The Importance of Multiplicative Thinking

launchlearningcent
Nov 17
3 min read

At Launch, we’re often asked: “Do children really need to memorise their times tables?” The short answer is yes – but not on their own. Quick recall is valuable but without understanding why multiplication works, students can become dependent on rote memory and struggle when tackling more complex problems. Strong mathematical thinkers don’t just memorise — they connect, reason and flexibly apply strategies. Multiplicative thinking is at the heart of this.

What Is Multiplicative Thinking?

Multiplicative thinking is the ability to see and work with numbers in groups and use proportional reasoning. It underpins key concepts such as fractions, division, ratio, area, algebra, and problem-solving. Experts such as Jo Boaler and Peter Sullivan emphasise that deep learning in maths comes from understanding relationships and structure, not just isolated facts. Students become more confident and capable when they understand how numbers relate.

Deep Conceptual Understanding

Students need to see multiplication as more than repeated addition. When they understand that:

6 × 4 means six groups of four
doubling one factor doubles the product
multiplication is related to arrays, area, and number patterns

…they begin to build true number sense. Conceptual understanding is essential before long-term fluency can develop. Without it, students often revert to guessing or counting when faced with unfamiliar problems.

Flexible, Efficient Strategies

This is where the magic really happens. When children understand the structure of multiplication, they can draw on flexible, efficient strategies — not just memory — to find answers.

Here are some strategies we love teaching at Launch:

×2 ➜ Double the number
×4 ➜ Double, then double again
×8 ➜ Double, double, double!
×3 ➜ Double the number, then add one more set
×5 ➜ Multiply by 10, then halve it
×6 ➜ Multiply by 5, then add one more set
×9 ➜ Multiply by 10, then subtract one set
×10 ➜ Make it 10 times bigger (add a zero!)
×7 ➜ This one’s worth learning by heart!

These strategies help students see patterns, connect relationships, and apply what they know in different contexts.

Fluency and Automatic Recall

Once students understand multiplication and can use strategies flexibly, they can build fluency — the ability to recall facts accurately and quickly. Fast recall matters because it frees up mental space for higher-level reasoning (a concept known as cognitive load theory). But recall should come after understanding, not instead of it.

How Parents Can Support Multiplicative Thinking at Home

Here are some simple ways to help — no worksheets required!

Talk About Strategies, Not Just Answers

Ask:

“How did you work that out?”
“Could you use doubling to help?”
“Is there an easier way to think about it?”

2. Play Games

Dice games (roll and multiply, race to double numbers)
Card games (Who can make the highest number? Use strategies to explain why.)
Skip-counting games with movement

3. Use Multiplication in everyday situations

“We need 3 bags of apples and there are 4 apples per bag. How many apples will we have?”
“If each cupcake tray has 6 cups and we need 18cakes, how many trays should we buy?”

4. Practise Fact Recall in Low-Stress Ways

Practise some facts when walking to school or in the car
Times tables songs
Apps or flashcards used playfully

Final Thoughts

At Launch, we believe every child deserves to feel confident and capable in maths. That confidence grows when children don’t just memorise — they understand, reason, and apply.

Times tables matter but multiplicative thinking matters more. When students combine conceptual understanding, flexible strategies and fluent recall, they become powerful thinkers who can tackle any mathematical challenge with confidence.