Mental math strategies outperform rote memorisation for harder facts
In many Australian primary classrooms, the times-tables chant still echoes down the corridor at the start of maths lessons. Students recite their way through, hoping rhythm carries them to the test. The trouble is that some products refuse to stick, and the harder a child drills a stubborn fact, the more it can feel like pushing a rope.
Rote learning asks the brain to file each combination separately. For facts like 2×5 or 10×4 the brain accepts gladly because the patterns are obvious. For others — 7×8, 6×7, 9×9 — the file gets crowded and items go missing. Mental math strategies work differently. They teach the brain to build an answer from facts it already owns, so a forgotten combination can be reconstructed on the spot.
The push toward strategy-based teaching has grown alongside recent national curriculum reviews. Schools in Victoria and New South Wales have moved lesson planning away from repetitive drills toward problem-solving tasks. Parents at the kitchen bench after school often notice the change first: fewer flashcard marathons, more conversations about how the answer was reached.
NAPLAN data from recent years showed that students who could explain their thinking generally outperformed peers who simply recalled answers. That evidence has shaped how departments of education encourage teachers to teach multiplication, and nudged the wider tutoring market away from memorisation-heavy programs.
Why rote memorisation stalls on certain facts
The brain stores information more reliably when it can connect a new item to something already known. When a child learns 6×6 by chanting the answer a dozen times, the brain has no scaffold to hang it on. Without a hook, the fact floats in short-term memory and slips away by morning tea. Teachers in Brisbane and Adelaide report the same sticking points: 7×8 trips up bright students, and 8×9 reliably appears in the wrong column on quizzes.
Repetition also carries a hidden cost: time spent drilling facts that do not consolidate is time stolen from facts that would settle with a small strategy. Fatigue builds, confidence dips, and maths becomes something to survive rather than enjoy.
How mental strategies use number sense already learned
A child who knows 5×8 and 3×8 already owns the ingredients to find 8×8. They add the two together and the answer is not memorised — it is cooked. This is the heart of mental math: turning arithmetic into reasoning. Strategies like doubling, halving, and breaking apart rely on patterns the brain recognises.
Australian curriculum guidance now asks teachers to highlight these connections explicitly. Rather than expecting students to memorise the entire multiplication grid, teachers model how the grid is built from a small set of anchor facts. A Year 4 student in a Melbourne classroom might find 9×6 by first calculating 10×6 and subtracting one group of 6. The fact is no longer a mystery to recall — it is a puzzle with a method.
Doubling and halving for the tough facts
Doubling is one of the cleanest tricks in the toolkit. A child who knows 4×7 can find 8×7 by doubling the product. Halving works in reverse: forget 8×6 but remember 4×6 and you simply double the known answer. These moves seem invisible to an adult but feel genuinely powerful to a nine-year-old.
The real gift of doubling and halving is that they work even when memory fails. A student sitting a timed quiz does not need every product memorised — they need a path to the answer they can trust. Doubling and halving provide that path with very little cognitive load, leaving more working memory for the next question.
Distributive thinking for larger products
Distributive thinking turns one hard fact into two easy ones. To find 7×6, a student splits the 7 into 5 and 2, then adds 5×6 and 2×6 together. This is not a trick reserved for gifted students. In classrooms from Perth to Hobart, teachers introduce it alongside the standard times-table sequence so every student has a fallback.
The approach also helps students see the structure of multiplication rather than treating it as a wall of digits. They notice that 13×4 can be solved as 10×4 plus 3×4, and that the same logic extends into multi-digit work in upper primary. By Year 6, students practised in distributive reasoning usually move into harder calculations with noticeably less anxiety.
Anchor facts as stepping stones
Every child has anchor facts they know instantly — usually the ones built on 1, 2, 5, and 10. Mental strategies use them as a starting point. To find 9×6, a student starts from 10×6, subtracts 6, and arrives at 54 in two moves. To find 8×7, they might start from 7×7 and add another 7. The grid feels less like a flat list and more like well-known nodes with paths between them.
Parents practising at home can reinforce this by asking how rather than what. Instead of "what is 9×6?", try "how could you work out 9×6 using something you already know?". The phrasing alone changes the conversation. A child who explains their strategy aloud builds a stronger mental model and is more likely to recall the method under pressure.
What Australian schools are doing differently
State-level guidance has moved away from timed drills as the main vehicle for learning facts. In NSW and Victoria, recent teaching frameworks ask educators to balance fluency routines with reasoning tasks, so students get the speed benefits of practice without losing the deeper understanding that makes facts stick. Many schools now use short daily slots for strategy games, paired discussions, and retrieval practice rather than marathon tests.
The shift is visible at parent-teacher interviews too. Teachers more often discuss which strategies a child reaches for, not just which answers they get right. A student who knows 6×7 because they doubled 6×6 plus 6 is, in the teacher's eyes, just as fluent as one who rote-recalled it — and arguably more flexible.
Putting the strategies to work
For parents and teachers ready to try strategy-based practice, the work begins with picking one tricky fact and modelling how to build it. Choose 8×7, walk through the doubling route, and then let the student try the next one on their own. Praise the reasoning, not just the correct number. Worksheets framed as problem-solving give students permission to think rather than guess.
A quick note on focus: older siblings helping with practice sometimes drift towards their own screens, and a quick browse of an unrelated casino review can swallow an entire study session. Keep devices out of reach during the ten-minute strategy slot, and the gains come quickly.
If you want ready-made materials that teach these strategies rather than just drill them, the printable library at Gialdini Worksheets offers packs built around anchor facts, doubling routines, and distributive reasoning tasks. Browse the collection, pick the fact families your child finds hardest, and watch the grid turn from a wall into a web of paths they can actually walk.