Change Game & More

My introduction of static addition was a little premature last week. So I backed up and introduced the Change Game to DJ.


This game starts by taking a random quantity of beads and making a royal mess of them on a tray. You then order the beads into their categories, units, tens, hundreds and thousands. Once ordered, you begin to count them.


You begin counting units and when you get to 10, you exchange them for a 10-bar. When you finish counting the units and have less than 10, you lay out the corresponding large number card, in this example 7. Then you continue with tens, exchanging for hundreds and then hundreds exchanging for thousands.


In the end we had 2 thousands, 6 hundreds, 7 tens and 7 units.


After doing the Magic Slide, we revealed the total quantity of 2,677.


The next time we played this game, I had DJ full the tray with a random quantity. He went a little overboard and selected all the unit beads (I have nearly 100), most of the tens, more than 20 hundreds and thankfully only 1 thousand. It took us a long time to count them, with A LOT of exchanging to do.


There's the final result. Only 3,557.


In other math news, DJ is anxious to learn how to count beyond 10. He understands 1 ten 3 units but he wants to know what 13 is called. So I've introduced the Tens Board. This is actually two boards (only one shown in this picture). There are nine 10's painted on the board and then there are nine cards numbered 1-9 that slide into the side slots covering the zeros on the 10s. Along with the boards we use 10-bars and a bead stair to make up 11-19. In the photo, you can see the 10-bar and red 1 bead next to eleven. Then a 10-bar and green 2 beads next to twelve, etc.

Ultimately this is just a vocabulary lesson. DJ has already learned what 10 & 3 means in quantity, so now he's just learning that we call that quantity 13.


I also introduced the Decanomial Square to DJ today. This is also sometimes called the Table of Pythagorus. It is a sensorial representation of multiplication tables and I have to say I really wish multiplication had been taught to me this way. I was expected to just memorize a bunch of meaningless numbers.

For DJ, when I began laying out the table starting with the red 1 card, I made it up to the pink 3 cards when DJ asked why all the diagonals were squares. Wow. What a realization! The diagonals are square because they represent 1x1, 2x2, 3x3, etc. I pointed to the thinnest pink card and told him that one represents one by three so it's not a square because one side is longer. He replied, "It's a rectangle."

Btw, this is a DIY Decanomial Square. I used Microsoft Word and printed the pieces on to cardstock, laminated the pages and cut them out. It only took one evening and is durable enough for my classroom of 1.


Finally, DJ completed all 4 Cylinder Blocks at once! I had begun to think that he wouldn't do this task because he's generally not interested in these anymore. But he pulled them off the shelf and actually put all the pieces back. I knew he was able to but I didn't know if he'd ever have the focus and perseverance to actually do it. Yay!