Let’s Count On Math™ is a Kindergarten to Grade 12 conceptual framework designed to help students see mathematics as a connected body of knowledge rather than as hundreds of unrelated concepts, rules, and procedures.
Instead of introducing each new topic as something completely different, the framework encourages students to continually ask three simple questions:
When necessary, students also learn to make change by rewriting values into equivalent quantities or representations before continuing with the mathematics.
By repeatedly returning to these ideas, students begin to recognize recurring mathematical structures that connect concepts across the K–12 curriculum. New learning is built upon familiar mathematical ideas rather than being learned in isolation.
The goal is not to change what students learn. It is to provide them with a consistent way of thinking about mathematics that can help reduce cognitive load, strengthen conceptual understanding, improve long-term retention, and make mathematics feel more connected and meaningful.
Let’s Count On Math™ is not a curriculum or a teaching method. It is a conceptual framework that can be incorporated into virtually any mathematics curriculum or instructional approach.
Ultimately, the goal is simple:
Help students Find the Counting… so they can Find the meaning.
No.
Let’s Count On Math™ is not a teaching method or classroom management model. It is a conceptual framework based on the underlying structure of mathematics.
Whether your classroom uses direct instruction, inquiry-based learning, cooperative learning, guided practice, learning centres, project-based learning, manipulatives, or a combination of approaches, students are still learning the same mathematics.
Let’s Count On Math™ complements these instructional approaches by providing students with a consistent way of thinking about mathematics. Throughout instruction, students are encouraged to ask:
Sometimes, before deciding how we are counting, students first need to make change by rewriting quantities into equivalent forms.
Because these questions are based on the mathematics itself—not on a particular teaching philosophy—the Let’s Count On Math™ framework can be integrated into virtually any classroom environment.
Rather than replacing the many effective ways teachers organize learning, Let’s Count On Math™ is designed to strengthen them by helping students see the underlying structure that connects mathematical ideas from Kindergarten through Grade 12.
Let’s Count On Math™ is designed as a Kindergarten to Grade 12 conceptual framework. Although Let’s Count On Math™ can be beneficial in any single classroom, it may have its greatest impact during the transitions between grades, particularly from elementary to secondary mathematics, where many students begin to see mathematics as a collection of disconnected rules and procedures. Providing a consistent conceptual framework during these years can help students organize new learning, reduce cognitive load, build confidence, and strengthen understanding.
The three guiding questions—
—and the idea of making change can be applied at every grade level.
The way these ideas are explored, however, naturally changes as students mature.
In the primary grades, students are learning to identify quantities, count objects, compare groups, recognize patterns, and build a strong foundation for number sense.
In the intermediate grades, the same framework helps students understand fractions, decimals, percentages, integers, measurement, rates, ratios, probability, algebra, and many of the algorithms that are introduced during these years.
In secondary mathematics, the framework continues to provide a consistent way of thinking about increasingly abstract ideas such as functions, exponents, logarithms, trigonometry, vectors, calculus, and statistics by helping students recognize the underlying mathematical structures that connect them.
Ultimately, the goal is not to change what students learn. It is to provide them with a consistent way of thinking about mathematics throughout their entire K–12 journey. As students encounter new concepts each year, they can build on familiar mathematical structures from earlier grades rather than starting from scratch. Recognizing these analogous structures can reduce cognitive load, lessen mathematics anxiety, and help new learning become more meaningful and easier to remember.
No.
Let’s Count On Math™ is not a mathematics curriculum. It is a conceptual framework for understanding the mathematics that already exists within virtually every K–12 curriculum.
Whether students are learning under the British Columbia curriculum, another Canadian provincial curriculum, the Common Core State Standards, the Australian Curriculum, the English National Curriculum, Singapore Mathematics, or another educational program, they are still learning many of the same mathematical concepts. They learn about numbers, operations, fractions, measurement, algebra, geometry, probability, functions, and many other topics.
Let’s Count On Math™ does not change what students are expected to learn. Instead, it provides a consistent way of thinking about those concepts by encouraging students to continually ask:
The framework can be used alongside virtually any curriculum because it focuses on the underlying mathematical structures rather than on a particular sequence of lessons, textbook, or instructional program.
As a result, teachers can incorporate the ideas into their existing classroom practice without replacing the curriculum or resources they already use.
Not necessarily.
Let’s Count On Math™ is not intended to replace the many effective ways teachers organize and deliver mathematics instruction. Rather, it is a conceptual framework that helps students understand the underlying structure of the mathematics they are already learning.
Many excellent teaching practices—including direct instruction, inquiry-based learning, cooperative learning, problem-solving, hands-on activities, learning centres, and classroom discussions—can all benefit from helping students recognize the recurring mathematical structures that connect concepts across grades.
The three guiding questions—
—can be incorporated into virtually any mathematics lesson, regardless of the teaching approach being used.
What is different about Let’s Count On Math™ is its emphasis on helping students see mathematics as a connected body of knowledge rather than as hundreds of isolated concepts, rules, and procedures. By continually identifying the quantities involved, recognizing when “making change” is needed, and connecting new learning to familiar mathematical structures, students develop a more coherent and meaningful understanding of mathematics.
The goal is not to teach different mathematics, but to help students see the mathematics they are already learning in a more connected, organized, and understandable way.
When people hear the word counting, they often think only of young children saying, “1, 2, 3, 4…”
At Let’s Count On Math™, the word is used in a much broader mathematical sense.
Mathematics begins by identifying quantities. In the early years, students literally count objects one at a time. As they mature, they develop increasingly efficient ways of working with those same quantities.
Counting evolves into the mathematics of later grades.
For example:
As students progress through school, the mathematics becomes more sophisticated, but the underlying idea remains the same: students are continually identifying quantities and deciding how those quantities should be combined, compared, grouped, transformed, or related.
Let’s Count On Math™ does not suggest that every mathematics lesson is simply “counting.” Rather, it suggests that identifying the quantities involved provides a logical starting point for understanding the mathematics. Once students know what they are working with, they are better prepared to decide how those quantities should be worked with.
The goal is to help students recognize that the mathematics they encounter from Kindergarten through Grade 12 is not a collection of hundreds of unrelated topics. Instead, it is a connected progression in which simple counting gradually develops into the more sophisticated mathematical methods, formulas, algorithms, and relationships studied in later grades.
By helping students recognize this progression, mathematics becomes more connected, more meaningful, and easier to understand. Students are no longer asked to learn each new topic in isolation—they build on familiar mathematical structures that have been developing throughout their entire K–12 journey.
Absolutely.
Mathematics is much more than simply counting objects. It is the study of quantities, how we work with those quantities, and how they relate to one another.
At Let’s Count On Math™, counting is viewed as the natural starting point for understanding mathematics—not the complete story.
When people hear the word counting, they often think only of young children saying, “1, 2, 3, 4…” In reality, counting evolves into the mathematics of later grades.
Students begin by counting individual objects. They then learn to combine quantities through addition, separate them through subtraction, count equal groups through multiplication, determine how many groups fit through division, compare quantities using ratios and rates, work with fractions, decimals, percentages, algebraic expressions, functions, probability, vectors, calculus, and many other increasingly sophisticated mathematical ideas.
Much of the K–12 mathematics curriculum focuses on number concepts, number operations, algebraic thinking, measurement, and quantitative relationships. As students progress through school, the mathematics becomes more sophisticated, but the underlying idea remains the same: they are continually identifying quantities and deciding how those quantities should be combined, compared, grouped, transformed, or related.
Mathematics also involves reasoning, modelling, generalizing, proving, communicating, and solving problems. These are essential aspects of mathematics. Let’s Count On Math™ does not suggest that every mathematics lesson is simply “counting.” Rather, it suggests that understanding the quantities involved provides a logical foundation from which these broader mathematical ideas can develop.
The goal is not to reduce mathematics to counting. The goal is to help students recognize that many mathematical ideas share common underlying structures. By beginning with quantities and showing how increasingly sophisticated mathematical methods develop from them, students often find mathematics becomes more meaningful, more connected, and easier to understand.
No.
Algorithms are an important part of mathematics. Many of the algorithms we teach today have been used successfully for hundreds of years because they provide efficient and reliable ways of carrying out mathematical calculations.
However, the world has changed.
When many of these algorithms were developed, a large proportion of the population worked in agriculture or manual trades. Formal mathematics was primarily needed by a much smaller number of people in fields such as commerce, engineering, navigation, and science. For many students, mathematics served as a filter rather than as an everyday necessity.
Today, the situation is very different. Nearly every student will enter a world that depends on technology, data, quantitative reasoning, and problem solving. Modern careers increasingly require people not only to perform mathematics, but to understand it, communicate it, and apply it in new situations.
For this reason, there is an increasing need for students to understand why mathematical procedures work, when they should be used, and how they connect to broader mathematical ideas.
Let’s Count On Math™ does not seek to replace algorithms. Instead, it helps students understand the mathematical thinking that gives rise to them.
For example, students can explore why multiplication comes before addition in the order of operations, why common denominators are needed when adding fractions, why like terms can be combined in algebra, and why factoring is often necessary before simplifying expressions. Rather than memorizing isolated procedures, students learn to recognize the underlying quantities, structures, and relationships that the algorithms are designed to work with.
When students understand the mathematics behind an algorithm, they are more likely to remember it, apply it correctly, recognize when it is appropriate to use, and transfer that understanding to new situations.
The goal of Let’s Count On Math™ is not to replace mathematical algorithms. It is to help students understand the mathematics that makes those algorithms meaningful.
In Let’s Count On Math™, making change means rewriting a value as an equivalent quantity that makes the mathematics easier to understand or work with.
Sometimes we can work with quantities immediately. At other times, however, the quantities must first be rewritten into a form that allows the mathematics to continue.
For example:
In every case, the value remains exactly the same, but the quantity being counted changes. By changing the quantity or its representation, students can work with compatible units, recognize familiar structures, and continue with the mathematics.
Making change is not a separate mathematical topic. It is a recurring mathematical action that appears throughout the K–12 curriculum whenever quantities must be rewritten into equivalent forms before they can be combined, compared, transformed, or related.
Within the Let’s Count On Math™ framework, making change is often the bridge between identifying what we are counting and deciding how we are counting.
One of the most effective ways to learn something new is to connect it to something we already understand.
In Let’s Count On Math™, asking “What is this analogous to?” encourages students to look beyond the symbols and recognize the underlying mathematical structure of a problem.
For example:
Although the numbers, symbols, and vocabulary become more sophisticated, the underlying mathematical thinking often remains remarkably similar.
Recognizing these structural similarities helps students build new learning on ideas they already understand. Instead of approaching every new topic as something completely different, students begin with familiar mathematical structures and extend them to new situations.
This can reduce cognitive load because students are not trying to learn every concept from the beginning. New ideas are connected to existing knowledge, allowing students to organize information more efficiently and recognize recurring mathematical patterns.
Because the unfamiliar is built upon the familiar, students often approach new topics with greater confidence. As mathematics becomes more connected and understandable, many students experience less frustration and reduced mathematics anxiety.
The goal is not to suggest that every mathematical idea is identical. Rather, it is to help students recognize recurring mathematical structures that connect concepts across the K–12 curriculum.
By continually asking “What is this analogous to?”, students begin to see mathematics as a connected body of knowledge instead of hundreds of isolated concepts, rules, and procedures.
The magnetic number line and instructional dice were designed to support the conceptual ideas behind Let’s Count On Math™ by making mathematical thinking visible, interactive, and easy to discuss.
The magnetic number line brings mathematics down to a height where both teachers and students can easily work with it during whole-class lessons, small-group instruction, learning centres, or individual exploration. Rather than simply observing a number line above the whiteboard, students can physically build, compare, group, regroup, and transform quantities while discussing the mathematical ideas together.
The movable number strips also encourage students to recognize and work with chunks rather than only individual units. Instead of always counting by ones, students learn to think flexibly using groups such as twos, fives, tens, quarters, thirds, or algebraic quantities. This emphasis on recognizing and composing quantities into useful chunks supports efficient mental mathematics, flexible number sense, and deeper mathematical understanding.
The instructional dice provide students with frequent, engaging opportunities to experience important mathematical ideas through repeated play and discussion. Activities such as making pairs to 5 or 10, counting equal groups, sorting like quantities, identifying patterns, and combining algebraic terms provide many meaningful repetitions of the same underlying mathematical concepts. These repeated exposures help build fluency, confidence, and long-term understanding rather than relying on memorization alone.
Together, these materials encourage students to continually ask:
The manipulatives are designed to support classroom discussion, reasoning, and conceptual understanding. They are teaching and learning tools that reinforce the Let’s Count On Math™ framework—they are not the framework itself. Teachers can successfully use the ideas of Let’s Count On Math™ with or without the classroom materials.
Absolutely.
The Let’s Count On Math™ framework is based on ways of thinking about mathematics, not on a particular set of classroom materials.
The three guiding questions—
—and making change when necessary, can be incorporated into virtually any mathematics lesson using the resources you already have.
The magnetic number line and instructional dice were developed to make these ideas more visible, interactive, and easier to discuss, but they are not required to use the framework successfully.
The website also includes free resources, lesson ideas, classroom demonstrations, and Counting Warm-Up Activities that teachers can use immediately in their own classrooms.
If the classroom materials help make the mathematics more meaningful and engaging for your students, that’s wonderful. If not, we hope the conceptual framework itself helps teachers and students see mathematics as a more connected, understandable, and coherent body of knowledge.
The goal of Let’s Count On Math™ is to improve mathematical understanding. The classroom materials are simply one way of supporting that goal.
I always welcome thoughtful questions, feedback, and classroom experiences from teachers, parents, administrators, and anyone interested in mathematics education.
Whether you have a question about the Let’s Count On Math™ framework, would like to share how you’ve used the ideas in your classroom, or simply want to continue the conversation, I’d be happy to hear from you.
You can contact me through the Contact Us page on this website or by email at:
info@letscountonmath.com
You can also visit the Let’s Count On Math™ YouTube channel (@LetsCountOnMath) for classroom demonstrations, lesson ideas, product demonstrations, and discussions about helping students develop a deeper understanding of mathematics.
After more than 40 years as a classroom teacher and elementary principal, my goal is simple: to help more students understand mathematics and to help teachers make mathematics more meaningful, connected, and enjoyable to teach.
Thank you for your interest in Let’s Count On Math™.
I hope these ideas help make mathematics more connected, meaningful, and enjoyable for both teachers and students.
