Friday, May 8, 2015

Math for May

DJ has been all about math lately. He is really keeping me on my toes because I didn't expect to need to be prepared for these activities for another 6 months or more!

The following activities in this post have been done over the past 2 to 3 weeks.

One of DJ's favorite games right now is called "Touch it quick!" We set the sandpaper numbers out in a random pattern and I call out numbers for him to touch as quickly as he can. As soon as he touches the correct one, I quickly call a new number. If he touches the wrong one or pauses, I just repeat the same number over and over until he finds the right one. We get going very fast with this and he usually ends in a pile of giggles.

We're finishing up the Number Rod exercises with the sensorial impression of addition. This starts with the 10 rod at the top. Then you lay the 9 rod next to it and say, "The 9 rod is not as long as the 10 rod. Is there a rod that we could place here to make 9 as long as 10?" DJ correctly answered 1 and placed the shortest rod in the empty space. I wasn't surprised by that because it's what he did the very first time I gave him the red rods months ago. But this time I said, "Yes, 9 plus 1 equals 10!" He looked at me strangely so I said, "9 and 1 together are as long as 10." To that he nodded in agreement. We then repeated with 8&2, 7&3 and 6&4. By the time we were finished, he was confidently saying "6 plus 4 equals 10."

We then did the activity in reverse, starting with the rods all matched to make 10s. I then said, "I'm going to remove the 4 rod, so this is not 10 anymore. Which rod is left?" DJ counted the rod and confirmed it was 6. So I said, "10 minus 4 equals 6." And we repeated for the other sets.

DJ still has zero interest in doing the spindle box, despite my strong encouragement. But he loves the cards & counters seen in this photo. The two activities teach similar lessons so I'm not too concerned. The main difference is that the spindle box highlights the meaning of zero, which DJ clearly understands and the cards & counters activity teaches the concept of even & odd. Following is an adorable video showing DJ identifying odd & even.

Next I introduced the Bead Stair to DJ. This is a set of bead bars from 1 to 10, each a different color. As soon as I put it on the shelf, DJ grabbed it and meticulously counted every bead on each bar. In time he'll become familiar with these colors because they will be used to represent these numbers in a lot of future math activities.

Then he decided to combine the Bead Stair with the Cards & Counters, which I don't think it an actual activity in the Math album, but I thought it was a great way to get familiar with the beads.

Watching DJ do these math activities and hearing him count everything and anything throughout the day, it has become apparent that he has a solid understanding of the numbers 0-9. And that is the indication that he is ready to move on to the next section using the Golden Bead Material. Oh my. Am I ready for this?

This is the Introduction to Golden Beads. The single bead sitting on the yellow disc is called "1 Unit". Then 10 beads are strung together and called "1 Ten". I had DJ count the beads on the 10 bar. Then I told him 10 Units equals 1 Ten. I showed him the square next and told him it is called "1 Hundred." then I had him count how many rows. When he finished I said, "10 Tens equals 1 Hundred." Finally I showed him the cube and told him it is called "1 Thousand". We counted how many squares were in the thousand cube and then I said, "10 Hundreds equal 1 Thousand."

With these materials he will begin to learn addition, subtraction, multiplication and division. When he gets to 10 of any one category, he'll exchange it for 1 of the next higher category so he won't ever need to count higher than 10 using this material. And yet, we'll be adding numbers like 3,472 + 2,694. And it is exactly this genius that originally sold me on the Montessori method.

Once he was somewhat familiar with the new language, hundred & thousand, I brought out a store of bead material. This isn't all I have, but it is all that will fit on my shelves right now. I desperately need more space! For now I have out 9 thousand cubes, 18 hundred squares, a box of 10 bars (I didn't count how many, I just filled the box), a container of unit beads and 2 small cups to hold the units.

The activity DJ is doing in the picture is that I've asked for a certain number of one category and DJ has to select the proper quantity and category from the store. In this case I have asked him for 4 ten bars. Prior to that I had asked him for a number of units which is why the box of units and cup are sitting out.

Since DJ seemed very comfortable with the Golden Bead material, I went on to the next step introducing the Decimal Cards. This is a set of large wooden cards with 1-9 in green, 10-90 in blue, 100-900 in red & 1000-9000 in green printed on them. The colors are important because the begin to introduce the 3-part hierarchy of our decimal system. 1 thousand is the unit level of the thousands hierarchy, then 10 thousand & 100 thousand finish the 3-part hierarchy of thousands. For now DJ will not ever go above 9 thousands but the colors are setting the foundation for this understanding when he goes to 1 million in elementary.

DJ has played with the Decimal cards a lot as he often pulls them out of my storage and they're sturdy enough that I don't mind him playing. But this week was the first time I formally presented them using only the 1, 10, 100 & 1000 and used the new vocabulary. The math album suggests I have him count the zeros to help him distinguish between the categories. Unfortunately, this backfired a bit on me. DJ easily recognized the 10 as ten and agreed it had 1 zero. But when I told him 100 was read as one hundred, he said, "No, it has 2 zeros so it's two hundred." And he was adamant about it and went on to insist the 1000 was three thousands because of the 3 zeros. Ugh. It's always amazing to me what he picks up so easily and then what seemingly simple concepts he seems to stumble on.

So that's what we've been doing lately. Is it summer break yet?

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