How Metaphors Make Math Make Sense

Math struggles can feel like standing on the edge of an impossible canyon — but every canyon has a bridge, even if you can't see it yet.

You're standing on one side of a canyon, waving frantically at your child on the other side. Between you? A whole lot of nothing—just thin air and the growing panic of "How am I supposed to get across this?"

That canyon? That’s math for a lot of kids—especially our brilliant, outside-the-box, neurodiverse thinkers. Numbers float out there like random puzzle pieces. Procedures feel like bizarre rituals. And no one remembered to build a bridge.

The problem isn't your child.

The problem is the way math has been taught since the dawn of time:

"Here are some numbers. Memorize the magic steps. Don't ask questions. Try not to cry."

Metaphors and analogies aren’t just nice little teaching tricks.

They’re the secret passageways that let your child sneak around the walls traditional math throws up.

They turn the “What even IS this?!” into “Ohhh, I see it now.”

(And honestly? Sometimes they make the rest of us adults finally get it too.)

And when you finally hand your child the right story—the right bridge—they don’t just understand math.

They own it.

So buckle up.

Today, we’re ditching the math trauma, grabbing some storytelling magic, and giving you a sneak peek into how premium, customized math instruction actually feels for a neurodiverse mind.

Why Neurodiverse Learners Need Bridges, Not Barricades

When students get to see, touch, and build math, the abstract becomes real—and confidence follows.

When I first started teaching, I had the optimism of a Golden Retriever puppy."Oh, math is just a set of steps! I'll show them the steps, and boom—everyone’s a math genius by Tuesday!"

Reader, they were not math geniuses by Tuesday.

Or by Friday.

Or... ever, if I kept that approach.

Here’s the uncomfortable truth they don’t warn you about in teacher training:The “steps” only make sense if you already secretly understand the concept.

Otherwise, it’s like being told to bake a soufflé when you’ve never seen an egg.

Neurodiverse learners—kids with ADHD, dyscalculia, autism, or simply wildly creative brains—don’t magically infer meaning the way traditional teaching assumes.They aren’t broken.They aren’t "behind."

They just don’t buy the nonsense that two random procedures somehow equal deep understanding.(And honestly, can you blame them?)

Instead of barking "Just follow the steps!" at a confused kid, we have to do something revolutionary: make the meaning visible.

That’s what metaphors do.They build a bridge between "this is nonsense" and "ohhhh, it’s like that!"

They take something wildly abstract—like, say, negative numbers—and wrap it in something human, like owing your brother five bucks because you "borrowed" his video game controller without asking. (Not that I'm speaking from experience. Ahem.)

True story: I had a student, Ethan, who treated negative numbers like they were radioactive.The more we practiced, the more confused he got—until he finally asked, "Wait, why would I even need to know LESS than nothing?"

Fair question, honestly. So we threw out the worksheet and built a video game quest instead: Ethan had to escape a dungeon, climbing from -10 (the dungeon depths) back up to Level 0 (daylight).Every move upward? Less negativity, more hope.Suddenly, Ethan wasn’t just tolerating integers.He was winning them.

The next week, he rocked his quiz like a boss. No tears. No drama. No threats to "accidentally" light his math book on fire. (Progress.)

The bottom line?If math feels like a locked castle guarded by dragons, metaphors are the secret keys your child needs.And if the traditional approach expects them to scale the walls barehanded?Yeah... we’re building a drawbridge instead.

What Makes a Powerful Mathematical Metaphor

Not all metaphors are created equal.(Somewhere, a thousand corny math posters just gasped in horror.)

Some metaphors are pure, brain-lightbulb-flashing magic.

Others?

They're like duct-taping a fork to a spaghetti noodle and calling it a bridge. Creative? Sure. Effective? Absolutely not.

So what separates a metaphor that actually helps your child get it from one that just leaves them wondering why adults are allowed to drive cars unsupervised?

Here’s the secret formula for a metaphor that actually works:

1. It’s sensory, not theoretical.

If the metaphor doesn’t make your child see it, feel it, or taste it (ok maybe not taste unless you’re teaching fractions with chocolate cake, which honestly...highly recommend), it’s going to float off into the mental void labeled “things I will now ignore.”

Example:

Instead of mumbling something soulless like "Multiplication is repeated addition," — aka the dental floss of math explanations —you say, "Multiplication is like stacking pancakes—layer after delicious layer."Suddenly, it's real. It's vivid. It's possibly making everyone hungry.(And if pancakes are involved, odds of engagement increase by approximately 472%. True science.)

2. It fits your child's brain like a tailored suit.

No metaphor is "one size fits all," unless you're aiming for “sad paper bag chic.”(Which, spoiler, we are not.)

Visual learners need colorful, dramatic imagery.

Story-driven kids need quests and cliffhangers.

Hands-on kids? Give them props, movements, and real stuff to manipulate. (And maybe a few things that aren’t breakable. Just saying.)

Example:

Explaining variables in algebra to a visual thinker?Don’t mumble about “mystery numbers.”Hand them a mental treasure chest locked tight—X marks the spot.

(And if they design an entire pirate ship backstory for their math homework? Honestly, extra credit. And I would like to pre-order that video game.)

3. It evolves as your child grows.

A metaphor is like training wheels—not a lifelong crutch.(Unless you really do want your college freshman solving systems of equations by drawing pizza slices. In which case, best of luck.)

The best metaphors lift off once they’ve served their purpose.First, fractions are pizza slices.Later, they're ratios and proportions running businesses, building bridges, mixing the perfect shade of lipstick (yes, makeup is basically chemistry, fight me).

The goal: Anchor the concept now, so later your child can navigate without needing a pizza map.

🚨 Metaphor Red Flags 🚨

If you hear any of these from a teacher, tutor, or math program, run—don’t walk:

• “Just memorize this, it’s easier.”(Translation: I’ve given up, good luck kiddo.)

• “You’ll get it eventually, it just clicks.”(And if not? Well, better luck in your next life, I guess.)

• “This is the way we've always explained it.”(Fun fact: Bloodletting was also "the way we used to do medicine." Look how great that turned out.)

  
  

If the metaphor doesn’t make your child’s face light up—or at least tilt their head like a very suspicious golden retriever—it’s not doing its job.

A real metaphor doesn’t just teach a concept.

It teaches your child that their brain was never the problem.

The approach was.

Quick Storytime:

One of my favorite students once told me that fractions "felt like monsters hiding under her bed."(And honestly? Fraction subtraction still lives rent-free in my nightmares, too.)

So instead of hammering through “numerator/denominator” for the hundredth time and watching her soul leave her body, we reinvented fractions as magic potions.

Half a potion? Half a bottle.Three-fourths? Three ingredients. (Dragon scale optional.)

Fast forward a few months:

She was making up her own fraction word problems—like "How many unicorn hairs do you need for a 2/3 strength invisibility potion?"...and passing her math tests with a swagger that would make any Hogwarts alum proud.

All because the right metaphor turned math from a monster into a superpower.

✨ Tiny Mic-Drop:

If math feels like a maze built by a sadistic wizard, the right metaphor hands your child a map, a compass, and a jetpack.

And that’s when the real learning takes flight.

In their hands, the building blocks of understanding — turning math into something they can touch, see, and believe in.

From Numbers to Narratives: Examples That Reshape Math Learning

Now that we know metaphors can turn a math meltdown into a math mic-drop, the next obvious question is:"Okay, wise guy... what do good metaphors actually look like?"

(First of all, appreciate the energy. Second of all, let’s get into it.)

Here’s the thing:

The best metaphors aren’t random.

They’re personalized, playful, and ridiculously sticky—the kind of mental images that your child can’t unsee even if they tried.

Here’s how the magic happens:

Fractions: From Pizza Parties to Music Jams

Old way:"Fractions are parts of a whole."(Cue the blank stare and internal screaming.)

Better way:

• Pizza Party:

  • "If you slice a pizza into 8 pieces and grab 3? You’re holding 3/8 of dinner.

    If Uncle Bob crashes the party and you have to split it more ways? Boom—your slice just got smaller. Blame Bob."

• Music Beats:

  • "A fraction is like a drum beat. If you have 4 beats in a measure and you hit the drum on 1 of them? You’re rockin’ a 1/4 rhythm. Congratulations, you’re now a drummer. Groupies not included."

✨ Why it works:

It’s tangible. It's funny. Your child will be able to feel the beat or taste the pizza (And possibly start a lifelong grudge against Uncle Bob.)

Algebra: From Mindless Balancing Acts to Language Translation

Old way:"Solve for x."(Which sounds about as thrilling as organizing your sock drawer.)

Better way:

• Seesaw Battle:

  • "Algebra is like a playground seesaw.If you add a chubby cat on one side, you better add something just as heavy to the other side, or that thing's going DOWN, and possibly flinging someone into orbit."

• Language Translation:

  • "An equation is basically a secret message. Your job? Crack the code so x stands alone. You're basically a math spy now. Sunglasses optional, but encouraged."

✨ Why it works:

Kids feel powerful when they’re decoding something.(Also, launching hypothetical cats into space = instant engagement.)

📚 Negative Numbers: Dungeon Levels, Not Doom

Old way:"Negative numbers are numbers less than zero."(Yawn.)

Better way:

• "Imagine you're trapped 10 floors underground in a video game dungeon.-10 means you're way deep. Every step up is one floor closer to daylight.Less negativity = more hope."

✨ Why it works:Kids don’t fear negative numbers anymore—they fight their way out of them.

📚 Decimals: Money, Honey

Old way:"Decimals are parts of a number."(Great. Tell that to a kid who doesn’t even like numbers.)

Better way:

"Decimals are just money in disguise.0.75? That’s 75 cents.0.1? Dime city, baby.If you can buy candy with it, you can understand it."

✨ Why it works:Money talks. Even reluctant mathematicians will show up when Sour Patch Kids are on the line.

Word Problems: From Tests of Endurance to Detective Mysteries

Old way:"If a train leaves Chicago traveling at 60 mph..."(Congratulations, you’ve now bored a child into a coma.)

Better way:

• Detective Mysteries:

  • "Word problems are riddles. You're the detective hunting clues.Numbers are your evidence. Equations are your suspect interrogations. If you set up the wrong crime scene? The case stays unsolved and you owe Sherlock Holmes an apology."

✨ Why it works:

Mystery = power.Instead of dreading word problems, kids get to play detective and outsmart the problem.

(And honestly, after reading some of those state test questions?Outsmarting them feels pretty heroic.)

✏️ Tiny Side Note for Parents:

If your child still hates math after hearing about cats flying off seesaws, solving mysteries, and building pizza empires?Congratulations: you officially have a future poet or defense attorney.Both excellent career options.

✨ Mic-Drop Moment:

When you turn numbers into stories—stories that your child can see, hear, taste, and fight dragons inside—you aren’t just teaching math anymore. You’re giving them the keys to their own brain.

And once a kid realizes that math isn't some random grown-up trick to make them miserable?

They don't just learn it.

They own it.

End scene. High-fives all around.

✨ Want ALL the Metaphor Magic?

These examples are just the opening act.

I’ve created a full downloadable guide packed with 100+ metaphors, real-world examples, and tips for using them to unlock math for every kind of learner—especially your wildly creative, outside-the-box kid.

🎯 Real metaphors.

🎯 Real strategies.

🎯 Real "holy cow, my kid actually gets it" moments.

👉 Click below to grab your free copy of Metaphors for Math Mastery!

Download My Guide

Trust me—you’re going to want this in your back pocket the next time math homework tries to pick a fight.

Beyond the Metaphor: When and How to Fade the Training Wheels

First we build the training wheels. Then we cheer when your child pedals beyond them. That’s real math mastery.

Here’s something they don’t tell you on Pinterest:

Metaphors are amazing...until they aren’t.(Kind of like chocolate cake. Fantastic at first. Regrettable by slice four.)

A metaphor is a bridge, not a permanent vacation home.And if we’re not careful, a tool that was supposed to launch your child into confidence can quietly turn into a crutch that keeps them stuck on Level 1 forever.

Let’s break it down:

When the Metaphor Becomes the Monster

You know it’s time to start fading the metaphor when:

• Your child can parrot the pizza story but still can't add 1/3 + 2/5 without visualizing an actual pepperoni slice.(Note to self: create less mouth-watering math metaphors next time.)

• They’re trying to "balance" every equation by literally picturing a seesaw and now they’re mad that gravity isn’t helping with Algebra II.

• They get too emotionally attached to the metaphor world.(Example: "But if the triangle is a pizza slice, why can’t I eat it?")

😂 Cute?Yes.Helpful long-term?Hard pass.

At some point, we have to gently (and lovingly) kick the metaphor out of the nest and let real abstraction spread its wings.

How to Fade the Training Wheels Like a Pro

Fading a metaphor isn't about yanking it away like a villain in a Disney movie.(Although let’s be honest, a dramatic math villain entrance would make Algebra class way more interesting.)

It’s about gradually shifting focus:

✅ Start by naming the real math concepts alongside the metaphor.

• "Just like you stack pancakes, in multiplication we’re finding the total of equal groups."

✅ Transition to more abstract visuals step-by-step.

• Draw diagrams.

• Create models.

• Use manipulatives but start labeling them with math terms, not just "wizard potions" or "dragon treasure."

✅ Celebrate when they solve without needing the metaphor.

• Seriously. Throw a metaphor graduation party. (Paper hats optional but highly encouraged.)

✅ And finally...Teach them that growing out of a metaphor doesn’t mean they’re losing creativity. It means they’ve leveled up into true mastery.

Because real math power?It’s being able to see the dragon, the castle, the map—and still solve the system of equations without needing the costume party every time.

✏️ Tiny Side Note for Parents:

If a tutor or program never talks about moving beyond metaphors...🚩 Red flag alert. 🚩

There’s a big difference between using creative bridges and building permanent math fairgrounds where no one ever leaves.

The best instruction always builds independence.Not endless rides on the "Pizza Slices Are Life" merry-go-round.

✨ Tiny Mic-Drop:

Metaphors are supposed to hand your child the torch.Not make them think they can only find the light if they're clutching a pepperoni.

When the metaphor fades away—and they still shine?That's when you know you’ve truly won.

Choosing the Right Educational Partner: What to Look For

Let’s get one thing straight:If you’re investing in your child’s math education—especially if your child thinks, learns, and feels differently—you are not just hiring someone to "help with homework."

You’re hiring someone to build bridges inside your child’s brain.(And if that doesn't make you want to be extremely picky, I don’t know what will.)

Here’s the unfiltered truth:Not every tutor, teacher, or program deserves the keys to your kid’s mind.

Some will hand your child a cookie-cutter worksheet and call it "individualized instruction."Others will teach like they're defusing a bomb—with exactly one script and zero room for unexpected sparks.(And if your child dares to think differently? Boom. Metaphorical explosion.)

✨ You, my friend, are looking for better.✨ You deserve better.✨ Your child absolutely needs better.

Here’s how to spot the real educational unicorns—the ones who understand the power of metaphors, individualized learning, and building actual math confidence, not just test performance.

1. They tailor the metaphors to YOUR child.

If a provider says, "Oh, we use metaphors for everyone!" but can’t give you a single personalized example after five minutes of talking...🚩 Red flag.

A truly individualized instructor doesn’t have a dusty box of metaphors sitting on a shelf.They listen.They observe.They build new metaphors on the fly, depending on how your child thinks, moves, jokes, worries, and dreams.

Test question you can casually drop into conversation:

"Can you give me an example of how you’d explain negative numbers to a highly visual learner who loves video games?"

If they stutter, sweat, or try to change the subject?Move along, my friend.

2. They know when to evolve (and when to shut up).

Some educators fall so in love with their own clever metaphors that they forget the goal:Independence.

You want a partner who sees metaphors as a temporary bridge, not a forever floatie.Someone who knows when to gradually nudge your child toward abstract reasoning—without pulling the rug out from under them.

(And definitely without giving a TED Talk about pizza every single session.)

3. They welcome questions (without flinching).

You need someone who lives for questions.The weirder, the better.

• "What if negative numbers are just time travelers going backwards?"

• "Why can’t we have a fraction bigger than a pizza?"

• "Is zero even real?"

  
  

✅ A great instructor will lean in.

✅ A mediocre one will panic and start rambling about the number line.

If a provider seems even slightly uncomfortable with the idea that your child might think differently, create differently, be different?Run. (Preferably while playing "Eye of the Tiger" in your head.)

4. They treat your child’s brain like it’s not already brilliant.

The best partners don’t just “help” your child.They respect them.

They see the fierce, sparkling mind hidden under the frustration.They talk to your child, not at them.They design teaching moments like they’re building custom blueprints for a skyscraper—not handing out Ikea furniture with instructions in Swedish.

Because here’s the deal:

Your child’s brain isn’t broken. It’s extraordinary.

And anyone you bring into their world should act accordingly.

✏️ Tiny Side Note for Parents:

You’re not "high maintenance" for wanting this. You're not "overthinking it."You’re just protecting one of the most precious and irreplaceable things in your world: your child’s belief in themselves.

And honestly?Good for you.(If anyone tells you otherwise, hand them a copy of this article. Gently. Or not so gently. Your choice.)

✨ Mic-Drop Moment:

A premium math experience isn't about flashcards, formulas, or fitting into someone else’s mold.

It’s about handing your child the tools to unlock their own genius.

And the right educational partner?They aren’t just teaching math.They’re helping your child rewrite the whole story of who they are.

Boom. Nailed it. Let’s go build some bridges.

Final Thoughts and Next Steps

Math shouldn’t be a lonely journey. With the right support, your child’s path becomes clear—and you're right there with them, every step of the way.

Here’s the thing:Math was never supposed to be a gatekeeper. It was supposed to be a gateway.

But somewhere along the way, between boring worksheets, one-size-fits-all textbooks, and "just memorize it" lectures, that gateway got buried under piles of confusion, frustration, and "Why even bother?"

Metaphors?

They're the shovels.

They dig through the nonsense and uncover a path that actually makes sense for your child—the one with the wild imagination, the nonstop questions, the brain that refuses to color inside the lines (and thank goodness for that).

When you give your child vivid, personalized bridges to understanding—when you hand them stories instead of scripts—you’re not just helping them survive math.

You’re giving them the tools to own it.

To see it differently.

To trust their own mind in a world that too often misunderstands how brilliant they really are.

✨ And that’s the real magic. ✨

If you're ready to see them light up because math finally clicks—If you want a partner who builds bridges instead of barricades—I would love to meet you and your incredible child.

Book your free consultation today,and let’s start building the path that was always meant for them.

(Click here to schedule your free consultation.)

Ready to see what happens when math finally makes sense?

Let's build that bridge together.

(Cue dramatic music and a well-earned parent high-five.)

You're child isn't broken. The way they'ev been taught probably is. Be the bridge. Change the story.

About the Author

Susan Ardila is a certified teacher, dyscalculia specialist, and educational clinician with over 12 years of experience supporting students with learning differences. Through MindBridge Math Mastery, she provides highly personalized, research-based instruction that empowers students to build confidence, develop strong math foundations, and rediscover their potential. Susan specializes in working with students who have dyscalculia, ADHD, and other learning challenges—helping them bridge the gap between frustration and success.

👉 Ready to take the next step? Book a free consultation.