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Kriston,

When I go to the homeschoolbuyersco-op.org they ask if I have a referral code when I go to sign up. I didn't complete the sign-up in case you get credit of some sort for sending me there.
Just let me know!

Aw! That's thoughtful of you, but I don't think there's any sort of referral bonus. Feel free to sign up and go to town.

BTW, I had a good hands-on day today, and I thought I'd share what we did since you were asking about it. This was not in any book or curriculum that we used. We just figured it out.

DS8 was getting a bit confused in his "Key To Algebra" lesson today, which involved isolating the variable and solving for X. If the problem was 6x + 4 = 2x, say, he was having trouble understanding that he needed to subtract 6x and not add it.

We pulled out the blocks. A big red block was used to represent X; a big blue block was used to represent -X, and little natural blocks were plain old numbers.

We put down a pencil to divide the problem at the = sign. On one side we placed 6 red blocks and 4 natural blocks and on the other side we placed 2 red blocks. He could then see that adding 6 red blocks wouldn't help because then he'd have 12 red blocks, not 0.

Instead he pulled out 6 blue blocks to "neutralize" the red ones, and used them on both sides of the pencil, leaving 4 blue blocks, or -4x, on one side and 4 natural blocks, or the numeral 4, on the other side.

It really helped him to see the concept. If words don't seem to clarify, blocks or drawings or something hands-on often do.

HTH!

Kriston

What a great use of simple everyday blocks! I did some poking around today looking at materials but we ended up going to the bank where they opened up their own savings accounts which produced a great discussion about interest rates - extremely low for savings accounts but higher for loans etc.
Both kids also seemed out of sorts today. Missing friends at school I think although no one wants to go back.
I am excited to order up some manipulatives and start playing though!

Thank you for sharing your day. I don't know that I would have come up with such a great concrete example. Nice one!

Oh, you would. Not your first day, of course. But you'll read stuff and join forums (like this one) that let people share ideas with you. And you'll figure out how your kids learn best. Then, if they get stuck, you'll find some way to help them.

It's easier than it seems. But it does explain why I keep lots of random bits and pieces on hand. If I hadn't had the blocks around, I wouldn't have grabbed them and made them work. Now, I might have grabbed something else instead, so it's not like blocks are the only way that would work. But it's what I had around, so I used them.

I'm sorry the kids were out of sorts. Have you found a homeschooling group in your area? Can you arrange afterschool playdates with school friends? Those things do matter!

The bank lesson sounds great!

P.S. It also shows that you don't need to spend a fortune on manipulatives. The natural blocks were 90% off, so I bought 1000 for like $10 or something ridiculous. The colored blocks were only 75% off, if memory serves, so I bought one bucket for a couple of bucks. Cheap! Why not buy them?

LOL! DS8 has been doing Plato Science, and the chemistry is really good. That means he has learned about acids and bases and chemical equations, so it made perfect sense to him to talk about neutralizing.

I'm totally laughing at the multi-variable equation.

Yes, it sounds like a really smart approach. My version certainly helped DS8 see it. And it translated very easily to the page. He immediately had an easier time of isolating the variable and solving simple equations.

We didn't start there. I prefer the page much of the time, too, personally, and DS8 likes paper and pencil. But for helping a kid who's not quite getting the concept, the hands-on balancing idea is a pretty handy trick.

I would call the "Key To Algebra" series some pre-algebra leading to maybe high school algebra 1. It is very light on problem solving. But it does get into graphing, polynomials and systems of equations, so I think it's a good primer before AoPS.