Continuing our series on The Evolution of Mathematics, let’s dive deeper into understanding why the math we’ve always done—and the algorithms behind it—work the way they do. In our initial post, we explored the idea that while math itself hasn’t changed, our approach to teaching it has shifted to emphasize understanding why algorithms work, rather than just how to perform them. In this post, we’ll focus on some effective strategies teachers are using to help students grasp these concepts on a deeper, more conceptual level. Let’s start by exploring the foundational tool of the ten frame.
What is a ten frame?
Simply put, it is as it sounds. A frame, rectangle, with 10 smaller squares inside of it.

Starting in preschool, students are introduced to a five frame—a half-sized ten frame—to help them recognize and understand numbers.
The five frame provides a structured way for students to visualize numbers from 1 to 5, allowing them to recognize number patterns easily. It works similarly to how we recognize numbers on dice without counting each dot; through repeated exposure, we learn to see the patterns instantly and associate them with a specific number.
In math, we call this skill subitizing—the ability to quickly and accurately determine the number of items in a small set without counting. Interestingly, the term “subitize” comes from a Latin word meaning “suddenly,” reflecting how we instantly recognize these patterns.

Subitizing is a foundational skill for developing number sense, as it helps students visualize and understand numbers, recognize patterns, and grasp relationships between numbers. In early grades, we often show students different groups of dots or objects and ask them to identify how many they see. This approach helps students spot patterns in smaller groupings, allowing them to quickly identify quantities without counting each item individually.
Patterning might seem like a small piece of the early learning puzzle, but it’s actually a powerhouse skill that sets kids up for success in math—and beyond. When young students work with patterns, they’re building essential logical thinking skills that will make tackling algebra and other complex math concepts easier down the road. Pattern recognition teaches kids how to sequence, skip count, and understand the relationships between numbers, which all lay the foundation for core math operations like addition and multiplication. But the benefits don’t stop there; working with patterns also strengthens spatial awareness and problem-solving abilities that students carry over to subjects like music, language, and art. By focusing on patterning from the start, we’re giving kids a toolkit that helps them see the world through a connected, mathematical lens.
Using a ten frame is a powerful tool for building number sense in young learners because it helps them visualize numbers in relation to ten, an essential concept in our base-ten number system. Ten frames encourage students to recognize numbers as combinations and patterns, which lays the groundwork for addition, subtraction, and mental math strategies. By arranging counters on the ten frame, students begin to understand quantities as groups (like seeing six as “five and one more” or eight as “five and three more”), making it easier to see how numbers relate to one another. This structure also supports the development of subitizing, or recognizing quantities without counting, which is key to building fluency and confidence in math.
As students progress, ten frames support their understanding of making tens—a key skill in mental math. For instance, in solving 6 + 5, students can move counters within the frames to “make a ten” and then add the leftover counter to arrive at 11.

We “make a ten” by moving 4 yellow counters to fill the first ten frame.

Working with these structured frames provides students with a hands-on way to understand number manipulation, building their confidence and fluency in basic operations and setting the stage for more complex math concepts.
This approach also highlights an essential concept: different expressions can yield the same result. For instance, in our example, moving counters in 6 + 5 allowed us to see it as 10 + 1. This shows that 6 + 5 = 10 + 1.

This understanding of equivalence is fundamental to algebra. By recognizing that what appears on one side of an equation must balance with what is on the other side, students develop a foundation for algebraic thinking. Building this skill early makes algebra more accessible and meaningful as students advance in their math studies.
Using ten frames provides a strong foundation for the next strategies we’ll explore in this series. Stay tuned for more!

Here are some of my favorite ten frame tools to have in a classroom:

RekenRods Ten Frame Boards

Giant Magnetic Ten Frame Set

Ten Frame Stamp

Write & Wipe Ten-Frame Mats

Ten Frame Dice

Multiple Representation Dice

Magnetic Ten-Frame Answer Boards