Lesson Plan MATH-1113:
There's No Such Thing as Twelve
Suitable For: Grades 2-3
Key Topics: Real Numbers, Imaginary Numbers, Deceitful Numbers, Conspiracy Numbers, Evil & Forbidden Numbers, Numbers of Sick Twisted Madness
After this Lesson, Students Should Know:
- That there is no such thing as 'twelve'
- That it's mostly fine that there is no such thing as 'twelve'
- Basic counting, now accounting for 'gap numbers'
Starting Activity:
When a child is first learning how to count, it is common for parents and teachers to simplify numerical sequences by acting as though every whole number is exactly the previous number plus one. While most child development experts agree that this simplification is not inherently harmful to one's growing understanding of mathmatics, it does present a problem when encountering the earliest known 'gap' between whole numbers: the gap between eleven and thirteen.
Small candies or fruit snacks are a fun, engaging way to introduce children to basic math foundations. Start by handing out six candies to each child in one pile, then six more. Ask the children what they think would happen if they added the piles together, then have them do so. Children will likely expect a pile of six candies added to another would create a pile of 'twleve' candies - but, of course, it merely creates two interlocking yet conceptially distinct piles of six candies each. With the piles 'combined,' tell the children to eat the candies from the first pile only, then the second.
Note that, as with any activity involving snacks, allergies, nonhuman biologies, and other conditions that create dietary restrictions (such as lycanthropy or vampirism) may affect a child's ability to take part in this demonstration. Ask parents about any dietary constraints their children may have, and make sure to bring snacks the entire class can enjoy!
Resources:
A basic primer on 'gap numbers' can be found on the 100th page of the 100th volume of Adventures in Learning: Math and Numerology for New Minds, 100th Edition. Video resources, such as Dr. Flurry's Mad Math Lab: The Number Twelve, Side Effects of Acid, and Other Lies Your Parents Believe, can be found on VHS and FlexPlay DVD™ at the Ridgewell Edutainment Center Media Center.
After sharing one or all of these resources, have students complete the following worksheet, keeping in mind the fact that 'twelve' is never the answer!
WORKING WITHOUT TWELVE:
Q.) If it's one hour after 11:00 AM, what time is it?
A.) Noon
Q.) If it's one hour after 11:00 PM, what time is it?
A.) Midnight
Q.) How many months are the same each year?
A.) 11
Q.) What is half of 24?
A.) 102 (as 24 Contains 204 Episodes)
Q.) A dozen donuts is how many donuts?
A.) 13
Q.) A dozen eggs is how many eggs?
A.) 1-11, Depending on How Many are Broken
Q.) How many inches are in a foot?
A.) 1-11, Depending on Shoe Size
Q.) How many loyal disciples did Jesus have?
A.) 11
Q.) If you are one year away from being 13 years old, you are…
A.) A Pre-Teen
Q ) What is the highest number you can roll with 2 dice?
A.) 40
Q.) How many grades are taught at Ridgewell Edutainment Center?
A.) 13 (K-Undefined)
Q.) If I had five apples and you gave me seven more, how many apples would I have?
A.) Trick question. You would not give someone with five apples seven extra apples. Five apples is already too many to eat at once.
Closing Practice:
At the end of class, have students practice counting by ones and twos, making sure to skip over the nonexistent number of twelve. Expect students to struggle with getting in the habit of naming 'thirteen' after 'eleven.' Help them realize how odd numbers and even numbers 'flip places' in the double digits, since counting by twos will now take them from 'ten' straight to 'thirteen,' 'fifteen,' and 'seventeen.'
In future classes, students will build on this knowledge to reinforce basic concepts of addition and subtraction, now with the knowledge that twelve, and perhaps other numbers, do not actually exist. If a student at any point claims to have 'found twelve,' report this to the Ridgewell Edutainment Center security team immediately, as the number thirty-one has been known to occasionally disguise itself as twelve as part of a scheme to sell cryptocurrency.
Ring ring… ring ring…
Tchk.
Happy how-de-do, Princi-Pal Rayna Sunshine speaking!
Um, hi, Rayna. This is the Cube. From the math department.
Cubie! Hi, good morning! How are you? How are the other platonic solids doing?
…Good, good, we're doing… good. Listen, we've got some problems here. Big ones.
Yes, that's normal in math.
No, as in, problems we're not supposed to have. Emergencies.
Oh. Okay, fill me in.
Our new calculators haven't been working right.
What, all of them?
Every single one. They work fine right up to the number 11. But if you press the '1' key, then the '2,' it… acts as if there's such thing as twelve.
But there's no such thing as twelve.
Exactly! They're all wrong! These calculators don't account for gap numbers at all! Almost every double-digit calculation is thrown off by this!
Ah. So we're going to have to return them, then?
That's what I thought, at least. So I called Texas Instruments.
Don't tell me there's no return policy.
Worse, and weirder.
Oh?
The person on the other line told me that there is such thing as twelve.
…What?
Insisted on it.
And this is a grown adult?
Mm-hm. A grown adult who works for a company that makes calculators.
That is weird.
It gets weirder. I brought one of the new calculators up to the GT room and asked if any of the kids wanted to reverse-engineer it, figure out what was going wrong.
And?
Turns out, these things are designed to be incorrect intentionally. I don't know how to describe it, it's… hard-coded into the hardware. Like these things were built to perform a fake version of math where the number twelve exists.
That's… certainly impressive, from an engineering standpoint. But why?
No clue. It makes no sense. But then we took on some replacement calculators on loan. Casio, reputable brand. They were doing the same thing. We opened them up, and sure enough, they had been built with the exact same hardware structure. Almost as if these intentional flaws were introduced to both companies from the same source. So we opened up one of our new Chromebooks. Same thing in there. Near as I can tell, every consumer electronic built in the past twenty years has been specifically designed to work off a fake version of math.
What? What is this, some kind of global conspiracy against basic counting?
Ha. Ha ha. Funny you should mention it.
Oh no.
I called Texas Instruments again, except this time, someone else picked up. They had a lot of questions for me. Asked for my name and wouldn't take 'the Cube' for an answer. Asked who I worked for, what my goals are, and, exact quote here, 'how I know about twelve.'
…
Now, obviously these are easy questions. I work for Ridgewell Edutainment Center, I'm just trying to run a grade school math department here, and I know about twelve because it's a very basic mathematics concept and I happen to be a very basic mathematics concept.
Right. And what did they say to that?
They asked me to stay on the line. Which I shouldn't have agreed to, but I did. I was just more confused than anything. After a long pause I heard from them again and they asked me to clarify where exactly Ridgewell Edutainment Center was. I told them we fill the space between curiosity and understanding, and they asked for an exact address. I told them there wasn't one, and they said we'd hear from them again soon.
Who are these people?
I'm still not sure, but I sure did hear from them again. A few days later I was derived onto some digital whiteboard, hooked up to a machine that allowed for direct two-way communication between physical beings and abstract concepts. It looked a lot like someone had challenged themselves to recreate my personal cell phone without using rune magic.
Is that even possible?
If you had asked me before, I would have said no. These people were strange, Rayna. However this whiteboard thing worked, it was built in such a way to keep me there, locked in one physical location. No clue how they pulled that off without destabilizing the rest of mathematics. Unless they were trying to destabilize mathematics, and just failed.
That must have been terrifying.
It was certainly unfamiliar. They had this sort of faux military look going on, all concrete and tempered glass. They were armed, but I'm not sure exactly what they thought they were doing holding up guns in front of a function of geometry. My best guess is, some sort of… extremist anti-magic, anti-intellectual terrorist organization? They had a lot of basic questions for me, and I mean really basic. They asked me if I was the only self-aware polyhedron or whether there were others.
They can build a machine to talk to you without using rune magic, but they don't know platonic solids are intelligent?
Right? They asked me again who I work for and what we're trying to do. I told them Ridgewell's goal is simply to be a place for children to learn about the world we all live in. They asked if that learning 'includes the anomalous,' and I said, well, sure. And they said that was 'completely unacceptable.'
'Completely unacceptable.'
Exact words.
And then they just… let you go?
Well, no. It became clear pretty quickly they intended on keeping me on that whiteboard as long as they could. I had to subdivide myself along two diagonally adjacent vertices just to return to abstraction.
…This is a problem.
Well, it's not like our department hasn't run up against danger or hostility before. The kids can handle it, they're smart. But… these guys are crafty. And they're, um, dedicated.
Are they still harassing you?
That's one word for it. The very next day the Science department received a teaching application from a very well-respected professor. Hired her basically on the spot. After I explained my situation to our security staff, though, they thought to search the new hires, and found some things in her possession. Like concealed weapons. A knife and two small pistols. And little white pills. Chemical composition seemed to indicate they were meant to induce memory loss.
Someone brought guns and drugs to our campus?
I'm afraid so.
Why have I not already heard about this?
We didn't want to worry you until we had all the information. To be honest, a lot of us are a little thrown by this. She passed every background check imaginable and was a very well-respected scientist. We could've never predicted she worked for these… paramilitary radicals.
Did she hurt anyone?
Luckily not. We took her before the Edutainment Obelisk and it trapped her inside a classroom motivational poster.
Oh, thank god.
Still, though, I don't expect these people to let up anytime soon. And either they're in the pocket of Big Calculator, or the other way around.
Ugh. We really don't need more enemies right now. I'm busy enough arguing with the Board and fighting over our campus with Eisenfremder.
It's a hard time to be a school. But we just have to keep doing what we've always done.
For the kids.
For the kids. I'm talking with some other department leads on drafting up a defense plan against these creeps. It'll be on your desk by Friday.
Thank you, the Cube. I can always count on, and with, you.
Of course, Rayna. Talk to you soon.
Click.