"The way [the story] describes mathematics uses excellent analogies and ways to think about [the concepts] that both give correct answers and make it much more interesting, fun, and memorable."
-Award-winning mathematics professor
-Award-winning mathematics professor
How to teach anything to anyone
How do humans learn? In very basic terms, learning is like piecing together a puzzle. Our brains have formed a picture based on our previous experiences and knowledge and when something new joins the party, it must figure out where in this existing jigsaw the new information fits in.
In short, to learn something you really need to already know something else. When my grandmother passed away, I took up crochet in her honor. I pulled out a pattern to begin and it looked something like this:
Hdc in next 3 sts
Huh? Turns out, I needed to learn a lot about crochet before I could even begin to crochet. Once I figured out how to translate the information stored in strange shorthand and characters, I needed to then learn how to execute these codes before I could even start accomplishing my goal of crocheting something.
This barrier of prerequisite knowledge turns teaching complex tasks or ideas into a huge mountain learners must scale. It’s also the reason why so many struggle in math and so many educators are plagued with insurmountable challenges every school year. Luckily, there is a way to make learning much easier. A story.
Have you ever wondered why certain fairy tales stand the test of time? In short, it is because they have found a way to simplify complex ideas into a digestible meal that is not only easily scarfed down by anyone, but also a craveable feast. In other words, a good story makes learning both easy and fun.
As a mother, I understand the importance of teaching my children right from wrong. I also understand this is not an easy task. I have gone down many ‘why’ holes in my life.
“You shouldn’t lie.”
“Why?”
“It’s wrong.”
“Why?”
“You are misleading someone and telling them something that isn’t true.” “Why?”
“What do you mean why? I don’t know why you’d do it, you shouldn’t!” For a child, understanding the intricate nature of lying, consequences, credibility, and mortality seems impossible. There is too much to understand before you can even begin to understand. Enter The Boy Who Cried Wolf.
In this tale, a young boy experiments with the ‘ding-dong-ditching’ of his day: screaming for help and laughing as the villagers come running only to find there is no real emergency. The lesson emerges when the boy encounters an actual threat but has used up all his good-will and trust, causing no one to heed to his calls.
It’s beautiful. Somehow in only a few pages, this story manages to help very young children understand the complicated topics some philosophers spend their entire career on. It unpacks a multifaceted issue into a bite-size takeaway that even a five year-old can grasp. When I lie it causes people to stop believing me, which can be very bad if I ever really need help.
Even better, it’s memorable. That is the power of a story. In Marco the Great and the History of Numberville I present middle school math concepts that are tricky for most students. Through imagery, analogies, and relatable situations, these same challenging ideas now feel obtainable and even intuitive, because a story is a powerful thing.
So next time you are looking to teach someone something new, tell them a story. Not only can it make understanding complex tasks accessible, it is also much more likely to stick in their brain and stay there.
by SK Bennett (Author), Carla DuPont (Editor)
April 17, 2023
Today is the day you fall in love with numbers.
Marco the Great and the History of Numberville is the first installment in a fantastical adventure series that will have readers learning math and enjoying every minute of it. In addition, the text includes over 300 practice problems and solutions as well as access to an entire digital world allowing students to dive directly into Marco's world with 40+ games to level-up their learning.
SYNOPSIS
Marco did okay in math. He could follow the complex blueprints provided to him, navigate the steps, and arrive at the answers that earned him a shiny grade near the front of the alphabet. That is, until middle school. As new and confusing letters started creeping into every question, Marco developed a problem. When a new figure 'pops' into his life, he is introduced to a fantastical world where numbers rule, where they live together in villages, engage in duels, build stadiums and cheer for their favorite team as players are flung through the air. Marco's imagination runs wild as he develops new powers and hungers for more.
But everything is not as it seems. Join Marco, his annoying little sister Maggie, and his best friends Oliver and Liam (a math whiz and a conspiracy nut), as they discover this magical world is more real than they ever could have dreamt. And find out... Will Marco master the Numberfolk before the Numberfolk, very literally, master him?
Marco the Great and the History of Numberville is the perfect choice for summer reading. Help your students catch up, get ahead, or just develop a deep understanding and love of numbers all while having a blast. Available for extended distribution for library and school purchases. Please contact partner@mathbait.com to bring Marco's amazing world to your students.
READING LEVEL
Marco the Great and the History of Numberville is a MathBait publication. The first installment in the series covers standards from 6th & 7th grade Prealgebra. The exact topics can be found at www.mathbait.com/marco-the-great.
Marco the Great and the History of Numberville is a MathBait publication. The first installment in the series covers standards from 6th & 7th grade Prealgebra. The exact topics can be found at www.mathbait.com/marco-the-great.
Marco the Great has a 4th-6th grade reading level and was written for a middle school audience. However, it is a great option for younger students as well, either independently or read aloud. Throughout his journey, Marco encounters bullying which may be uncomfortable for younger readers. Parents may skip the related passages (pages 22, 60, and 112), if desired, for the given audience.
Excerpt
Chapter Five: Letters
Despite the enjoyment his tutoring sessions brought, he had not yet fallen in love with the educational jail known as Mrs. Sanders’ class. The best of the day was word problems. In an unusual change of events, as his classmates struggled to translate sentences to numbers and letters, then to numbers, and finally back to words again – for the first time, Marco found himself at the head of the class.
“A new robot toy was released, and you are excited to buy it.” Mrs. Sanders always tried to make word problems have some interest to her students. While it was a nice thought, they all boiled down to an equation of some sort with all the context removed anyway. “It is listed for $50, but there will be a sale offering 20% off. How much will you save if you buy the game on sale?”
Oliver’s hand shot up. Marco’s best friend, like his sister, possessed a genetic supernatural power that made them number savants. While everyone else struggled to move an inch, they could come in and easily jump a mile. The fact that Oliver was also the class clown and always in trouble helped balance the nugget of jealousy that ached in the pit of Marco’s stomach.
“Yes, Oliver?” Mrs. Sanders pointed to her student. “You will save 20%,” Oliver answered with a smirk. Quiet giggles erupted from all corners of the classroom.
After a sharp look, Mrs. Sanders painted her smile back on and responded, “You are correct. But how much money would that be?” In an instant, the class became the robots from the problem and following their programming, they all put their heads down and began scribbling on the paper in front of them. Unlike his cyborg peers, Marco put his head down, but wrote nothing on his paper. He had a different idea. Remembering what he had talked about with Mr. Pikake – that numbers are ours to control – he let his imagination take over.
Knowing that ‘percent’ meant ‘out of 100’, Marco saw the number 100. A vacuum cleaner was sucking out 20s from the number. SLURP! Now, it was an 80 and a 20. SLURP! Now two 20s and a 60. Marco kept sucking at the number until it lay on the ground as five disoriented 20s. He turned his attention to the $50 from the question. He changed the settings to rip the 50 into five pieces as well in one mouthful. SLURP! Five 10s shot out the back.1
He slowly raised his hand. Oliver shot Marco a look that read, ‘What are you doing?’ “Marco,” Mrs. Sanders called.
“10?” Marco answered reluctantly.
Mrs. Sanders looked at the clock which read 9:58, “No, it’s not quite 10 yet,” she responded. “No. The question. You’d save ten dollars.”
Her face frozen in a state of shock, Mrs. Sanders looked down at her paper and back up at Marco. “Oh, um, yes. That is correct, Marco. Nice job.”
Riding his math high for the rest of the day, Marco was silently thrilled when Oliver took it upon himself to recount the event for Liam at lunch.
“You should have seen it, man!” Oliver exclaimed. “The teacher couldn’t even solve it as fast as Marco.” He turned to add, “Your tutoring must be going well.”
Marco pushed and pushed but couldn’t hide his smile. His green eyes were bright with excitement as he began to tell his friends about Mr. Pikake. “He’s a little crazy, I’m not going to lie. It makes things fun. It’s like a video game, but rather than zombies, we are hunting numbers.” Pretending to be a character in the boy’s favorite game, Marco mimed out a zombie hunt.
“Are they evil numbers trying to eat your brain?” Liam laughed. Although Marco hadn’t thought about it before, the way Mr. Pikake talked about numbers gave him the sense there was something dangerous about them. Realizing how bizarre that was, he shook the thought from his head.
1 What did Marco do here? The question Mrs. Sanders really asked was ‘What is 20% of $50?’ Since five 20’s make 100, he needed to know 5 of what would make 50. He split 50 into five pieces to discover each piece is a ten, meaning 20% of $50 is $10. You can do this with any question where the percentage is a factor of 100. My dog ate 12 pounds of food last month, and he ate 25% more this month, how much did he eat? Since it takes four 25’s to make 100, how many fours make 12? Well, three, of course. So, 25% of 12 is 3. Fido ate his normal 12 pounds plus the 3 more, meaning he ate a total of 15 pounds of food this month – what a pig!
Chapter Five: Letters
Despite the enjoyment his tutoring sessions brought, he had not yet fallen in love with the educational jail known as Mrs. Sanders’ class. The best of the day was word problems. In an unusual change of events, as his classmates struggled to translate sentences to numbers and letters, then to numbers, and finally back to words again – for the first time, Marco found himself at the head of the class.
“A new robot toy was released, and you are excited to buy it.” Mrs. Sanders always tried to make word problems have some interest to her students. While it was a nice thought, they all boiled down to an equation of some sort with all the context removed anyway. “It is listed for $50, but there will be a sale offering 20% off. How much will you save if you buy the game on sale?”
Oliver’s hand shot up. Marco’s best friend, like his sister, possessed a genetic supernatural power that made them number savants. While everyone else struggled to move an inch, they could come in and easily jump a mile. The fact that Oliver was also the class clown and always in trouble helped balance the nugget of jealousy that ached in the pit of Marco’s stomach.
“Yes, Oliver?” Mrs. Sanders pointed to her student. “You will save 20%,” Oliver answered with a smirk. Quiet giggles erupted from all corners of the classroom.
After a sharp look, Mrs. Sanders painted her smile back on and responded, “You are correct. But how much money would that be?” In an instant, the class became the robots from the problem and following their programming, they all put their heads down and began scribbling on the paper in front of them. Unlike his cyborg peers, Marco put his head down, but wrote nothing on his paper. He had a different idea. Remembering what he had talked about with Mr. Pikake – that numbers are ours to control – he let his imagination take over.
Knowing that ‘percent’ meant ‘out of 100’, Marco saw the number 100. A vacuum cleaner was sucking out 20s from the number. SLURP! Now, it was an 80 and a 20. SLURP! Now two 20s and a 60. Marco kept sucking at the number until it lay on the ground as five disoriented 20s. He turned his attention to the $50 from the question. He changed the settings to rip the 50 into five pieces as well in one mouthful. SLURP! Five 10s shot out the back.1
He slowly raised his hand. Oliver shot Marco a look that read, ‘What are you doing?’ “Marco,” Mrs. Sanders called.
“10?” Marco answered reluctantly.
Mrs. Sanders looked at the clock which read 9:58, “No, it’s not quite 10 yet,” she responded. “No. The question. You’d save ten dollars.”
Her face frozen in a state of shock, Mrs. Sanders looked down at her paper and back up at Marco. “Oh, um, yes. That is correct, Marco. Nice job.”
Riding his math high for the rest of the day, Marco was silently thrilled when Oliver took it upon himself to recount the event for Liam at lunch.
“You should have seen it, man!” Oliver exclaimed. “The teacher couldn’t even solve it as fast as Marco.” He turned to add, “Your tutoring must be going well.”
Marco pushed and pushed but couldn’t hide his smile. His green eyes were bright with excitement as he began to tell his friends about Mr. Pikake. “He’s a little crazy, I’m not going to lie. It makes things fun. It’s like a video game, but rather than zombies, we are hunting numbers.” Pretending to be a character in the boy’s favorite game, Marco mimed out a zombie hunt.
“Are they evil numbers trying to eat your brain?” Liam laughed. Although Marco hadn’t thought about it before, the way Mr. Pikake talked about numbers gave him the sense there was something dangerous about them. Realizing how bizarre that was, he shook the thought from his head.
1 What did Marco do here? The question Mrs. Sanders really asked was ‘What is 20% of $50?’ Since five 20’s make 100, he needed to know 5 of what would make 50. He split 50 into five pieces to discover each piece is a ten, meaning 20% of $50 is $10. You can do this with any question where the percentage is a factor of 100. My dog ate 12 pounds of food last month, and he ate 25% more this month, how much did he eat? Since it takes four 25’s to make 100, how many fours make 12? Well, three, of course. So, 25% of 12 is 3. Fido ate his normal 12 pounds plus the 3 more, meaning he ate a total of 15 pounds of food this month – what a pig!
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SK Bennett is an award-winning educator, instructional designer, mathematician, and home school mom of five. She spent years designing courses for top companies and institutions before deciding it was time to embrace her belief that learning should be fun and math should never be all about memorization and rote procedures. Inspired by her favorite stories, she set out to create Marco's world - where learning is an adventure and math is never ever boring.
Bennett has also been published in a book of poetry as well as her academic research contributions to improving mathematics education through an emphasis on conceptual understanding.
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