years are divisible by four.

I pointed out that Erika doesn't yet know what "divisible" means, and launched into an explanation involving dividing up various numbers of cookies among the four members of our family. This led to the following hilarious exchange with Karl:

Karl: Wait, I have an idea! If we had that number of cookies you said...
Me: Ten?
Karl: Yeah, ten. We could each have two cookies, and then when Mama and Erika went to Karate, we [Karl and John] could eat the other two!

John then pointed out to him that we could also break the remaining two cookies in half so we could share. But I was very amused by Karl's idea; he clearly thought it was so clever!

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!

This morning, Erika had a math insight in the car. She said, "did you know that two tens are twenty?" I responded in the affirmative, so she went on to say, "and that three tens are thirty?"

She eventually got all the way to 100 with it, and also remarked, "if you count to twenty, it's like counting to ten twice!"

I have not tried to teach her this, though she has made use of an abacus, a chart going to 100, and Cuisenaire rods, all of which would encourage thinking about this kind of thing.

Go, Erika!

Today we got a Judy Clock used from someone on Homeschool Classifieds, and of course the kids wanted to use it right away. While Karl was napping, Erika asked to do math, so I suggested that we do some work on telling time.

I'd been planning to use the Math Mammoth Clock Worktext with Erika next year, but since she was interested today, I bought it and printed out the first few pages. Of course I could have just talked with her about it and let her play with the clock, but I find that Erika is much more willing to do enough work with an idea to really get it when we use someone else's curriculum. She doesn't respond well to having me suggest that she needs more practice with something, but she's willing to put in the practice when it was the curriculum author's idea. The concepts in the Math Mammoth workbook made sense to her, and she even successfully wrote things like "half past seven" and "six o'clock." I think it likely that she'll continue to be interested.

After we'd worked with telling time for a while, she asked to do some number line work, and then did half a page of Miquon as well.

She also finished lesson 49 in the Ordinary Parent's Guide to Teaching Reading today, which we started using a few weeks ago when she expressed interest in a more formal approach to reading instruction. She seems excited that tomorrow, we'll be starting initial consonant blends -- something she's certainly encountered before, but not with the same degree of depth. I'd say that she doesn't particularly LIKE the Ordinary Parent's Guide, but it is helping her make progress with reading.

Right before dinner, the kids were watching an episode of a German TV show, "Die Sendung mit dem Elefanten," which happened to feature a science experiment. It involved lighting a candle in a plateful of water and then putting a glass over the candle to watch the candle extinguish and water get pulled up into the glass.

We decided to duplicate it after dinner and have further discussion. ( Some photos of the experiment )

Erika seemed to have a pretty good understanding of what was going on, especially since John was able to remind her of recent conversations they'd had about the three things fires need.

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." :-)

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.

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.

I bought some used Cuisenaire Rods to go along with my Miquon math materials. Even though I'm not planning to use the Miquon materials yet, I wanted to get some Cuisenaire Rods so I could do some of the exercises myself and figure out how many of them we needed.

Just from giving the kids the opportunity to play with them once, I can see that I need a lot more!

( Picture of kids playing with Cuisenaire Rods )

I also got the "First Grade Diary" yesterday, which gives the experiences of the developers of the Miquon Math program teaching first grade one year. It's very helpful, and makes clear that the kids in the Miquon school had access to LOTS of Cuisenaire rods during their frequent free play sessions.