Sunday, December 20, 2015

Week 15: To 100 and back again!!

DJ completed the Hundred Chain this week! He was incredibly proud of himself. He had been intimidated by the Hundred Chain when I first showed it to him so he really surprised himself when he was able to do it.

He has been working hard on the Tens Board learning to count from 21-99. That work focuses on each group of ten at a time (say 21-30) so DJ never really felt like he had counted all the way to 100. But I noticed the he was not only developing proficiency with the numbers, he was also becoming more focused with counting each bead as he built them - a skill that is critical for success with the bead chains.

The Hundred Chain is the first step in the next phase of Linear Counting where the child uses short & long chains (from the Complete Bead Material) to practice counting and also begin to learn skip counting, squaring and cubing. Now that DJ knows the vocabulary for the words from 1 to 20, all of the tens from 20 to 90, and the words hundred & thousand, he has all he needs to know to count and read any number from 1 to 9,999. He has been working with these numbers with the Golden Beads, but in that work he reads numbers as "2,349 is two thousands, three hundreds, four tens, nine units". It is in linear counting that he learns to read it as two thousand, three hundred forty-nine.

The Hundred Chain begins by laying it out on the mat and then counting each bead one at a time. For the beads 1 to 9, DJ had nine green arrows to label the beads with, each arrow having the number written on it.

Once he reaches 10, he then finds a blue arrow (slightly wider) with ten written on it. There are no labels for 11 to 19, but he keeps counting until he gets to 20, places the twenty arrow, then 30, 40, etc. Finally at the end the is a wide red label for 100. If DJ loses his place at any time while counting, he just goes back to the previous label to start up again.

After all of the labels were placed, I showed DJ that he could then use the labels to practice skip counting by reading 10, 20, 30, 40, etc all the way to 100 and then read them backwards saying 100, 90, 80, etc. That is the "new work" to learn with this material so, of course, DJ wanted no part of it. He actually said "no, no, I'm not going to do that." Hah.

Another use for this material is to begin learning that "ten squared equals one hundred". The 100 Chain is also called the "Short Chain of 10" and it is made to fold up to show that ten 10-bars makes a square. The next work that DJ will do is counting the Thousand Chain, all called the "Long Chain of 10," which represents "ten cubed". That chain also folds up into ten squares that can then be stacked to make a cube. After completing the Thousand Chain, DJ will then repeat the process for every number from 1 to 9. The "Short Chain of 9" is 81 beads long, or 9 squared. And the "Long Chain of 9" is 729 beads long, or 9 cubed.

DJ had so much fun doing the Hundred Chain that he completed it AGAIN the next day on his own and then begged and begged for three days to do the Thousand Chain! That is a BIG work though, so I'm holding off until after Christmas for him to start it. I do think it is the mat that his Grandma made for this work that is inspiring him to want to do the Thousand Chain. You can see in the pictures here that we have it rolled out only far enough to hold the Hundred Chain but it is a full 30 feet long, ten times longer than the Hundred Chain. To roll it out completely it starts at the sofa and goes all the way down the hallway to the far wall of the dining room - essentially the entire length of our house! Now THAT is going to be a fun work.

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