I am a volunteer math tutor. My student is in fifth grade. He was evaluated in August and found to be at the first grade level in math. (His reading is very close to grade level.)
He has epilepsy, memory problems and ADD, and has made slow but good progress.
This week I discovered he has a right-left problem that I wasn't aware of before. We were doing some color coding and there was a need to write the word "Red" on the board to label something. He wrote a backwards R, crossed it out, and said he couldn't do that. I asked if he'd like to write it lower case, and then he did, more happily. That was the first time I observed a left-right reversal.
The next day we were working on a multiplication activity, laying out chips in an array to model multiplication. We rolled the dice and got 7 * 3. He arranged the chips on the table in a 7 by 3 grid. Then I said, let's imagine that this shows us the apple trees a farmer planted. Let's say the farmer planted three rows of seven apple trees. He said, "There are 21 trees." (He's very proud of having learned how to multiply -- which we accomplished by skip-counting.)
I wrote the number 21 on a piece of paper, and asked him to multiply by 100. I reminded him of the shortcut we had done the day before, drawing two zeros after the number. He did that fine. I asked if he wanted to put the comma in, and he placed it wrong initially, so I helped him with that. Here's what the final result looked like:
Then I asked him to read the number out loud. He made two attempts:
"One thousand, two hundred
"One hundred, two thousand
I checked to make sure he wasn't trying to be funny -- he wasn't.
Then I wrote a number in words, and asked him to write the number. The text number was
Thirty-two thousand, six hundred forty-seven
Here's what he wrote:
When I suggested that the leading zeros aren't needed, and that erasing them wouldn't change how big the number is, he said, "No, don't erase them, I need them or I'll feel very confused."
Now, we did similar exercises about a month ago without any trouble. He was okay with numbers below a million. I noticed that past a million, all the digits started to swim around in his visual field.
It seems the right-left reversal is a symptom that comes and goes. But I need to find a way he can remind himself that numbers get bigger to the left. But without using the word "left," and remembering that anything involving right and left is liable to get confused.
I think I need a simple graphic mnemonic he can use to remind himself which side the ones column goes on, and which direction we go in order to get bigger numbers.
Suggestions? Please, nothing too fancy. This is a student who needs simple procedures. When his working memory was measured, it was found to be at the 6th percentile for boys his age.
What he can reliably do now: he can add one, two or three digit numbers together vertically with pencil and paper. He can carry reliably. He can add two digit numbers mentally in the context of the game, as long as there's no carrying. If there's carrying, he usually prefers to use pencil and paper.
He can also plot a number up to one thousand fairly reliably on a number line, and also go the other direction. It seems that once we get over three digits, things start to go haywire for him.