Tag Archives: problem solving

Dominoes for Teaching Fractions, Decimals, or Division

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Choose a set of rules for dominoes, then pick one of the following variations on score-keeping:

For Addition of Fractions

  1. Each player keeps track of points individually. For competitive games, individuals keep track of their own scores. For cooperative games, each player keeps track of the total score of the game.
  2. As players place tiles, the numbers represent fractions rather than integers. The number on the end touching the existing tile is the numerator, and the number on the free end is the denominator.
  3. Each time a tile is placed, the player must add the resulting fraction to the point total.
  4. If playing a version where doubles are played sideways, use this as an opportunity to enforce the concept that it doesn’t matter which number is the numerator; the answer is still 1 point for that tile.

For Long Division and Addition of Decimals

  1. Each player keeps track of points individually. For competitive games, individuals keep track of their own scores. For cooperative games, each player keeps track of the total score of the game.
  2. As players place tiles, the numbers represent division problems rather than integers. The number on the end touching the existing tile is the dividend, and the number on the free end is the divisor.
  3. Players must divide the numbers appropriately to how the tile was played, and add the resulting decimal number to the score total. The facilitator may choose to specify a certain number of digits to be used (i.e. – “round to the nearest hundredth”) depending on the skill level and desired outcomes of the game.
  4. If playing a version where doubles are played sideways, use this as an opportunity to enforce the concept that it doesn’t matter which number is the dividend; the answer is still 1 point for that tile.

For Division with Remainders, Rounding, and Addition of Integers

  1. Each player keeps track of points individually. For competitive games, individuals keep track of their own scores. For cooperative games, each player keeps track of the total score of the game.
  2. As players place tiles, the numbers represent division problems rather than integers. The number on the end touching the existing tile is the dividend, and the number on the free end is the divisor.
  3. Players must divide the numbers appropriately to how the tile was played until a remainder is found. Then, players properly round the answer to the nearest integer and add it to the score.
  4. If playing a version where doubles are played sideways, use this as an opportunity to enforce the concept that it doesn’t matter which number is the dividend; the answer is still 1 point for that tile.

 

The Parable of the Anachronistic Alchemist

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A prodigy graduate physics student at UC Berkeley in California’s bay area worked secretly to create a time machine. The device was designed to transport up to two people and their clothing, two small cases of gear, and enough fuel for a return journey through time and space. Calculations regarding Earth’s location in space over time were integrated into the operating systems, allowing the driver the ease of entering a date, time, and Earth surface coordinates into the console.

Our student had a fondness for alchemists from history. Their obsession with such goals as turning lead into gold did not impair their judgement when it came to the process of discovery. In fact, these individuals began to carefully record the results of their experiments, and ultimately created the fundamentals of what is known today as the scientific method.

When the time machine was complete, our student dressed in destination-appropriate clothing, bid adieu to the cat in ancient Greek, and arrived moments later outside Alexandria in the middle of a summer night in the year 176. After an incredible adventure that is not relevant to this story, our student returned to the vehicle with a new friend who was an alchemical practitioner, and a deeper understanding of the ancient Greek language.

Our student brought the alchemist to Berkeley’s campus, sneaked him in to the chemistry library, and showed him the wonder of one of her favorite collections of knowledge.

“Nearly two thousand years of exploration and discovery have lead us to this and more,” our student said in ancient Greek.

The alchemist looked around with excitement. Book after book the alchemist pointed out, and our student translated the title. Sometimes they read in the books. As time went on, the alchemist grew wary.

“This cannot be,” he said. “Elements that are not alive? Metals as discrete, separate elements that do not mature into precious metals? Everything here is based on these concepts, and these concepts are false. Therefore, this library is full of nothing but lies.”

Our student was perplexed and tried to discuss the matter further, but the alchemist wished to return home. Our student complied, leaving him back in ancient Alexandria where she had found him. Back at home, she contemplated the situation. It did not make sense for someone who was dedicated to truth and reason to dismiss something just because it conflicted with previously held beliefs.

Graduation finally came, and our student took the podium. Her encounter with the alchemist flavored her speech to her fellow graduating scientists.

“…truly embracing discovery can be difficult because it means letting go of preconceived notions, and preconceived notions are comfortable. They help us understand the world, so losing them is scary. As we go forth into the real world let us remember, in former president Roosevelt’s words, that ‘the only thing we have to fear is fear itself.’ Go forth. Let yourself be afraid. Discover truth.”

Snippets from the Week

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Any names presented have been changed.

A Morning in Line

This particular food distribution location is my favorite one. I intend to write a post in the future about the full extent of why, but one of the reasons is that folks there are pleasantly social. This distribution location doesn’t use lines in the traditional sense. Instead, they use a “take a number” system. The result is that folks actually talk to one another. With the freedom to move about a pretty church courtyard from group to group, it almost feels like a family reunion full of folks you’ve only ever met in passing.

Ages of patrons waiting for food ranged from 20s to way too old for estimation. Most folks looked well over 40. Many of them had long-wrinkled skin and used wheel chairs or other mobility assistance devices. Several of them asked my name, and I began making new friends.

As usual, I managed to be using the restroom during the morning prayer. I wouldn’t call myself an atheist per se, but I also do not have a desire to pray to a God I don’t believe in. Silently refraining from joining the group prayer prior to food distribution earned me nasty looks from other patrons on my first few visits. Conversely, the folks running “God’s Pantry” took no apparent offense to my discrete abstinence from prayer.

I emerged from the restroom with freshly washed hands clutching my numbered ticket. I asked one of my new acquaintances if I had missed anything important during announcements. He told me that there was a registered nurse there that day, and directed me to her.

I asked the nurse about some concerning symptoms I had. She urged me to see a doctor at my earliest convenience. I thanked her, and went back to waiting my turn.

An Afternoon in Class

My calculus teacher wrote the number of students who received each letter grade on our first test on the white board:

  • 6 – A
  • 6 – B
  • 12 – C
  • 5 – D
  • 4 – F

“What a lovely bell curve,” I thought to myself as I awaited my exam. The teacher walked about, placing each one face down on the desks. Finally it was my turn.

I stared at the back of my test, then flipped it over as if I was ripping off a bandage. My heart danced a little with joy at what I saw.

“What did you get?” asked my study buddy from the desk behind me.

I showed him the big “96% Nice Job!” across the top of my page. He grinned. His score was a 97%. High-fives were had.

An Evening in the Store

I am a superstar at the retail store where work. I’ve got the brain of a problem-solving engineer and the heart of a compassionate teacher. The combination makes me perfect for any employer who wants proactive employees.

I can do anything on the sales floor except work in the coffee shop, including all the things with special training, which means I often don’t get my assigned tasks completely done. My bosses are okay with that, though; they know I am putting out fires.

On this particular evening, the line at the returns desk became wondrously long, so I hopped back there to help out. My last customers consisted of a couple who had come to return their coffee maker because the latch button which allows the coffee to be poured from the carafe had broken off. Their receipt had not expired, but we were out of stock on that model.

It took some convincing as they had their heart set on that exact model, but I walked the couple back to the coffee display to see if we could find something similar that they liked. We couldn’t, but I got an idea, and I pulled out my walkie.

“Nancy, do you copy, Nancy?”

“Go for Nancy,” my manager responded.

“I have some folks with me who would like to return a coffee maker, but we are out of stock on the model they want. It’s just a small piece on the carafe that’s broken, though. Is it okay if we just switch it out for the display model’s carafe?”

“Is theirs still in good enough condition that our display will look nice?”

“I think so. It shouldn’t be too hard to glue this piece back on for display.”

“Yeah, that’s fine. Go ahead and do it.”

I peeled the sticker off the display carafe, and handed it to the customers in return for their old one. They left after expressing their happiness. In the break room, I used a cleanser which contained hydrogen peroxide to dissolve the coffee scent from the inside of the pot. It worked remarkably well, although there was still just enough of a hint of it that I hoped it might help drive more sales. When the outside was clean, I put the sticker from the original display model on it. It shined beautifully.

A Night in the Emergency Room

“I’d like you to stay on a clear liquid diet for the next 24 hours or so,” the ER doctor said to me.

I couldn’t decide whether to laugh or cry.

“I can’t really do that, but I’ll try,” I said.

“Clear liquids are things you can see through,” the doctor explained. He must have thought I had not read the papers the nurse had handed me. “So, things like Jell-O, and…” I interrupted during his pause.

“No, you don’t understand. I live off of food bank food. I don’t get a choice. I will do my best, and I’ll try to be gentler with the food I eat, but there’s no way for me to get my hands on clear liquids other than water. They don’t give us Jell-O at the food bank.”

“Oh…okay…” the doctor said, then went about discharging me. Long story short, suffice it to say that the CT scans show I did not have a concussion or internal bleeding, and the blood work was negative for everything, which is a fantastic combination. I know that “Obamacare” has hurt a lot of people in the middle class and probably could have been implemented better, but if it wasn’t for our current healthcare system, I would never have been able to afford a brain scan when nausea and other problematic symptoms followed a head injury.