Teaching Times Tables with Understanding (Not Just Chanting)
If you've ever taught multiplication, you've probably seen the same pattern emerge.
A student can confidently recite their times tables during a class chant, yet when presented with a simple multiplication problem, they hesitate. They begin counting on their fingers, guess at an answer, or wait for someone else to respond. Ask them why 6 × 4 equals 24, and they're unsure. Ask them to solve 24 ÷ 6, and it suddenly feels like a completely different concept.
It's easy to conclude that the student simply needs more practice.
More often than not, the issue isn't a lack of practice - it's a lack of understanding.
The student has memorised a sequence of facts without developing an understanding of what multiplication and division actually represent.
When educators and homeschool families ask how to teach times tables, the conversation should begin with understanding, not memorisation.
Understanding Comes Before Fluency
Learning times tables is an important part of mathematics. Automatic recall allows students to solve problems more efficiently and frees working memory for higher-order thinking.
However, automatic recall is not the starting point.
It is the outcome of meaningful learning.
There is nothing inherently wrong with practising times tables through songs, chants, games or repetition. These can all support fluency once understanding has been established.
The difficulty arises when memorisation becomes the first step rather than the final stage of learning.
When students are expected to remember facts before they understand equal groups, arrays and multiplicative relationships, those facts often remain isolated pieces of information. They may be recalled during a chant but are difficult to retrieve or apply in unfamiliar situations.
Understanding gives multiplication facts meaning.
Fluency makes those facts efficient to use.
Students need both.
How Mathematical Understanding Develops
When considering how to teach times tables, it helps to think about how mathematical understanding develops.
Students don't move directly from knowing nothing to instantly recalling multiplication facts.
Instead, they gradually build understanding through carefully sequenced experiences.
They begin by exploring mathematical ideas using concrete materials.
They represent those ideas visually.
They discuss what they notice using mathematical language.
Only then do they record the ideas symbolically.
This progression helps students connect what they can see and build with the mathematical symbols they are eventually expected to use independently.
Within the I-CRAVE Maths® Methodology, this progression provides the foundation for teaching multiplication and division in ways that are both meaningful and memorable.
Teaching Times Tables Through the I-CRAVE Maths® Methodology
The I-CRAVE Maths® Methodology supports conceptual understanding before procedural fluency, helping students develop confidence as well as competence.
Identify
Before solving a multiplication problem, students first identify what the mathematics is describing.
Are there equal groups?
How many groups are there?
How many are in each group?
Developing this understanding helps students choose an appropriate strategy instead of relying on guesswork.
Concrete
Students physically build multiplication using manipulatives such as counters, integer blocks or other hands-on materials.
For example, to solve 4 × 5, students create four equal groups containing five objects.
They move the materials.
They count them.
They compare different arrangements.
Multiplication becomes something they can experience rather than simply remember.
Representation
Once students understand the concrete model, they represent it visually.
They might draw equal groups or create arrays to record what they have built.
These visual models strengthen understanding while preparing students for more abstract thinking.
Students also begin recognising important mathematical relationships.
They notice that four groups of five and five groups of four produce the same total.
They discover that multiplication and division belong to the same fact family.
These patterns emerge naturally because students can see them.
Abstract
Only after students understand the concept do they record it symbolically.
They connect:
4 groups of 5
Array of 20
4 × 5 = 20
20 ÷ 5 = 4
20 ÷ 4 = 5
Rather than seeing these as separate equations to memorise, students recognise them as different ways of describing the same mathematical relationship.
Verbal
Mathematical language is an essential part of learning.
Students explain what they have built.
They describe their reasoning.
They read equations aloud using accurate mathematical vocabulary.
Listening to students explain their thinking gives teachers valuable insight into what students genuinely understand and where misconceptions may still exist.
Explicit
Throughout the lesson, instruction remains clear, structured and carefully sequenced.
The teacher models each step.
Students practise with support.
Responsibility is gradually transferred as understanding develops.
Misconceptions are addressed early before they become established habits.
What This Looks Like in Practice
Imagine introducing the 6 times tables.
Rather than beginning with repeated chanting, students first build six equal groups of two using manipulatives.
Next, they build two equal groups of six.
They compare the models.
They draw the arrays.
They describe what they notice.
As the lesson progresses, students begin recognising patterns.
They discover that reversing the factors does not change the total.
They connect multiplication and division through related fact families.
Later, when asked to solve 6 × 8, students have several ways to reason.
They may immediately recall the fact.
Or they might think:
"I know 5 groups of 8 is 40, so one more group makes 48."
Or:
"I can picture the array."
Or:
"I know 48 divided by 6 is 8."
These are signs that multiplication has become connected knowledge rather than isolated memory.
The same sequence works equally well in homeschool settings, where children often benefit from spending additional time building and discussing concepts before moving to written equations.
Why This Approach Works
Research across cognitive science and mathematics education consistently supports building conceptual understanding before expecting procedural fluency.
Cognitive Load Theory reminds us that working memory has limited capacity. Asking students to memorise abstract facts before they understand what those facts represent places unnecessary demands on working memory.
Explicit Instruction reduces this load by introducing concepts in carefully sequenced steps, providing clear modelling and guided practice before independent application.
The Science of Learning also demonstrates that durable learning occurs when new knowledge connects with existing understanding rather than existing as isolated pieces of information.
Within a Response to Intervention (RTI) framework, this approach is particularly valuable.
Students who struggle with multiplication often do not require endless repetition of facts.
Instead, they need opportunities to revisit the conceptual foundations that may have been missed the first time.
Once those foundations are secure, retrieval practice and purposeful repetition help develop the automatic recall needed for fluent mathematical thinking.
What Changes for Teachers
Teaching multiplication conceptually changes more than student outcomes.
It changes the way teachers observe learning.
Instead of seeing only correct or incorrect answers, teachers begin seeing student thinking.
Misconceptions become visible.
Assessment becomes more meaningful.
Planning becomes more intentional because teaching decisions are based on understanding rather than assumption.
For homeschool educators, lessons often become calmer and more enjoyable because children are no longer trying to memorise ideas that don't yet make sense.
For classroom teachers and intervention specialists, the I-CRAVE Maths® Methodology provides a consistent framework that supports students across a wide range of learning needs while reducing the guesswork that often accompanies intervention.
Most importantly, students begin developing confidence because the mathematics makes sense.
Understanding First, Fluency Second
Fluent recall of multiplication facts is an important goal.
But fluency built on understanding is far more powerful than fluency built on chanting alone.
Times tables are not the destination.
They are one part of a much bigger journey towards mathematical understanding.
When students understand equal groups, arrays, fact families and the relationships between multiplication and division, they no longer rely solely on memory.
They reason.
They explain.
They solve problems with confidence.
And over time, the facts become easier to remember because they are connected to understanding.
Children don't remember times tables simply because they have chanted them.
They remember them because the mathematics makes sense.
When understanding comes first, fluency follows. And when fluency is built on understanding, confidence follows with it.
Ready to Strengthen Your Maths Teaching?
Maths Australia provides practical, research-informed training that shows educators and homeschool families exactly how to teach times tables with clarity and confidence using the I-CRAVE Maths® Methodology.
If you're supporting students who are disengaged, struggling with multiplication, or missing foundational concepts, explore our educator training and accreditation pathways.
Learn more at: https://mathsaustralia.com.au/training