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.

Save for Later

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.