My Daughter and I Play a “Math Game”

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Most all games we play (if we dig deep enough) are, in fact, math games or games that require some kind of mathematical thinking. Then there are games like Juggle, a spatial and logical game with a bit of computation, that have the explicit purpose of engaging us in and learning more about mathematics. Juggle is the game we play on this occasion so I set the timer to 45 minutes and we begin. As I watch my daughter interact with the game and respond to complex situations, there are a few things I notice.

Patience – Early in the game, when my daughter placed a piece in a place that would not allow her to complete the board, I wanted to say something and explain her error. But I wondered if it would be better if she discovered it rather than me instructing her. On her next turn she immediately removed the piece and fixed her error. After that, she was careful about not repeating the misplacement with other pieces. Isn’t that the result I wanted all along? And it happened without my interference, without me turning a game into a lesson, without me (in her mind) trying to show I know more than her. Sometimes, the best way to respond to a teachable moment, is to keep my mouth shut and observe. There are certainly times to intervene but this was not one of them.

My Strategy is Not Superior to All Others – I have a way of playing Juggle that I think is the best way. It’s logical and seemingly effective. So, everyone should use it. Right? Well, again I resisted my urges and did not compel my daughter to use the same strategy. She chose a different route and we played to virtual tie. Was luck on her side? That can happen in this game. But I don’t think that was it. Her strategy was flexible, responding to the results of her dice rolls whereas mine was more rigid, trying to make the dice rolls conform to my strategy. Neither approach was wrong but there is clearly more than one route to success and because chance is involved, the best strategy may be one that not only responds to your strengths but is situational. A discussion of strategy after a game makes sense but trying to impose my strategy before or during the game would have been counterproductive.

Some Games Should Have a Time Limit – In the Math Pentathlon tournaments, there is a 45 minute time limit for each game. One purpose is that that hundreds of kids need to get through 5 games in one day. But it also worked well for us. We didn’t get fatigued, bored or frustrated as we might if the game dragged on. We gave ourselves a 5 minute warning which worked beautifully as our tactics were different in the last few minutes. I’m not saying that all games should have a time limit, in fact, there are cases in which adding the element of time makes children feel rushed and discourages thinking. We should dissociate speed from learning mathematics but time periods can be used, with care, when considering a reasonable stopping point.

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What Does it Mean to Do Math?

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MIDDLE SCHOOL MUSINGS #1

The GURPS Basic Set which contains rules for the paper and pencil roleplaying game designed by Steve Jackson describes an ability that you can bestow on a character you are creating.

Lightning Calculator – You have the ability to do math in your head, instantly. If you have this talent, then you (the player) may use a calculator at any time, to figure anything you want – even if your character is fleeing for his life at the time!

This description seems to imply that doing math and calculating are the same thing. Do you agree or disagree? Make your case.

I Can’t Carry Anymore!

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Encumbrance, in role playing games, means how much you can carry.  This is usually determined by the weight of the items you are carrying.  A common definition of encumbrance is “a burden” and for most tabletop role playing game enthusiasts, it’s an apt definition in more ways than one.  So, it’s often ignored.  I mean, who wants to limit how much of the dragon’s treasure you will bring back to your own den?  In role playing videogames, it often can’t be ignored because it’s an integral part of the game.  Champions of Norrath (2004) attempts to give players the best of both worlds, a limiting factor for realism and an unrealistic way to horde your winnings.

Champions of Norrath is an action oriented role playing videogame.  The action comes from hitting and shooting things while the role playing comes, in part, from collecting gear to improve your character’s performance.  Often when I compel my warrior, Morg, to pick up something, he will bleat, “I can’t carry anymore!”  In which case, I transport Morg to the store and lighten his load in exchange for gold coins.  In this game although weapons, armor and other equipment have weight, gold coins do not.  This is a treat since Morg is currently holding 1,114,064 gold coins.  But it’s also a bit silly.

Grade 6 Content (6.NS.B.2)

Investigate

Q1: If 1 gold coin weighs 1 ounce, what is the weight of the gold Morg is carrying in pounds?

Q2: If a car weighs 3,000 pounds, about how many cars would it take to equal the weight of the gold Morg is carrying?

Key:

If 1 gold coin weighs 1 ounce, then the weight of 1,114,064 gold coins is 1,114,064 ounces.  There are 16 ounces in a pound so,

1,114,064 ounces / 16 ounces per pound = 69,629 pounds, the number of pounds in gold coins that Morg is carrying.

If a car weighs 3,000 pounds then Morg is carrying,

69,629 pounds / 3,000 pounds per car = the weight of more than 23 cars in gold coins.

That’s one way to bury the local cutpurse.

No Squares Here

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RECOGNIZE AND CATEGORIZE SHAPES – Grade 4

Everyone wants to count triangles in this figure but what about rhombi, parallelograms and trapezoids? Hexagons and pentagons? Dodecagons anyone? The abundance of parallel lines make this a good figure for 4th graders to study, both as a review of some of the shapes addressed in previous grades and as an opportunity to classify quadrilaterals based on the presence of one or two sets of parallel lines.

2.G.A.1 – recognize triangles, quadrilaterals, pentagons and hexagons

3.G.A.1 – recognize rhombi as examples of quadrilaterals

4.G.A.2 – recognize parallelograms and trapezoids* by their attributes

Investigate

Q1: What shapes do you see?

Q2: How many of each shape are there? Count all same sized shapes as one shape. [For example, there are 4 different sized triangles.]

Q3: How would you organize each of these shapes into categories?

Q4: How many categories do the rhombi belong to? Make your case.

*Although students are composing trapezoids as early as grade 1, it’s not until grade 4 that students are considering its defining attributes. Use the inclusive definition of the trapezoid, a quadrilateral with at least one set of parallel sides.

How Tall is a Giant?

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INTRODUCTION TO SCALING – Prerequisite for 5.NF.B.5a/b – This lesson addresses only one dimension when considering scale thus it may be used as a precursor to thinking about multiplication as scaling using a pair of factors.

CONTEXT – The height of a giant can vary greatly.  The evidence of this comes from Giants, a tabletop RPG supplement written by Bruce Humphrey and published in 1987 by Mayfair Games Inc.  According to this “reference for the society of giants,” there are many races of giants and though scholars have scoffed at their physical impossibility, their existence cannot be denied.  Instead of delving into the biology of giants (see Giants pages 5 and 6 if you must), our focus today is on their height.

Titans, 24 feet tall, first giants and progenitors of the other giants

Sea Giants, 18 feet tall, noble and personable giants from the depths

Frost Giants, 15 feet tall, resilient hermits from the icy realms

Fire Giants, 12 feet tall, impetuous and powerful warriors

Hill Giants, 10.5 feet tall, aggressive and stubborn hunters

Investigate

Q1: How many feet taller is each race of giants when compared to a 6 foot tall human?

Q2: How many times taller is each race of giants when compared to a 6 foot tall human?

Q3: How many times taller is each race of giants when compared to a 6 inch tall tufted titmouse?

Q4: How many times shorter is each race of giants when compared to a 60 foot tall sauroposeidon?

Activity: Draw a picture of yourself and a representative of each giant race, all to scale in regards to height.

Create

Activity: Make a new race of giants.  What will they be called?  What characteristics will they have?  How tall will they be?  How will the height of the new race compare to the heights of other giants and animals?

Forgotten Realms #1 – 4

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Let’s consider the first four issues of the Forgotten Realms comics from 1989 written by Jeff Grubb and penciled by Rags Morales.  It’s a 4-part series named “Hand of Vaprak” and as Grubb explains in his blog, these characters are fully aware that are living in a “fantastic universe.”  So it’s more adventure than ordeal and the characters are allowed to have fun.

It’s a magical word.  Magic spells, magic potions, magic vehicles…  Magic gets the characters in and out of danger.  So, it shouldn’t surprise you that 3 of the 6 main heroes and the dominant adversary in this series are spell casters and that they are all battling over an incredibly powerful magical artifact.

It’s a light-hearted world.  If you were like me in 1989, you wanted your fantasy to feel as real as possible.  That meant no silly, tongue in cheek nonsense.  So, oddly, Forgotten Realms is a better match for me now that I’m cured of that confining perspective.  And I’ll even admit that I chuckled a bit at this exchange in issue #2:

Assistant: The company of dragonslayers is no more…

Mage: What happened to them?

Assistant: They encountered their first dragon, milord.

It’s a Dungeons & Dragons world.  If you are acquainted with the roleplaying game you will feel right at home.  The D&D character classes and races, the names of spells and monsters, and even the almost sizzle of an almost thrown fireb– (see issue #3) are all here.

Supergirl: Wings

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Supergirl: Wings by J. M. DeMatteis (writer), Jamie Tolagson (artist), Ken Lopez (letterer), Sherilyn Van Valkenburgh (colorist); Published by DC Comics, 2001

I’ve never had an interest in Supergirl.  In fact, any derivative of Superman was a turn off.  The original Superman was so ridiculously powerful and yet so ridiculously humbled by a green rock.  This didn’t work for me.  So why read expanded versions of those themes?  Well, let’s be fair.  Superman has changed.  Science fiction and fantasy writing has often succeeded in creating characters that are not human, yet are equally or even more human (exhibiting the best/worst of human traits) in their actions, thoughts and feelings.  Comics have trended this way over the decades and even Superman has become more Watson than the other worldly Sherlock.

But none of that was part of the calculus when selecting this comic.  It really came down to two things.  It was in the preowned dollar bin and it had a really cool cover.  The cover let me know that this comic was about more and less.  More depth.  The angel with a closed form is breaking the fourth wall by staring at me, the reader, with literally burning hatred and disgust.  And yet, she is a creature of light.  Counter that with the darkness, the sin, that consumes the vulnerable woman in the background.  The commanding devil is also looking our way and if you peer closely, you’ll see the woman in red is too, from the corners of her eyes.  Surely this comic would provide more layers of thought on our existence and supernatural forces around us.  But I also theorized it was about less.  There couldn’t be a lot of punching, kicking, KAPOW!-ing around in this title.  So I expected less of the action and snarky comments that became a hallmark of many superhero comics.  At least in this stage of my life, that would be a good thing.

Now, this comic is weird.  It’s part of the Elseworlds collection in which “heroes are taken from their usual settings and put into strange times and places.”  There actually is some action and quite a few DC regulars are sprinkled throughout, though not in their typical form.  All of that with a deep subtext we are to take seriously, seems like a train wreck if not done with exceeding care and love for the work.

When I opened to the first page, I was immediately disappointed.  There are nine constricting horizontal panels on this page which make for a lot of focus and perseverance to read and piece out what is going on.  But I did and it was well worth it.  After turning the page, I found a single piece of art that opens over the next two pages.  The artwork following the cramped panels, makes for an incredible motion.  A spring.  You move your eyes down the first page, building tension, finding yourself at the very bottom of the page, only to turn the page and explode upwards into a starry sky of wonder.

But that’s only the first three pages.  What about the rest?  Well, this book is deserving of multiple reads and I’ve only done two, so far.  Two was enough to realize the parts I felt were unnecessary on first reading were found to be critical on the second.  Whether that’s my own deficiency or the consequence of layered art is unimportant.  What is important is that Supergirl: Wings is worthy of diligence.  I would enjoy this comic with or without the DC branding.  And that says a lot.  This is not just a DC Comics fan pleaser.  It’s a good story with many sometimes subtle, sometimes overt tributes to the DC pantheon.