Educating Risa

Last Thursday, during our “week off workbooks”, the boys and I headed to the Royal Tyrrell Museum of Palaeontology in Drumheller, one of our favourite places. It was a lovely day, and I was excited to see some new exhibits: ‘Alberta Unearthed’, featuring 25 of the most significant fossil finds in Alberta in the past 25 years (i.e., since the Tyrrell opened, in 1985); and ‘Women in Palaeontology’. The best of the submissions from last year’s Prehistoric Art Contest for kids were also on display, and the boys found these quite inspiring. (For details on this year’s contest, see here).

We began our day with a stop at Horseshoe Canyon a little before Drumheller, in what seemed like gale-force winds. The badlands landscape is always worth the stop, IMO:

After saying hello to the family of ceratopsian statues outside:

We headed straight for the new Alberta Unearthed exhibit. I really enjoyed it. Some of my favourites were the 62-cm (about 25-inches) across ammonite; that’s my iphone in the second pic to give a sense of perspective. The pictures don’t do justice to how iridescent it was. Imagine the shiniest penny ever, with glimmers of green and reds and gold. Simply stunning.

I also liked seeing the ‘Black Beauty’ skeleton. This is a T Rex that has been coloured by the mineral manganese seeping into the bones. One of the most distinctive dino skeleton fossils anywhere:

The kids were surprised at how big some dinosaur’s eggs were:

My very favourite fossil was this almost entirely intact Gorgosaurus:

I’ve never seen a better preserved claw:

And I loved the details about the find on the display board, with the highlighted / captioned sentence: “Nineteen people and two all-terrain vehicles were required to flip this specimen…”

Up next was the ‘Women in Palaeontology’ exhibit along a corridor:

It began with Mary Anning, as you’d expect:

But quickly moved on to unfamiliar (to me, anyways) names, like Englishwoman Mary Ann Woodhouse (wife of Gideon Mantell; she was the finder of the famous iguanadon tooth, as well as illustrator of his books); German Tilly Edinger, founder of palaeoneurology—study of fossil brains; and Canadian-born Karen Chin, the world’s leading expert on coprolites (fossilized poop).

It wasn’t the most kid-friendly (hands-on) part of the museum, but I talked to the boys about this section in great detail over lunch. Led to some interesting discussions about the nature of prejudice, the accuracy of ‘history’, the downplaying of contributions to world culture/knowledge from various groups (women, people of colour, non-Christians), etc. Daegan was so taken by the injustice of it all (‘Why do I know Gideon Mantell’s name, but not his wife?’) he told Jim about this display when we got home. Of course, lunch was also spent on lighter matters, like how to make letters of the alphabet out of french fries.

After lunch we spent some time with hands-on displays:

and even made our own hands-on display. Here’s Gareth using this microscope originally aimed at a mite on a midge trapped in amber to check out his new carnotaurus toy:

One of my favourite hands-on displays shows the role of camouflage in the evolutionary process. It’s simply harder for a predator (Gareth) to catch the camouflaged (red) butterflies among the red flowers, giving them a better chance at reproducing (a mix of yellow, orange, and red butterflies light up):

Total catch:

We also spent quite a bit of time checking out the best submissions to last year’s Prehistoric Arts contest. Daegan wants to enter this year:

This was the overall winner in the upper grades category. Impressive, no?

We then did one last tour of the museum, hitting some of our favourite spots:

Despite being through this museum several times in my life, I find something new every visit. On this trip, I learned why the K-T Boundary—the dividing layer of rock above which dinosaur fossils are not found—has a K in it. Since it divides the Cretaceous from the Tertiary period, shouldn’t it be C-T, not K-T?

And both boys spotted this display, of a tooth coming in in a dinos mouth. No doubt teeth are much on the boys’ minds lately, with Gareth recently losing his first tooth, and Daegan getting his orthodontic palate spacer appliance in on Tuesday:

On the way back to the car, after saying goodbye to the dino statue family:

Daegan found a cricket (grasshopper?), which he shared with Gareth, pointing out its long ovipositor, and beginning to lecture us about how the females use this in fall to lay their eggs deep in the ground to survive the winter. I was reminded once again of Daegan’s on-going dilemma: Should I be a palaeontologist or entomologist when I grow up, Mom?

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This past weekend the family took part in one of many free “Alberta Arts Days’ celebrations around the province. We were at the Louise Riley branch of the library, where Calgary’s own ‘Birdman’, Andrew Stiles, put on a workshop. (You can read more about him at his blog here.) It was fantastic! He began with a short slide-show presentation on birds in the Calgary area, and how his own love of birds, and building birdhouses, began. The kids were fully engaged by the great photos and the little tidbits and stories Andrew told. We then headed outside to build our birdhouses. Here’s ‘The Birdman"’ showing the kids a prototype of the boxes they’d be building, and explaining which pieces of wood (pre-cut) to start with:

I really liked how he got the kids making the birdhouses themselves. Over the course of the next hour or so, the boys used a hammer, a saw, a file (to smooth the rough edges) and even a power drill!

Gareth found it easiest when Jim would get the nails started:

The Birdman had boards sawn about halfway for the lids. It was the kids’ jobs—with parental help—to finish the sawing. I think this is the first time either of my kids has used a real saw. They did great; all fingers and toes still accounted for!

Here’s the finished product:

And the boys labelled and decorated it afterwards. Gareth even drew a cardinal:

While there were enough supplies to build one birdhouse per kid, Daegan and Gareth decided out family should just build one joint house—and it’s not like we’re lacking for birding gear in our backyard. This also gave Jim a chance to help two other young boys who were there sans parents; he actually helped build 3 birdhouses that afternoon. “What a guy!” (said in best Red Dwarf voice).

All in all, a wonderful way for our family to participate in Arts Days. Many thanks to Birdman Andrew Stiles, as well as the Calgary Public Library.

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This morning Jim and the boys headed to their weekly Wildwood Running Club, for kids ages 6-12 and their parents. Daegan did this program a couple years ago as well—and the boys are having such fun with it. When I returned from a quick grocery shop, the club was heading back from an activity where they ran through the evergreens that are planted in rows as a windbreak (Edworthy Park is an old homestead of the Edworthy family, one of the first families in Calgary). After each weave through the trees, the kids collected a coloured popsicle stick, until they had all 7 colours of the rainbow. It always amazes me how such simple ideas as this are so well-received by children. My two spotted me and dashed over in a hurry to show me their sticks.

The kids then played a relay game to build the biggest pile of leaves. They broke into two teams, where one kid per team ran to the other end of the field to gather leaves, then ran to put them in a pile, and sprinted back to their team to tag the next runner to go. It is such a lovely environment for the kids surrounded by nature, and I like how the emphasis at running club is on fun and cheering on your team:

They soon told everyone to go and gather leaves all at once, in a big pile. Charge!

Once a fair-sized pile was built up, they called all the kids in for the big finale. Everyone pick up a big armful of leaves from the pile…

And…..wheeeeeeeeee!!!!

Needless to say, the kids loved this. So one more time everyone…..wheeeeeee!

The boys love this program. The people running it are friendly and helpful, and have the kids doing proper warm-up, longer runs, games, sprints, and so on. They make good use of the resources in the park, with its different pathways, playgrounds (the kids preferred cool down activity!), and nature. No running that same route over and over again here! No running endless “laps around the track”  (snore!) we all did in highschool. There’s a nice mix of ages and genders among kids and parent volunteers too. And the cost simply can’t be beat: $15 per kid for 6 weeks of running. Awesome!

I am so appreciative of these sorts of community resources that make raising kids and homeschooling that much easier. So what sorts of things do you take advantage of that are on offer in your community?

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Yesterday the boys and I did a fun activity tying into our learnings about the human body: we made a model of our blood, based on this activity an acquaintance of mine did with her daughter. I began by asking the boys, “What is blood?” and we attempted to find a reasonable model for it. “A red liquid” said Gareth, so we got out some water and red food colouring:

“That’s too watery…too thin,” said Daegan. So we tried some other red liquids, like paint and ketchup. We thought they looked closer to blood, but I told them boys there was a problem with all 3 models: blood was more complicated than this, and not quite a ‘simple red liquid’.

I then posed a different question, and got out 4 empty bowls and blank labels: What is blood made up of? Gareth quickly said, “red blood cells”, so he got to measure out 1/2 c. of ‘red blood cells’ (red hot candies).

Daegan then added “white blood cells”, and put 5 of them (dry lima beans) in a bowl:

Gareth: “Those things…you know…those things that stop you from bleeding when you get a cut. I just can’t remember their name.” Platelets, I reminded him. One Tbsp of platelets (dry lentils), please!

So we got to this point, but the boys were stumped as to what the missing component of blood was:

I told that that if my blood was like they modelled so far, it would have a hard time moving around in my body—all the parts we have so far are solids. “Water!” exclaimed Gareth. “There’s a watery part to blood!” “Oh, plasma!” added Daegan, finishing the thought. He poured out 1/2 c of plasma (light corn syrup). (Note: I kept all the ingredients hidden in the kitchen until the boys came up with the corresponding blood component. I was curious to see how much they had learned from our readings and DVDs):

So now we had a pretty good answer to my earlier question:

And all that was left to do was combine them. After explaining to Gareth that no blender was required—and in fact, if we blended it all together as per his suggestion we’d end up with a misleading model, as he’d see in a moment—the boys mixed things together:

Yielding:

I then asked the boys why blood looks red. “Oh, it’s because of the red blood cells in it” quickly grasped Daegan. “That’s right,” I said, adding: “The liquid part of blood—the plasma—is in fact a slightly yellow-ish clear substance, like our corn syrup,” (which in retrospect I wish I had added some yellow food colouring to). We compared this again to our original red water/red paint/ketchup models, and I thought we were done.

“But other things can get in blood,” said Gareth. “Like germs.” So off I went to the pantry to find a germ model, and came back with a couple green split peas. “Or dirt.” said Daegan. “You can get dirt in your blood when you get a scrape.” Back again to the pantry for a chocolate chip, to be sacrificed in the name of science.

The boys put the germs and dirt in the blood, and then made the white blood cells attack (complete with all kinds of sound effects!):

(Siren wails!) Attack! Munch! Munch! Slurp! Slurp!  

I hope you have fun trying this activity at home. I included lots of detail in this post—yes, perhaps bordering on the pedantic—for a few reasons. I wanted to show you how easy it can be to adapt an idea you see elsewhere for your own home. I included some Socratic-type questions (my natural and preferred ‘teaching style’); I incorporated other skills into the activity (measuring, pouring); I ran with the children’s suggestion about germs and dirt though that was not even on my radar originally. Have fun making this activity work for YOUR kids in YOUR homeschool, and if you put a different spin on it, drop me a comment or send me a link to your blog!

On a related note: A few days ago, we’d watched the Bill Nye DVD on this topic—Blood and Circulation—which contains an outstanding song Blood Stream, based on the B-52s hit Love Shack: “blood stream, baby, blood stream…”. You can see the Bill Nye version here. The boys asked me to play them the original B52s song, which I did during our ‘gym time’ when we were playing musical statues (i.e., freeze when the music stops), and it was a wonderful ‘rabbit trail’ to follow. Hands on activities, candy, AND fun music from Mom’s youth? No wonder the boys are having so much fun with this human body unit!

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My friend Alicia, an amazing and inspiring homeschool Mom and published poet, is offering a free 10-week online course called Poetry For Kids. You can find this first week’s lesson and suggested activities here. This week’s lesson is focused on cliches, and trying to find fresh ways of saying things / evoking imagery in one’s poetry. The boys and I did the “fill in the blank” cliche-busting exercise, and came up with:

It was a fun exercise to do, and while not every answer quite ‘worked’ for me, some of my kids’ suggestions surprised me. “Soft as oatmeal”, “chickadee days” and a “Mary Poppins ending” all create a clear image in my mind. What are your favourites? (And yes…all the ‘butt’ related answers came from the 6-year-old. Sigh.)

Hope you get a chance to play along with some of the Poetry For Kids activities. I am very appreciative when folks offer up some activities from their area of expertise, and even more so when their area of expertise is one of my areas of weakness. So thank you, Alicia, the the poetry  course. I’ll stick to math.

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A couple days ago I learned of a new-to-me website called Top Documentary Films (link here), and on it I was thrilled to find The Story of 1, a math documentary featuring Terry Jones (of Monty Python fame) that I’ve been looking for for a while now. (Update: If the previous link is no longer working, try here, at the Documentary Heaven website; again free). It was superb! Both boys found it entertaining and educational (yes, even the 6 year old), as did I. The video takes us on a journey through the history of numbers one (and later on, zero), from the spoofed prehistoric 1 climbing out of the primordial soup (the boys giggled away at that part!) through the Sumarians, Egyptians, Greeks, Romans, Hindus, etc. through joining up with 0 in the modern world run on computers. There was lots of humour, from the titles of the segments “1 becomes a Greek God”, “1 joins the Army” (Romans), etc. to comments like “the gift the Ancient Sumerians gave mankind: the chartered accountant!” I loved learning about the Aboriginal tribe with no concept of numbers beyond ‘one’ and ‘many’; where the word ‘bankrupt’ comes from; how the term for the modern numerals (‘Arabic numerals’) is misleading, as although they did indeed come to Western Europe via the Arab world, but they were the brainchild of the Hindus; and the explanation of binary numbers…well, it was so good the boys and I were inspired to try it ourselves. (More below). Whether your thing is math, history, or corny humour—and whether you and 6 or 96—there is something in this documentary for everyone. My highest recommendation!

Daegan got a lot out of this video, and was inspired that night to practice drawing different numerals: Egyptian, Roman, and modern ‘Hindu-Arabic’:

And tonight the boys and I replicated the activity done during the documentary, in which mathematician Marcus du Sautoy explained binary numbers to Terry Jones using egg cups. (We used washed fruit cup containers). I started off by setting up our usual base 10 system (in blocks) beside binary, or base 2, cups:

Let’s begin where it is easiest, in the ‘tens’ place (second from the right in the blocks). Notice that as you move to the left (get larger), each place value increases by a multiple of 10. The hundreds are 10×10 (or 10-squared, or 10 to the power of 2); the thousands are 10x10x10 (or 10 to the power of 3), and so on. It is similarly with with binary, or base 2 system: each place value (‘cup’) to the left increases by a power of 2. 4 is 2×2, 8 is 2x2x2, 16 is 2x2x2x2, etc. Note too that we can express 10 as ‘10 to the power of 1’ and 2 as ‘2 to the power of 1’. The limiting case in both systems—the ‘ones’ or units as they are now more often called—is the base to the power of zero. Anything to the power of 0 is 1. (It’s one of those weird quirks of math; if this bit is fuzzy don’t sweat it).

Now, we’re all quite sure that every whole number we can think of can be expressed in our base 10 system, using the digits 1 through 9, with a 0 as a place value holder. But would you believe every number can also be expressed in binary, using nothing but ones (for a full cup) and zeroes (for an empty cup)? I know the boys didn’t believe it, and it is far from obvious: these cups are labelled 1, 2, 4, 8, and 16. How the heck do I make 22? Or 14? Or 3, for that matter?

So we made a chart, with the ‘normal’ base 10 numbers on the left, and the way we can express those numbers in binary notation—using nothing but ‘1’ and ‘0’—on the right. Here’s the completed chart (again, don’t worry if this doesn’t make sense yet—it will! Even my 6 year old was able to understand this!):

We then started building numbers by putting eggs in the appropriate cups. 1 was simple—an egg in the 1 cup—and looks the same written in binary as base ten: ‘1’. The picture below shows 2, which we’d write in binary as 1-0 (say ‘one-zero’, not ‘ten’); again, 1s show the ‘cup’ or place value filled, zeroes mean that place value is empty:

And 3, or 11 (‘one-one’) in binary; both the 2-cup and 1-cup are filled because 2+1=3.

And 4, or one-zero-zero (100), along with a hammy Gareth:

Can you figure out how to make 7? Yup—it is 4+2+1, so fill those cups for 111 (one-one-one):

So what number does 1010 represent in binary? If you said 10, congrats—you’ve got it!:

We continued on this way, and soon the boys felt confident enough to record the binary numbers in our chart, as well as create them:

I made a video of the boys building numbers 12 through 17 in binary (I’ll add it when I figure out how!) And yes, that’s the 6-year old rattling off (out of shot) the binary representation of 13. I am utterly amazed at Story of 1s ability to make binary numbers accessible to a child this age!

We ended the session by me asking the boys what the biggest binary number they could currently make (with 5 cups, or place values) was, and they quickly sorted it out. Gareth said it would be written “one-one-one-one-one” (11111) and Daegan added it up: 31. (16+8+4+2+1).

Who knew egg cups could be such a useful math manipulative, eh?

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I came across a new way to practice your times tables, based on a honeycomb shape with all the different products (using factors from 2 to 9) in it:

All the numbers (products) have a unique answer (factors), except for the shaded middle row which have 2 answers apiece. So the student ‘sweeping’ the grid would start on the top row: “2 times 2” “2 times 3”…until the shaded row “2 times 6 and 3 times 4” “2 times 8 and 4 times 4”….to the end “9 times 9”. The idea is to have students practice until they can ‘sweep’ the whole honeycomb in 60 seconds or less (though I will de-emphasize speed here.). You can find a video about this game here. And I got the basic honeycomb grid in the picture above here.

Now, I quite like this idea in general, for a few reasons. First, laying it out in terms of answers (products)—there are only 31 of them—simply looks less overwhelming than a traditional times table grid. The commutative property of multiplication is implied—or, to put it in simpler English, a child need only say one of ‘2 times 3’ or ‘3 times 2’ when sweeping over the 6 honeycomb; not both as in a traditional multiplication table/grid. Second, it goes about multiplication from a different perspective, giving the products only. A child with a decent visual memory should quickly learn which numbers are products, and which aren’t: one simply doesn’t need to worry about 47, for example, when it comes to memorizing times tables, a fact that is not so obvious to some when memorizing conventionally (7 times 7 is…49? Or is it 47?). Third, I think this grid is quite adaptable: once your child has mastered a fact, you can colour than product in, cover it with a token, etc. I am also going to try writing these numbers in sidewalk chalk on our driveway and see how Daegan does jumping between the products, both doing the sweeping himself and answering questions I fire at him. 

If you try this out with your kids, let me know how it goes. I’ll update this post once Daegan and I have played around with this multiplication honeycomb a bit more and let you know his thoughts. 

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Have you heard about this sale? Scholastic is having a sale on 800+ of their titles, all PDF books to be downloaded for $1. You can find the sale here.  I ordered a bunch over the weekend, including titles like:

Easy Make and Learn Projects: Human Body (we’re doing Human Body this year)
25 wacky and Wonderful Stories that Boost Vocabulary (Daegan wants to learn about prefixes, suffixes and roots, and this humourous book looks perfect!)
Paragraph Power (D is learning to write paragraphs)
Grammar Cop (notice this humour theme so far?)
25 Mini Plays World History (reader’s theatre as an intro to history works awesome for us)
Great Map Games (elementary map skills are another theme this year)
Read Around the World with 20 Great Picture Books (we’re bibliophiles!)
Mega Funny Division Stories (nice complement to MUS Delta)
Math Practice Puzzles (puzzles over dull drill anyday!)
Origami Math (how fun!)
Funny Fairy Tale Math

and the list goes on and on. I used some of the new material as our math ‘warm-up’ today: Gareth did a few pages from an Algebra Readiness book, while Daegan did some math facts practice in this fun ‘riddle’ format. They both loved the new materials.

I was able to make this an even better deal by using the code 10THANKS in the coupon code slot, saving $10 from my order. Not sure if the code is still working—a friend of mine had some difficulties tonight—but worth a shot. Oh, and you’ll have to hurry—the sale ends tomorrow. Happy shopping and I hope you find some fun additions for your homeschooling / afterschooling!

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You know how sometimes things just come together in life, with little effort on your part (and other times you feel like a salmon swimming upstream, upstream, upstream!)? Well, today was one of those easy days, as the boys and I headed off for a tour of a local chocolate factory. This tour was organized by a local HS Mom weeks ago, and the timing could not have been better, with Jim just finishing Charlie and the Chocolate Factory as a read-aloud last week; our watching the 2005 Johnny Depp movie of the same name last weekend; and the 1971 Gene Wilder movie version has just come in at the library so we’ll be enjoying it for tomorrow night’s family movie. I don’t think I’ve ever had an easier unit study!

We had a few minutes to check out the large retail store before heading downstairs for the factory tour:

The boys liked some of the displays upstairs, like this one showing cocoa beans and other ingredients Bernard Callebaut uses in their chocolates:

We then headed down a flight of stairs to a long narrow hallway. There were windows all the way along so you could see the factory, and different parts were labelled (e.g.,  “panning machine”, “cooling tunnel”, and “mould spinner”, which you can see in the centre of the pic (to the left of the fan) whizzing Santa’s around. Yes, Christmas season is such a large one that they are creating chocolates for it already!):

We were able to watch chocolate-covered pretzels being made, first by being placed on the conveyor belt to be covered in chocolate by machine:

Then white chocolate decoration was added by hand:

Lots of the white chocolate ended up on the belt not the pretzels, and it was collected in a bin at the end. I figured they’d melt it down and use it again, but the tour guide said that it would be thrown out as some milk chocolate was cross-contaminating it. Now you know where you can find some tasty treats dumpster-diving if that is your kind of thing!

There was also a collection of ‘reject’ pretzels, which looked perfectly tasty to me. Many were two pretzels stuck together because they went through the enrobing machine too close together. Hungry yet?

The acceptable pretzels were then bagged, again by hand:

On the other side of the hallway were pictures and captions explaining various steps in the chocolate-making process. Gareth wanted me to take a pic of this large bunny as it reminded him of Bugs (we’re also in a Looney Tunes phase right now). I learned they hold the mold closed with magnets, and you can see the little circle inserts on the edges where the magnets would go:

On the way back upstairs I asked the boys to stand by the carved chocolate inukshuk for a pic, and they hammed it up in a predictable way:

There were free samples as well (surprise! they disappeared too fast to get a pic!) and I bought the boys a small treat each: their ages. (Despite looking all dreamy-eyed at the 9, upon arriving at the cash Daegan decided he’d rather have a dark chocolate bar with hazelnuts. Fine by me, and cheaper too! ):

The tour was quick, and the boys enjoyed it. It was also uber-popular with local HSers (how many of us were in that hallway? 40? 50?) which made it hard to hear the tour guide. Jim said he would like to go sometime and the boys are keen to go back (more free samples!) so perhaps we’ll try to arrange another smaller showing. Thanks again to local HS Mom Jessica for arranging this! I feel so grateful to be part of such a strong and generous homeschooling community in this city!

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The boys and I have been working our way through the simply fabulous list of “living math books” from Julie Brennen, who runs the LivingMathForum e-mail group. You can find the list of books, organized by topic (addition, fractions, geometry, etc.) here. And what is a “living book” you may ask? A “living” book is one in which the author has a voice and a passion for the subject: a picture book, story, novel, or even text argued from a single viewpoint; it is not a “neutral voice, just-the-facts-ma’am textbook”; neither is it a patronizing ‘dumbed down for children’ book. It was Charlotte Mason who coined the term, and discussed its opposite, which she dubbed “twaddle.” Google away on those terms for more info, or read this helpful post here. We’ve enjoyed several living math books and series over the years (see here and here and here), and our most recent ones that stick out were Ten Times Better, by Richard Michelson; and The History of Counting, by Denise Schmandt-Besserat.

Ten Times Better turned out to be a far better book and better fit for our family that was apparent from the cover. I’d gotten it out of the library ages ago, and it had laid around, unread—until I got notice this week that it was due back. When I finally got around to reading it aloud to the boys as part of our math lessons that day, we all loved it! It is a series of playful poems (and playful artwork!) featuring different animals, with the first animal saying what he/she thinks the best number is, and why. And the second animal saying, in effect, “Oh, yeah? This ten-times-bigger number is better!” So the book starts with an elephant singing the praises of ONE (as it has one trunk), and a giant squid saying TEN (as in tentacles) is clearly better than one! And on it goes with very logical choices for the animals: a 3-toed sloth, a 9-banded armadillo, a giraffe with 70 spots on its neck. And my children’s favourite animal and line of poetry: “I have 60 teeth” says crocodile, “I’m a great  masticator. (That means I chew first, and ask questions later.).” A delightful book for kids learning multiplication and into animals.

The History of Counting was a book that caught Daegan’s attention; Gareth half-listened as he played on the floor nearby. It does exactly as its title suggests, outlining some of the major steps in humankind’s “invention of counting”, from using pebbles / physical markers (counting without numbers), to body counting (“1 is left little finger…11 is left neck…16 is right ear” up to a very limited number: 28), to using different words to represent the same number of different things (like we use “twins” to mean two babies who share a womb, but “duo” to mean two people in other contexts, like music), and so on. We visit the Sumerians (whose ‘base 60’ lives on today in our number system: 60 seconds in a minutes, 60 minutes in an hour, 360 degrees in a circle),  Egyptians, Phoenicians, Greeks, Romans, Arabs, Hindus, etc. up to modern day arabic numerals and the importance of zero and place value. Daegan was particularly engaged with the section on Roman Numerals, and the way the book showed their severe limitations when it came to computation. This is a very abstract concept for a 9-year-old, that’s for sure—understanding why place value was such a big leap over Roman Numerals—but attempting the addition problems in the book:

1084+1797

vs. the same numbers written in Roman Numerals:

MLXXXIV + MDCCXCVII

drove the point home. And even more so when I suggested he try multiplying those numbers instead of adding them! Happy reading!

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