Concept 2 of 7
Speedy Tables: Multiplication
Today's big idea
Multiplying is counting equal groups, so 4 x 3 is four rows of three.
Rows and columns of dots turn a times fact into something you can count.
How it works
👀 What's going on?
Adding 7 + 7 + 7 + 7 + 7 gets you to 35 eventually. Writing 7 × 5 gets you there at once. Multiplying is not a new kind of maths; it is adding, folded up so it fits in one step.
💡 Here's the trick
Look at the rows above. 4 × 3 means four rows of three, and counting every dot gives 12. Because it is a rectangle, you can turn it on its side: three rows of four is the same 12. That is why the order never changes the answer.
🪄 How to do it
- 1.Read the multiplication as groups, the way the rows above are grouped.
- 2.Add that group as many times as the other number says, or use the table if you know it.
- 3.Use the shortcuts: times 0 is always 0, times 1 leaves it alone, times 10 puts a 0 on the end.
✍️ Try it
Work out 6 × 7 by adding groups. Then work out 9 × 8. Finally try 34 × 6 by splitting 34 into 30 and 4.
Six sevens are 7, 14, 21, 28, 35 and 42. For 9 × 8 the table gives 72. Check it by noticing that 10 × 8 is 80, and one 8 less is 72. For 34 × 6, split it: 6 × 30 = 180 and 6 × 4 = 24, so 180 + 24 = 204. Multiplying the tens and the ones and adding is exactly what the column method does with bigger numbers.
⚠️ Watch out
You might be thinking a bigger first number always makes a bigger answer. 3 × 8 and 8 × 3 are both 24, because turning the rectangle sideways changes nothing. What does change the answer is muddling times with plus: 3 + 8 is 11, nowhere near 24.
🌟 Why this matters
Price for several items, tiles on a floor, minutes in a few hours: all of them are equal groups. Knowing the tables by heart is what makes the rest of maths feel fast.
Exam tip: A fact you know instantly frees your thinking for the part of the question that is actually hard.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What is 8 × 6?”
- 1
What does 8 × 6 mean?
Eight groups of six. Or: 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6. 🎯
- 2
Use a known fact
5 × 6 = 30 (easy table). Now add three more 6s.
- 3
Add the last groups
30 + 6 + 6 + 6 = 48
- 4
Answer ✓
8 × 6 = 48
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
3 × 4 means 3 groups of 4. Drop one group at a time and watch the total grow.
MULTIPLY · ROUND 1 OF 3
3 × 4
3 groups of 4
RUNNING TOTAL
tap “add a group” to start
Quick check
✅ VERIFICATION
What is the same as 8 × 5?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Arrays & the Turn-Around Trick
3 × 8 = 8 × 3 — the same rectangle.