Monday, June 22, 2015

Fast Summer

My last post was entitled "Slow Going Summer." I think I am going to retract that statement and replace it with the title of this post. The last two weeks seemed to just speed by and the weekends were gone in the blink of an eye. (That rhymed.) It was our first full two weeks of our new summer schedule and it was certainly full. It left me feeling energized but wondering if we are going to be able to fit it all in. 

Here is a bit of what we did the last two weeks in the classroom. For some reason our more recent lessons haven't been as photography friendly. Sometimes I need two hands and sometimes I just plain forget to snap one. So this is a sampling of what went on.
An introduction to the golden beads!! D is starting work with the golden beads. I kind of can't believe it. I've been looking at those early math materials on the shelves all year and wondering when we'd get to them. Well the time has come to get to them, and get to them he did.

In about two sittings he was able to independently identify which was the unit, the ten bar, the hundred square and the thousand cube. This first presentation introduces the child to the different number categories in a sensorial manner, "look at the unit, now feel the thousand cube. It feels much heavier and larger than the unit." Then we added language and named each object/category/quantity using the three period lesson. (A small note here: my albums recommend using glass beads only and note that plastic beads, whether strung or fused, don't have the heft and weight that the glass beads do to truly give the child the best sensorial impression. We have plastic beads from Montessori Outlet. For a second I thought about getting glass beads just for these first exercises. The only reason I didn't was because I wasn't going to be able to get my hands on them fast enough. D needed them NOW.) (Another note to those needing to move their classrooms half way across the country: don't wrap your golden beads in bubble wrap or plastic. Ours were in non-climate controlled storage for three months and this made the plastic stick to the beads in some places. The beads aren't overly sticky, but since I like things to be perfect, they aren't exactly perfect either.)

After D was able to name each quantity, we played a fetching game where I asked him to collect a certain number of a single category quantity. I'd say, "please bring 3-hundred squares." He'd go to a mat across the room to our "bank" and count out three hundred squares and bring them to our mat. Then he'd count the hundred squares once again to verify that he had indeed brought three, the right amount. D was able to do this fetching game easily thanks to the 1-10 numeration work he had just completed.

After this exercise, we will be working on identifying a quantity in a single category. (Like I would collect a group of three thousand cubes, present these to D, and ask him how much is on the mat.)
I've read that the typical child starts with the golden beads and then proceeds with the collective exercises that demonstrate all four operations (+ - * /.) In D's case he was so interested in counting EVERYTHING that I thought that we'd proceed with the teens and the tens work in parallel. These are the first exercises in the linear counting section of the Primary Math album. The direct aim of the teens exercises is to give the child a sensorial impression of the quantities of 11-19 and how they each relate to the quantity of 10. We will also introduce the traditional names of the quantities. These works will aid D in his quest to count to 100 "all-by-himself."
This material includes bead bars from 1 to 9, and (9) ten bars. We use a long narrow grey felt mat on top of our work rug to isolate space for our work. I first showed D how to set up the upside down pyramid of bead bars. The nine bead bar is placed at the top and the one bead bar is placed at the bottom. 

I then realized that the children have already seen this configuration working with the red rods and the number rods. I also realized that we have been doing the snake game upside down. The black and white bead stair should also be orientated with the nine-bead bar on top and the one bead bar on the bottom. Oops. It amazes me to see these consistencies throughout the Montessori sequence. When you see something that is similar to something you've seen before, even if the new thing is a bit different, it always brings up a sense of comfort, confidence, and calm--ahhh, this seems familiar. What a brilliant way to guide learning and exploration.
So admittedly, we didn't get further than the upside down pyramid in our first presentation. He just wanted to count the bead bars, again and again and again. It was really neat to see that confirmation that we've hit this sensitive period right. Whew.
On a separate occasion, we again took out the golden ten bars and began forming the quantities 11-19. At the top is eleven: one golden ten bar on the left and a single red bead bar on the right. The iteration at the top of the shot is 12, then 13, and so forth. You can also see that D didn't feel the need to organize his bead bars into that upside down pyramid. 

We set up the beads in this manner and then added language in a three period lesson. He knew many of the names already, but 13 was pretty difficult. We are still in between the second period and third period at this point.

In the next exercise the adult will name a number and the child will build it. After this, the adult will build a number and the child will name it. Then lastly the child will build the numbers in order.

Typically, this work comes between ages 4 and 5.5 years.
Still later on we brought out the teen boards. This equipment consists of two rectangular wooden boards, with six horizontal bars affixed to each of their faces equally spaced. The bars create a space for other wooden cards to be slid underneath them. The first board has 5 tens printed on it and the second board has 4 printed tens. The set also comes with 9 number cards with the numbers 1-9 printed on them. Finally, the entire set is housed in a wooden box. I think we got ours from Alison's Montessori. This is a very heavy work, and the boxes are almost too cumbersome and large for D to be able to carry them from the shelf to the rug. 

The boards are placed on the vertical felt narrow rug, end to end. We place the card numbers on the right hand side stacked in the correct order with the 1 on the top. I took the first card with the "1" on it and slid it into the top slot over the first zero to create "11." I also said, "this is eleven." After this, D took the stack of cards, and slide them into the remaining slots over each zero from top to bottom and said, "twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen." When I asked him to "show me fourteen" he wasn't sure quite which one it was. I think he had just remembered the numbers in sequence and could recite them in order only. 

In a later lesson another day, he was able to "show me [x number.] which is the second period of the three period lesson. 

During a still later lesson he was able to tell me "what is this" and name the printed number I indicated. He can also complete the first exercise when the adult asks the child to build the printed teens numbers randomly. I'll say, "please make 14." He'll pick up the 4 card and place it in the fourth slot and say, "14." 

There are two more exercises where the adult builds a number and the child identifies it by name and then when the child builds the numbers in order before we start pairing the bead quantities with the printed numbers on the boards. But at this point, I think he has done both of those other tasks by accident without formal introduction and he is ready to start pairing beads and numbers symbols which is the third and last stage of the Teens Lessons.
D also got started with the Tens lessons. In the shot above he is comparing (10) ten bead bars to a wooden hundred square to make sure they are equivalent. (This exercise isn't part of the formal lesson.) In this presentation there is a box of 45 golden ten-bead bars in a wooden box, and a long narrow felt mat which we place on top of a work rug.

In this presentation, we unroll the narrow grey felt mat (from Alisons Montessori) vertically and we start forming quantities at the top. I placed 1 ten-bead bar orientated vertically at the top of the mat and said, "this is ten." Then underneath I placed 2 ten-bead bars side-by-side orientated vertically and said, "this is two tens. We also call this twenty." Then I repeated the process with thirty. We continued with the three period lesson naming ten, twenty and thirty, which he was able to do easily. Afterward, he wanted to see all of the remaining quantities to 90 laid out and wanted to know what they were called. There are no further exercises for this first tens sensorial experience besides a three period lesson to learn all of the names of the quantities. The direct aim of this lesson is to help the child learn the traditional names for the tens 10-90 and to associate the name with the symbol. This lesson usually is presented between 4 years and 5.5 years of age. 
After the tens beads are presented and the child can name the quantities, or in this case, when the child asks to see the "next work" we move on to the tens beads and boards. This work includes two tens boards similar to the teens boards in design and style, except they are printed with the numbers 10-50 and 60-90. We continue to use the box of 45 golden ten-bead bars and the long narrow felt mat. The prerequisite lesson is the tens bead work. 

In this presentation, we set up the boards end to end, with the board printed with the numbers 10-50 on the top. I placed one golden ten bead bar next to the symbol 10 and said, this is ten. Then I placed two golden ten bead bars next to the symbol 20 and said, this is 20. And then we continued in a similar manner through 90. I don't remember if D took over counting out the ten bars and naming the quantities or not. He was interested in the number cards that came with this set, and the fact that the font on the number cards was slightly different than what was printed on the boards.

Then he wanted to write all the numbers on small index card pieces and stick them on the cards and the boards with double-sided tape.

The direct aim of this lesson is to help the child learn the traditional names for the tens 10-90 and to help the child learn that two tens is 20 and so forth. In addition, this work will help the child associate the name of the number with the number symbol. The child usually gets to this work between 4 and 5.5 years of age. The work that comes after this is the Tens Stage 3: Beads and Boards 11-99 lesson when the child will learn how to create all numbers from 11 to 99 and this is traditionally when we use the number cards D decided to recreate.

After D paused on relabeling the tens board materials, he set to work writing all numbers from 0 to 19 on small index card pieces. He is lefty to be sure now and always grabs his pencil with his left hand. Thanks to MBT who sent me these cool lefty-or-righty pencil grips (sorry don't know what they are really called) D easily holds his pencil the right way. Maybe I'll get one child out of three to hold their pencil correctly. The only thing I don't like about the grip is that it makes it hard for the child to sharpen his/her own pencil independently.

Anyway, back to numbers. Here D is using both the sandpaper numbers and the teens beads to create quantities and then write their number names. He was very very very proud of this work and he was super focused through it all. He is in his sensitive period for these numbers RIGHT NOW and it is really cool to see. I just keep reminding myself to "BACK OFF" and just let him explore what he needs to explore in the way HE needs to explore it. This isn't a formal lesson, or even an extension of a lesson. D made up this exercise. But something inside him just NEEDED to do THIS: write down numbers. He is using the correct pencil grip, the Montessori materials he feels he needs, and is doing constructive independent work. What more could I ask for. 

Afterward, D really did seem calmed, refreshed and ready to move on. After a period of intense work D is always more interested in other materials and works in the classroom. I am still amazed to see first-hand the phenomena that Maria Montessori first witnessed.


Oh, we are working, working, working on learning our letter symbols. Though we squarely hit D's sensitive period for numbers, I seriously missed his sensitive period for sandpaper letters. He no longer wants to feel the sandpaper letters, so now I am trying other tactics to get him to practice forming his letter symbols and help along his muscle memory. 

We do the sand tray a bunch and we also go through a lot of shaving cream. He loves writing letters in shaving cream in the shower. I'd love it too if they came up with an unscented shaving cream.

Typically the child would have focused on learning the sandpaper letters in one quick 3 week period. After finishing the sound to symbol association they would quickly move on to using the moveable alphabet to begin creating words, then phrases, then sentences, and then stories. The moveable alphabet allows the child to communicate his/her thoughts without having to have the motor coordination to hand write. At this point the child has had thorough aural training and can segment most any word. With the knowledge of which letter symbol goes with which sound, they can then spell most any word and therefore begin to communicate that which they desire to share. On average this stage begins somewhere between 4 to 4.5 years of age.

After much work with the moveable alphabet the child is ready to begin drawing these letter symbols by hand. After prerequisite work with the geometry cabinet, the tactile materials, the leaf cabinet, and sandpaper letters the child will begin work with the metal insets. I've mentioned these before as well as D's seeming disinterest. So, he is focusing more on the mazes to help develop mastery of the hand in using a writing instrument including, pencil pressure, keeping within an outline, and control of movement. The metal inset work typically begins close to 3.5 years of age. 

The sand tray is also introduced as a work to develop handwriting. This is a shallow tray filled with sand in which the child can trace symbols. After some control has been achieved with the metal inset work, this work helps to further develop coordination and control of movement. 

After the sand tray comes the chalkboards. There are a few different types of chalkboards. The one D is using here has no lines. Typically, the child would sensitize the fingers, select a letter symbol, trace it, give the sound and then would write the letter on the board with a piece of chalk and say its sound. This material again works to refine the child's hand coordination and control of movement. Successive chalk boards introduce lines that help the child form and space their letter symbols accordingly.

Now, I must also add to this very abbreviated list of handwriting preparation D did not follow this sequence. We were in transition during his sensitive periods and all of our belongings were in a storage crate or three. But since we missed these sensitive periods, we are picking up the pieces and trying to build a foundation of skills that will help serve him and patch up any gaps. I am not quite sure how much of what to do and when to do it, but I am trying to let him lead, and am listening to him tell me what he needs and when he needs it. I am also returning to some of the books I've read in the past that explain a bit about what to do with children who haven't had the needs of certain sensitive periods met to figure out how we should better proceed.

D is interested in words, and how to express himself, and even in reading what others have written. So I am hoping that he will catch himself up and master the skills he needs to be able to express himself as he desires.
Here D is working with the chalkboards and in this case, creating something a little outside the scope of letter symbols.

He does like to use the sand tray, and here he should be using it on a table where he can attain better writing posture. But for now, he pulls it out and sets it wherever when he feels so inspired.

I made this sand tray from a few pieces of balsa wood (to cover the handle holes) and a tray I found at Jo-Ann Fabrics.

Wow, that was a lot about D's primary work. I guess I had a lot to say because neither of the other children did this at home.
S found our Zoology nomenclature materials (from Montessori R&D) on the shelves and decided to explore them a bit. I was thrilled that she just decided to look through these materials on her own accord. I did give her some suggestions about where to find more information about a few of the questions she had about the content in these booklets. True to form she was most interested in the worm-like classes of invertebrates. Yuck. Here she is looking up the bones of amphibians in one of our bone books. (Sorry, I just don't remember which book.)
Then she got out our Animalium book and started looking for pictures of worm-like animals. She then decided to make a booklet of her worm drawings. A wonderful, if a bit icky, independent project if I do say so.
S also seems to like grammar just like T. It must be the Montessori lessons because I sure as anything did NOT like grammar when I was in school trying to learn it.

Here I have her the first verb lesson. I actually took this lesson from the Cultivating Dharma album. You can read more about this lesson here.
Here S is working through the first verb lesson in the KotU album. First we talked briefly about the black pyramid that it represents the old, stable, noun. Then I introduced the grammar symbol that depicts the verb. A red ball is spherical, it can move easily, and it is red like the hot sun. Just like the sun gives energy to the earth, the verb gives energy or movement to the sentence. S seemed to like this idea.

In this work, we introduced a new grammar box for the verb. S selected the first filler box that contained sentence cards and word cards. She chose a first sentence card and read both sentences out loud. Then she formed the first sentence with the word cards and then chose the alternate verb word card. Then she acted out the command. In this case she spoke a word and then whispered a word. Then she placed the appropriate word cards in the appropriate grammar box compartments. 

After she had completed all of the sentence cards, we explored word order a little further. I told her that "speak a word" and "whisper a word" are called permutations. Then we rearranged the sentence to read "a word" and I asked her "can you do what it says?" She replied, "no." Then I arranged the cards to read "a word whisper" and asked if she could do what it said. She said "no," and then immediately rearranged the cards into the order that made grammatical sense: whisper a word. We repeated this with another pair of sentences to further explore word order and how order affects meaning. These exercises help the child become aware of the construction of our language and that generally the verb can be found in a central location within the sentence, and that it will rarely appear at the end.
Finally, I showed her the verb energy chart where we see that the verb shines on the noun family (the noun, adjective, and article) and gives energy to the noun family. Generally the verb gives the noun energy, movement, and action.

After this, S will continue to work through the other verb grammar filler boxes that explore other aspects of the verb.
T challenged himself to work through the rest of the grammar boxes by the end of the summer. (He was in part challenged by Kal-El who just finished all of the grammar boxes.) He received all of the initial presentations in the 2013-14 school year. Here he is working on adverbs and I think he wrote down his own definition of what an adverb is in his work journal afterward.
We have started the Stories of the World. You can go here to read a bit more about it, or Google MBT's blog for "SotW" and read her descriptions of this curriculum from a Montessori homeschooling perspective. 

After reading the first chapter about what history is about, T decided to create his own personal timeline. I think that this particular work is in the KotU history album as its own separate presentation. So, even if you don't have or do the SotW curriculum it is in the albums nonetheless.
D spent three days taking apart and putting together the puzzle map of the US. (He spent three days doing this one time.) He has already done the prerequisite map of the world (the continents map) and the puzzle map of North America. With 49 pieces (Hawaii isn't a separate piece) this puzzle is a bit more difficult. But over three days, with the help of the blank control map, D was able to put all the states back in their places. The direct aim of this work is to aid the child in refining their sense of visual discrimination of shape and to indirectly prepare them for geography.
I think he asked me the names of most of the states. He certainly knows his home state! That piece went in first.

S and T have been working on geometry a bit though here it looks like fractions. Here we are working on adding and subtracting angles and this lesson is the KotU geometry album. 

First I introduced this concept verbally. I said something along the lines of, "what if we put two red fraction circles in the Montessori protractor and see what they measure as a combined pair? Oh, each of these two quarter pieces here measure 90 degrees and together they measure 180 degrees. I wonder if you could find another pair to combine."

Afterward, I introduced how to write this expression on paper. "Let's add 1/3 and 1/5." We measured each individual angle separately and then we wrote each measurement down: 120° + 72° =. Then we measured the two angles together and found that they were 192° and we wrote this down as well.

Then S tried adding more than two angles together.
And then T and S started subtracting angles pretty much by accidental exploration. Oh, we can add them together, or we can take one away from another and get something else entirely.

Then T was playing around with the fraction circles and came up with this and the idea to build a board game. 

They even made a dodecahedron die to go along with the game. 

After these adding and subtracting angles lessons using the Montessori protractor we will move on to using a regular protractor, drawing angles, and measuring them as well as learning new terminology like bisect and amplitude. Still after this, we move on to learning about lines.
One afternoon I just took S aside for a little one on one time. She loved the attention and the easy quick focused lessons, and I loved that we didn't get interrupted and that we got some special time together.

We started off with a little bit of the large bead frame and naming quantities. Then we pushed on to some more elementary early numeration math lessons. This lesson is part of the commutative and distributive laws of multiplication lesson. I thought I had written about this lesson before, but either I didn't or I can't find it now. So, this is the commutative property of multiplication. We used a box of bead bars (in this case for the decanomial from Montessori Outlet) our cut out signs (which are HUGE and they are from Alisons), and grey and white number tiles from the checkerboard (ours are from Montessori Outlet.) 

In this problem above, S set up 7*8 and 8*7. Then we laid out 8 white seven bars below the first equation and 7 brown eight bars below the second equation. S counted them up (she is still working on those math facts) and found that both equations equal 56. Then she placed 5 ten bars and a 6 bead bar below each equation to indicate their total product. She found that both equations equaled the same thing.
S continued to explore using the same commutative property principle. She said that this work was really fun. The child should continue to explore combinations on their own and then they can draw them on graph paper to continue the work. After the child can create equations fluently, we introduce the "commutative property" terminology. The next topic we will explore is the distributive law. 

This lesson is in the early numeration sequence in the elementary math album. S will be officially entering 2nd grade so she could be considered a year behind on the math. I am not particularly concerned because she proceeds easily when it is a subject she enjoys, and I've found that her sensitive periods come pretty consistently about 6 months behind the Montessori average. She has the same sensitive periods as Montessori suggests but just not at the same average age. 

Whew! So that is a bit of what we've been doing in the classroom. What have you been learning this summer?

Thursday, June 11, 2015

Slow Going Summer

Even though the official start to summer isn't quite upon us, it sure feels like summer in these parts. The outdoor shade thermometer said 91 degrees at 2:30pm. The thermometer I put in the sun at that time read 115 degrees.

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 102 = 42 + 2(4*6) + 62. (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 102 actually equals 42 + 2(4*6) + 62. (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?