Numerator vs. Denominator: What Each Part of a Fraction Means
Confused about numerator vs. denominator? Mathnasium tutors explain what each part of a fraction means, how they work together, and where students go wrong.
Picture a classroom where math doesn’t look like math at first glance. A second grader is hopping along a strip of tape on the floor while counting by twos. Across the room, a student is laying out tiles to form a rectangle and explaining what it shows. Another is snapping in rhythm while saying multiplication facts out loud.
None of them is holding worksheets, yet every one of them is practicing math.
That’s the idea behind multisensory math.
By pulling in sight, sound, touch, and movement, students start to experience numbers instead of just memorizing symbols. It’s a wonderful way to spark curiosity and get students to engage. Most importantly, it can make math click like it hasn’t before.
Let’s explore this approach, looking at how and why it works.
“Multisensory” might sound like jargon, but it simply means using more than one sense while learning.
For a younger student, that could mean clapping while skip-counting. A middle schooler might sketch a number line before solving an equation. A high schooler might measure the sides of a polygon instead of just reading the definition in a book.
These strategies may look like fluff, but they’re ways of exploring math by engaging different senses. Some students are auditory learners, some are visual, and some are kinesthetic. Multisensory math allows us to experience math and approach it in a way we learn best.
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It all comes down to neuroplasticity, which is the brain’s ability to reorganize and form new connections. When students use more than one sense, those connections grow stronger. A review in Trends in Cognitive Sciences noted that learning through multiple senses leaves a more durable imprint than learning through just one.
Think of a student working with fractions. They might handle a tile and look at its size, or speak the name of the fraction aloud. Each of those actions gives the brain a different way to store the idea, which makes it easier to call back later.
Educator David Sousa, in How the Brain Learns Mathematics, points out that involving motor and sensory regions during math lessons builds a wider toolkit for reasoning.
We see this play out in our center: students who tense up at worksheets often loosen once they can move pieces around or explain their thinking out loud.
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Educators sometimes call this the Concrete–Representational–Abstract (CRA) sequence. Students begin by using objects like blocks or counters (the concrete stage). From there they move to drawings or diagrams (the representational stage). Finally, they work with just numbers and symbols (the abstract stage).
This progression is important. A study on effective math interventions showed that the CRA method significantly helps students, especially those struggling, by providing a clear pathway from the tangible to the abstract.
At our Cherry Creek center, we see this all the time. A student struggling with fractions may start by fitting tiles together, then drawing a quick sketch of a circle cut into parts. Only after those steps do we shift to writing the equations. By then, the numbers make sense because they’re tied to something the student has seen and touched.

Multisensory math allows kids to explore abstract concepts the way they learn best
Here are a few ways multisensory math shows up in practice:
Visual and tactile: Base-ten blocks for regrouping, fraction circles to compare sizes, quick sketches on a whiteboard.
Auditory: Clapping or chanting facts, explaining steps out loud, turning a formula into a short rhyme.
Movement: A human number line made with tape on the floor, a ball tossed back and forth while skip-counting, hopscotch to solve equations.
Tech tools: Virtual manipulatives, apps that let students drag and drop, interactive whiteboards.
The point isn’t to add bells and whistles. It’s to make sure students have more than one route into the concept so it sticks.
We’ve seen multisensory strategies make the biggest difference for students with specific challenges.
Kids with dyscalculia often need to see numbers in action. Arranging counters or tiles can help them notice patterns that otherwise stay hidden.
For kids with ADHD, rhythm and movement can keep them engaged. A chant with claps or a quick walk to the board gives them a way to use energy without losing focus.
For kids with math anxiety, turning practice into play changes the tone. Solving a problem while hopping to an answer feels different from sitting for a test.
These approaches align with the evidence-based tiers of intervention outlined in the Every Student Succeeds Act (ESSA), ensuring the methods are engaging and recognized as effective.
The biggest change we see is a shift in how students see themselves. They stop thinking of math as a fixed ability and start to believe they can grow. Mistakes become part of the process. Effort feels worthwhile.
We’ve had students who once shut down at the sight of a problem begin to keep going, even if they need a few tries. That resilience is just as valuable as the math itself.
Sometimes classroom strategies aren’t enough. If your child consistently avoids math, forgets concepts even after practice, or feels too anxious to participate, one-on-one support can make a big difference.
At Mathnasium of Cherry Creek, we build from these multisensory methods but tailor the pace and level to each student. We expect mistakes and use them as stepping stones. Small wins are highlighted so progress is visible and confidence grows alongside skills.
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At Mathnasium of Cherry Creek, multisensory strategies, tailored pacing, and positive reinforcement turn mistakes into growth and build lasting confidence.
Mathnasium is a math-only learning center that welcomes K-12 students of all skill levels.
Using a proprietary teaching method called the Mathnasium Method™, we teach math in a way that makes sense to each student, empowering them to unlock their full potential in math.
Our approach begins with a diagnostic assessment. This gives us a clear window into your homeschooler’s strengths, the areas where they need more support, and—equally important—how they learn best, whether your student is more verbal, visual, or maybe hands-on.
Using assessment-based insights, we create a personalized learning plan tailored to your student’s specific needs. Our tutors follow that plan closely, delivering face-to-face instruction in an environment that’s as engaging as it is confidence-building.
During sessions, we adapt to each learner’s style and use a mix of written, verbal, visual, mental, and tactile techniques. We also incorporate gamified challenges and rewards to keep students motivated and progressing.
For families in Denver, CO, Mathnasium of Cherry Creek brings this proven teaching approach close to home.
Read how one parent described their child’s Mathnasium experience:
Our specially trained math tutors offer personalized instruction and live, face-to-face online support to help students truly understand and enjoy math.
Schedule a free assessment to get started!
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Mathnasium of Cherry Creek is not the nearest center to you?
Mathnasium of Cherry Creek is a math-only learning center for K-12 students in Denver, CO. Trusted by over a million parents, Mathnasium uses personalized learning plans and the proprietary Mathnasium Method™ to help students catch up, keep up, and get ahead on their math journey.
Our specially trained tutors deliver face-to-face instruction in a supportive and fun small-group environment, working with students both in center and online to develop a deep understanding of math, build confidence, and improve academic performance.
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