Monday, January 10, 2011

Best Homeschool Lessons: The Witch of Mixed Fractions Doom

Several years ago, desperate to inspire a clean-up, I plagiarized an idea from Mrs. Piggle-Wiggle. Donning a cloak, I cackled evilly, "Aha, my pretties. You are disobeying your mommy, excellent. [Stage whisper] If their clean-up is not done in thirty minutes, I will kidnap them and turn them into little minion slaves. Hehehe."

The kids named my alter ego "The Witch of Doom" and set about to thwart me.

Since then, the Witch of Doom has made many appearances. From cockroach pie for Halloween, to a series of bedtime stories detailing the deaths of her many minions, she has become a fixture in family folklore.

Below is a math problem I devised for Eric involving her struggles with mixed fractions.

Part I: Problem

The Witch of Doom is making a polyjuice (transformation) potion. Her nefarious plan is to steal one of Eric's hairs, drop it in her potion, and become his temporary doppleganger. (The effects of a properly-prepared polyjuice potion last one hour.) While impersonating Eric, she intends to poison Mom.

The recipe calls for 5 cups of dragon's blood. The Witch finds only 1 1/3 cups in her cabinet. "Dratted acorn dregs!" she curses. "I forgot to re-order."

Digging through her disorganized storage shelves in the dungeon, she finds a partially-used box of dehydrated dragon's blood. The instructions say to reconstitute 1 tablespoon of the powder with 3/4 of a cup of water. She measures 2 1/2 tablespoons remaining.

Muttering to herself about moronic minions who make miserable lab assistants, she hobbles out to the moat and kills an alligator. Her reference book, Queer and Curious Concoctions, gives the following ratio for emergency substitutions:

3/5 cup fairy dust : 1 cup alligator blood = 1 cup fresh dragon blood.

The Witch has plenty of fairy dust. (A barely-literate previous minion made a clerical error and ordered 50 #10 cans instead of 5, giving her a lifetime supply.)

How many cups of alligator's blood does she need to finish her recipe? How much fairy dust must she stir in?

Note: she doesn't have a decimal-based measuring cup. Use standard English measurements.


Not allowed: 3.85 cups
Allowed: 3 3/4 cups + 1 1/2 teaspoons.


[Eric calculated correctly, of course.]

Part II: Aftermath

As you correctly calculated, the Witch needs 1 3/4 cups + 2 teaspoons of alligator blood. She also needs 1 cup + 1 1/5 tablespoons, or 1 cup + 1 tablespoon + 3/5 teaspoons of fairy dust.

Since she lacks instruments to measure 1/5 of either tablespoons or teaspoons, she calculates that 3/5 teaspoons = 4.8 eighths-of-a-teaspoon. "Close enough," she growls impatiently, and rounds to 5/8 teaspoons.

Her mathematical calculations are correct. She prepares her potion, drinks it, and tries to infiltrate the Berry home.

On her way there, she has an epiphany. "Why on Earth did I waste time mixing fresh, dehydrated, and imitation dragon blood?" she berates herself. "I could have simply taken 5 cups of alligator blood--there was more than enough--stirred in 3 cups of fairy dust, and saved myself all that math and mixing!"

"Or," her latest minion suggested, "You could have re-ordered dragon blood and waited until it arrived to try your plan."

This was the most intelligent thing the minion (#18, Karl) had ever said. It is thus unfortunate that the Witch rewarded his suggestion by turning him into an alligator.

(Of course, the Witch of Doom might also have tried a variety of other options, including upgrading her laboratory with modern, metric-friendly books and instruments.)

The Witch arrived at the Berry home, sauntered into the kitchen, and poured a drink of milk, surreptitiously adding in the poison. "Mommy dearest," she called, attempting to imitate Eric, "I made this for you."

Alas, all the Witch's hard work proved inadequate. Mom took the cup but then stared. "Who are you?" Gail demanded suspiciously.

The polyjuice potion had worn off early!

"Barking behomoth bananas!" the Witch shrieked. (Thus further damaging her cover.) "But I measured everything exactly!"

She had, indeed, computed and mixed accurately. Had she bothered to double-check her Handbook Reference to Heinous Potions, however, she would have remembered that polyjuice belongs to the Finicky class, where substitutions for fresh ingredients have no efficacy.

The 1 1/3 cups of fresh blood were only 4/15ths the total mass of the potion; though operating at full strength, they conferred only 16 minutes of transformation.

The reconstituted powder was 1/3 the magical potency of fresh blood. It conferred only 7 1/2 minutes of disguise.

Instead of 60 full minutes, the Witch of Doom only got 23 1/2, several of which she wasted in travel and in re-stocking her moat.

By the time Mom saw her, the Witch had a blurry shape and was flickering oddly. No wonder Mom looked at her askance.

Thwarted yet again, the Witch of (Unfulfilled) Doom retreated sulkily back to her dungeon, where she decided to upgrade her infrastructure, train a new minion, and plot for another day.

--Yes, technically the "solution" was longer than the actual "problem," but it was so much fun! Plus it teaches important lessons about magic, science, leadership, and preparation.


Brian Thomas said...

Since fairy dust is (I'm presuming) approximately the consistency of flour, which packs, why is the witch measuring by volume? She should really invest in a kitchen scale and measure by mass for more effective (and tasty) potions!

Krenn said...

Why haven't I heard about the Witch of doom before? the kids really came up with this name themselves?

I wonder if i can use that as a villain idea the next time i run a hackmaster session for little people...

Gail said...

@ Brian -- excellent idea, thanks. The Witch has modernity problems. She also has minion problems. More on that in another homeschool lessons post.

Gail said...

@ Ronald -- Yes, the kids came up with the name themselves. I tried to pass myself off as a generic "Wicked Witch" or maybe Baba-Yaga. I have referenced her before in passing. See my post of kid quotes from October 2009.


Gail said...

@ Ronald -- oh, and you are welcome to use her as a villain. She's not a super fleshed-out character. I think her succession of minions make for better story fodder, generally.

Carolyn said...

I thought that Mommy was suspicious because REAL Eric does not do spontaneous nice things for his mother. I'm sad that that twist did not make it into the plotline!