Tuesday, May 23, 2017

Homeschool History: A Cookie and Jello Map of Ancient Greece

The kids made this cookie and Jello map of Ancient Greece as an introductory overview of the geography of Ancient Greece, although it would work just as well--even better, perhaps!--as a culminating project. Looking at photos of the cookie map now, a few weeks after the kids did it, I can immediately see some places--Mycenae! Thera!--that we didn't label but have since studied, and a couple of places--Troy! Sparta!--that the kids have had to look up the location of again, since it didn't stick. But back then we were more concerned with the location of places like Thrace and Macedonia, and the kids DO remember where those places are after this activity, so there you go.

We've made cookie maps of geographical locations many times before, so that part of the process is fairly cut-and-dried for the kids now. They can independently roll out the dough, carefully cut the map out with the tip of a sharp knife, peel up the unwanted dough, and bake it, watching it carefully to remove smaller pieces before they burn.

But unlike other maps that we've made before, Ancient Greece has tons of islands, the placement of which I wanted to secure in the final map. And I wanted something to represent the sea, something that was NOT icing... shudder. I had the idea of blue Jello, but I wasn't sure that it would work. I shopped it around to some of my mom friends at our weekly homeschool playgroup, and they weren't sure that it would work, either, but they gave me the idea to freeze the baked cookie map before adding the Jello, in hopes that the map wouldn't absorb all of that liquid before it could set.

It worked only okay, but that was enough for us!

The blue that you see all over the cookies isn't from the Jello being absorbed by the cookie, although it was, a little--that's from us slopping the liquid Jello all over the darn thing while trying to move it and get it settled in the refrigerator. Next time, I'll probably clear a shelf in the fridge (and good luck to me on THAT!), then have the kids pour the Jello in after it's stable.

We also didn't notice until Syd was trying to pour the Jello in and kept running out, but that giant half-sheet baking pan that I've had since the first time the kids asked for a themed birthday party is not perfectly flat anymore. Is any pan that large EVER perfectly flat? It looks flat, but every time Syd poured, the Jello would settle in the Aegean Sea, leaving next to nothing for the Ionian Sea. You can see it in the photo--the Aegean Sea has all the Jello, while the Ionian Sea has just a hint.

Regardless, even a hint of ocean was enough for our purposes. Time for decorating!

As you can see, we're still benefiting from the map coloring lesson in Math Labs for Kids, as the kids used the greedy algorithm to color in the kingdoms of Ancient Greece. Syd also made labels for most of the important locations--

--and they were added to the map with much fanfare and even more candy decorations:

The finished map is certainly one to be proud of!

We'll be seeing some of these places during our trip to Greece later this summer, when it'll be even sweeter to see them in person than it was to eat them!

P.S. Here are some of the other cookie maps that we've made over the years:

Monday, May 22, 2017

Work Plans for the Week of May 22, 2017: Sparta, Prehistoric Fashion and a Three-Day School Week

Last week was GREAT! It was a fabulous, productive week full of work and play for both the kids and me. Check out Syd, who was supposed to be helping me make egg carton and beeswax fire starters, but discovered midway through that sun-warmed beeswax is even better than modeling beeswax:

Our weekend was just the same--obedience school and an open-house at the kids' sleep-away camp, as well as cookie baking and an astounding amount of time spent with books and movies. I read The Man Who Walked Between the Towers to the children late on Saturday night, and then Matt remembered that Man on Wire is actually on Netflix right now, so instead of sending the kids to their own beds we all camped out on our bed to watch it. THAT was so inspiring that I now have a beginner's slackline kit on my to-buy list!

This week will be either just as great, because we only have three days of school, or stressful and hectic, because we have a LOT of field trips and classes and meetings instead of school. As homeschoolers, I'm not sure if we can handle two whole days during which we have to be up and ready to go by 8 am. We'll see!

Books of the Day this week are science picture books, Native American folktales, a novel that I read last week and thought Will would like, and the first book in the Chronicles of Narnia for Syd. Other daily work includes cursive copywork for Will, time for creative writing for Syd (she's been working for weeks on a story entitled "Shopping Shipwreck"--it's pretty great), typing practice on Typing.com for both, progress on their MENSA reading lists, keyboard through Hoffman Academy, Wordly Wise 7 for Will (she's almost finished!) and a word ladder for Syd, SAT prep through Khan Academy for Will, and Greek language review. Trying to include Matt in our Greek language lessons is turning out to be a huge roadblock to progress, as he's turning out to be quite adept at wiggling out of the lessons, so we may have to drop him. There is no space for weakness in our homeschool!

And here's the rest of our week!

MONDAY: After some extra hands-on lessons last week, Syd understands the concept of dividing fractions now, but still needs more reinforcement to cement the algorithm. She hates and I LOVE these worksheets from Math-Aids; whenever a kid needs more drill in a certain area, I always check Math-Aids first, and they almost always have worksheets that apply. When she's got dividing fractions down, her Math Mammoth curriculum is circling back to geometry, while Will's is circling back to percents this week. Their hands-on math this week, therefore, has to do with neither! In this short week, I just needed something that wouldn't take a lot of time or preparation, and ratios do apply to both fractions and percents. Monday is also mind bender day for Will. Some day, it would be nice to find a firmer logic curriculum, but until then, these puzzles will get your brain moving!

Syd is close to the end of Junior Analytical Grammar. When she's finished the book, both kids will spend some time on Latin and Greek root words before I make Syd start Analytical Grammar, which she is going to LOATHE. Will is still working through the first season's Review and Reinforcement workbook twice a week; when she's finished with that, she'll start the second season of Analytical Grammar--Will likes worksheets, fortunately, because she likes something concrete that she can zip through and be done with.

While Will has class after class and camp after camp and activity after activity this summer, Syd is going to be spending the summer working hard to earn her Girl Scout Bronze award. She and some sister Scouts are meeting later to share their brainstorming work and to debate and decide on their Take Action Project, and because Syd has a plan that she's very fond of, she's going to spend part of her day today working on a presentation of that plan. How about that for a school assignment that directly applies to the real world? Will, on the other hand, is going to work on helping me finish up our troop budget and helping me make an analog record-keeping system that will live inside of a notebook, the better to travel and trade off with, my Dear.

Our Story of the World volume 1 chapter this week is a comparison/contrast between Athens and Sparta. Sparta is further south than we'll be traveling on our Greece trip, but we'll be spending a LOT of time in Athens! On this day, the kids will read/listen to the chapter, verbally answer the quiz questions, then complete the mapwork directly onto the road map of Greece that we'll be taking with us on our trip.

For Syd's birthday, I gave her this book of fashion history. I didn't tell her at the time that it was going to be the spine for a fashion history unit study for the two of us, but she's game, and we're starting this week! On this day, we'll read about the clothing worn during prehistoric times, and then I'll hopefully interest Syd in exploring some more with her small wooden loom. She was really into it for a while before setting it aside, but I bet that when I show her the colorful yarn that I bought her, and what a Pinterest search will reveal, she'll be inspired once again. I just wish that she had two looms, so that I could play alongside her!

TUESDAY: On this evening, we have a Girl Scout meeting/cookout to practice outdoor cooking skills, in preparation for a future troop camping trip. My two are bringing fresh fruit that travels and stores well for camping, and will research each fruit's nutritional information, then create a display or label to share that information with the other girls. At the cookout there will also be burritos, fire-baked potatoes, foil packet green beans, and gourmet variations upon the s'more--I think they're going to eat well!

In the years that we've been homeschooling, I've gotten a lot better about not reinventing the wheel while also avoiding most packaged curricula. This has coincided, of course, with the development of so many more freeschooling options, from MOOCS to open courseware to podcasts to YouTube channels of significant educational value. And that's why instead of creating my own lesson on the democracy of Ancient Athens, I just have to point the children to this excellent TED-Ed lesson.

This Junior Archaeologist badge book is a doozy--38 pages, and several hands-on activities!--so the kids are taking an extra week to work on it. Fortunately, as with all the other Junior Ranger books that they've encountered, they're loving it.

In our weather unit, we're moving on from temperature to air pressure. On this day we have an activity planned to demonstrate how air pressure works; in upcoming lessons, the kids will build a working model of a barometer and use that to measure air pressure for a period of time.

WEDNESDAY: The kids and I will be volunteering at the Children's Museum, running tabletop activities related to cars and physics. This is one of the funnest and easiest of volunteer assignments, and perfect if you enjoy interacting with all kinds of children.

THURSDAY: Sparta is probably my favorite city-state, and I am going to take a LOT of pleasure in helping the children dress up in Spartan armor! They have to research what they need themselves, but of course I know what they'll come up with, and I already have gold duct tape winging its way to me from Amazon, and Matt on the lookout at work for cardboard sheets that MUST be at least three feet in diameter. Return with your shield or on it!

Most of the day, however, will be spent on our local university's campus, where we have an afternoon appointment with a librarian at the special collections library. She has promised to show us some lovely examples of medieval illuminated manuscripts, parchment, bindings, and even scribal errors. I am, as you can imagine, pretty darn excited about our visit.

FRIDAY/SATURDAY/SUNDAY/MONDAY: What a nice, long weekend we'll have! The kids have their all-day nature class on Friday, we'll do some traveling over the weekend, and if I can have as relaxing of a Memorial Day as I had last Saturday, I will be happy and ready and eager for another...

...hmm. Looks like we have another three-day school week next week, too!

What are YOUR plans for the week?

Friday, May 19, 2017

Homeschool Science: The Physics of Temperature and a Homemade Working Thermometer

We weren't meant to spend more than maybe a month, tops, on this meteorology unit. What we really want to be studying is astronomy, and we'll have to get to it soon if I want to have us set up to watch the total solar eclipse as our culminating activity, but meteorology has never been something that's interested the kids enough to study before, and so we just need to zip through it just so the kids have some basic background information, and some context for relevant bits of knowledge.

There will be no weird gaps in our homeschool curriculum!

This unit is kind of taking forever, though. Like most of our studies, it's heavy with hands-on activities, but since they're hands-on weather activities, they keep either requiring specific conditions outside that we have to wait on (can't identify clouds if there aren't any!) or take days and days to complete (this week, the kids are working every day on a temperature-gathering experiment, and it's a huge pain in the butt).

Even this particular lesson was kind of a pain in the butt, because we had to put it off when we discovered that Syd had used up all of our clear straws on a huge, messy (though delicious) milkshake project. We finally got it done this week, though, and happily, it was so awesome that it was worth the wait!

In order to understand how a thermometer works, you have to understand the physics of temperature. This Crash Course Physics video gets too hard for Syd less than halfway through--

--but does contain plenty of reinforcement of the main takeaway, that heating expands solids, liquids, and gasses, and cooling contracts them. The rate and intensity depend on the substance, but if you know that rate and intensity of a particular substance, you can use its expansion and contraction to then measure the temperature around it.

And boom! You have a thermometer!

We studied how to physically use a thermometer as a measuring tool in a previous lesson (I probably should have told you about that lesson first, but bizarrely, I chose not to. I'll tell you about it later, I guess!), and the difference between the various scales of temperature measurement. So when we finally scored some clear straws (at the movie theater, in partial recompense for the ridiculously high ticket prices for Guardians of the Galaxy 2), the kids were all set to make a working thermometer for themselves, using sugru, a Starbucks Frappuccino bottle (I bought some different types of coffee drinks to test out for an upcoming camping trip, and this one was NOT a winner--it tasted weirdly chemically and...oily, kind of?) and this tutorial:

The kids were able to follow the tutorial independently, although I'd advise you to let the thermometer rest for a couple of hours before you use the eye dropper to add a couple of inches of water to the straw. Our rubbing alcohol was already at room temperature, but the water that the kids got from the sink must have been cold, because just by sitting on the counter the thermometer soon maxed out its temperature reading, with the colored liquid all the way at the top of the straw and dripping down.

But yes, after you fix that the thermometer works just as you'd like it to, and you can move it inside and out, around to different parts of the house, put it in the refrigerator and then take it out later and watch the water level rise while you're eating dinner, etc. 

P.S. If that Physics of Temperature video wasn't too hard for you, you should also check out this second video on the subject, and then this video on thermodynamics. If we were going in a different direction with our study of heat, the kids would have LOVED to spend some time burning and melting stuff to determine melting and boiling points, etc., but I'll save that fun activity for another time.

Wednesday, May 17, 2017

How to Divide Fractions with Cuisenaire Rods

Although by now my kids well know that with almost every math problem there's an algorithm hiding in there somewhere, and that the algorithm will be even quicker and easier than the model and so they want to know it RIGHT NOW, I still try to whip out the mathematical models whenever possible, and especially whenever a kid is having trouble remembering or utilizing the algorithm. If, for instance, a kid can't consistently remember the algorithm for dividing fractions, that's because she doesn't understand dividing fractions. If she understands how it actually looks to divide a fraction, then she'll have a better idea of the answer that she's looking for, and that will likely remind her of the algorithm that she needs to use to get that answer.

You know how when you're trying to spell a word that you don't fully know how to spell, or trying to grammar check some tricky grammar, you often know when that word or sentence "looks" right, or when it doesn't? That's because you've read so much that you understand how words and sentences are formed, even if you don't completely remember the algorithm for your particular word or sentence. It's the same with math. If you understand how to physically divide fractions, and you're presented with, say, the expression 1/2 divided by 1/3, then even if you don't completely remember the tricky algorithm involved (which is to invert the divisor and then multiply), you should at least know that the answer isn't 1/6. You'll probably, in fact, be able to look at the two terms and know that the answer will be greater than 1,  and that might be enough to remind you of the algorithm.

Here, then, is a quick-and-easy way to model fraction division using Cuisenaire rods. It takes longer than simply calculating using the algorithm, but it makes dividing fractions make SENSE, which, if you learned how to do it using only the algorithm, is a pretty big deal and might blow your mind even now.

Take this problem:

Syd's math curriculum asks her to work the following: 2 divided by 5/6. I asked her to interpret it in this way: "How many times will the fraction 5/6 fill into two wholes? Or, how many 5/6s are in two wholes?"

Step 1, then, is to wrap your head around one possible interpretation of a fraction division problem: how many times will the divisor fit into the dividend? You can work some whole number problems to illustrate that interpretation, if you like. How many times will 7 fit into 35? How many times will 10 fit into 120? You can even work those with the Cuisenaire rods first, using the method that I'm about to show you, to prove that the problems are essentially no different.

Step 2 is to set up the problem with Cuisenaire rods. Since we're being asked to divide 5/6, then the whole is clearly 6/6, or a six bar, and there are two of them, so set up two six bars. You need to divide that by 5/6s, so gather up some five bars to represent that, and some single units in case you're figuring out remainders. The five bars make up 5/6 of the six bars, and those singles will represent fractions of the five bar. One single unit is 1/5 of a five bar.

That alone is going to tell you that if you do have a fraction remainder, it's going to be in fifths. The remainder, if you have one, is always going to have a denominator the same as the numerator of the divisor, because that numerator is what you're actually dividing. It's not something you notice when you divide whole numbers, because when you divide whole numbers in our society, you're using the Base Ten system, and so denominators are ALWAYS in tenths (or hundredths, or thousandths, etc.). Not so when you divide fractions!

Step 3 is to notice how many of the five bars, which are 5/6 of the six bar, it takes to equal the two six bars, which are each 6/6. When you line them up together, you can see that to equal two whole 6/6s, it takes two whole five bars and two single units. Those two units represent 2/5 of the five bar.

2 divided by 5/6 = 2 2/5

Note that this model takes a LOT longer to explain than it does to do. I'd recommend just modeling the actions with the kid, not necessarily all of my blather that engulfs the simple and clear actions with a bunch of verbal baggage. The kid can see perfectly well what you're doing, and doesn't have to hold all the explanations in her mind for her mind to *know* it, if that makes sense. It's the way that when you read to a kid, you're not all, "Here's the subject of the sentence. It's a pronoun, but that's just because there's a noun that we just saw in the previous sentence, so we don't want to see that again so soon. And here we have a helping verb, which comes before the action verb. You know that next you'll see the direct object, unless you have an indirect object first. Oh, no, actually we've got a prepositional phrase next! How fun!", but nevertheless the kid internalizes all of those patterns well enough that when she's old enough, she'll know that something is wrong with a sentence that lacks a verb.

If your kid is just beginning to learn dividing fractions, you can do lots of these models, as many as the kid can stand, before teaching the algorithm as the tricky shortcut that gives you the same answer. Syd, however, had already been presented with dividing fractions, and was just struggling to remember the algorithm, so every time she completed a problem using the model, I then had her rework the problem with the algorithm to show her that they give the same answer, and to reinforce the connection between the two. It still takes more time and more practice until the algorithm is second nature, because it is NOT an intuitive one, but it all goes easier when it makes logical sense!

Monday, May 15, 2017

Work Plans for the Week of May 15, 2017: The Ancient Olympics, Medieval Manuscripts and the Temperature This Week

The kids had a lovely, short school week last week--or, at least, I suppose they did, as I was busy all week finishing up a giant etsy order. They completed all of their school work, both the book work and the projects--
Syd wrote her name using the futhorc.
--helped me outside when I asked (both my perennial sunflower and my thornless raspberry, both of which leafed out and grew when I first planted them exactly the way the instructions said to, are now wilting. I have no idea why, other than possibly that plants hate me?), and still had loads of time for their own play and projects. Syd's birthday brought her a bounty of new toys, so she, in particular, has been quite busy grooming her ponies and having tea parties with her dolls and dressing them for outings, etc.

Matt helped me finish packaging the last of my etsy order over the weekend, so that I was free to enjoy a happy Mother's Day with my family. We did all of my favorite things: an indulgent breakfast in bed (both the kids are now competent cooks, so a Mother's Day breakfast in bed is now quite the pleasant experience), nerdy presents (a wine bottle light, and Fantastic Beasts and Where to Find Them, AND this DIY speaker kit which claims to require a full two hours of soldering--squee!!!); a long hike--

--a movie (Guardians of the Galaxy 2, FINALLY!), and then I lounged and read while the rest of them cleaned house. And THEN we ordered pizza and started to watch the latest Doctor Who as a family, but as soon as the first corpse appeared I covered Syd's eyes, and then when the pack of corpses appeared I sent her out of the room entirely because after last week's episode, she was too scared to take a shower in the bathroom by herself and we had to leave the door open and keep coming in to check on her--this season is DARK!

So it was a good week, a great weekend, and without a giant etsy order over my head this week is shaping up to be excellent, as well, as perhaps I can get many smaller things knocked off of my to-do list this week, and not just the one huge thing.

The kids' daily work for this week is the usual: typing practice on Typing.com, progress on their MENSA reading lists (we do a LOT of independent reading in our homeschool, because Will loves reading more than anything else, and Syd loves listening to audiobooks more than anything else--might as well utilize those passions!), Wordly Wise 7 for Will (she ought to finish that book within the month, and then we'll take a bit of a break before beginning Wordly Wise 8) and a daily word ladder for Syd (she'll finish her book this month, too, but won't get much of a break before I make her get back to finishing up Wordly Wise 4), a Hoffman Academy lesson and then keyboard practice for both, SAT prep through Khan Academy for Will, and Greek language review, using a variety of sources.

Memory work is the same as last week, with the addition of measurement conversions, and Books of the Day this week include some classics that I thought the kids would enjoy (Will is going to be trying out both Little Britches and National Velvet--I'm sure she'll like National Velvet, but she'll probably end up skimming Little Britches), a couple of short non-fiction books on Ancient Greece, and this book on fairy houses for Syd.

And here's the rest of our week!

MONDAY: In Math Mammoth this week, Will is finishing up her chapter on graphing and data, and Syd is finishing her chapter on fractions, decimals, and ratios. While working with decimals, Syd had a little trouble with figuring out when and where to round. You remember how hard she worked learning to round the first two times around, so we're going to review rounding today, all of us, by playing this game. I like that it requires strategy as well as rounding skills, and I think we'll enjoy it.

For both math and grammar, the kids complete that day's lesson and give it to me. I mark their errors and on that day or the next school day, they have to correct those errors and give it to me again. If there are still errors, we go over them and work them together. Both kids HATE this, and I have no idea why. They act like I'm a condescending jerk just because I want to walk through multiplying fractions or identifying helping verbs with them. Will's strategy to attempt to avoid this scenario is to throw a giant fit and get a lecture from me and then have to do it anyway; Syd's strategy is to "forget" to show me her work and simply continue the next day with the next lesson until I realize that it's been days since I've seen her answers and go find them and mark them all at once. That's what she did last week for grammar, so for the first three days of Junior Analytical Grammar this week, I've told her exactly which lesson she needs to check and rework the incorrect answers to. You'd think she'd realize that she'd do better on subsequent lessons if she's just let me check her previous work, but both of my children are as stubborn as their father.

Will only has grammar review on Tuesdays and Thursdays, so on this day she and I work a mind bender. They're VERY fun, and in a couple of weeks, when Syd finishes Junior Analytical Grammar (if we stay on track this time...), I might have them both working mind benders three or so times a week during the break, they're so fun.

Even though both kids learned cursive years ago, neither every really uses it in their daily writing, so I have to enforce daily writing in cursive to keep their skills up. Will hates journaling and story prompts, so occasionally needs a break from them during which I just let her do cursive copywork. Currently, she's copying Seamus Heaney's translation of Beowulf for five or so minutes a day. Syd usually loves creative writing, and is in fact in the middle of writing a story entitled "Shopping Shipwreck," but is taking a break from that this week to write the thank-you notes for her birthday gifts. Two birds with one stone!

We're still pausing Story of Science so that we can catch up to it in the history of Greece; on this day, we're reading about the gradual settling in of the Dorians and Sea Peoples after they drove the Mycenaeans away from Greece; those pirates and barbarians are now the Greek people, and are starting new traditions in their new cities, one of the most interesting of which is the Olympics. We're actually going to see Olympia, Greece, next month, so you can bet that we're going to pay special attention to this lesson! On this day, the kids will listen/read the chapter in Story of the World volume 1, and then do the quiz orally with me, and the mapwork on the AAA map of Greece that we'll be taking with us. I got pissed at Will last week when after I'd told her twice to use a thin-nibbed pen and write small so that she didn't write over anything else, she used a too-large marker and obscured part of our planned route by scrawling "Mycenae" over their former city as well as the highway and 30 miles of surrounding countryside. Hopefully, even though she behaved like an obstinate jerk about it at the time, she'll take care to write smaller this week. I'm an obstinate jerk, too, so if she doesn't, I have no problem with begging a second map from AAA and then making Will do all her work over again.

We had our lesson on the physics of temperature last week, so this week the children are running an experiment to explore how various natural insulators affect temperature. We have three outdoor-friendly thermometers, which the children will install in various locations outside (one needs to go in the garden soil, and I have suggested that the inside of the chicken coop might be a good location for the second, but the third is dealer's choice) and then record their readings three times a day through Thursday. It would be a bit much to ask of just one of them, as we're a little too loosey-goosey in our schedule for two kids to both remember to check three thermometers three times a day, but I'm crossing my fingers that the kids can work out a system between themselves to get the work done.

Syd FINALLY finished all the work for her Girl Scout Junior Scribe badge this week, and attended a webinar on earning the Bronze award, so now she's all ready to go for it! She's meant to be observing her community to figure out its needs, but she knows that she wants to work in some capacity with animals, so she'll be "actively observing" by emailing local shelters and rescue groups and asking them what they need. Understanding the need to do this is a vital life skill--too many people take it upon themselves to do things for non-profits without that non-profit's go-ahead, and then that non-profit is left with, at best, a tertiary need met when a primary need could have been met instead, or at worse, a bunch of crap donations that they have to spend their own time and resources figuring out how to utilize. You should always ASK before you give.

TUESDAY: We were all set last week to make a working thermometer, so that the kids could observe the physics of temperature in action, when we discovered that Syd had used up the last of our clear straws making milkshakes for everyone as last week's cooking project. We stocked up on clear straws over the weekend (at the movie theater, obviously--we don't BUY straws!), and I hid them in my homeschool closet, so milkshakes or no milkshakes, we'll have straws aplenty for thermometers on this day.

Even though we're studying ancient history as part of our science unit (and for our upcoming Greece vacation!!!), the kids also wanted to study Medieval history this semester, and as a former Medieval scholar, myself, I am happy to comply. After spending three weeks on the Anglo-Saxon period (Celts! Beowulf! Runes!), we're finally going to allow Britain to be Christianized, The kids will read the chapter from Story of the World volume 2, then complete the mapwork from the activity book and do the quiz orally with me.

WEDNESDAY: As part of our study of the Ancient Olympics, the kids are going to organize and run a family Olympics on this day, to be held after Matt gets back from work. They'll need to research the Ancient Olympics and include the following components: 1) an opening ceremony; 2) at least five events, at least one of which must be adapted from the original Olympics, and at least one of which must be something creative and modern; and 3) something, traditional or contemporary, to award the winners. There will be some learning, sure, but mostly I think it will just be a fun family evening.

Will and I have a little bit more work to do on the last activity of her Girl Scout Cadette Budgeting badge (she's helping me create the budget for our Girl Scout troop for the coming year), but if we can finish that up before Wednesday, then she'll be free to start a new badge! She has several in hand that she wants to complete, including three retired badges that will be extra fun for her, and look extra interesting on her vest.

THURSDAY: Medieval monasteries are vastly important in the Middle Ages, and I actually have a couple of field trips that I'm planning this month to explore them further. Yes, medieval monastery-themed field trips in Indiana! There are two Catholic monasteries in Southern Indiana, both of which welcome visitors, and our local university's special collections library has a nice collection of medieval manuscripts. On this day, however, we'll be having a lesson on the illuminated manuscripts created in many Medieval monasteries, and then we'll be trying our hands at illuminating our initials. Syd loves to draw, and Will loves to color, so I think they'll both like this lesson and activity.

I encourage Syd to figure out her baking projects in advance, because I don't make last-minute trips to stores, but for the past couple of weeks, she's been choosing her projects based on what (little) we happen to have in the pantry, and I have to say that they've turned out amazing! Two weeks ago, she baked scones with frozen blueberries, and they were the most delicious scones that I've ever eaten, so delicious that she made me more scones, this time with chocolate chunks, for Mother's Day. Last week she tried to make milkshakes with the ice cream that we'd bought to use up the ice cream cones that we'd bought for Syd's castle cake. Instead of making milkshakes, she learned that our Vitamix quickly liquifies ice cream, but she turned it into a kind of milkshake/smoothie by adding frozen bananas and frozen strawberries. Thanks to the fruit, I felt quite justified in having milkshake/smoothie for lunch!

Who knows, then, what she'll come up with this week?

Do NOT let me forget to make the snack for Pony Club on this day! I'm supposed to be Snack Mom for the unmounted meetings, and usually I make something cute and sometimes even horse-themed, but last month, about a week and a half AFTER the unmounted meeting, it suddenly occurred to me, "CRAP! I didn't bring a snack to Pony Club!" Will says that her leader whipped out some cheese and crackers, since it was at her house, and nobody ever said anything to me. I feel like a monster. This week's snack will be extra delicious and even more horse-themed than usual... if I don't forget again.

FRIDAY: By Friday, we're ready to start winding down, and it's not unusual for one or both kids to still be working on something from earlier in the week, so even though I could have added a couple more assignments to this day, I decided to just let it rest with our daily work and the completion of this Junior Archaeologist badge book. If we do finish early and want some more learning, I've got plenty of craft projects and library documentaries that we can entertain ourselves with!

Hopefully, the kids will have been able to run their temperature experiment Monday-Thursday, so that on this day they'll be able to compile, organize, and present their data, and come up with a meaningful interpretation of the information.

SATURDAY/SUNDAY: For the first time in forever, the ONLY weekend activity that we have is Luna's obedience school on Saturday morning.  We could, therefore, take a day trip to one of those Southern Indiana monasteries, or we could stay home and work on the many outdoor projects that I've been nagging the family to help me with.

OR we could stay home and read in the hammock, watch movies in bed, and eat scones. That could be fun, too.

What are YOUR plans for the week?

Saturday, May 13, 2017

Homeschool Math: Use the Decanomial Square to Explore Binomial Squares

If you took algebra in middle school, you probably remember that squaring a binomial makes no sense.

Let's say you've got to square the expression (a+b). You square the first term, take twice the product of the two terms, and square the second term:

a squared + 2ab + b squared.

And you're all, "Umm... okay?" And your teacher is all, "Just memorize it. It'll be on the test."

And you do. And you earn an A on the test. And then you forget what you've just memorized, on account of it makes no sense and you have nowhere to put that information, nor anything to use it on other than more algebra.

Well, there's a deep, dark secret at the heart of Algebra 1, and that deep, dark secret is that the binomial square?

It is REAL:

Will hasn't been asked to square binomials yet, and Syd certainly hasn't, either, so this is something that we're exploring well in advance, so that when each child is then asked to square her first binomial in her math curriculum, I can say, "Oh, that! Remember that we do that with the decanomial square. You remember what that looks like." Takes the fear out of math before the kid even knows there's something there to fear.

To start, I asked the kids to build the decanomial square and then to place the labels that let us use algebraic notation to name each piece of the square. Then, I asked each of them to pick two random squares from the decanomial square, and to place them kitty-corner to each other (kitty-corner, you probably know, is the official, scientific term). Then I asked them to figure out how to complete the puzzle to make a square:

I did have to redirect Syd, as her first instinct was to piece together the sides with many small pieces. I told her that the perfect solution would be just two pieces, one for each side.

And you can see as well as I can what both kids discovered, that it's two identical pieces that complete this square:

If they don't quite notice that these two pieces have the same lengths as square a and square b, they do notice that as soon as I ask them to write down the expression that represents what they have:

You can see in the image above (you can also see that I need to recondition our very old dry erase board) that Will has written the expression correctly: c squared + cb + bc + b squared.

She's written "cb" and "bc" because that's how they're labeled on the square, one in row c and column b, and one in row b and column c. But she can see that they're perfectly identical, so that and her knowledge of the commutative property of multiplication (a*b=b*a) allows her to simplify cb+bc into 2cb.

The simplified expression, then is this:

You can also look at the square that you've made and pick another way to write the expression, one that's even simpler: each side is made of length a + length e, so to represent the square as a whole, you can simply write (a+e) squared.

(a+e) squared = a squared + 2ae + e squared

Congratulations! You've just squared your first binomial!

See, that wasn't so hard, was it?

Friday, May 12, 2017

Once Upon a Time There was a Fairy Tale Birthday Party

Once upon a time there was a little girl who loved birthday parties. Every year she had a birthday party with a different theme, and she got so much pleasure out of making her party fit that theme, from invitations to decorations to games to food, that the whole family loved to chip in and help her, just to see how happy she was.

Of course, it didn't bother her mother terribly much when this little girl grew up some and could do MUCH more of the planning and prep work all by herself!

For instance, guess who baked this entire cake all by herself? Who assembled it and decorated it completely independently?

The birthday girl herself!

Matt carved the watermelon into the shape of a crown, and I assembled the fruit wands:

My plan had been to use those watermelon cut-outs there as the wand toppers but let me tell you--cut watermelon is MESSY! It was dripping sticky juice down the entire wand, and while I'm not squeamish about kids getting messy when they're at my house, the line must be drawn somewhere.

To round out the dinner, we also made a tray of cheese sandwiches and peanut butter sandwiches, all cut out with a crown cookie cutter, and then some chips and mini un-iced cupcakes (from the leftover birthday cake batter). The party guests demolished the lot, so I think they liked it!

When the children arrived, I taught them how to make balloon swords--

--and another kid knew how to make balloon dogs, so we all happily played with balloons for a very long time before I was able to heard them into the playroom for our first game: Pin the Kiss on the Frog Prince:

Matt drew the frog, Will painted it, and Syd drew and cut out all of the kisses. Competitive games stress Syd out, so the kids just took turns for fun, and there were no prizes.

One of my favorite things about Syd's group of friends is how engaged they are. They love everything! Every activity you introduce, they're super into it. Every game you play, they give it their all. And what's more, they're so connected, as well--they love watching every other kid take her own turn, shouting advice as she wanders way to the left of the frog, laughing when she puts her kiss on its butt, congratulating her when she takes off the blindfold, over and over and over, for every kid, for every single turn. And some kids took several turns!

After giving that frog prince many, many, MANY kisses, we broke for dinner, and then came back to the playroom for the game that I had been looking forward to the most:

Yes, we played Toilet Paper Princess!

This game was just about the cutest thing that I have ever seen. We had enough guests to make three groups, each with a princess and two ladies in waiting. The ladies in waiting had approximately ten minutes to dress their princess for the ball, and then we had a princess fashion show.

I had planned on doing this once, but you know we ended up doing it three times in a row. Surprise, surprise--all the little girls wanted a turn at Princess!

And here's the token male, sitting in the corner looking bemused:

This game took a full hour, and after all of that shrieking and giggling I am not ashamed to tell you that I sent every single one of those children outside, taking the dog with them, and told them not to come in until they were ready for cake.

Of course they were all in and out and all around, shrieking and giggling and fighting with balloon swords, but it gave me time to swallow some ibuprofin and sit down in the kitchen with Matt for a while. I'd had a nice, long break by the time the pack of them came barreling in for good, reporting that there'd been some drama with the Freeze Tag game, and I declared that if there were some tempers that needed to be sweetened, then it must be time for cake!

I can't get over that perfect, perfect cake that she made for herself, all by herself:

And her sweet face, surrounded by her family and friends, just having been sung to, just about to make a wish:

She couldn't have had a better birthday--

--or a better bunch of kids to share it with.

I'm curious how her birthday parties will change as she gets older. The last time that Will requested a birthday party, she was nine (and there were also balloon swords at that party, and a kid-decorated castle cake, AND the candles on this cake are the same ones that I made for that first castle cake!). I'll happily have giant birthday parties for Syd as long as she wants them, then, with the sure proof that one day, whenever that day may come, she will no longer want her mommy to throw her a birthday party. I did suggest to Syd, though, that perhaps next year she might want to host her birthday party all by herself, without Mommy to organize the games and demonstrate the craft.

As soon as I said that, though, I bit my tongue in regret. Because sure, I'd have an easier week the week of her party, if I didn't have to do the prep work for games and activities, and an easier day the day of, if I wasn't cutting out a million little sandwiches into cute shapes and making fruit wands and watching yet another balloon sword-making tutorial on YouTube, but to not be there to watch every single kid take her turn at kissing the Frog Prince? To not be the emcee for the Toilet Paper Princess runway walk, for every single princess?

Not having to take double the dose of ibuprofin that night would NOT be worth missing out on all of that sweetness.


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