Concept 1 of 7
The Hopping Map: Adding by Jumping
Today's big idea
Add big numbers by hopping: jump the hundreds, then the tens, then the ones.
246 + 375: +300 to 546, +70 to 616, +5 to 621.
How it works
👀 What's going on?
Add 246 + 375 without lining up columns? Jump along a number line instead.
💡 Here's the trick
Look at the picture above. Adding is moving forward. Land on the first number, then hop the hundreds of the second, then the tens, then the ones. Where you land is the total.
🪄 How to do it
- 1.Start on the first number.
- 2.Hop forward by the hundreds, then the tens, then the ones of the second number.
- 3.Read where you land.
✍️ Try it
Hop 253 + 124. Then hop 418 + 235.
253 +100=353, +20=373, +4=377. And 418 +200=618, +30=648, +5=653.
⚠️ Watch out
Hop the biggest place first and count each jump carefully. To subtract, count UP from the smaller number to the bigger one, which is brilliant for round numbers: for 800 − 465, hop 465 → 500 (that is 35), then 500 → 800 (that is 300), so the answer is 335. No borrowing across zeros. The same count-up handles thousands too: 4,000 − 2,750 is a hop of 250 then 1,000, giving 1,250.
🌟 Why this matters
Hopping keeps a picture of adding in your head, and counting up turns a scary subtraction like 800 − 465 into two friendly jumps.
Exam tip: count up whenever the top number is round and full of zeros.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Add 324 + 253 by hopping on a number line.”
- 1
Start on the first number
Put your marker on 324.
- 2
Hop the hundreds of 253
324 +200 lands on 524.
- 3
Hop the tens
524 +50 lands on 574.
- 4
Hop the ones
574 +3 lands on 577.
- 5
Answer ✓
324 + 253 = 577
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Add by hopping. Land on 246, jump the hundreds of 375, then the tens, then the ones.
246 + 375 = ?
Hop +300: 246 + 300 lands on…
Quick check
✅ VERIFICATION
Add 312 + 245 by hopping: 312 + 200 = 512, then + 40 = 552. What is the total after the last hop of + 5?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Number Smashers
Add the hundreds, tens and ones, then join them.