If you’re thinking about placing your child in SAI, here’s another reason to do so.

SAI works in two directions.

First, in SAI we look ahead to algebra. We give kids a solid, lasting preview of several foundational aspects of algebra (such as powers, variables, and factoring).

Second, in SAI we look back at arithmetic. We teach unique principles – broad unifying ideas – that connect the algebra they’re learning with the arithmetic they already know (such as place value and basic facts).

This dual outlook helps kids make sense out of math. These unique principles we teach in SAI not only help with algebra – they also make more sense out of fractions, place value, and units of measurement.

SAI is a rich, hands-on experience that uses color, shape, size, texture, music, games, and manipulatives to turn kids on to math.

Be sure to reserve a spot in SAI while there’s still room!

IMHO, the main reason why people flunk algebra is because of the almost exclusive symbols-only approach to algebra. Here’s a comparison: think money.
When we learn about the U.S. money system, we use all of the following, starting with some of the following as early as age 2 or 3:

• real object: coins – pennies, nickels, dimes, quarters, etc. – and bills;

• concrete objects: play coins and play currency, including Monopoly money;

• equivalent real objects: 1 penny buys 1 chocolate football;

• verbal descriptions: “Son, you can earn 5 pennies if you put away all the basement toys before lunch” – “Dad, I found a quarter! That’s 25 cents, right?”

• written symbols for money: 5 = 5 pennies = 5¢ = $0.05; 1 quarter = 25¢ = $0.25 = 5 nickels; 7 dollars = $7 = $7.00 = 700¢.

Now… think about learning money using only the written symbols.

That’s essentially how most people learn algebra – using only the written symbols. And that’s why too many people bomb algebra.

I’ll be commenting here on several time-honored, popular card games that are great vehicles for practicing and sharpening your child’s math fact skills and number sense. You’ll have to look up the rules for play elsewhere; my remarks point out the mathematical value of playing these games.

In this blog, we’ll look at the card game Ten-Twenty-Thirty. [For how to play the game, go online to the following Youtube video: https://www.youtube.com/watch?v=ogDqB8aWsHw. Please note my comment [below the video] where the teacher in the video overlooks a combination of cards that would add to 20.]

Ten-Twenty-Thirty can be played solo, or cooperatively in pairs, or in small groups of 3 or 4. The object of the game is to have as few cards left as possible. There’s a lot of math at different levels in this game.

First, simple addition. We have add a set of three cards (always three!) to get a sum of 10 or 20 or 30. This is great practice for basic addition facts.

Second, there’s mental math. If the first two cards I’ve turned over are 6♣ and 5♥, then I’m doing mental math to find the sum (so far) is 11.

Third, there’s subtraction at this point as well. I’ve turned over a 6♣ and a 5♥ with a sum of 11,  so now I’m hoping the next card will be 20 – 11 = a 9. So if I want to anticipate what the next card is, then I’m practicing some subtraction.

Fourth, there’s some implicit experiential algebra involved with anticipating what I’d like the next card to be. Let’s say the cards laid out (without regard to suit) are 5, 10, 8, 6, 3. What is the value of the next card I’ll turn over? I simply don’t know! So let’s call that next card x. So now the cards on the table are 5, 10, 8, 6, 3, x. Let’s examine the 3-card sets that might give a sum of 10 or 20 or 30:

• the two left-most cards, with the x on the right: I want 5 + 10 + x to equal 20.
5 + 10 + x = 20. How much is x? Here, must equal 5.

• the left-most card with two right-most cards: I want 5 + 3 + x to equal 10.

5 + 3 + x = 10. How much is this x? Here, x must equal 2.

• the three right-most cards: I want the 6 + 3 + x to equal 10:
6 + 3 + x = 10. How much is this x? Here, x must equal 1 (the ace).

So, by anticipating what I’d like that next unknown card to be (the x), I’m doing some algebra. Note well: a player can do this mental math work without realizing the implicit algebra that’s taking place. But even for players who aren’taware of this algebra connection, those players are still acquiring experience with algebra.

In summary, this game of Ten-Twenty-Thirty is great practice in several ways:

– players get lots of experience with simple addition (and some subtraction);

– players get a lot of practice with mental math; and

– players acquire solid experience in implicitly working with a variable (the unknown number of that next card) and solving for that variable.

P.S. A few years ago, a nationally known university professor with a PhD in math told me that he still occasionally picks up a deck of cards and plays Ten-Twenty-Thirty. Hooray for math!

With all the emphasis I put on skip counting, sometimes I get asked, “But what things can my child skip count?”

As I thought about that question, I started thinking back to… stuff … that I had my own kids count from time to time. This isn’t rocket science – it’s mostly a matter of keeping your eyes open. Just look for anything that either comes in same-size groups, or things that are already arranged in ways that they’re easy to count by 3’s or by 4’s or whatever.

A suggestion: be careful about letting your child too often skip count by 2 or 5 or 10. If your child really needs to master counting by 2’s or 5’s or 10’s, that’s fine. But once these numbers are mastered, (which doesn’t take long), focus on the other numbers.

Here’s my list – these are things that our kids actually skip-counted from time to time.

• coins on a table (we had an unusual amount of quarters one day, so we made stacks of four)

• clothes pins in a bucket (little fingers could hold three at a time, so we counted by 3’s)

• books on a shelf (in this instance we skip counted in several different ways, because all the items were right there on a shelf and just could be touched rather than being moved or picked up)

• desks in a room (skip count by whatever number makes sense – e.g., if they are in rows of 6 count by 6)

• seats in an auditorium (use whatever number your child can use to group the seats, e.g., groups of 3 or 4 work easily.)

• eggs in groups of 2 or 3 or 4

• days on a calendar (yep, in groups of 7)

• players on a bench or sideline (I think we did this in groups of 3 or 4, depending on how players happened to be standing or sitting)

• number of players in the starting line-ups of all the baseball teams in the National League (counting by 9’s, for 8-10 teams at a time; American League teams have 10 in their starting line-ups)

• six-packs of pop at the store

• eight-packs of pop at the store

• sets of 4 windows in a large apartment building

• baseball cards in a 3-ring binder full of plastic sleeves (nine cards per page)

• ….

Well, I think you get the idea. I tried to make these skip counting practices just a fun thing to do. When my kids were ages 4 to 7, almost everything that Daddy or Mommy suggested was fun to them. So we had fun with this. I hope you will too.

 

One year we had a student named Chelsea in our summer algebra program SAI who a few years later turned up in one of my math classes at the high school where I teach. In our summer program she was very alert and astute and positive – she seemed to learn a lot from SAI. In my high school math class, she was just as teachable and positive, and she went on to a few more years of high school math after she finished my class.

All of a sudden Chelsea is a senior, just a few days away from graduation. I hardly ever saw her in the building because even the math classes she took were in a different part of the building from my room. So when I saw her walking past my room after school one day, I called her over to see what her plans were after high school. We chatted pleasantly for a few minutes, and then I realized I had a question to ask her.

So I said, “Chelsea, I know you’ve always been a good student here in high school, so I want to ask you: Do you remember the SAI class you took with me that summer a year or two before high school?”

She said that of course she remembered it. Then I asked her, “Given that you’ve always been a good student, as you look back on SAI, do you think it helped you do better in high school math? Or would you have done just as well anyway since you’re such a good student?”

This is what was cool: her whole face lit up with her great smile and she very enthusiastically said, “Your SAI class really helped me, because when I started taking regular algebra during the school year, I already knew the that x and x2 were different, and I already knew how to factor quadratics. But a lot of my classmates weren’t clear on things like that. So while they struggled with those things, I was already at the next problem or done with the assignment. For sure, SAI was very helpful for me.”

That was gratifying and encouraging for me to hear first-hand from a student what I already pretty sure of: SAI made algebra much, much easier for a very bright student. That’s cool. That’s why we do this. SAI enriches a student’s mind so much, with dynamics like color, shape, size, texture, music, movement, activity,and symbols building a deep and lasting understanding of foundational math concepts.

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