Look what we did today!! This is called the 45-Layout or Bird's Eye View. This is a BIG work but DJ had a lot of fun with it. We actually did almost all of the work on the carpet until we got to the last stack of 9 thousand cubes and couldn't get them to not topple over. So we moved the entire layout for the final picture!
This is DJ laying out the units. Sorry this picture is so blurry but it's the only one I took of this step. Here he has the cards in a line, his little cup started with 45 beads and he's distributing them next to each number, one bead next to the 1 card and nine beads next to the 9 card. (BTW, transferring this section to the wood floor was a PAIN! Those little beads rolled everywhere!)
In this step he is laying out the tens cards and then he distributed the 45 10-bars from 10 to 90. When we did this at first, I had him lay the 10-bars horizontally but at some point I remembered that I think they are supposed to be vertical so I switched them when we moved to the wood floor. But I can't think of why it would matter so I'm not sure if I'm right or not.
Next he distributed the 45 hundred squares. When he finished this step he really noticed the size differential from one hundred square to nine hundred squares and he started saying "smallest" (pointing to the one hundred), then "bigger, bigger, Bigger, BIGGER ... Bigest!" as he went up the line. And that is exactly the purpose of this exercise. He is getting a very tangible sense of the difference between 9 of something and 900.
Finally, he distributed the 45 thousand cubes into taller and taller stacks. This was by far his favorite step of this work and when we finally finished (after moving the whole setup to keep the towers from toppling) he cheered and clapped his hands.
Take a look at this awesome Golden Bead work mat that DJ's Grandma Jacque quilted for him! She finished it last week and I had tucked it away in the corner of the living room because we're not ready for Golden Bead addition yet. (Or so I thought!)
Well, DJ found the quilted mat today and demanded we use it. So, I presented Golden Bead Static Addition to him. Static addition means that each step in adding equals no more than 9, so there is no need to "carry" a ten to the next category up. In this photo you can see that we started with 2,512 beads. I had laid out the number cards and DJ found the corresponding bead materials.
Next I selected number cards for 3,123 and DJ found the beads. Once DJ learns Dynamic Addition he'll be able to choose his own quantities with just reminders to use small thousands so they won't add up to more than 9000.
After gathering our two addends, we combined the two piles together into the larger bottom section of the mat and DJ began adding up our sum. Here he's pouring out the units to count them. After confirming there were 5, he found the large 5 card from the box.
Next he counted the 10-bars and found the 3-tens card from the box of numbers.
After counting the hundreds and finding the corresponding card, he counted the thousands.
Here is the final solution but we're not done quite yet.
I took each set of cards and stacked each one with all the cards to the left so only the zeros are visible except for the top card. I did the "magic slide" for each one, sliding the cards to the right, revealing the number. I then read each number to DJ saying "two thousand five hundred thirteen plus three thousand one hundred twenty two equals five thousand six hundred thirty five."
You'll notice for the addends, we used small number cards. This is a subtle hint to the child. Two smaller numbers are added together to become a large number. When we do subtraction we'll start with the large cards and subtract a smaller number (represented with the small cards). I love how there are so many sensual impressions of math to help cement the understanding of the concepts!