One of the most effective ways to learn something new is to connect it to something we already understand.

Although mathematical ideas often appear very different on the surface, many are built on the same underlying structure. Students frequently struggle because they see each new topic as something completely different, when in fact it is often another version of a familiar idea.

At Let’s Count On Math™, we continually ask:

What is this analogous to?

Instead of seeing mathematics as hundreds of unrelated concepts, students learn to recognize familiar mathematical structures that appear throughout the curriculum. A Kindergarten activity involving sorting dogs and cats is analogous to combining like terms in algebra. Sharing cookies equally is analogous to division. Building equal groups is analogous to multiplication. Comparing the lengths of two objects creates a ratio, which is analogous to comparing distance and time (speed), rise and run (slope), or favourable and total outcomes (probability).

Although the numbers, symbols, and vocabulary become more sophisticated, the underlying mathematical thinking often remains the same.

Recognizing these structural similarities can reduce both cognitive load and mathematics anxiety. Rather than beginning each new topic from scratch, students build on ideas they already understand. Familiar structures provide a foundation for new learning, helping students approach increasingly complex mathematics with greater confidence.

The YouTube video below illustrates how the same mathematical thinking that is learned in Grade 7 shows up in Grade 10/11. Although the symbols become much more sophisticated, the underlying reasoning remains remarkably consistent. Showing students the examples side-by-side gives them a familiar model for understanding something quite complex and can reduce anxiety as well. For more examples, see the Practical Examples page.

When students are shown the structure, they can recognize the mathematics – and mathematics begins to make sense.

Find the Counting. Find the Meaning.