Alpha's Adventures in Mathematics: Book 1

Recap

Rescued from the streets of Korea and brought to a shelter, Alpha quickly began to plan his escape - using his superpower MATH! That was until he learned that the dogs in this shelter were only there for a short time, until they found their forever home! So he settled in with his new friends to see what adventures, and math, awaited.

And now..

Chapter 3: Life at the Shelter

A little known fact about Jindos. We HATE water! I mean, I see a puddle and I do anything to avoid it.

It's a good thing then that I can jump super high.

So the next morning, when one of the shelter ladies led me into a room full of tubs of water, I literally freaked out! And no amount of chicken was going to distract me this time.

I pulled and dragged and gave my biggest, saddest please-don’t-dump-me-in-the-giant-tub-of-water eyes . It was to no avail. Before I knew it, I was scooped up and dropped, quite unceremoniously, into a soapy, bubble-filled tub.

Shelter Lady: 1

Me: 0

After the initial shock, I started to calm down and realized that this bath wasn’t like the puddles outside. It wasn’t cold. It wasn’t stinkyInstead, it was warm and smelled like coconut. 

Teeny tiny bubbles floated here and there and everywhere. And the ladies bathing me were scratching behind my ear and in all the places dogs love to be scratched.

As I sat in my bath, I started looking at the bubbles soaring out of the tub. Fascinating orbs that, even though there were different sizes, were all the same exact shape: a sphere.

I wondered why that might be and tried to imagine bubbles as squares, pyramids, cubes or even multi-sided shapes.

Then I started thinking about how a bubble is made. When soap is mixed with just the right amount of water it becomes sticky. You can use this stickiness to blow air inside it, forming a bubble.

I started thinking about things that function the same as bubbles and remembered seeing kids with balloons during street festivals. They would take a stretchy material, rubber, and fill it with air or helium if they wanted it to float on a string above them. The balloons would always have rounded edges, no matter their shape. 

This is because air will fill any space it’s put into, expanding into every little nook and cranny.

So when a bunch of air molecules fill up a balloon or bubble, they want to be perfectly spaced, or as scientists say, optimally spaced. A sphere is the best way to do this because it doesn’t have any corners or edges to get bunched up in.

The size of the bubble depends on how much soap is used, how sticky the soap is, and the pressure of the air blown into it. (You don’t want it to pop!)

Help Alpha

Alpha wants to investigate how air molecules fill up space.

To do this he drew a couple of different shapes: a square, a triangle and a circle (see above).

First he calculated the area of each shape (see From Pam for how he did this) and made each shape so it had the same area. 

Then he filled each of the shapes with little circles, each as close to the same size as he could. 

Then, he counted how many circles fit inside each shape and then multipled the area of each circle by how many circles he could fit in the shape.

Finally, he subtracted the area of all the circles from the area of the shape and compared which one had the smallest area left over.

It turned out the circle had the least amount of space left over, this meant that the circle was the optimal shape for holding air molecules.  

From Pam

In order to calculate area Alpha had to use a few equations. Let's see what he did...

Alpha learned from the school classroom the following equations (note: * means to multiply): 

Area of square or rectangle = l * w
Area of triangle = b * h / 2
Area of circle = π * r2

He knew that l is the length of one side of a rectangle and w is the width of the other side (in a square both l and w are the same). He also knew that b is the base (or bottom) of a triangle and h was the height. Finally, for the circle he knew that r was the radius (the distance from the very middle of the circle to the outside) and π is the number 3.14. The tricky part was where it said r2. But he remembered learning that a 2 written like that meant 'squared' and to 'square' a number meant to multiply it by itself. 

So let's try some out. If Alpha had a square with length of 5, what's the area of it? (remember, in a square l and w are the same)

Answer:

Area = l * w
Area = 5 * 5

Area = 25

Great work!

Now let's try a triangle with a base (bottom) of 8 and a height of 4. 

Answer:
Area = b * h / 2
Area = 8 * 4 / 2
Area = 32 / 2
Area = 16 

Fabulous!

Now, the tricky one, a circle. If the radius of the circle is 6, what's the area?

Answer:
Area = π * r2
Area = 3.14 * 6 * 6
Area = 3.14 * 36
Area = 113.04

Great Job! 

Try At Home

Using circle stickers or punch outs from a hole punch draw some different shapes and see how many circles fit inside the shapes. This will be more accurate than drawing the circles. But make sure that all your shapes have the same area (like the Help Alpha).

You can do the same challenge as Alpha as well.

Explore More

The number π isn't actually 3.14. That's what we call an estimate of it. In fact the number π starts off as 3.14 but doesn't have an end. It also never repeats itself. We round off, or estimate π to be 3.14 to make it easier to use for calculations.

There are many places you can learn about π:

From Pam

To distract himself from the on-coming needles Alpha thought back to one of the classes he sat outside of and knew that you could set up equations to figure out unknown amounts.

In this case, it was how much medicine he was being given. To do this, he named the amount of medicine in the first needle “a” and the amount in the second needle “b. And then “x” was how much medicine would be injected.

This let him set up the equation:

a + b = x

He could then put the numbers he knew back in and figure out “x”. So this gave him:

a = 25
b = 45
So…x = 25 + 45
x = 70

70ml of medicine, woot!

After the bath, I was taken to see a lady in a white lab coat. She seemed nice enough, but something made me suspicious… She patted me all over, checked my eyes and ears. Then disappeared and came back with two HUGE needles! They must have been twice my length and three times as wide. (At least, that’s how I remember it. Maaaaaybe they might have been a bit smaller.) But the point here is that these large, pointy objects were coming straight at me.

I could clearly see the needle markings that showed the medicine measurement. One was filled to the line that said 25 ml and the other to the 45 ml line. To distract myself, I closed my eyes and created a math equation to figure out how much medicine I was getting. 

Help Alpha

Using Alpha's equation, but knowing that he received 7ml less medicine than he thought, can you create a new equation to calculate how much medicine Alpha actually got? 

Challenge: there are many ways to set up a new equation, see how many you can create!

I felt quite proud of my math skills and soon I heard the lady say, “All done.”

And I hadn’t felt a thing...

I looked back at the needles and noticed that one had 7 ml left in it. This meant that I hadn't received 70ml of medicine after all, I'd have to re-calculate. Yippie!

Once the vet was done poking and prodding me, I went back to the main yard where there were big bowls of food and water, enough for all the dogs there to eat. I helped myself to some food and circled the yard a few times, making sure to say hello to Henry and Carlos, who introduced me to some of the other dogs as well.

I spent two months at the shelter, making friends and getting healthier from all the delicious food. I even had a few more baths and they weren’t so bad. I continued to work on escape plans, just in case, but things seemed to be going well enough that they weren’t needed for now.

I even learned the names of the ladies who’d come to rescue me, EK and June.

Then one day, EK came to me and said she had some good news. They’d found someone who was looking for a puppy just like me. Finally, it was time to go to my forever home. But to get there, I was going to have to do a lot of traveling.

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