# Happy 100 Days

I have no memories of ever going to kindergarten nor ever going to first grade. My first school memories are from the second grade. We read Aesop’s fables, did some multiplication, worked with fractions, went to gym, did some “four score and seven years ago” play rehearsals, played NES (well, at home, but talked about NES at school) (I know, I’m dating myself), and I think we did some square dancing, but that may have been fourth grade, not really sure.

So, I was surprised to hear about what seemed to be a generally, well-accepted, classroom celebration of “100 days of school”. I didn’t know it was a thing, until I saw a tweet by kindergarten teacher, @tritonkory, requesting videos and other fun stuff from the twitter-edu-sphere to show to her class. You can see the fun at #mrsgs100day.

So, I decided to make this little animation.

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I gave @tritonkory her own page and you can see the full version at http://www.mathmisery.com/mrsgsclass/.

## The Math

If you’ve watched through the whole animation, you’ll see that it makes a “100-pointed star” with a twist.

At the elementary math level, before students are taught multiplication, sometimes a concept of “skip counting” is introduced, or “counting by” is introduced.

Let’s count by twos, beginning at zero until we reach a positive multiple of 5. Thus, we count $$0, 2, 4, 6, 8, 10$$

Now, in the area below, there are two boxes, one for “Number Of Points” and another for “Increment” or the skip count. Set “Number of Points” to 5 and “Increment” to 2 and press the “Animate!” button. You will notice that this will animate the construction of a five-pointed star, by connecting every other dot together. In other words, start at the current dot and move in a clockwise manner to the dot that is two dots away. If we count by twos, the animation finishes when we reach a count of 10.

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Number Of Points:
Increment (Skip Count):

Try this with 6 points and an increment of 2. Then we will see that the star is finished when we reach 12, like so.
$$0,2,4,6,8,10,12$$

But notice that we made this star with two triangles. That’s because when we skip count by twos we encounter the number $$6$$, which is the number of points on the star. Thus, we “finished” the star too soon and were left with three points that were not connected.

This may seem a bit confusing, but the whole idea is that if we skip count by twos, we encounter numbers that we’d encounter if we skip counted by the sixes (and we are considering a six-pointed star). Every time we encounter a number we would encounter if we skip counted by sixes we will have come back to our starting point.

Try this, 8 points and skip count by 3 to get $$0,3,6,9,12,15,18,21,24$$ Notice that $$24$$ is the first number that we’ll encounter if we also skip count by eights $$0,8,16,24$$ and if we animate our star with those choices then we will come back to our starting point after eight lines, making a complete star!

But, if we try 8 points and skip count by 2, we’ll get $$0,2,4,6,8,10,12,14,16$$ which means that we’ll make an eight-pointed star out of two four-pointed stars.

This can be a fun way to get the especially young students (kindergarten, first grade, second grade) to start developing a sense of “multiples” and can be a precursor to introducing multiplication and division. For older students this can be tied in with the idea of least common multiple.

Finally, you’ll notice that the 100 day animation has the lines curving. This was done by using a special type of curve called a Bézier curve. I’ll discuss Bézier curves some other time, but if you are curious, have a look at the Wikipedia article on it. My control points happen to be the center of the circle and that’s what creates the bend.

Finally, finally: those animations required math and programming!