### Math Monday:: Domino Math!

Don’t faint, but I’m actually posting a Math Monday blog today!

I’ve picked up a few more readers, so I’ll explain…

I am a recovering mathphobe. I hated math growing up, panicked about it in school, felt stupid doing it for my whole life. I can’t really even remember simple addition problems, let alone memorize multiplication tables. In 4th grade, everyone got ice cream sundaes at school for remembering their times tables up to 12…and I hadn’t even cleared them past the 4′s. No ice cream for me. Not only was I humiliated (I had to go sit by myself outside while everyone ate their prize in the classroom), I really really wanted some hot fudge. I pretty much concluded I was an imbecile, end of story.

Then my daughter came along with the same issues with math, and I felt like obviously that meant everyone dealt with it but some people learned to do math better because they were smarter. And then my son was born and he started multiplying in his head by kindergarten. And I thought…wait a minute…some people actually have minds that get it! That don’t struggle like mine and Naturalists. I found out about dyscalculia and felt like I finally had some answers.

Then Naturalist and I discovered sacred geometry, which made math and numbers so much cooler. So much more right brain and visual spatial!

So we started up a Creative Math Club, and doing math our way. Using art, music, and anything else we could get our hands on to make math very experiential.

Serendipitymama (with her cool blog, here…) tweeted me (I’m childplay on twitter, come say hi!) to ask if I’ve done any math mondays while here in So. Cal. I said no, because I think of the creative math club back in Colorado as the main part of math mondays. Without them, I feel mathless. A form of worthless, but with math.

But it turns out, that’s not really true. We do math all the time! Especially because Sassy loooooves dominoes. She carries around her own bag of them everywhere we go! So, in my first math monday video ever to debut here on Child’s Play, I bring you video documentation of what math looks like with Sassy and I! It involves being by a pool, singing in an opera voice, using watercolors, and a shout out to all the ‘rapping birds’.

The great thing about dominoes is that it’s so easily transformed into math games for older kids, simply by changing the operation. Instead of adding, you can multiply the numbers, divide, or subtract. And if you have creative kids (which I’m betting you do, because you’re reading this blog and we’re all about creativity over in this part of the blogosphere!) then they can pretty much come up with their own games with nothing more than some dominoes and some pens and paper!

In case you need some help, here are some links:

Domino Math Book (grades 1-4) that we enjoy!

Domino Math Book (grades 2-6) that we also enjoy!

Fun (free) domino games with domino math mats.

### Math Monday::Memory Games = Better Math Skills

I noticed with Naturalist and myself that a lot of our problems with math actually have very little to do with the numbers and lots to do with our poor short term memory. (well, actually, we also have big problems with numbers, too, but one thing at a time!)

If you have a mathphobic kid that you are trying to help out, I suggest doing fun memory exercises rather than keep focusing on the rote memorization stuff or straight computation. Because the foundation for doing any of that well is a strong memory. How can you memorize math facts if your memory is full of swiss cheese holes?!

This is a great thing to do if your child has panic attacks surrounding math, or who says they hate it with a passion. If you can make math fun, then they have a harder time hating it, and when they stop hating it, they relax, and when they relax their brain works better. So spend your math time doing fun games instead! And if you can combine fun games with candy, then it’s all that much better.

Here’s a few that we like to do…without pictures because I’m in over my head with life a little bit this week. But I’ll explain it really well for you.

Take a handful of M&M’s. Put up a barrier of some sort, so you can see them on the table but your kid can’t, then arrange 4 of them in a pattern. Lift up the barrier for 2 seconds, then lower it, then have them recreate the pattern in front of them. If they can do that without a problem, increase it to 5 M&M’s. Then 6, then 7…the point is to build up to as many M&M’s as they can. You may need to adjust the time they can see them from 2 seconds to something longer. Then switch and have them come up with the sequence and you try to reconstruct it.

If you don’t want to use candy (but really why wouldn’t you?!), this can be recreated with just about any colorful toy. Legos work really well! Just sequence the colors in a specific pattern, let your child see it, then cover it up again, then have them try to reconstruct it with their legos. Keep building up to a greater and greater number of legos. You can also vary the time they reconstruct it…have them wait 30 seconds after you cover yours back up, or a minute, or even 5 minutes after they see it.

This has been a fun way for Naturalist and I to work on our memory skills, which in turn has helped our math recall. And, we’ve gotten to eat candy in the process! It’s a win win!

Other Resources:
My favorite fun math skills gamebook…125 activities to build skills for better math, and not necessarily through math computation drills! Mega-Fun Math Games and Puzzles for the Elementary Grades: Over 125 Activities that Teach Math Facts, Concepts, and Thinking Skills (Jossey-Bass Teacher)

our family favorite memory game, this one is so much fun, and no math at all!!! But totally develops memory skills that will help with retaining math facts/ideas. Tell your kid it’s time for math, then play this game, they’ll think they’re in heaven! STARE! Game

(STARE! JUNIOR if your kids are younger!)

### Math Monday::Gumdrops & Toothpicks

Dec 15, 09

Tis the season for Christmas candy! To take advantage of all the gumdrop packages on the grocery shelves, the Creative Math Club went ahead and organized a gumdrops & toothpicks day. Each kid had two packages of gumdrops and a container of toothpicks to use, and we started our meeting by making 2D shapes with them–officially called regular polygons because the equal sized toothpicks make them automatically equilateral (all sides have same length) and equiangular (all sides have equal in measure).

I made a spreadsheet with 20 spaces for regular polygons, starting with a triangle. It also had spaces to fill in how many edges and vertices it had, as well as space for what the angles measured. Edges are the sides, denoted by how many toothpicks are used…vertices are where two sides meet up, denoted by how many gumdrops are used. Once the kids modeled a 2D shape, they measured the angles with a protractor and then they filled in the spreadsheet information.

The wikipedia article on regular polygons has the names for the polygons up through 20 sides, and then the names for even bigger polygons like the megagon.

I found it really fascinating to watch how the angular shapes changed the more toothpicks we used. A triangle opened up into a square, which opened up into hexagons and octagons. By the time we got to the 20 sided icosagon, it more closely resembled a circle. Those were used as necklaces and embellished into peace signs.

Once we were done investigating 2D polygons, we moved on to 3D polyhedron shapes. But! Not just ANY polyhedron shapes, we focused on the five platonic solids. I also made a spreadsheet for this, with spaces for the polyhedron name, how many edges, how many vertices, and how many faces it had. And then we went to town building, from simple to more complex. I used a hands on resource page, here, as a rough lesson plan.

Tetrahedron:

Cube:

Octahedron:

Dodecahedron:
(which apparently I forgot to take a picture of)

Icosahedron:

we talked about how Plato associated each of them with one of the four elements, and also how they were the shaped dice used for games like D&D (any kid who’s a gamer will enjoy this association a lot!)–those dice are actually called polyhedral dice that we use for most if not all of our math games!

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Being creative math, I’m not promising that everyone filled in their spreadsheet 100%, or that there wasn’t a fair amount of creating other shapes going on. But I am promising that we all had a good time discovering shapes (2 and 3D) and characteristics using gumdrops & toothpicks!

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If your kid really gets into hands on building with gumdrops, I highly recommend the Zometool, which is based on this kind of constructing, and it takes it into different interests like chemistry (making chemical reactions), biology (making viruses), etc. It’s a big hit over here.

Links to resources I used to prepare for this that I’ve bookmarked on delicious is here.

### Math Monday::Pentominoes, part 2.

When I last left off our pentominoes investigation, the kids had made the pentomino shapes out of square pieces of paper and laminated them. The sheets of pentominoes looked like this, and then we cut them out:

So now that they each had 12 pentomino shapes as their game pieces (review of what a pentomino shape is linked through here) it was time to make the game board. The board was for a solitaire game of pentominoes–the goal being to get every one of the 12 pieces to fit inside the game board without any piece overlapping or going outside the board. So, we brainstormed. The question: how can we determine the size of the game board using the pentominoes as a reference.

No one really had any ideas, so I rephrased. ‘What we want to know is, how many pentominoes will fit exactly into a game board. How much room does each pentomino take up? (5 squares, because they’re each 5 squares.) So how much room total will you need if you want to fit them all in a game board?’ This kicked some activity off…counting started…some kids counted each square individually, some kids picked up their pieces and counted by 5′s, and some kids just did the mental math 12 pentominoes times 5. They all came up with 60 squares.

I wrote 60 down. So our game board needed to fit 60 squares, no more or less. To use mathmatical speak, the area of our board shape needed to be 60. Now that we knew that, we could find the dimensions of the board and then make one out of contruction paper.

So the next question was, what size board would give us an area of 60.

Not a lot of ideas.

Rephrase: “to find the area of something, you multiply the length times the width. We want to find the length and the width…what two numbers multiplied together equal 60?”

At this point, they could use calculators, multiplication cards with the math facts, or their own mind. Numbers started trickling in.

“1 and 60!”
“4 and 15!”
“6 and 10!”
“2 and 30!”
“3 and 20!”
“5 and 12!”

With those factors, we could start to narrow down our game board shape. Some of the dimensions wouldn’t fit any pentaminoes in them, like the 1 by 60 board, so we crossed that out. We kept crossing out number combinations until we arrived at the 4 shapes that were possible.

Each game board has it’s own possible solutions, so I used the wikipedia article here to explain which board would have the most possible solutions and which board would have the least. They decided on what their game board would look like, then started measuring and cutting it out.

and then, of course, we laminated them. Any excuse to pull out the laminator!

So then they played around with trying to fit their pentominoes onto the game board.

There is a section on pentominoes in the book Shape Patterns (Let’s Investigate) which I notice is for sale on Amazon, used, for .88! (In fact, Amazon has most of the ‘Let’s Investigate’ book series for great used prices…I’ve found these books to be the best math related investigative books anywhere!)

In the shape pattern book there are a handful of two player pentomino games. A few of our favorites were:

*Two people each play with all their 12 pentominoes. They take turns laying down their pentominoes (without a board). Points are scored for each square of another pentomino that you touch with your own pentomino. You cannot overlap, but you can leave gaps and flip the pentomino around. Highest score wins.

*Two people take turns choosing pentominoes from one (12 pentomino) set. Each player has one minute to arrange all their (6) pieces into a 5 by 6 rectangle. No overlapping, but they can be flipped and turned. Every square outside the rectangle counts as one point…the winner is the one with the lowest score.

And we just played with the pentominoes for the rest of the time.

Yay for math!

### Math Monday::Play Math!

I’ll have to wait until this week’s Creative Math Club to finish off the Pentomino Math part of Math Monday, so in the meantime I’ll share the things we’ve found that have made math really fun for us.

Our journey towards not hating math has come slowly, over the past 4 years. I’m hoping that with these Math Monday posts, I can help speed up the process for other people. Because math can and should be really fun, engaging, experiential, and exciting! Once it became this for my daughter and I, even we could not keep from hating and avoiding it.

This list of things that helped us play around with math is especially for those kids (and parents!) who have serious issues with numbers. It’s for those people who find math boring, or painful, or inhumane.

Think of it as my ultimate nerdy and totally mathmatical gift buying list for those who love math or want to learn to love it. Just in time for Christmas!

The first ‘aha’ moment we had came while reading A Beginner’s Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science. I can’t even tell you how much we love this book. For the first time, numbers became mysterious, magical, important, archetypal. We became philosopher mathmaticians while reading it, which suits us better than computational mathmaticians.

However, computation is a big part of math, so after being mathmaticaly inspired, we agreed to try out some computation stuff. Our favorite way to do this was through books that made math into games. If you or someone you love is mathphobic, put down the math curriculum schoolbooks immediately, and pick up some of these:

Family Math Book Series…experiencing math through games:
Pre K-K: Family Math for Young Children: Comparing (Equals Series))

Elementary school: Family Math (Equals Series)

Lots of different kinds of Dice Math books

and here are other general math game books

Computer and video games that are so cool, you won’t know you’re doing math/science:

Experiential Math:

at first I bought the beginner set, and then my kids caught the fever and wanted to build epic big structures, so I’d go with this one:

Goobi 202 Piece Master Magnet Construction Set Rainbow …my 5 year old is building away with these as I type.

And finally, Kinesthetic Math…for people that like to move!:
Addition & Subtraction: Math Mat Challenge Game

Multiplication & Division: Learning Resources – Factor Frenzy

So that’s what we’re enjoying at our house–all the things that have helped us not be so afraid of math in our daily lives.

### Math Monday::Pentominoes!

{as an aside, let’s just all pretend that I actually write and post these on Monday, it would help keep the whole ‘math monday’ alliteration theme going…and help me keep my dignity…}

A few weeks ago, our Creative Math club met together and did even more things with the square inch pieces of paper that Sonja and I had cut out for the Square Numbers Math activities. I went to town with my paper cutter one night and ended up with about a bazillion squares before I realized it.

When the kids arrived, they just sat around the table and played with the squares for a little while. Then I focused it a little more and asked them to choose 5 squares, and see what kind of pictures or shapes they could make. Some were really pretty!

And finally, after a few minutes of that, I told them we were going to play a game, but that first we needed game pieces made from 5 squares. Each piece needed to have 5 squares connected–no more, no less. There would be a total of 12 game peices per person. Their job was to put the 5 squares together to see if it was a game peice…each piece had a specific rule to follow in order to use it to play the game with, but, I wasn’t going to tell them what the pieces looked like, I would only tell them yes or no if it was a piece as they showed me their ideas.

This is a technique I discovered works really well with visual spatial, right brain thinkers. Rather than tell them the rule, or explain how something works, I just give them the free reign to experience it for themselves and then tell me the rule or how it works. The rule for the game pieces is simply the definition for pentominoes…shapes that are formed by joining a series of 5 squares attached edge to edge (not edge to corner!). Or, another way of putting it: A pentomino is a polyomino composed of five (Greek ????? / pente) congruent squares, connected orthogonally.

So, the kids would arrange 5 squares, then ask me if it was a game piece. Out of these 3 examples, only the two on the ends are pentominoes, because the middle one joins the squares at the corners.

If you’ve ever played Tetris, then you’ll recognize the pentomino shapes…even though Tetris only uses four block shapes.

Slowly they honed their skills, and it didn’t take long for them to figure out the characteristics of the pentomino shapes.

Once they all had their 12 pieces glued to a sheet of construction paper, they cut them out and then I brought out my most favorite thing in the world….the laminator. It’s hard to express how much love I have for this thing, I’m totally addicted to laminating things. The kids were also totally addicted to watching their pentominoes go in with a thin sheet of plastic over them, and come out laminated and sturdy.

Now, they had their game pieces ready…but we’d run out of time. So, we’ll make the game boards next week and use the pentominoes in a very mathmatical and fun way. And then next math monday I’ll explain what games we played with them. In the meantime, here’s an Online Pentomino Gameand another online Pentomino Game.

To finish up our Math Club, we played Blokus, which is a family favorite in our household, and one that uses pentominoes and other shapes to create a simple and addicting game. This has been in heavy rotation around here for the past year, solid.

So, here’s a quick note about pentominoes, and why I love them. They are totally mathmatical, but totally non computational. Meaning, you don’t have to sit around with a calculator or worksheet. Pentominoes are meant to be played with, flipped around, discovered, explored, and used in a very hands on way. If you have a mathphobic kid, or are mathphobic yourself, I highly recommend getting a hold of some Pentominoes games and puzzles for a while. Math is fun! Just play with them! If you can’t resist a more ‘schooly’ way of dealing with them, there are lots of school standard type Fiction and Non Fiction books about Pentominoes.

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and then I just now saw this Blokus 3D Game, which looks pretty cool!

### Math Monday:: "Simon Says…" Angles Math

In the spirit of Trampoline Math, our Math Club last week opened with some new Simon Says activities. Our exploration into square numbers and then the Pythagorean Theorem also led us into discussing angles and triangles.

The angles being: obtuse (bigger than 90 degrees), accute (smaller than 90 degrees), and right (90 degrees exactly). The triangles being equilateral (all 3 sides are equal in length), isosceles (2 sides are equal in length), and scalene (no sides equal in length). We also covered right triangles…the special kind of polygon where two of the sides form a right angle.

Was that as boring to read as it was to type?! Yes, methinks so. So, I’ll tell you how we talked about angles and triangles the fun way…using our bodies.

Acute angle, using your arms, arm, or fingers:

Once the kids got comfortable making angles, they started making them with whatever part of their bodies they could. Note that there are three different models of acute angles: Naturalist is using one arm and bending it way closed to make her angle…her friend T is using two fingers spread only a little wide to make his, while golfer is doing the two armed style. Later on they used legs, feet, wrists..anything with a hinge.

After a few warm ups to get everyone on board the angle train, we started Simon Says…Simon Says make an acute angle, Simon Says make an obtuse angle, Simon Says make a right angle with your leg, Simon Says make an acute angle with your arm…etc. etc.:

As you can see, this is multi-age friendly. Lots of laughs were had.

With only 3 angles, it didn’t take long for that part of it to be over with, so then we moved on to the triangle part of it. All the kids were in one group, and when I named a triangle they had to choose who would help make it with their body. For instance, I said, “Equilateral Triangle” and even though I’m pretty sure none of my kids could give the definition correctly, they knew that they had to find 3 kids that were the same height. It’s just another way of processing information…they don’t really connect to a triangle on a sheet of paper, and having 3 equal sides doesn’t really matter to them…until they have to construct one using their friends.

So here’s as close as we could get to equilateral:

They tried to build an isosceles triangle standing up, which didn’t really work…it looked more like a pentagon:

so they had to reform to make it on the ground:

I have to say, one of the most fun parts was rolling the younger kids into position…Sassy in particular is very ticklish:

Most interesting of all was making a right triangle. We knew, from the Pythagorean experiments we’d done the last week, that important numbers were 3,4, and 5…because if you take the squares of 3, 4, and 5 you end up with a right triangle. The kids set about finding a similar ratio that applied as a relationship to their sizes, and decided that my three would be perfect to make it:

Aren’t my kids simply and elegantly gorgeous? And photogenic?! Anyway, getting back to the triangle, sure enough, they were able to make a perfect right triangle:

would you like to see another angle of the right triangle? of course you would:

I found this fascinating to watch. The word ‘hypoteneuse’ doesn’t mean a whole lot to my kids until they started making their own body triangles, then they realized that the tallest person would always be the hypoteneuse, and that was always the line across from the right angle.

We did some other things, namely, building and playing with shapes:

but I’ll save that for another time.

For now, I’ll end with the observation that kinesthetic math is a powerful learning tool, and easily adaptable to most math concepts in a variety of ways. Math Simon Says has been a really versatile tool in our multiage gathering!

### Math Monday::Pythagorean Theorem

For our latest Creative Math Club, Sonja (who I’m happy to say is rested and recovered from her family’s bout with the flu!) prepared some activities having to do with the Pythagorean Theorem. We geared this one towards the older set of kids, those between the ages of 10-15. We had an amazing turnout for the day so ended up splitting off into groups arranged by age…the under 6 set of kids, the 7-9 set of kids, and then the 10-15+. There were kids and parents everywhere!

We had lots of inch squares for everyone to play around with and mosaic for the first 10 minutes or so, just to get in the mode of squares and numbers. Once the older kids had settled into the routine, Sonja wrote out a number line from 1-10 and then had the kids square each number:

Sonja was starting to teach them the Pythagorean Theorem, but in a backwards way. Or, rather, in an investigative way. So instead of giving them the formula a(squared) + b(squared)=c(squared) she led them in an investigation to discover that using squares. Once they had squared all the numbers between 1-10 (some kids knew the answers by doing it mentally, other kids made a square using the square pieces of paper…)

Sonja challenged them to find a sequence of 3 numbers where the square of that number plus the square of the next number equaled the next number squared.

I hope I’m explaining that clearly, lol. So, looking at the numbers 1-10, they were to find the sequential numbers where the first number squared plus the second number squared equaled the third number squared. Lots of number crunching ensued. They were using their mental math skills, or the square pieces, or calculators. They were also, because they are in fact creative kids, taking larger square sheets of paper and constructing paper houses out of them. Which is totally off topic, but I figure that any kind of investigation (on or off topic) is better than no investigation at all. And with creative kids, it’s the most random experiences that can lead to the best kind of learning. So, all forms of square ‘play’ was allowed, whether it was a direct contribution or not.

In any case, they eventually discovered that the numbers 3,4, and 5 are the only consecutive numbers where the squares of the first two numbers equals the square of the third number.

Sonja had prepared some new squares…not the square inch shapes, but 3 inch squares, 4 inch squares, and 5 inch squares. Each kid got one of each, and were asked to construct a triangle with them.

What they came up with was a right triangle:

At this point, we had a discussion about angles and triangles. The definition of ‘right angle’ was important, and then Sonja was able to tie the triangle they had made with squares, into the Pythagorean Theorem. Which is to say, anytime there is a right triangle, the Pythagorean Theorem of a(squared) + b(squared) = c(squared) applies. This also introduced the idea of the hypoteneuse being like the third number, or, the c part of the triangle.

By this time, the kids were starting to get antsy from sitting at a table, so we ended that part of it without doing much application of the formula as far as plugging in numbers and measuring–we can do that another math club. What we did was one last cool application of the idea by using a 12 foot long piece of string.

Sonja asked, if we are building a house, and we need all the corners to be square, or have right angles, so our house is a perfect square, how can we do it using only this rope and our knowlege of the Pythagorean Theorem? The kids gave different ideas, and then Sonja had them measure and mark the rope off into sections of 1 foot. They ended up with a rope marked off at every foot. She told them to think about what consecutive numbers made up the answer in the first part of the lesson, they replied “3,4 and 5″ so she had someone grab hold at the 3 feet mark, then had someone grab hold 4 marks after that, and the last person grabbed hold 5 marks after that which happened to be at the 12 foot mark. She then had them take it down to the floor and make a triangle out of it. This is what they saw….a right triangle appeared!:

So. Freaking. Cool!

So, that was our brush with the Pythagorean Theorem. Personally, I remember learning the Theorem as just a string of numbers to memorize without any connection to why or how it works. I really enjoyed re-learning it this way!

### Math Monday::Halloween Symmetry!

With Halloween being not to far away, at least for us here in the USA (which reminds me of a hysterical story involving our attempt to trick or treat with the kids when we lived in Budapest…but I’ll save that for later…), we’ve been crafting like crazy. Also, the leaves are almost all off the trees, so I thought I’d post a Math Monday using symmetry before all the leaves are gone, baby, gone.

First, paper cut symmetry…it’s the same principle as making paper snowflakes…the idea that you can fold paper, cut it, and it creates a symmetrical pattern. This is a fun one–take square pieces of paper, we used 8 by 8 decorated pattern paper, but even construction paper will work. Since this is symmetry, you’ll fold it in half. On one half of the paper, draw half your shape:

We drew:
pumpkins
ghosts
cats
spiders

Then, once you’ve done that, you can cut around the mark:

…and open the paper up again to see how it looks! Here’s a bat…

and a cat from Naturalist:

There is something called a ‘line of symmetry’ which is illustrated perfectly when the figures are unfolded. It’s the line in the middle that divides a shape where the two sides on either side match.

A great video to watch with your kids on symmetry and line of symmetry is through this link.

A quick note: if your child struggles with writing, it may be frustrating for them to draw the image and/or cut it out. Golfer didn’t enjoy that part at all. So I let him direct me in the drawing and cutting, and then he got to take our images and tape them to all the windows:

Something else we’ve been doing is the good old leaf rubbings. Everyone goes outside and pics a few (or more!) of their favorite fallen leaves. They can’t be too brittle, or it won’t work…so, leaves that aren’t too dry yet.

Bring the leaves inside, lay them on a piece of paper and place another sheet of paper over the top. Get a crayon in a nice fall color, unwrap it, and use the side of it to gently rub over the paper. This will give a nice rubbing of the veins and outline of the leaf. Point out the lines of symmetry and talk generally about how one side of the leaf is so similar to the other. Do this for every leaf, varying the fall colors you use, then cut them out and tape them everywhere.

This may lead to an interesting observation about all the symmetry there is in nature (if the video hadn’t already sparked this discussion!). If you child is interested, go on a photo safari for nature symmetry. (Symmetry in Nature) Sassy and I did this, but my card reader is about 2 seconds away from not working anymore, and it failed to upload any of those pictures. But I’m sure you know what I mean! Snap a picture of everything that you see outside that is symmetrical.

This is a perfect ending to a fun time…especially if you’re coming in from outside where it may be cold–a great excuse to put on a pot of hot chocolate and look around at all the lovely decorations you have scattered all over your house!

### Math Monday::It's hip to be square!

Yep, we’re still being square over here for Creative Math Club. We had a few new kids, so we basically just went back over how to find a square number using square pieces of paper (cut lovingly by moi the night before…it was a good excuse to get the super cool paper cutter from Costco…).

We also started putting together a square number book, where each page had the square number on it with all the different notations that equaled that number. For instance, the first square number is 1, so that page looked like this:

First, we wrote down the “1″, because that’s how many squares there are on the paper to make the square number. Then I asked them how many squares there were going across (1) and how many squares there were going down (1) which gave us 1*1. Then I explained that another way to say it was “1 squared” while I wrote down the 1^2 sign. I didn’t do the square root sign right away, first we explored the other numbers so I’ll skip it for now.

It took us about an hour to get the first 4 square numbers explored like that, with all the different notations on the paper, until we ended up with this:

Once they all were pretty comfortable with understanding how to use all the different notations to explain the square number they were making, I introduced the square root idea.

Usually, Sonia would be doing all the explaining because she is, in fact, a math tutor. I am, in fact, a mathmatical idiot. But, she was out with the flu so I did my best. I had a little break down when explaining the square root idea, lol, and luckily another mom was there to help me get the notation correct. Personally, I think my mistakes are as good a tool for learning than what I get right. So many kids are afraid to fail or afraid to be wrong, but when the person ‘teaching’ can say, “Oops! I totally got that wrong! But I found out the correct way to do it, so let me go over why it wasn’t right before and learn it the correct way…” then the kids are less afraid of having to say the same thing. Also, I feel that my absolute fumbling ineptitude helps break the ice a little bit, and gives the kids more confidence. As in, “I’m terrible at math, but this lady is even worse! And she’s doing it, so maybe I can keep trying too…” At least, that’s what I’m hoping.

So, anyhoo, the square root was done–like I mentioned last Monday–by saying, the number of the side of the square is…. and then they’d get it.

We spent another 15 minutes after doing all the mosaic work to look for patterns. What did the numbers on the papers have in common? Could they predict the next square number without knowing it? Could they predict the next number notation in the sequence, ie., 1*1, 2*2, 3*3, 4*4, …?

And then we all took a break and ate more square food.