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4×1=4, 4×2=8, 4×3=12… You can probably even hear the chant in your head, right? But is memorizing the multiplication tables the same as learning them?
If we memorize the tables without understanding what lies behind each result, we become dependent on a very useful, but often misleading, learning tool: memory. Want to know why?
The Danger of Empty Repetition
The answer is simple: a lack of connections. And that leads to a lack of fluency.
If you know that 4×6 is 24, but hesitate when faced with 6×4, you probably don’t have a memory problem—you have a fluency problem. If you get confused with the same multiplication when the context is new or more complex, that’s also a sign of missing fluency.
Here’s the thing: if we don’t see patterns or build meaningful strategies, we haven’t really learned the multiplication tables. We’ve reduced them to a mechanical memory exercise that can collapse at the slightest challenge.
So, how can we help children truly learn the multiplication tables?
Building the times tables with meaning
To avoid this, we need to introduce the times tables through concrete and visual contexts. When children can see and touch what’s happening, multiplication stops being abstract.
A good example is building the 2 times table. We might start with everyday situations: bicycle wheels, animal legs, paint stains that double when folding a sheet of paper… Each situation adds another piece to the puzzle.
And so, through reasoning, strategies, and contexts, we can build all the results of all the tables.
Then Comes Memorization
Knowing the multiplication tables by heart is important. But memorization should be the last step—the logical outcome of everything we’ve seen before: asking questions, observing the environment, making connections, organizing, discovering patterns, and solving problems where kids apply what they’ve learned. Memorization is the natural result of meaningful, connected learning!
And then yes: we can be proud when they chant 4×1=4, 4×2=8, 4×3=12… (although it’s even better if they can answer out of order). And most importantly: they’ll be able to say they’ve learned the multiplication tables, and they’ll be able to deduce and recall them in any context without relying only on memory.
Stepping into a 3rd grade classroom
Shhh… Quiet, students are working! The Innovamat team steps into classrooms to observe, document, and analyze what’s happening. This allows them to reflect on teaching practices and share effective learning strategies with the world.
Today we’re visiting a 3rd grade classroom at Belmar School District, in Belmar, New Jersey. Here you’ll see Albert Vilalta beginning to build the table of 2 with the students. Notice how he guides them from repeated addition to the first steps of formal multiplication. Come along!
⚠️ This is a 360º video. To get the most out of it drag your mouse across the screen (or swipe on your phone) to change the angle and explore the scene from different perspectives.
Beginning of the session – Warm-up
The session begins with a simple activity: counting by twos in different contexts. For example, “Nine chickens—how many legs do they have?” This question is a concrete and natural starting point for number talk.
Students work in groups, discuss, and share their solutions. When it’s time to share, the teacher doesn’t ask “What’s the answer?” but instead challenges them: “Convince me!” With this strategy, the focus shifts to the process, not just the result.
As children count by twos, they build a bridge between repeated addition and the idea of multiplication. The teacher helps them notice: reciting the results of the table of 2 in order is the same as counting by twos! Moving from one result to the next means making a jump of 2 forward.
But the connections aren’t solid yet: it’s time to let thinking emerge.
Mistakes as opportunities and the importance of debate
Some students suggest expressions that sound logical but don’t fit the context: “7×14,” “2×7”… Even though the product is 14, these don’t correctly describe the reality of the chickens and their legs.
Instead of correcting immediately, the teacher lets the error breathe. The kids laugh when they realize a chicken can’t have 7 legs. The mistake then becomes the starting point for discussion: “Why doesn’t 7×14 work in this case?”, “What does 2×7 mean here?” and “Why do we need to think of 7×2?” In this way, error—far from being failure—becomes a driver of learning.
Building the 2 times table through contexts
One natural conclusion from this discussion is the need to be mathematically precise with words. The session moves forward: in a whole-group activity, each child writes on their mini whiteboard and says aloud how many bicycles and how many wheels are shown in the picture.
But they can’t explain it just any way. The teacher sets rules and gives an example: “3 groups of 2 is 6.” He then shows how to represent this: 3 × 2 = 6. At this stage, it’s very important not to read the cross (×) as “times,” but as “groups of.”
Each context adds a new result to the table of 2. The teacher writes each representation on an 8.5×11 sheet and posts it on the board. The results are not shown in order; that way, it doesn’t look like a list to memorize, but rather a network of connections that helps students find answers without reciting previous results.
Once all the results have been built through reasoning, connections, and representations, it’s time to organize them. The teacher suggests putting them in order from smallest to largest and guides the discussion, letting students discover the pattern step by step.
Closing: Consolidating the Table
To wrap up, students work on different representations in their individual practice notebooks: drawings, abacuses, contextual problems, etc. The goal is to consolidate the table of 2, not as a repeated list, but as a set of relationships they have constructed.
This is the practice logbook they work on to consolidate what they’ve learned today.
Notice how in some activities the hens are shown sitting so kids don’t count their legs. For students who need more support, an adaptation would be to show the same elements without hiding parts—for example, showing the hens’ legs.
Finally, the teacher reflects with the class: What did you observe? What patterns emerged? How does this connect with counting, with “doubling,” and with symbolic representation?
The key takeaway is that after this shared experience, students no longer memorize in an empty way: they understand that 7×2 isn’t just “14,” but “seven groups of two units.”
If you’d like to access the complete teaching guide, you can find it here.
