Hands-on Rounding, or, I cannot Make This Concept Any Clearer

Rounding is just non-intuitive.

Not only do you have to wrap your head around the fact that you're going to pretend that a number is a different number, but you have to remember that even though it's called rounding DOWN, you don't round down by subtracting 1 the same way that you might think that you round up by adding 1 (that's not *really* how you round up, but if you're nine, that might be how you've explained it to yourself).

Oh, and rounding up if the digit is 5? That doesn't actually make sense; it's just a convention to memorize.

I wanted Syd to understand the concept of rounding, not just memorize a rule that doesn't make sense to her, so using this post on hands-on rounding as a spine, we went over it again from the beginning.

The post doesn't mention using a hundred board, but we've relied on our hundred board a lot throughout Syd's entire math education, so once again we began a lesson by having Syd build it:

I've got three sets of these 1-100 tiles, two DIY sets and one for the light table/overhead projector, so I could leave the 100 grid intact and give Syd a second set of tens to use in making a number line between two consecutive tens:

This part was all review, as she had no trouble with any of it.

Syd built a number line between two consecutive tens a few times, each time with me handing her the numbers in between at random. We then reviewed rounding to the nearest ten by noting on each number line which consecutive ten a number fell between, and which consecutive ten it was closer to.

Numbers ending in 5, of course, round up merely through convention, as we also discussed.

To end the activity on this day, Syd and I played a game with two 10-sided dice. One of us was "Rounded Up" and the other was "Rounded Down;" we each took turns rolling the two 10-sided dice, making a number from it, then deciding if that number rounded up or down and giving a point to the correct category.

Although the points go to the correct category regardless of whose turn it is, when it's your turn to roll, you can do your best to build a number that gives you the point. It's tricky, though, because you can't always build a number that goes your way!

I let this lesson settle for a few days while Syd worked on different concepts in her Math Mammoth, then we had another lesson on rounding to the nearest hundred and thousand.

Syd didn't seem confident in building a number line between two consecutive thousands, so I had her do so using the hundred flats from our Base Ten blocks as physical markers, with each hundred written on a torn piece of paper--use what you've got! I then used a domino to mark a place on the line--9,600, say--and gave Syd another domino to use as a game piece to hop to each thousand:

The thousand with the fewest number of hops to get to it, obviously, is the thousand that the number is closer to.

After this, we turned to our light table, and I asked Syd to build another number line between two consecutive thousands:

I used the dry-erase marker to modify the 0-100 tiles to make them into numbers in the thousands (30, for instance, became 5,300), then asked Syd to place them on the number line. She found this a LOT harder than working with a number line between two consecutive tens. Her number line got so wonky, in fact, that I abandoned the tiles work, gave her a different number line--9,000 to 10,000--and asked her to simply draw in the hundreds in between.

As she did so, I noticed that she did not have 9,500 in the middle--actually, it was very close to 9,000---so I asked her to check her spacing. She was VERY not happy with this, because she knew then that she'd made an error, and she HATES making errors.

Aside: That's an attitude that we work on a lot, by the way. I see it as a very destructive type of thinking that will keep her from establishing a strong and persistent work ethic, so I speak constantly of the fact that knowledge and skill do not enter one's brain by magic, but instead require a lot of training to achieve. When one has the correct answers immediately, one is not learning, but reviewing. Learning is the space in which we try to spend much of our school days, I tell her, and we know that we are in that space if we are struggling and making mistakes.

Hopefully one day that will sink in!

Because Syd was tipped off that she'd made an error, all of her will became focused not on finding and correcting her error, but instead on defending it to the death. She insisted her spacing was perfect. I noted that there was only a finger's width of space between each integer up to 9,500, but that the others on the way to 10,000 were really far apart. She decided to deliberately misunderstand me, and began screaming that I wanted her to write everything with one finger in between, and that was impossible. I excused myself to my room, and told her that she should choose another activity, and we'd finish the lesson later. I then read quietly for an hour while Syd screamed the house down in the next room.

Of course, eventually one must finish one's schoolwork if one wants an hour of screentime, and one DOES want this hour, so much, much, much later, Syd went back to work with a good attitude renewed:

I was still pretty over it, so Matt finished the review with her, and then they played the same dice game, this time with four 10-sided dice, with the goal, again, to decide if the number rounded up or down to the nearest thousand:

Afterwards, I quizzed Syd by throwing out more numbers, and she was able to round them all correctly! She was also SUPER happy to do so, because she knew that she was getting them all correct.

Have I mentioned that this child exhausts me? Oh, my word, she exhausts me!

But, of course, so does the other one...

Work Plans for the Week of September 14, 2015: Hawaii!

School last week went reasonably well, even though Syd did spend one entire afternoon melting down over rounding to the nearest thousand. I'm starting to think that these meltdowns are a short circuit of her brain working in the background, however, because when Matt sat down with her in the evening to work on the concept with her some more, she had it completely mastered.

The kids happily read their Books of the Day--

--didn't fuss too much over their memory work, spent the evening in our bomb shelter while air raid sirens blared, and tried out my pattern block stained glass template idea, which, while it worked okay, in the end the kids preferred simply playing with the pattern blocks:

We also managed to spend the last reasonably warm afternoon of the year at the lake, which was just what we all needed.

This week, we're focused on Hawaii, because a vacation isn't fun unless you study for it! I'm also introducing 1941 events in World War 2, finally, so that next week we can immerse ourselves in Pearl Harbor. Memory work for the week consists of the spelling words from last week's Wordly Wise chapter (I think it's going to take us two weeks to complete each chapter--one for grammar, and one for spelling), bee anatomy, the eight major Hawaiian islands, Mandarin numbers 1-5, and, for Will, fraction terminology. I should have included multiplication terminology for Syd, but I didn't take a look at her Math Mammoth for the week until after I'd written the kids' memory work onto our chalkboard, and I'm too lazy to redo it.

New for memory work this week are cursive workbooks for each kid. Syd has New American Cursive book 2 (the secular version), and Will has Teach Yourself Cursive. I'll be asking them to complete one page every day, and neither seem too bummed about it... yet.

Books of the Day consist of books on volcanoes, caves, a couple of animal biographies, and a graphic novel for Will about a Holocaust survivor. Other than a few children's biographies, I'm planning to go very light on the Holocaust, and even then, that reading will be mostly for Will.

And here's the rest of our week!

MONDAY: Math Mammoth should be pretty straightforward for both kids this week, with Will starting a unit on fractions and Syd starting one on multiplication. They've studied these concepts before, of course, so hopefully they won't struggle too hard to extend their knowledge. If something does trip them up, however, we can do the hands-on enrichment of it next week.

The kids' Mandarin class starts this weekend, and while I don't expect that we'll always be working ahead like this, the extra review involved in making flash cards ahead of class can't hurt.

Last week, the kids got a good foundation of what volcanoes are, and why and how they work. We'll be doing more reading/viewing on the subject, but the last volcano activity before our trip is to research the location of the Ring of Fire and mark it on our big world map. Alternately, I actually have a map with volcanoes and earthquake sites already on it, so if we're low on time, we might just put that on the wall and then discuss it. After all, we'll be getting some hands-on knowledge of volcanoes soon enough.

We've got our regular volunteer gig at the food pantry later today. I won't be dropping Will off at the library afterwards as I usually do, as she's in trouble for leaving a library book outside (again), so she'll instead be spending the afternoon doing chores to pay it off. Mwa-ha-ha!

TUESDAY: I mostly want the children to understand that Hawaii once had a monarchy, and that it was overthrown (by non-native citizens), so on this day, we'll be reading and discussing this infographic on Hawaii's monarchy, and watching this documentary on Hawaii's last queen. In Hawaii, I'm hoping that we can visit at least one royal site.

This day is a short one in terms of our own schoolwork, since we've got our homeschool group's playgroup and the kids' evening robotics class. But if you consider that the children are going to be spending two hours at a ROBOTICS CLASS, then you can understand why I'm keeping our own work short. They've got to have time to play!

WEDNESDAY: I messed up my spreadsheet here, when I tried to copy and paste something, so you can't see that Syd has a Friday Zone taping on this day. It's Halloween-themed, so she and I have been making her Halloween costume early, in preparation for it. I'm sure that I'll be happy next month to have it already done, but right now it's kinda stressing me out! She and I will spend the entire afternoon on campus, then, since she's also got ballet there a couple of hours later and a couple of buildings over, making this another short day for our own schoolwork. Good thing that being part of a television production is so educational!

And no, Will wanted no part of that television production. Sigh...

Although we're mostly focused on Hawaii and World War 2, I wanted a couple more enrichment activities to cement our experience visiting the Nina and Pinta, so the kids and I are going to attempt to make these cardboard models. I printed one set of instructions at the regular size, and another set 10% larger, so hopefully we'll be able to muddle them together with lots of cardboard and even more hot glue. Wish us luck!

THURSDAY: The last extra activity that I want the kids to do for Will's Girl Scout Cadette Comic Artist badge is to create a week's run of comic strips, just like they read in the newspaper every day. I'm going to suggest that they collaborate and make it a funny version of their own lives, as many comic artists do, but I won't insist.

We'll be continuing--and ideally finishing!--our cardboard models on this day, and the kids will research and put Columbus' voyage on our world wall map. They've read descriptions of his voyage many times by now, but really being able to see it in context is always the best.

FRIDAY: The kids will put the 1941 timeline cards in their World War 2 notebooks on this day, and then over the weekend Matt will give us a history lecture that unpacks those events. Next week, we'll focus on Pearl Harbor!

That papier mache unicorn head that we began last Friday probably won't be completely dry until this day, so we can work on the bottom of it and perhaps smooth the sides a little more. It might be ready to paint next Friday?

I want the kids to become experts on a few different Hawaiian plants and animals that they can then be on the lookout for during our vacation, so I'll have them doing a few of these infographics in the next couple of weeks.

As for me, I'll be spending my week completing a Fluttershy costume, starting on the whopping seven Crafting a Green World posts that I need to write and schedule before our vacation (as well as the three that I need to write for this week!), working on a commissioned project that I also need to finish before we go, working on Girl Scout registrations that I ALSO need to finish before we go, and deciding if I'd rather spend the time sewing more shorts or the money buying more shorts for Will, who has already grown out of all of her summer clothes.

It's okay to be stressed out, though, because I'm going on vacation pretty soon!

The Nina, the Pinta, and other Kentucky Standards

Okay, Christopher Columbus' sailing ships aren't *exactly* Kentucky standards, but they were waiting for us at the river's edge in Louisville last week, when one of our homeschool groups took a trip two hours south to visit them:

The ships can't sail on the river, of course, so they each have anachronistic auxiliary power to get them where they're going.

This is the hardwood that was used to make the ships. It's as heavy as a piece of concrete that size! These replicas were built in Brazil, because that's where you can still find traditional Portuguese shipwrights. They built both ships using only hand tools and authentic methods

The Nina is the most accurate replica ever built. The Pinta, however, was purposefully built a little larger than the original; the Nina is so small that the Coast Guard won't allow tourists on her upper deck, but on the slightly larger Pinta, we're allowed up.

The Santa Maria, however, is larger than the other two, and so wasn't recreated by the Columbus Foundation at all, except in this model. She'd be too large to visit most of the ports that the Nina and Pinta travel to.

They look like pirate ships, don't they? I was surprised to see that they're black! That's because they're coated in pine tar to make them waterproof.

This is the windlass, used to haul up the anchor. See the holes? You crank that lever down, then put it in another hole and crank it some more.

This cast iron anchor is authentic; it was recovered from a shipwreck.

  

Because I am a nerd, and I have a sense for my people, I somehow managed to discover that one of the crewmembers is a huge Harry Potter fan. We got talking, and then she was like, "I also cosplay. Do you know what that is?"

DO I?!?

And that's how I stood on the deck of the Nina, looking through a stranger's phone at pics of her awesome cosplays as characters from Avatar: The Last Airbender and The Hobbit. And I forced her to listen to me tell her all about Krrish, my favorite Bollywood superhero film series.

Oh, and she also has a sweet lycra mermaid outfit.

After we got our fill of the Nina and Pinta, it was less than a mile's walk down the riverwalk and through downtown to another Kentucky favorite, the Kentucky Science Center!

There was a new area, with a new climbing apparatus, since our last visit, and I hesitated outside of it, uncertain if it was for toddlers or for everyone. A docent passed by, so I asked him.

"Oh, it's for everyone!" he assured me. "It's weight-tested to support even adults!"

So obviously the next time he passed by I shouted down to him from the top of the structure, so that he could wave at me and give me the thumbs-up.

The Kentucky Science Center gets mad props from me for having many exhibits that I've never seen before in any hands-on museum--and you know I've been to my fair share of hands-on museums!

There's this area with mirrored panels on wheels so that you can make your own mirror maze:

There's this area where you can hook up a variety of components to make your own gravity-powered roller coaster:

There's this clever gross motor skills area, formed by drilling giant eye hooks into a pergola-type support, tying rope to each eye hook, and then covering the rope with pool noodles. The kids ADORED it:

And there's this ball ramp set-up in which each of the components sticks to a giant magnet wall:

It was a whirlwind day, especially considering we had to walk back to the car and drive two hours home again in time for the kids to make their evening robotics class. As soon as I'd dropped them off there, I immediately had Matt take me to a Mexican restaurant so that I could eat tortilla chips and bean burritos and drink both my margarita and most of Matt's, as well.

Fitting recovery from a day spent with sea and science, yes?

Field Trip: To the Zoo!

It's been a long time since we've been to the Indianapolis Zoo, and yet it's still a familiar, welcoming place to be. We still know all the shortcuts to all the drinking fountains, the best shady benches, and the fact that you should really go into the exit to the Forest exhibit and out the entrance, because otherwise you'll have to backtrack later.

Of COURSE we sat in the splash zone. It's just not the zoo if you don't smell like dolphin all day!

The orangutan exhibit is actually new since our zoo membership lapsed, although during our family overnight here, we visited the "backstage" area where the orangutans were already in residence. 

This meerkat's incredible dedication to its guard duty cracked me up, and also, Syd still100% remembers her traumatizing experiences watching Meerkat Manor as a toddler. 

We were in the Plains area, and actually at the cheetah exhibit, less than 48 hours before one of the Cheetahs made its Great Escape. All we saw, however, were cheetahs like sleepy kitties drowsing in the shade, but this elephant was up to pretty great things:

This is the flamingo that nearly bit Will when she reached under the fence to steal a dropped feather. Perfectly within its rights, I say.

It was a super hot day, and it wasn't just the elephants who enjoyed the water!

Sleepy koala! Long after the kids had grown bored with the koala, we stayed to eavesdrop on this older woman who was experiencing the happiest moment of her life to date there. Every time the koala twitched a sleeping limb, she'd squeal and then start cooing to it in baby talk. It. Was. Great!

My favorite place to watch the dolphin show is in the underwater dome.

See that blue blur next to Will's ear? That's a blue morpho, fluttering around looking for a landing spot. See the looks on the kids' faces? That's each of them desperately wishing for the butterfly to land on her.

Winner!

Seriously, Syd was the butterfly whisperer on this day. I told her that she must smell like fermented fruit.

Will was SO stoked to spot this bee. The kids are going to add it to the citizen scientist program's registry on Friday.

Both of these kids are VERY good at petting dog sharks.

I, personally, don't really love zoos--observing animals in captivity bothers me--but both kids have always adored them, and therefore zoos have always been an important part of our curriculum. I try to think of the zoo animals as heroes for their species, sacrifices that are here to teach compassion and conservation, and for my kids, at least, they've done their job in spades. Both of my kids are very aware of the plight of animals in a world overtaken by humans, and they, at least, will grow up to be adults who always have that in mind in the course of all of their decisions.

Even if Will says that she no longer wants to be a zoo worker when she grows up. Now, apparently, she wants to be a pilot.