Concept 2 of 9
Number Smashers: The Partition Method
Today's big idea
Smash each number into tens and ones, add each pile, then recombine.
46 + 37: 40+30=70, 6+7=13, then 70+13=83.
How it works
👀 What's going on?
Add 48 + 35 in your head? Smash each number into its tens and ones, and it gets easy.
💡 Here's the trick
Look at the picture above. Split each number into tens and ones. Add all the tens together, add all the ones together, then join the two piles back into one number.
🪄 How to do it
- 1.Smash each number into tens and ones (48 becomes 40 and 8).
- 2.Add the tens pile, then add the ones pile.
- 3.Join the two piles: tens-total plus ones-total.
✍️ Try it
Smash 52 + 36. Then smash 47 + 28.
50 + 30 = 80 and 2 + 6 = 8, so 80 + 8 = 88. And 40 + 20 = 60 and 7 + 8 = 15, so 60 + 15 = 75.
⚠️ Watch out
When the ones pile tops ten, do not drop the spare ten. 8 + 5 = 13 is 1 ten and 3 ones, and that spare ten is exactly what the column method carries.
🌟 Why this matters
Smashing shows WHY carrying happens, and it makes adding in your head far easier. To subtract, smash both numbers and take each pile away.
Exam tip: a quick smash is a great way to check a column answer that looks wrong.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Add 48 + 35 by smashing into tens and ones.”
- 1
Smash both numbers
48 = 40 + 8, and 35 = 30 + 5.
- 2
Add the tens pile
40 + 30 = 70.
- 3
Add the ones pile
8 + 5 = 13 (a spare ten!).
- 4
Put them together
70 + 13 = 83.
- 5
Answer ✓
48 + 35 = 83
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Smash each number into tens and ones. Add the tens pile, add the ones pile, then put them back together.
46 + 37 = ?
Add the tens: 40 + 30 = ?
Quick check
✅ VERIFICATION
Smash 54 + 23: the tens make 50 + 20 = 70 and the ones make 4 + 3 = 7. What is the total?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Adding 2-Digit Numbers
Line up the columns, then add each one.