Between some standardized testing, appointments, service people invading our home, figuring out summer sports schedules and logistics, getting sick, and going to the zoo and the caves, we haven't been in the classroom quite as much. This doesn't mean that someone hasn't hit their sensitive period for numbers though!

I wrote more about D's math here. This is the number rods exercise 4: the impression of addition. This shot is actually the end of the exercise. We first set up the number rods in order on the mat the regular way with the ten rod at the top and the rod of one at the bottom.Then I asked D to place the number cards near their corresponding number rod which he did. Then I asked D, "can we find a rod to place at the end of the rod of 9 to make it the same length as the rod of 10?" He found the rod of one and placed this end to end with the rod of nine, and counted entire length to verify that the length was equal to ten. We then isolated the rod of 8 and repeated the process. When we reached the rod of five, I showed him how to flip it over to show that two rods of five equal the rod of ten. This exercise gives the child their first sensorial impression of addition.

In the shot above D has paired all of the rods to make lengths of ten.

D has also completed the number rod exercise 5 which is the sensorial impression of subtraction. On a different day, we set up the number rods in order and paired each rod to make lengths of ten. We verified that the rod of 6 and the rod of 4 together make 10 by counting both lengths end to end. Then I said to D, "what if I put the rod of 4 down here below the rod of 5, how much is left? Six is left. Ten minus 4 equals 6." And we continued in the same manner with the remaining number rod pairs until the entire set was sequenced back in order. Then we took the rod of 10 and I said, "if I could cut this rod exactly in half, I would have two fives and I could take one away. So five minus five leaves five." This is the child's first sensorial impression of subtraction.

Here D is touching each band of color to count the rod's length.

He also has traces of that sensitive period for order!

He was very proud of his work so he used the kid camera to take a picture. The direct aim of all the number rod exercises is to help the child associate the quantities 1 to 10 with their numerical symbols and introduce the sequence of numbers. The rods and cards lesson typically comes at around age 4, after the number rods and the sandpaper numerals lessons, and before the spindle box.

He's mastered and finished the spindles exercise. I wrote more about this work here.

And he's completed the cards and counters initial presentation and extension work.

We have cut out numerals and counters from I think it is Montessori Outlet. There are two "1's" and one of every number from 3 to 9 and a 0. There are also 55 red counter dots and these items stow away in a dual compartment wooden box.

I began the presentation on a mat in error. We just needed more table space than our small placemat sized table mat allowed. I started by setting out the wooden numeral one on the table to the left of our space. I proceeded to place the two to the right of the one and then the three to the right of the two. After this, D gladly took over. He figured out that the one and the zero made ten. He also orientated most of the numbers correctly, though not all. (It was difficult for me to not correct him, but I know he will see the correct orientation over and over in the coming months and this will help him catch his own errors.)

Then I set out a single counter centered below the numeral one. Then I said that we use a special pattern when we set out the counters and proceeded to place two counters side by side centered under the numeral two. After this, I set out three counters under the numeral three, with the "extra odd" counter centered below the pair above. D took over at this point and followed the pattern setting out the correct number of counters all the way to ten. This was the end of the first presentation.

The second presentation, we set out the numbers and counters as we did the before, but I used the bump method to show that there is a difference between even and odd numbers. I made sure not to introduce the language for "even" and "odd" just yet. I simply, started at the bottom edge of the table and traced vertically upward with my index finger until I hit the counter centered below the 1. Then I traced from the bottom edge of the table vertically upward with my index finger until I was able to trace between the pair of two counters centered below the 2 and I pushed the 2 upward a bit.

Here D is pushing the two vertically upward a lot.

We proceeded to "bump" the odd counters and pass through the even counters to "push" the numeral upward.

The third lesson added language. As I "bumped" I said "odd." As I "pushed" I said "even." Afterward I explained that there are two types of numbers; odd numbers and even numbers.

The albums suggest the child begin these lessons between 4 yrs and 4.5yrs after the zero activity. The direct aim of the lesson is a first introduction to odd and even numbers.

The last lesson in the numbers 0-10 section of the primary album is one that requires memory. This lesson really demonstrates the child's understanding of the numbers 0-10. In a traditional classroom, many children would come together to play this game, but in our classroom, I have exactly one primary child. So we played the game as a solo exercise.

I wrote the numbers 0-10 on small slips of paper. I folded these slips and placed them in a basket. We laid out a work rug, and I asked D to select one of the slips of paper, read it, remember the number, fold it back up, put the paper on the rug, and go and fetch that many of something in the environment. At first he wasn't sure what item he should be gathering. I asked him "can you find that number of something in the environment? What has that many pieces?" After this he caught on.

Here he is fetching "8" puzzle pieces.

As he brought the items back to the mat, he counted out the quantity he had collected to verify it was indeed the quantity he intended to bring. Then he selected another slip with a number on it and set about fetching that many of another item. When he was all done with the fetching part, he opened each number slip, and recounted to verify again that he had brought the correct number of items. He thought this lesson was pretty fun.

Now that we are finished with the 1-10 lessons, it is on to the golden beads and I think the teens beads and boards as well.

We don't do many workbooks in our classroom, but I have a few for test prep. And that is what S was doing here. I didn't tell her it was test prep though. T and S think workbooks are "fun" so she asked to do a few chapters.

S is now working on these readers from Waseca. This is the part of the complete set of Parts of the Biomes readers. I think here she is changing out the sets from "sun" to "soil." She likes the little readers, but I hate, hate, hate, the laminating. I am thinking that my next purchase from Waseca needs to be something wooden that you can't cover in plastic.

S is still working on her Daily Math World Problems. I think that she is nearly finished with this book and may actually be ready for book 2 soon. I guess I shouldn't be too alarmed that it has taken her the better part of a year to get through this material. She has only been reading for about 7 months and she is in first grade after all. (This book is for grade one.)

S is working steadily on the grammar boxes. She has been more disciplined with and interested in this work than T was. Here she is working on comparative adjectives.

A little bit, or a lot rather, of practical life. Yuck.

T is done with the All About Spelling book 1. It has only been a few months! He really liked these lessons, but I suspect it was because they were about spelling rules he already knew very well. Book 2 will be a bit more difficult since we will be covering a lot of new topics, so it will be interesting to see how quickly he moves through these next 24 or so lessons.

S is also doing the AAS sequence too and she just finished up the last lesson in Book 1. She loves these lessons as well and found book 1 supremely easy. This is also coming from someone who has been writing for about a year, but only reading for about 6 months.

T thinks that coloring in these dots takes a long time. This is exercise 3, the paper square of 10. This exercise is part of the Transformation of a Square lesson sequence in the Squaring and Cubing section of the KotU math album. This work prolongs the child's work from previous exercises. (We first started this sequence here.)

Here T is making binomials. These are printed paper squares of ten. Each square is ten "beads" by ten "beads." He is coloring in his first square in one color, his second square in another color, and then the two equivalent rectangles in a third color. In the photo above he is creating 10

^{2}= 4

^{2}+ 2(4*6) + 6

^{2}. (I figured out how to create superscripts in html! It is <sup>txt</sup> for those who are thus inclined and somehow didn't know already.)

Afterward, T cut out his colored ten square, taped it to a piece of graph paper and wrote out the binomial equation and solved it proving that 10

^{2}actually equals 4

^{2}+ 2(4*6) + 6

^{2}. (The actual bead square of ten in the shot above denotes a trinomial equation.)

After T has decided he has collected enough paper squares, we'll move onto using graph paper, which further prolongs the children's work from the previous exercises. This next step also moves us closer to something that looks like the familiar geometric multiplication T already knows. And still after this, we will move onto expressing the binomial and trinomials algebraically.

Now, notice the suntan the kids have now in June. I wonder what they will look like at the end of August.

We are moving into a new summer phase right now. We get out early to beat the heat and do our tennis practice while there is still a bit of shade on the courts. Then we eat breakfast, do chores and get changed for swim lessons. Then we head to the pool. (Thank goodness I found classes for two levels at the same time.) Afterward, we head home, shower, and lunch. After a quick free-time break, we are in the classroom during the hottest hours of the day working our brains and we usually end around 4pm or so. Then it is free-time, dinner, and an early-ish bed-time. Fridays, there are no swim lessons. Thursdays, there is no school, but we have evening tennis lessons. July we'll change it up a bit, with no lessons, but we'll have camps in the mornings. And to finish off the summer, August we'll be back to the same schedule in the pool and on the court.

I've noticed that this schedule keeps the kids happier, more relaxed, and more engaged. Everyone eats and sleeps better. I also feel that we have a bit of schooling to catch up on since we missed schooling last spring, and then again the first two months in the fall because of our move. This is why we are focusing in the classroom more formally during the summer.

That is our summer outlook! What is your summer shaping up to be?

Great work! Kal-El just finished AAS book two. He is LIKES spelling now ??? He says that he hopes to do book three and four next year to be caught up to grade level. Me Too finished book one a month or more ago and didn't feel like starting book two yet.

ReplyDeleteLove the coloring in circles work. I have to show that to Kal-El. We finished everything today. Just history and spanish this summer and Kal-El will do vocab. Working on signing up for swimming and tennis today but hubby hasn't returned my phone calls.

Tell D I that is some very grown up numbers work. Tell S that I wish she could come change over materials at my house.

The kids are chomping at the bit to start the next AAS book. I guess it is a good thing that we are doing school this summer??

ReplyDeleteT is just banging on ahead with that math. It will be interesting to see if he takes the foot off the pedal this summer and focuses on other things, or just lays into it and continues to zoom ahead. The pressure is kind of off this summer, and we are being planning, but more relaxed about classroom progress.

Tennis and swim. Balls and water. I think that the kids would like tennis in your neck of the woods better. Cooler. But I am thinking that your kids would like swimming better in our neck of the woods. They'd get a darker tan for sure.

I will tell S. She'll probably want me to look at airfare prices.

Oooh you guys are doing "going outs" (or field trips) too! There are a few places I want to hit up this summer. Good to see what you all are up to! Way to go D on all the math! And I love that S is sitting in the itty bitty chair. That's what my kids do, not sure why??

ReplyDelete:) going to the zoo and the caves wasn't really the kids planning a trip based upon interest in a certain area. And I hadn't presented any relevant lessons beforehand either. Thanks for giving the benefit of the doubt, but we aren't quite doing "goings out" yet. It was more like husband and I said, where should we go for D's birthday outing?

DeleteCan't wait to see you guys again soon! How are you guys doing?