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Do your students struggle to multiply larger numbers? Maybe they know their basic facts but are lost when faced with something like 25 × 16? That’s where knowing how to teach halving and doubling comes in!
And the best part? It’s rooted in number sense—not memorization or tricks!
This is not a strategy I was taught in school, but I wish I was! It’s a little more advanced so I share it with my students who have already got a decent grasp of the concept of multiplication. Those still need visual representations such as arrays aren’t ready for this as it will likely add confusion.
Let’s look at how to teach halving and doubling so students really get it.
How Does the Halving and Doubling STrategy Work?
Here’s the simple rule:
- If you halve one factor, you must double the other so the total product stays the same.
Think of it like balancing a scale—one side gets smaller, the other gets bigger, but the weight (the product) stays the same.
It’s essential to make it clear that we double and halve (use multiplicative reasoning), NOT add and subtract in order to keep the relationship between the factors the same.
TEACH these basic MULTIPLICATION STRATEGIES FIRST…
Let’s look at an example: 25 × 12
Instead of multiplying these numbers as they are, we can transform them into something much easier:
✅ Halve 12 → 6
✅ Double 25 → 50
Now the equation is: 25 × 12 = 50 × 6, which is MUCH easier to solve mentally: 50 × 6 = 300.
If we want to take it a step further, we could double and halve again to make 100 x 3, making it even easier still!
Why Does The Double and Half Multiplication Strategy Work?
The easiest way to conceptually understand why this strategy works, is to go back to visual representations of multiplication, such as arrays.
Consider 4 x 5 as an array. If we double and halve, we get 2 x 10. You can see in the arrays that the number of squares (the product) hasn’t changed, we have simply changed how they are arranged.
How to Teach Halving and Doubling
As you know, we love math inquiry and student-led investigations over here! Let students experiment with multiplication questions that benefit from this strategy by asking questions such as:
- Represent 4 x 12. Now represent 2 x 24. What do you notice?
- Arrange these 24 counters into 8 equal groups. How many are in each group? What if you have 4 equal groups? How about 2 equal groups? What do you notice?
- What is 14 x 8? What are some other multiplication questions that would give the same product? How do you know?
- Does doubling and halving always work? When doesn’t it?
Considerations when Teaching Doubling and Halving
- Start with manipulatives such as cubes or blocks to build conceptual understanding.
- Transfer the manipulatives to visuals by using arrays or drawings.
- Introduce mental calculations with smaller numbers that can be solved using basic multiplication facts.
- Apply their solid understanding to larger numbers.
When Should Students Use Halve and Double?
While it’s a great mental math tool, Halves and Doubles work best when:
✓ One number is even – Since we’re halving, at least one number should be divisible by 2.
✓ One number ends in 5 or 50 – Doubling numbers like 25, 50, or 75 makes them friendlier (e.g., 25 → 50, 50 → 100).
✓ A larger number can be broken into known facts – Like turning 16 into 8.
Common Misconceptions & Pitfalls
🅇 Forgetting to do both steps. Emphasize that if they halve one number, they must double the other.
🅇 Trying it with odd numbers. Since halving an odd number creates decimals, while possible, it’s not making the question easier to solve.
🅇 Not recognizing when to use it. This strategy isn’t always helpful! Discuss which numbers it works best for and which are best suited to other strategies.
Making It Stick: Activities & Practice
✓ Quick Mental Math Warm-Ups – Give students equations where one number is easily doubled (e.g., 25 × 12, 50 × 18).
✓ Partner Challenges – Have one student pick a multiplication fact and challenge a partner to find an easier way to solve it using Halve and Double.
✓ Use Visual Models – Arrays or number lines can help show how numbers are being transformed.
Final Thoughts on Halves and Doubles
Teaching halving and doubling helps students think flexibly about numbers instead of relying on rote memorization. By guiding them through hands-on visuals, number talks, and real-life practice, they’ll develop a deeper understanding of multiplication—and get faster at mental math!
Multiplication Strategies Posters
If you’d like a set of multiplication strategy posters, check these out.
They’re focused on building a deeper understanding of multiplication and number sense, rather than memorizing facts and tricks!
What are your favourite ways to build multiplication fluency? Let’s chat in the comments!
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