Concept 1 of 7
Story Translators: Making Math Real
Today's big idea
Decide if each thing that happens makes the amount go up or down, before you calculate.
Back for what goes out, forward for what comes in. No arithmetic needed.
How it works
👀 What's going on?
Your friend texts you: 'I had 1,200 coins. I gave 350 to Aarav, and Mom gave me 500 more.' There isn't a single + or − sign anywhere. That is what makes word problems feel harder than sums, even when the numbers are easy. Every word problem hides an equation inside a story, and your job is to find it.
💡 Here's the trick
Read the picture above. Selling 3,200 apples pushes the pile back. The delivery of 1,500 pushes it forward. The back jump is longer, so the shop finishes lower than it started. Work out which way each event pushes before you touch the numbers. Clue words like altogether and more often mean add. Gave away and left often mean subtract. They are helpful hints, but they are hints, not rules.
🪄 How to do it
- 1.Draw each thing that happens as one jump on a number line, like the picture above.
- 2.Decide what each step does to the total: does it grow (add) or shrink (subtract)?
- 3.Use clue words to double-check your choice, not to replace your thinking.
✍️ Try it
You have saved 1,800 rupees. You spend 450 on a book. Then you get 700 for your birthday. Do you end up with more money or less than you started with?
Two things happen, so draw two jumps: back 450, then forward 700. The forward jump is the longer one, so you end up with more. The shop above ended lower and this ends higher. In both, the longer jump decided it, not the order the events came in. Deciding the direction is this concept's whole job. The next one, The Hopping Map, uses the same number line to land on the exact number.
⚠️ Watch out
You might be thinking, but it said more, so surely we add! In a longer problem that word can trick you. 'She had 20 sweets, gave away 5, then got 8 more' needs a subtract and an add. Trust the picture over any single word.
🌟 Why this matters
Maths outside the classroom almost always arrives like this, as a story with no signs in it. Working out change at a shop, or whether pocket money covers two things, starts with deciding what to add and what to take away. Strong problem solvers always settle the direction first.
Exam tip: Olympiad papers are built this way on purpose, so they almost never hand you a bare sum.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A stall had 7,000 tickets. It sold 2,500 in the morning, then got 900 more printed. Did the pile grow or shrink overall?”
- 1
Count the events
Two things happen: tickets sold, tickets printed. So my picture needs two jumps. 🗺️
- 2
Which way does each one go?
Selling means fewer than before, so jump back 2,500. Printing means more, so jump forward 900.
- 3
Compare the two jumps
Back 2,500 is longer than forward 900, so the story travels backwards overall.
- 4
Answer ✓
The pile shrank and I never worked out a total. The word “more” was there, but the pile still got smaller.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Map the story first. Each thing that happens is one jump, and you decide which way it goes.
STORY 1 OF 3
You start with 4,000 books. Then 900 were borrowed, and 1,300 new books arrived.
Does that make the amount grow or shrink?
Quick check
✅ VERIFICATION
A tank had 9,000 litres. 2,000 litres were used, then 4,000 litres were added. Without working out the total, how does the amount at the end compare with the start?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Hopping Map
Add or subtract huge numbers by hopping one safe step at a time.