Understanding Math by Making Connections

Have you ever been in the middle of a math lesson when one of your students suddenly asks, “When are we ever going to use this?” It is a question that many of us hear at some point, especially as math concepts become more abstract. The truth is that our students often struggle with math, not because they cannot learn it, but because they cannot see how new ideas connect to what they already know. When our students begin to recognize how math fits into their experiences, previous lessons, and the world around them, lightbulb moments happen. Math stops feeling like isolated problems on a worksheet and starts to make sense. Helping our students make those connections is one of the most effective ways to support their understanding of math.

Why Making Connections Improves Understanding Math

Our students are surrounded by information every day. That does not always mean they naturally connect ideas across lessons or experiences. In many classrooms, math can unintentionally feel like a series of disconnected units. Our students might study fractions one month and geometry the next without ever seeing how those ideas relate to each other. When math feels disconnected like that, it becomes harder for them to remember what they learned or apply it later. 

When our students begin connecting ideas, understanding math becomes much more attainable. Instead of memorizing procedures, our students begin to recognize patterns and relationships among concepts. For example, when we have our students connect multiplication area models to fraction multiplication, they realize they are not learning something completely new. They are building on something they already understand. Those moments help them feel more confident because the math feels familiar rather than overwhelming.

Connections also help our students see that math has a purpose beyond the classroom. When our students can relate math concepts to everyday situations, they are much more likely to stay engaged and motivated. You can have students estimate the total cost of supplies for a class party or calculate how much time is left before recess. When we highlight those moments, our students begin to realize that math is not just a school subject. It is something they use to solve everyday problems.

Using Prior Knowledge to Support Understanding Math

Each one of our students walks into the classroom with experiences that shape how they think about math. These experiences form what we often call prior knowledge or schema. Prior knowledge includes what our students already understand about math concepts, how they feel about math, and the situations where they have used math in their daily lives. When we tap into that prior knowledge, new learning becomes much easier for our students to grasp.

One helpful way to begin a lesson is by asking students what feels familiar about the topic. If you are starting a lesson on multiplication of fractions, you might ask students where they have seen area models before. Many of them will remember using them when learning multiplication earlier in the year. By bringing that idea back into the conversation, you are helping students realize they already have tools that can help them understand the new concept. That small moment of recognition can make a big difference in how confident they feel.

We can also activate prior knowledge through quick discussions, math journals, or simple reflection prompts. Asking questions like “Where have we seen something like this before?” or “What part of this problem reminds you of another lesson?” encourages students to think about connections between ideas. These short conversations help students to build bridges between past learning and new concepts. Over time, this habit helps them understand math because they begin to recognize relationships between topics on their own.

Teaching Three Types of Connections for Understanding Math

Students do not always make connections automatically. In fact, many of our students need explicit instruction and modeling to learn how to think this way. Otherwise, they stare at us blankly and insist they have never seen the concept before. Many of us have heard students say things like “I don’t remember this” or “I never learned this.” When we teach our students to look for connections, those moments become opportunities to remind them where similar ideas have appeared before.

One helpful approach is to teach students three types of mathematical connections: math to self, math to math, and math to the world. These categories give students a clear way to think about how new concepts relate to other experiences.

Math to Self Connections

Math to self connections focus on personal experiences involving math. We want students to connect math concepts to everyday situations they encounter outside of school. You might have students estimate the total cost of snacks for having friends over, or think about how measurement is used when baking with their families. Activities like reflection journals or math inventories can help students notice these moments. When students begin to recognize math in their own lives, understanding it becomes much more meaningful.

Math to Math Connections

Math to math connections help students see how new concepts build on ideas they already learned. This is one of the most impactful ways to deepen mathematical thinking. If some of your students previously used area models to understand multiplication, they can apply that same visual model when learning fraction multiplication. When students see how math concepts build on each other, learning becomes less intimidating.

Math to World Connections

Math to world connections help students recognize that math exists everywhere. Many of our students believe math only lives inside textbooks or classrooms. That misconception changes when we help them start seeing math in the real world. You can have your students start noticing symmetry and angles in playground equipment or identify geometric shapes in buildings and bridges. These observations help students realize that math is used to design, build, measure, and solve problems in everyday life.

Modeling Connections to Strengthen Understanding Math

Helping students make meaningful connections requires intentional modeling. During math lessons, think alouds are a great way to demonstrate how connections work. As you solve a problem, you might pause and say something like, “This reminds me of when we used area models earlier in the year. Remember how we broke the rectangle into sections to multiply? That same idea can help us here.” Hearing those thoughts out loud helps students see the process of connecting ideas and gives them language they can start using themselves.

Another helpful strategy is using connection prompts, or sentence starters, during lessons. These short questions guide students as they begin practicing this type of thinking on their own. Prompts such as “What part of this feels familiar?” or “Where might we see this in real life?” encourage students to reflect on what they are learning. We can keep these prompts visible on anchor charts, bookmarks, or small cards that students can reference during lessons.

Over time, these small reminders help students build the habit of making connections automatically. Instead of seeing each lesson as a completely new challenge, they will start recognizing patterns across topics. This shift strengthens their understanding of math because they begin using prior knowledge to support new learning. The goal is not simply for students to complete math problems, but for them to truly understand the ideas behind them.

Real World Activities That Deepen Understanding Math

One of the most engaging ways to help students see connections is through real-world math activities. When students explore how math shows up in the world around us, they begin noticing concepts they may have overlooked before. Geometry is a great example of this because shapes, angles, and symmetry are commonly used in architecture and design.

An engaging way to help students notice these connections is through a find the geometry in architecture activity. Students will be able to examine real images of buildings and structures to identify geometric features. As they look at the architectural photos, they look for shapes, angles, lines, and symmetry that appear in the structures. The activity encourages students to see geometry in a completely different way.

Your students will complete a recording sheet in which they locate specific geometric features in the image. They might identify parallel lines in windows, outline and measure three angles, circle polygons they find in the structure, or locate lines of symmetry within the building. These tasks help students apply geometry vocabulary in meaningful contexts rather than simply memorizing definitions.

This type of activity works well after students have been introduced to basic geometric vocabulary. I recommend that students have prior knowledge of identifying features such as polygons, quadrilaterals, intersecting lines, angles, and lines of symmetry while recording their observations on a task sheet. The goal is not just to name shapes but to recognize how geometric concepts appear in real-world structures. I also recommend deciding ahead of time whether you want students to work in pairs to practice math talk or work independently. 

Activities like this help students move beyond memorizing vocabulary and instead apply their knowledge in meaningful ways. When students begin noticing geometric patterns in everyday structures, understanding math becomes clearer. Suddenly, math feels more like a tool they use to understand what's around them.

More Helpful Math Resources

If you are looking for more ways to help your students build stronger connections in math, be sure to explore the resources available in my TPT store. Inside my store, you will find a variety of math activities and classroom resources designed to help with understanding math through meaningful practice and clear visual support.

You will find activities that provide additional practice, visual supports like math posters that reinforce key concepts and math talk, and engaging tasks that encourage your students to apply what they are learning. These types of resources help your students see how mathematical ideas build on one another rather than feeling like separate units.

If you are ready to give your students more opportunities to practice making connections and strengthen their understanding of math, take a few minutes to browse my collection of resources. You may discover new tools that help your students feel more confident as they explore math concepts throughout the year.

Helping Your Students With Understanding Math

Helping students make connections in math is not an extra strategy added onto a lesson. It is a teaching approach that strengthens students' overall thinking about math. When we consistently encourage students to connect new ideas to prior knowledge, everyday experiences, and real-world situations, math begins to feel more logical and accessible.

Instead of viewing each topic as something completely new, students see how ideas build on each other over time. This approach helps them retain information longer than just memorizing. They are understanding how concepts fit together.

Creating opportunities for students to make connections can transform how math feels in the classroom. Their confidence grows as their knowledge increases, and math becomes approachable. Those moments of recognition lead them to truly enjoy and understand math.

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If you are looking for ways to help your students make stronger connections in math, be sure to save this post for later. Pinning it to one of your teaching boards on Pinterest makes it easy to come back to when you are planning lessons or looking for new ways to help your students with understanding math.

 

Tapping into Multimodal Learning in the 21st Century

When it comes to learning styles, you’ve probably heard the classic V-A-K framework: visual, auditory, and kinesthetic learning styles. We were encouraged to identify students' preferred learning styles and weave them into our lessons while still exposing everyone to the other styles for a balanced approach. Here we are in the 21st Century, teaching our students who toggle between YouTube tutorials, fast-moving games, TikTok how-tos, and AI tools before the school bell even rings. Their brains are used to quick shifts, layered information, and a blend of senses happening at once. That means our teaching has to shift as well. That’s exactly where multimodal learning comes in.

Instead of focusing on which “type” of learner each student is, we should now think about how many different ways we can help our students make sense of an idea. When instruction offers multiple modalities, what our students see, hear, say, build, sketch, write, model, or move, it opens doors for every learner. Multimodality isn’t about sorting our kids into categories. It’s about designing rich, flexible learning experiences that meet the reality of today’s diverse classrooms.

Why Multimodal Learning Matters in the 21st Century

Students today live in a sensory-rich world where visual and auditory information constantly overlap, interact, and compete for attention. They swipe through videos, play interactive games, listen to podcasts, and use AI tools to explore new ideas, often at the speed of curiosity. When we bring multimodal learning into the classroom with that same intentional variety, it feels familiar to their brains. Purposeful shifts in how information is presented keep them alert, engaged, and mentally anchored in the lesson.

Modern classrooms also reflect a wide range of backgrounds and needs. We teach multilingual learners, students with unique neurological profiles, and children who arrive with very different levels of prior knowledge. When we lean into multimodality, we give each of our students an entry point into the same content. Rather than expecting everyone to learn in a single way, we create learning experiences that honor the idea that understanding grows stronger when it comes from multiple angles.

Using Visual Modalities to Support Multimodal Learning

Visual thinking remains an incredibly powerful pathway for understanding, especially when it’s one part of a bigger multimodal plan. When students can see an idea through illustrations, diagrams, color-coding, or sample models, abstract concepts suddenly feel more manageable. Visuals help students build mental connections, find patterns, and remember information long after instruction ends.

Think about an image you may share with students. A timeline in social studies, a visual cycle in science, or even a color-coded grammar example gives students something concrete to connect with. Good visuals provide support for what students are learning. They give students a way to make sense of unfamiliar concepts or connect vocabulary to something they already know. Luckily, great visuals are relatively easy to find or create for the classroom. Whether it is an anchor chart, a diagram, or a visual checklist, visuals should be a key part of your lesson because they are highly connected to learning.

One visual checklist I have used is my Eye on the Target Problem Solving Stick. This visual cue helps students visually walk through their assignments as they problem solve. It’s a simple example of how vocabulary and standards can be differentiated visually, but that exact approach can support so many different subjects. If you want to explore more visual supports for problem-solving, you can take a look at Eye on the Target for additional ideas.

Using Auditory Modalities as Part of Multimodal Learning

Even in our highly visual world, listening is still a powerful learning tool. Spoken explanations, read-alouds, storytelling, and partner discussions all help students make sense of content in a way that feels conversational and human. When you introduce a new topic through a story, or when students rehearse their thinking out loud, they strengthen their comprehension and build confidence before ever putting pencil to paper.

One of the easiest ways to integrate auditory learning is through picture books or oral storytelling. These moments bring emotion, pacing, and clarity to the content. If you teach customary measurement conversions, the Land of Gallon story is an example of how a straightforward narrative can anchor understanding in a memorable way. The more students hear language wrapped around concepts, the more naturally they begin to talk about and internalize those ideas themselves.

Using Kinesthetic Modalities to Build Meaning

Movement is another essential layer of multimodal learning. Not because some students are labeled “kinesthetic learners,” but because physical engagement helps the brain connect ideas more deeply. When students get up, manipulate objects, or interact with space, they build meaning in ways that worksheets alone just can’t replicate.

Human number lines are an example of kinesthetic learning. When students physically step into the role of numbers, decimals, or rounding benchmarks, they suddenly understand the relationships between values much more clearly. Similarly, "build and compare" activities offer the same sense of discovery as students use math tools, create models, and test their thinking with their hands. Vocabulary learning becomes more memorable when students move between stations, act out words, or rotate through tasks that anchor meaning in both body and mind. If you’d like to try ready-made activities, make sure to grab a copy of the kinesthetic vocabulary supports.

Where Technology Fits into Multimodal Learning

Technology has quickly become one of the most natural pathways for multimodality. Students intuitively understand digital spaces. Tech tools give us endless ways to blend visuals, audio, movement, and interaction. Students might watch a short video model, use voice tools to explain their thinking, collaborate inside a digital document, sketch on a touchscreen, or build a diagram using an online template. All of these experiences offer rich layers of input and output that make ideas more accessible.

As AI tools become part of daily life, they also open up new multimodal entry points. Students might ask AI to summarize a concept, generate an illustration, check an explanation, or model a process. When used thoughtfully, these tools don’t replace learning; they expand the modalities available to students, so they can choose the pathway that helps them understand the content most clearly.

Ready to Plan Multimodal Lessons With Ease?

Incorporating these different techniques into your lessons does not have to be complicated or time consuming. Let's start with one misconception: You do NOT need to incorporate all of these into every lesson. Instead, start thinking of your lessons and activities as a cluster or unit. During the course of teaching a specific skill or concept, try to include as many of these as possible. This helps to ensure that each student has multiple opportunities, in multiple ways, to connect with the information. 

Please don't let this thought discourage you. You are already doing some of this. As you introduce or teach a new skill, you usually talk and model or show examples. This hits visual and auditory modalities right away. Add a video to the mix as a technology element, or pair it with a picture book read-aloud to explain the concept in a different way. Next, students have the opportunity to practice. Aim for practice activities in various formats: a worksheet, a hands-on interactive activity, a partner game, a digital activity, or a write-the-room scavenger hunt. Not only do these connect with different modalities, but changing activities will keep learning fresh and fun. Need to reteach? Try an activity that uses a different modality than the one you originally used. 

It doesn't have to be hard to use multimodal learning in your classroom; it just takes intent. As you change the way you think about lesson planning, it will become easier until it is just second nature.

Ready to bring even more multimodal learning into your classroom? I’d love for you to explore the resources in my TPT store. Everything there is designed to help you plan lessons that naturally weave together different modalities so students can interact with content in meaningful ways. From hands-on activities to visual supports and digital resources, you’ll find materials that make it easy to reach your diverse learners without adding extra stress to your planning time. 

A Modern Look at Learning Styles

Visual, auditory, and kinesthetic experiences still matter, but not because they define who our students are. They matter because learning becomes stronger when ideas are experienced from multiple directions. A modern classroom thrives when our students are invited to see, hear, discuss, sketch, model, build, imagine, act out, and explore concepts across multiple modalities.

The goal is no longer to match instruction to a preferred “style” but to design lessons that naturally weave together different modes of thinking. When students engage with content through multimodal learning, they remain present, curious, and ready to participate. They also build a deeper and more durable understanding because they’ve interacted with the content in more than one meaningful way.

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If you want to come back to these ideas when you’re planning future lessons, save this post now. Multimodal learning is one of those topics that becomes more powerful the more you put it into practice. Having these examples on hand makes it easier to weave multiple modalities into your lessons. 

4 Fun and Effective Ideas for Multiplication Fact Practice

When multiplication fact practice started to feel more like a chore than a challenge, I knew it was time to change things up. I wanted my students to understand multiplication more deeply, rather than relying solely on memorization. The magic happened when I focused less on speed and more on strategy. Once my students could explain their thinking and make connections, their fluency naturally improved.

The Why Behind Multiplication Fact Practice

For me, multiplication fact practice was never about who could finish first. It was about helping my students see how numbers worked together. When they understood what multiplication meant, they could reason their way through new problems instead of relying on memorization. That’s when fluency became meaningful.

The Common Core Standards and NCTM describe fluency as "flexible, accurate, and efficient." The focus is on thinking, and not solely speed. I completely agree. True fluency shows up when our students can look at 6 × 7 and think, “That’s 5 × 7 plus one more group of 7,” or when they can use a known fact to find an unknown one. That’s real number sense in action.

I used to tell my students that their goal wasn’t to beat the clock. It was to understand the why. Once they could reason through problems, their speed would improve naturally. They stopped fearing math drills and started looking forward to discovering patterns and shortcuts that made sense to them.

Rethinking Fluency

One of the biggest shifts I made was rethinking what fluency really looked like. I realized that speed alone didn’t tell the whole story. A student who solved slowly but used a strong strategy showed a deeper understanding than one who blurted out answers without thought.

In my classroom, I focused on building fluency through reasoning and critical thinking. I loved asking questions like, “How did you get that answer?” or “Can you think of a different way to solve it?” Those moments of reflection gave my students permission to slow down and reflect on their process.

Over time, something amazing happened. Once my students got comfortable using strategies flexibly, they naturally became faster. That confidence came from practice that emphasized meaning rather than strict memorization. Redefining fluency in multiplication fact practice allowed each of my students to feel successful, regardless of their starting point.

Multiplication Stories for Conceptual Understanding

One activity that helped strengthen understanding was Multiplication Stories, which encouraged students to think about multiplication in a different way. It provided students with the opportunity to create their own word problems using real-world data from tables, such as art supplies or groceries. The twist was that their story had to meet specific criteria, such as “the product must be even,” or “the answer must be greater than 20 but less than 35.”

I would have my students start by choosing two numbers from a table. Then, they would build a multiplication story around them. They wrote a detailed word problem, created a matching number sentence, and illustrated it with a drawing. The stories became mini math adventures, filled with creativity and critical thinking. Once they finished, they swapped stories with their classmates to solve the problem. This gave them an authentic audience for their work.

I loved how this activity naturally built math vocabulary. My students used words like "factor", "product", "even", and "multiple" in context instead of isolation. They were reasoning, writing, and problem-solving all at once. If this sounds like something you'd like to try in your own classroom, grab my free Multiplication Stories Freebie and give it a try!

Multiplication Fact Practice That Builds Confidence

While the multiplication stories helped students grasp the meaning behind the operation, they also needed frequent opportunities to apply this to help it stick. That’s where my Oh Deer! Multiplication Facts Practice Game resource came in. Instead of another worksheet, students were drawn into a quick draw style game that got them thinking, talking, and reviewing multiplication facts in a low-pressure way.

The game includes question cards that target key multiplication foundations such as repeated addition, skip counting, arrays, patterns, and simple story problems. Students take turns drawing cards and solving the problems. But. . . there's a fun twist that will make you say "Oh Deer!" just to keep the excitement and engagement high.

You can use this activity during math centers, small groups, or as a partner activity for early finishers. Because the questions emphasize the meaning of multiplication rather than speed, students get meaningful practice and grow more confident. 

This game gives you a seasonal, skill-focused way to build fluency without turning math into a race. Students feel successful, you get authentic practice, and everyone has a little holiday fun along the way.

Using Games and Movement for Multiplication Fact Practice

I’ve always believed that math should be interactive and engaging. This is what Multiplication and Division Facts Tic-Tac-Toe offers. This game turned fact practice into something my students genuinely looked forward to. Each partner took turns answering multiplication or division problems correctly to claim their space on the Tic-Tac-Toe board. The goal is to get three in a row while reviewing math facts.

The best part of this game-based multiplication fact practice is that it works for every learner. Your students who need extra support practice fluency without pressure. Those who are ready for a more challenging experience can play a faster-paced version. Since the resource includes both multiplication and division grids, it makes an easy bridge between the related operations.

I often used Tic-Tac-Toe as a math center, a warm-up, or even a math choice activity on Fridays. It encouraged collaboration, conversation, and laughter while naturally and authentically reinforcing fluency. Games like this reminded my students that practice doesn’t have to feel routine. Movement and play can be just as effective as pencil-and-paper practice. 

Visual Multiplication Fact Practice

For my visual learners, seeing the math made all the difference. This visual support for multiplication concepts can take many forms. I used number charts, arrays, and models to help my students make sense of multiplication relationships. When they could visualize the groups, products, and patterns, multiplication fact practice became much more meaningful.

One of my favorite visual activities is to show students a real-world application of math. Using this cupcake image, I helped my students think more deeply about math because they could see it. I always started with the open-ended questions that got students thinking about how the image could connect with the concept, in this case, multiplication. Our math talk conversations would be so rich as students made connections between what they knew and the picture. With this image, students would realize that the cupcakes looked like an array. This quickly helped them jump into creating an equation and seeing the patterns of 4s and 6s. This approach turned static numbers into patterns that my students could actually “see.”

The more I used this approach, the more my students began to notice patterns on their own. They started realizing that multiplication was all around them and that it wasn't just something they had to learn in math class. With this realization came a new excitement about multiplication and its usefulness. These visual math talk activities quickly became a highlight of our class.

You can easily use this technique in your classroom, too! Just grab a photo that shows an application of the math skill you are working on. For multiplication, photos of objects laid out in an array or in equal groups are the perfect starting point. But don't stop at multiplication, your students will love connecting many math concepts to real-world images.

The Real Goal of Practicing

At the end of the day, the goal of multiplication fact practice isn’t just memorization. It’s about reasoning with numbers, seeing patterns, and building confidence. Automaticity, the ability to recall facts quickly, is beneficial, but fluency is key. Fluency means being able to solve flexibly, accurately, and efficiently.

When we redefine fluency this way, we give our students the freedom to think. We create learners who can explain why something works, rather than simply repeating what they’ve been told. That’s where true understanding happens. That’s when math starts to click.

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Love these ideas for multiplication fact practice? Pin this post to your favorite math board so you’ll have it ready when you’re planning engaging activities for your students!

Strategies and Tips for Grouping Students

When I was in the classroom, I grouped students for activities multiple times a day. The way I grouped them always depended on the learning goal. Sometimes it made sense to pair them with a partner. Other times, I wanted them working in small groups or with classmates they didn’t typically choose on their own. That’s the beauty of intentionally grouping students. It provides the flexibility to tailor the group structure to the lesson's purpose. It also helps your students develop important collaboration skills, learn to work with a diverse range of peers, and stay engaged.