Concept 2 of 7
The Hopping Map: Adding & Subtracting Step-by-Step
Today's big idea
Add or subtract big numbers by hopping one step at a time on a number line.
Start at the first number. Hop right to add, hop left to subtract.
How it works
👀 What's going on?
The stadium is filling up before a big match. 25,000 fans are already inside, then 10,000 more come through the gates, and then another 3,000. Working the crowd out in one go feels jumbled, and it is easy to lose track halfway.
💡 Here's the trick
Look at the number line above. Start at 25,000, hop right 10,000 and you land on 35,000. Hop right another 3,000 and you land on 38,000. Each hop is one small problem instead of three at once. Because the path is drawn, you can see exactly where a slip would be.
🪄 How to do it
- 1.Start at the first number, the way the line in the picture above starts at 25,000.
- 2.For each new number, hop right to add or left to subtract.
- 3.Land, write that number down, then take the next hop.
✍️ Try it
A game score is 20,000. You win 5,000, then a trap costs you 3,000. Where do you finish?
Start at 20,000. Hop right 5,000 and land on 25,000. Now hop left 3,000 and land on 22,000. Notice the two hops went opposite ways. That is fine. Each hop only cares about its own sign.
⚠️ Watch out
You might be thinking you can save time by hopping the 5,000 and the 3,000 together. The risk is that the two hops go opposite ways. Bundle them up and it is easy to add the 3,000 instead of taking it off, landing on 28,000 instead of 22,000. One hop at a time keeps each direction in view.
🌟 Why this matters
You already do this without a line when you count on from a price to work out your change. Hopping in friendly steps is how most people add in their heads, at a shop or a bus stop.
Exam tip: Hops let you check a big sum quickly without redoing the whole column method.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“16,000 − 4,000 − 3,000 — what's left?”
- 1
Put the frog at the first number
Start at 16,000 on the number line. 🐸
- 2
First hop — jump left
Subtracting 4,000 means hop left. 16,000 → 12,000
- 3
Second hop — jump again
Now hop left by 3,000. 12,000 → 9,000 🎯
- 4
Land at the answer ✓
16,000 − 4,000 − 3,000 = 9,000
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Hop RIGHT to ADD. Drag the frog to where it lands — then it snaps to the mark.
Mission: 30,000 + 20,000 + 5,000 = ?
Hop 1: drag the frog +20,000
🐸 Frog is at: 30,000
Quick check
✅ VERIFICATION
You start at 8,000 on a number line. You hop right 3,000, then hop left 500. Where do you land?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Number Smashers
Split by place value, then add the matching pieces or take the chunks away in stages.