Math Mondays::Be a Square!

Creative Math Club has started back up for those people in my area who also belong to the Out of the Box group on yahoo. The Math Club isn’t that old…we had it every week for 3 or 4 months in the springtime, and then stopped when summer appeared. I knew it was a success when my math phobic and totally math averse 12 year old asked if we could still do it on the weekends during summertime instead of stopping it altogether.

Creative Math is different from regular math in that it mixes art, music, and exploration with numbers and rules. Schools have stopped doing math this way because it takes a little longer to ‘discover’ math than it does to teach rote memorization for the NCLB standardized tests. It’s a shame.

This month, we’ve declared October to be Month of the Square. You know, square:

The younger kids tackled the actual shape concept, which I’ll cover another time. The older kids (4th grade and up) covered the exasperating concept (for me) of square numbers and square roots. And there were no tears! Or frustration! Or willful disobedience about it!

But first, the most important thing when hosting a math club for math averse, creative and divergent thinkers is good food, so everyone brought along square food. And if it wasn’t exactly square, we still ate it but just discussed why it wasn’t a square. We had chocolate squares, graham cracker squares, cheese cut into squares, square crackers, etc. etc.

The older kids sat at a table with a variety of square materials. First, they played around with square mosaic tiles (found at any craft store). This was done without any math discussion at all…just pure creative play.

After 15 minutes or so of mosaic patterning, correlating math patterns were brought up. In the example above there are a myriad of corresponding math facts. The kids were able to pattern it out without much prodding, for instance, if you look at the colors you start with:
1 black
3 white
5 red
7 black

One kid mentioned this, another kid noticed they were odd numbers, yet another predicted the next number would be 9, then 11, then, 13… Sonja, who was leading the older kids table, asked if they noticed what kind of number you got from adding two odd numbers together, odd or even.

Then, someone else notice that:

You may notice the square number pattern happening, but the kids didn’t, so we left their observations out there to linger until they were familiar with the actual square numbers. Some did notice, however, that the pattern was take the answer from the last equation and then add it to the next odd number in sequence. This interplay lasted another 15 minutes.

Next, the tiles were put away and some paper squares were brought out. Let the mosaics begin!

Free play with the paper squares took another 15 minutes, and then Sonja started directing their focus a little bit by asking, “How many squares do I need to make the smallest square?” The kids looked around and picked up 1 square paper….1. “This is the smallest square number. Number 1, and it is a square. What is the next smallest number that makes a square?” The kids looked around, played a bit with the papers, and set four of them together. “4” “4 is a square number, it’s not just a quantity, but also can be a shape…the shape of a square! Numbers that can form a square when you put them together in a grid are called Square numbers. See how many square numbers you can form!”

Some kids were methodical when finding square numbers, like this little girl who ordered them sequentially on her paper:

Some kids layed out a 12 by 12 grid…just as sequential, but more compact. Similar to the tiled pattern up above, only this time they had a correlation between the number patterns and the significance of them to ‘square numbers’.

And then some, as you notice in the background of the pic, used their papers to make happy faces. Since this is a freeform type of group, I really try hard not to mind if a kid isn’t necessarily sticking to the plan. Turns out, the happy face kid (who happens to be the Golfer) didn’t need to see or make the squares to know the square number pattern. He is more mathmatically minded and once he realized a square number was any number times itself he knew what the numbers were without referencing a visual square in his head. So, he made happy faces!

Naturalist made a mosaic that had a great deal of symmetry, and even mimicked two triangles forming a square:

We probably could have stopped there, but the kids were still happy around the table, and they had all grasped the concept of what a square number was by making square mosaics. So, Sonja introduced the idea of square roots. The usual diagram:

Only, when Sonja made the square root sign, for each line she said a word: The…Side…of the…Square…of number 4. Meaning, look at the square with 4 squares in it. How many squares are on the side? 2! That’s the square root, or side of the square. We practiced finding square roots in this manner until the kids grew restless. All told, they were at the table for 2 hours doing math and art at the same time…making mosaics and square numbers all at once!

And then, we ate square food like kings.

Math rocks!


17 Responses

  1. I just realized that the sum of each square goes positive &negative…1, 4, 9, 16, 25, 36, 49, 64, etc. I loved the patterns in Brooke’s design.

  2. Finally math that looks like fun and isn’t scary! I don’t know when kids are “supposed” to learn about square roots but I know Owen who is eight wouldl ove this.

    Thanks for posting these activities Tiffani – it helps when I have just run out of ideas πŸ™‚

  3. Finally math that looks like fun and isn’t scary! I don’t know when kids are “supposed” to learn about square roots but I know Owen who is eight wouldl ove this.

    Thanks for posting these activities Tiffani – it helps when I have just run out of ideas πŸ™‚
    P.S. – Sorry, forgot to tell you great post!

  4. I had an EXTREMELY hard time with math in school. Then I moved to a different town and we used a similar style of math learning as this- Things finally started to click for this visual/creative girl.
    I wish they would have done this earlier with me, I would have been a ‘whole lot smarter’ (or at least not felt so stupid). And you know what, later on when I had to take the standardized tests (pre-NCLB but standardized test none the less) I did better in the math segment. if they aren’t doing this anyomre in the schools it is a shame, all us non-math types are loosing out!

  5. Beautiful method. Love that it was fun and enjoyable.

  6. hmmm…….
    strangely familiar……

  7. Great ideas there once again. I wish we lived closer so we could come too (like in the same country would help lol)

  8. This literally makes me want to cry! I feel so stupid when it comes to math. Reading your blog opens my eyes to what is available if someone takes the time to actually teach this in a way that makes sense. Your kids are soooo lucky!

  9. Fabulous!! I NEVER knew that the number of squares along the side of a square is the square root!!! I really never knew that!! I am SOOOOO trying this activity with the kids. Thanks so much! πŸ˜€

  10. I just got chills. I’ve always been good at math and square roots were just something that made sense with numbers. But just seeing them! WOW! That is so amazing. And it’s been staring me in the face this whole time (I love to doodle geometric shapes in meetings) and I never made the number-to-art connection. So cool.

  11. […] Math Mondays::Be a Square! […]

  12. […] 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 […]

  13. […] 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 […]

  14. Huh! I can do squares and square roots, but I never knew why they were called such before. Amazing how things can make such common sense and never have been taught to me that way.

  15. Hi there, I’m a math-phobic looking for ways to engage my kids in math and I could see they were beginning to struggle and dread it the way I was. So when I found your lessons, I was thrilled and have been using so many of your math club ideas with my kids to great success. We just finished our lessons on squares and it was a blast! Thank you! I’ve just posted it on my blog if you are interested to have a peek!

  16. Love this lesson!!! Thanks so much for posting it! πŸ˜‰

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