Dragon Dance the Rest of the Day

What started out on Chinese New Year as simply the perfect opportunity to get out the dragon puppet kits that I purchased on clearance from some big-box arts-and-crafts store long ago, so that the girls could make them, along with red cake, as our little celebration--

--turned into something else. It turned into this face:

And this face:

And then a lot of this dancing, to some Chinese children's folk music tuned into on Spotify:

How magical these kids are, to take a cheap-o out-of-the-package activity that I basically tossed at them just to clean off my shelves, the most half-assed New Year's celebration ever, and to make it into magic, too.

For the rest of the day, those two dragon puppets were The Greatest Things EVER in my daughters' eyes. They flew, they danced, they roamed upstairs and down, they played out elaborate roles in their pretend sagas:

Needless to say, math and handwriting and geography waited just fine until the next day.

P.S. I haven't seen the dragon puppets since. No doubt they were tossed down at the children's feet the moment that I called for dinner or bedtime, and, like the Velveteen Rabbit on Christmas Day, utterly forgotten. Children's magic...so wild, so fickle, so fey.

Montessori Math: Building Big Numbers with Base Ten Blocks

As we've casually, slowly, and happily meandered through our first couple of homeschool years, we've gradually evolved into ways that keep us happy, engaged, and productive. We're no longer the unschoolers that we were for over a year, and yet we still do not follow a curriculum, and, believing that play is still the most important work of my so-big seven-year-old and five-year-old, I still strictly limit the amount of formal, structured work that I ask my girls to perform each day.

In other words, no matter what you're doing with your own kids, you can feel free to agree that I'm doing it all wrong.

The girls' schoolwork is almost entirely guided by their interests--Ancient Egypt, werewolves, the desire to be in the next community fashion show, the desire to earn exactly enough money to buy herself a certain ipad app. I see my role as to surround the girls with all the resources at my disposal involving their interests, to guide them through formal study of their interests to deepen their knowledge (and thus appreciation) of these areas, and to set up and moderate as many hands-on, context-deepening, multiple-intelligence activities as is desired. We do this until their knowledge is, for the time being, sated, adding other areas of interest and focusing and re-focusing and coming back to former loves as the little ones wish.

Our number-building study came about when, for some reason, it kept coming about that Willow needed to add multi-digit numbers. She needed to add the tax to the list price of an ipad app to calculate how much money was going to come out of her piggy bank for it, then she had a lot of change to add up to see if she had enough, and when I did the math in front of her, talking her through the carrying the ten and such, it was mysterious and fascinating and something that must be learned!

We watched the Khan Academy video on addition with carrying for background, but obviously when it comes to actually mastering the skill, you've got to back that train on up. Here's the progression:

1. Before she learns the shortcut, Will needs to understand the concept of carrying tens and hundreds to the next place value.
2. Before she understands the concept of carrying tens and hundreds to the next place value, she needs to understand how numbers are built from hundreds and tens and units.

We've played with that second concept plenty, so that it was a comfy review for Willow before we moved onto the first concept (where we'll be for a while), but such regular review is very important, because not only does it continue to cement the concept, but it also aids contextualization--Will sees that multi-digit addition with carrying is built upon the concept that numbers have place value, and when we go back to this review again before we start subtraction with regrouping, she'll see it again.

To build numbers in a way that highlights their place value, in a way that internalizes the basic fact of each number, in a multi-sensory, hands-on way, you need two things: Montessori-style number cards, and a BIG set of Base Ten blocks. Base Ten blocks consist of one-centimeter-square unit blocks, ten-bar blocks that are ten centimeters long by one centimeter wide and represent "ten", hundred flats that are ten centimeters long by ten centimeters wide and represent "one hundred", and a thousand cube that's the size of a stack of ten hundred flats and represents "one thousand." We're happy with one regular set of Base Ten blocks, and an extra purchase of eight more thousand cubes, on account of I wanted nine of them total.

To start the number-building unit, Will cut out a few of the following math journal prompts, and glued them, one to a day, in her math journal:

Building Numbers With Base 10 Blocks Math Journal Prompts

She didn't do all of these prompts, but Sydney, when she finishes the patterning math stuff that's currently fascinating her and starts on number building, probably will.

Each day, Will reads the prompt in her math journal and gets out the appropriate supplies. To build the number 487, for instance, she first gets out our Montessori number cards. She chooses a 400 card, an 80 card, and a 7 card, and lays them out in her work area left to right. Next, she gets out her Base Ten blocks--

--and builds the number, with four hundred flats next to the 400 hundred card, 8 ten bars next to the 80, and 7 units next to the 7:


To finish, she stacks the number cards from biggest to smallest, and behold! The number appears:

We also own a set of Base Ten stamps, so that Willow can write the number and record how it's physically built right in her math journal:


On days when we didn't feel like dragging out all the blocks and the stamps and doing some elaborate math, Willow played with this Montessori number-building app to further reinforce her skills:

I like the step-by-step, physical building work involved in this activity because I want the concepts, and the ones that come beyond, to be something that the girls can mentally visualize. I think it helps them to actually, physically see what a thousand looks like, and to see that a big number is made up of so many thousands, and so many hundreds, and so on.

Here are the manipulatives that we're using:

Teach Your Children Algebraic Notation!

Our family loves a casual game of chess. Matt and I are evenly matched--he's a more creative player, although I have a better structural knowledge of strategy--and Willow plays a great overall game for her age, although she hasn't yet mastered setting up a checkmate.

If you merely love a casual game of chess, then you likely don't need to learn algebraic notation, the method of recording the sequential chess moves of your entire game. If you find intellectual pleasure in chess, however, then you must learn algebraic notation, because I guarantee that you'll love what the knowledge of algebraic notation can open you up to. And if you have children who enjoy chess, then you must teach them algebraic notation, as well; not only is it a great precocious math skill, but otherwise they, too, are closed off from studying and mastering the game. The study of chess is full of just the sort of things that delight little children--tricky pawn tricks, secret strategies, patterns that carry you straight to checkmate if you only recognize them as they're unfolding, etc.

Here's a little of what you can do:

algebraic notation in action

Will's a reluctant writer, so don't tell her that this is writing practice! Finding a specific point on a grid is a crucial math skill, and translating the board's play to paper builds her three-dimensional visualization skills, which will be powerfully useful throughout her life, everywhere from performing high-level physics to nagivating her way on the highway one day.

I date-stamp her game notations just as I date-stamp all our schoolwork, and I have her write them in one spiral-bound steno notebook. When she's a more mature player, she'll be able to play these games back and alter the outcomes using better decision-making. Also--what a cute memento of a childhood!

replaying a game using notation

Of course, right now Will usually chooses to replay a game, using her notation, immediately upon its conclusion--this is called a Post-Mortem, and it's actually an important strategy in chess study, as you have the unique opportunity to study the board and recognize better/alternate moves while your reasoning for making the original moves is still fresh in your mind. In chess club or at a competition, your teacher or coach will go through the Post-Mortem with you, and it's also an opportunity for them to see where your skills stand--needless to say, this opportunity is lost if you don't know algebraic notation.

Will simply thinks it's fun to play both sides. Sneakily, the Post-Mortem also requires her to read and translate the algebraic notation back to the board, again strengthening her math, logic, and three-dimensional visualization skills.

re-playing famous games

Here, Willow and Matt are re-playing Bobby Fischer's The Immortal Game, with Matt (and later me, because Matt doesn't have the practice at algebraic notation that Will and I do and got overwhelmed, poor dear) calling out the moves using algebraic notation, and each player moving where the notation says to. This sounds dry, I know, but if you like chess it's actually really fun--the game moves fast, since you're not sitting and thinking up the moves yourself, and it's a GOOD game, because it's one that great players have played, with exciting tricks and tricky traps and fabulously bold machinations. Usually the game that you're reading through will be annotated, as well, to point out both the genius moves and the boneheaded ones, and it's fun to see.

When we do these re-plays, I always position Willow on the winning side, to give her practice at developing a checkmate. It's especially fun because, when a great game is playing out in front of you, even a little child can often see and exclaim over these genius or boneheaded moves--there was much outraged shouting during this particular match over Donald Byrne's dead-end strategy of simply moving his king back and forth in the endgame. It's an excellent model, because you can see how the center is developed and how the pawns get sacrificed and how truly excellent it is to fork your opponent's pieces. Several times, after Fischer did something amazing, we rewound the pieces and played it out again to better see how he set it up.

And yes, that's how we spent last Friday night. Do not judge.

studying chess problems

Will's not normally a kid who loves worksheets, but nevertheless these are fun for her, probably because of their novelty. Worksheets set up chess problems, from simple "What are the possible moves for the knight here?" to the more challenging "Find the mate in two moves" types. Since these worksheets abstract chess from the board-and-pieces manipulatives, they distill into some serious intellectual work--consider the difference between solving 19+24 with Base 10 manipulatives, and solving the same problem on paper! Many studious chess players can go one step further, and work these problems, and even entire chess games, entirely in their heads, the same way that you and I mentally solve 19+24.

Will's also a member of our community's scholastic chess club for children, which is nice because she can play with children her own age and has access to coaching that we otherwise wouldn't be able to afford. She's also a scholastic member of the USCF, which means that she receives a children's chess magazine quarterly and can earn rankings when she competes--a leg up in case she decides to get serious about competitive chess later in life. Sydney's not yet interested in chess, so it's divide and conquer so far: Matt attends chess club meetings with Will, and I accompany her to competition. I'm looking forward, though, to Sydney's inevitable decision to try chess out for herself--just think about how much more fun we'll have when this game is truly an activity that the entire family enjoys together!

Until then, it's something special that Will has with just her parents, which, of course, is also pretty great.

What I've Been Busy With

Whew! Now just two more orders to make tomorrow, and then I'm going to do something entirely non-productive.

The Third Biggest Milestone--

--lagging only behind toilet training and sleeping all night in their own bed (and, well, breathing on her own, but you can't count Syd milestones that way, lest you first count down a list of at least forty medical-related milestones, from 1. breathing on her own to 41. finally getting our insurance companies to cover her $200,000 hospital bill), is witnessing the children put on all their own snowgear, from snowpants with the elastic ankles and zipper up the front and overall straps, to snow boots that go under the elastic ankles, to sweaters that need to be buttoned or zipped, to the hat that's pulled on just right to keep hair out their eyes, to the coat that needs buttoning AND zipping, to both mittens, even that tricky second one that you have to put on with your other hand in a mitten!

Of course, it's handy to have a sister to assist you.

Chocolate Pumpkin Icebox Pie from the Pantry Stash

I am saving money. Week by week, sometimes day by day, sometimes one challenging minute at a time, I'm setting aside bits of hoarded cash--a $3.99 ipad game that Willow wanted me to buy for her, but that I asked her to pay for herself. Plus tax, that's five dollars in my stash.

A trip to the Children's Museum of Indianapolis, sans the typical visit to the gift shop. That's a good fifty bucks in the stash.

A choice not to order take-out at all last week. That's thirty bucks in the stash.

I'm saving money for a (hopeful) September trip to Disney World, if you must know. Yes, it's silly and expensive, but the girls and I want to go, and Matt is willing to indulge us, and so I'm saving money.

One of my most controversial money-saving experiments, and one that I'll have to evaluate for a couple more months before seeing if it's actually worth it, is attempting to do without one of our weekly trips to the grocery store each month. We spend approximately $150 a week at the grocery store, so that's $150 straight to savings every month if we can pull it off. The theory behind the practice is that we have ample food supplies in the pantries and the freezer--stuff that I bought at good price in bulk ages ago, stuff that I have a lot of and don't regularly use, stuff that got lost and then re-purchased and then found again during the Great Kitchen Remodel. I certainly don't need the excess, and I certainly don't like the clutter that an entire case of canned tomatoes, or three half-used jars of tahini, or a giant bag of powdered milk out of which approximately one quarter-cup has been taken, adds to the minimal storage in this house.

Wouldn't it be nice to save money AND declutter our food storage, and spend a week eating a nice canned  tomato-pesto soup with homemade bread and last year's frozen corn, and chicken and dumplings from that frozen chicken we need to process, and DIY pizza with homemade dough and all those bits and bobbles of leftover cheeses, and barley with our stir fry one night instead of rice, and peanut butter and marshmallow fluff sandwiches for lunch one day, because why on earth do I have half a jar of marshmallow fluff in the back of the pantry?

That's the idea, anyway.

So with a can of pumpkin (minus the quarter-cup that I used making pumpkin-spice latte creamer), a cup of chocolate chips, and a pie crust that I found in the back of the freezer (I DO know how to make a pie crust from scratch, but Matt doesn't, and he's the one who made the pumpkin pie last Thanksgiving. Apparently frozen pie crusts come in pairs?), I whipped together one of our favorite desserts, the chocolate pumpkin icebox pie from Chocolate-Covered Katie. I often make desserts from Chocolate-Covered Katie, and I'm always pleased with them--they're healthy-ish, since they're minimally sweetened and made mostly from highly nutritious foods, they're delicious and satisfying, and they feel better in my tummy, probably because they don't have all the usual crap. I have a big sweet tooth, and it's highly UNUSUAL for me to be satisfied with desserts that aren't southern redneck rich, so these are extra happy foods.

The chocolate pumpkin icebox pie calls for lots of nutrient-dense pumpkin, a pie crust that you could make far more healthily than Matt's leftover Pillsbury pie crust, a cup of melted chocolate chips, whose sugar content you can monitor when you select the brand, and some extract (I used vanilla and orange extracts, because that way I could use up the last little bit in the orange extract jar, and I really liked the resulting flavor). It looks like this after it's set:

But less than an hour after all four of us came back from sledding, the entire pie looked pretty much like this:

I usually make hot cocoa from scratch these days, so I had no idea that we still had all these envelopes of powdered hot chocolate! Another no-groceries-week score.

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