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Math is a language. Translation goes both ways.
Most school teaches math one direction: here's an equation, solve it. That's the easy part. The hard part — the part most adults still can't do well — is the translation. Take a real-world problem and turn it into math. Take a math statement and turn it back into a real-world thing.
The cadets who learn this skill stop being afraid of word problems. Word problems are just translation exercises. Once you can translate, the math itself is the small part.
By the end of this workshop you'll have diagnosed which equation matches a word problem, written equations from descriptions, written descriptions from equations, and built a translation pair of your own — both directions, your problem.
Step 1 · Read
Got it?
If you understand the loop — words to math, math to words — tap below.
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Step 2 · Diagnose
Match each word problem to its equation
Three problems. Two equation choices each. One is right. The other is a trap that almost matches but doesn't. Pick carefully.
PROBLEM 01
A T-shirt costs $15. You buy 4 of them. How much do you spend?
15 × 4 = 60. "Same thing happening 4 times" is multiplication. The trap (15 + 4) treats the count and the price as the same kind of number — they're not.
PROBLEM 02
You had 20 dollars. You bought a $7 sandwich. How much do you have left?
20 − 7 = 13. "How much is left after spending" is subtraction. The trap (20 × 7) is the most common kind of math mistake — picking an operation that looks fancy instead of the one that fits.
PROBLEM 03
Six friends split a $48 bill equally. How much does each pay?
48 ÷ 6 = 8. "Split equally" is division. The trap (48 + 6) is what happens when you panic and pick any operation. Slow down. Read for the verb. "Split" means divide.
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Step 3 · Translate forward
Words → Math. Write the equation.
Read the problem. Write the equation that matches. Don't solve it — just translate. Use whatever symbols you'd use ( + − × ÷ ), letters for unknowns (x, y), and a clear shape.
PROBLEM
A book costs $12. You buy 3 books and pay with a $50 bill. The change you get back is x. Write the equation.
Try writing it with subtraction and multiplication. We'll check the shape, not the spelling.
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Step 4 · Translate backward
Math → Words. Describe the situation.
Below is an equation. Your job: describe a real-world situation it could represent. Don't solve it — just turn it into a story. Any topic. Be specific.
EQUATION
y = 8 × n
What real situation produces "y equals 8 times n"? Maybe each of n things costs $8. Or each n seconds, you save 8 of something. Your story, your specifics.
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Step 5 · Build a pair
Write your own translation pair
You translate both directions now. Write a real-world problem of your own (it can be small — counting candy, splitting time, anything), then write the equation that matches it.
Your problem (in words)
Be specific. Use real numbers. Make it a problem with an answer.
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Your equation (in math)
Use letters for unknowns. Use operators ( + − × ÷ ). Make the shape match the words.
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Step 6 · Reflect
A real problem in your life right now that math could help you think about
Translation works on real things, not just textbook things. What's a question or decision you have right now — how to spend money, how to split time, how to compare two options — that math could help with?
15 characters minimum
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First Equation — constellation formed
You can translate now. Words to math, math to words. Word problems lose most of their fear when you stop trying to solve them and start trying to translate them. Last workshop teaches you how to defend the answer once you have it.