Multi-Step Word Problems

🧩 Multi-Step Word Problems

Part 1 of 5 — What Makes a Problem "Multi-Step"?

Topics in This Part

🔑 Key Idea: A multi-step word problem cannot be solved with a single calculation. You have to find a hidden answer first, then use it to reach the real answer.

One-Step vs. Multi-Step

A one-step problem needs just one operation:

Maya has 12 stickers. She buys 8 more. How many does she have? One step: $12 + 8 = 20$.

A multi-step problem hides a number you must find before you can answer:

Maya has 12 stickers. She buys 3 packs with 8 stickers each. How many does she have now?

You can't just add — first you must find how many stickers are in the 3 packs:

$\text{Step 1: } 3 \times 8 = 24 \text{ stickers in the packs}$ $\text{Step 2: } 12 + 24 = 36 \text{ stickers total}$

💡 The number 24 is the hidden answer. The question never asks for it directly, but you need it to finish.

Concept Check 🎯

The 4-Step Plan

Use this plan on every multi-step problem:

⚠️ Watch Out: Many students answer the hidden question by mistake (like writing "24 stickers" instead of "36"). Always re-read the question at the end to make sure you answered what was asked.

Find the Hidden Step 🔽

A school orders 4 boxes of markers. Each box has 10 markers. The teacher then gives away 15 markers. How many markers are left?

Choose the correct operation for each step.

Your First Two-Step Problems 🧮

Solve each. Enter just the final number.

1) A farmer collects 6 eggs each day for 5 days. He uses 9 eggs. How many eggs are left? 2) Liam saves 8 dollars a week for 4 weeks. He spends 12 dollars. How many dollars does he have left?

🧩 Multi-Step Word Problems

Part 2 of 5 — Choosing the Right Operations

🔑 The Skill: In a multi-step problem, each step might use a different operation. The hard part is matching the clue words in the story to $+$, $-$, $\times$, or $\div$.

Clue Words for Each Operation

💡 "Each" is tricky! "5 bags with 6 apples each" means multiply ($5 \times 6$). But "share 30 apples so each friend gets the same" means divide ($30 \div 5$). Read the whole sentence, not just the word.

Concept Check 🎯

Worked Example: Two Different Operations

A bakery makes 9 trays of muffins with 6 muffins on each tray. They sell 40 muffins. How many muffins are left?

Step 1 — "9 trays with 6 each" → multiply: $9 \times 6 = 54 \text{ muffins made}$

Step 2 — "sell 40" / "how many left" → subtract: $54 - 40 = 14 \text{ muffins left}$

✅ Check: $14$ muffins left $+ 40$ sold $= 54$ made. And $9 \times 6 = 54$. ✓ It matches!

Pick the Operation 🔽

A library has 7 shelves. Each shelf holds 20 books. Then 35 books are checked out. How many books remain?

Mixed Operations Drill 🧮

Solve each two-step problem. Enter the final number.

1) 5 friends each pick 7 flowers. They give 6 flowers to a teacher. How many flowers do they keep? 2) A store has 48 apples. They put them equally into 6 baskets, then sell 1 whole basket. How many apples are sold?

🧩 Multi-Step Word Problems

Part 3 of 5 — Money, Time & Measurement

🔑 Real-World Math: The most common multi-step problems are about money (making change), time (figuring out how long), and measurement (combining lengths or weights). The same 4-step plan works for all of them.

Money Problems & Making Change

Noah buys 3 notebooks that cost $4 each. He pays with a $20 bill. How much change does he get back?

Step 1 — "3 notebooks at $4 each" → multiply: $3 \times \$4 = \$12 \text{ total cost}$

Step 2 — "pays with $20, change?" → subtract: $\$20 - \$12 = \$8 \text{ in change}$

💡 Change = Money Paid − Total Cost. Find the total cost first (that's the hidden step), then subtract it from what was handed over.

Concept Check 🎯

Time & Measurement Problems

Time example:

A movie starts at 3:00 and lasts 2 hours. Then there is a 30-minute drive home. What time do you get home?

Step 1 — movie ends: $3\!:\!00 + 2 \text{ hours} = 5\!:\!00$ Step 2 — drive home: $5\!:\!00 + 30 \text{ min} = 5\!:\!30$

Measurement example:

A ribbon is 8 feet long. You cut off 3 pieces that are each 2 feet long. How much ribbon is left?

Step 1 — ribbon cut off: $3 \times 2 = 6 \text{ feet}$ Step 2 — ribbon left: $8 - 6 = 2 \text{ feet}$

⚠️ With time, remember there are 60 minutes in an hour, not 100. With measurement, make sure all your numbers use the same unit before you add or subtract.

Money Word Problem 🔽

Sofia has $25. She buys 2 books for $6 each and 1 bookmark for $3. How much money does she have left?

Money, Time & Measure Drill 🧮

Enter the final number only (no $ sign or units).

1) A toy costs $7. You buy 2 toys and pay with $20. How many dollars of change do you get? 2) A board is 15 feet long. You cut off 4 pieces, each 3 feet long. How many feet are left? 3) Practice starts at 4:00 and lasts 90 minutes. How many hours long is practice? (decimal is fine)

🧩 Multi-Step Word Problems

Part 4 of 5 — Estimating & Checking Your Answer

🔑 Be Your Own Checker: A good problem-solver always asks "Does my answer make sense?" Estimating (rounding to easy numbers) is the fastest way to catch a big mistake.

Estimating to Check

To estimate, round each number to the nearest ten (or hundred), then do the easy math.

A class collects 38 cans on Monday and 41 cans on Tuesday. They split them equally among 4 boxes. About how many cans per box?

Estimate first: $38 \approx 40$ and $41 \approx 40$, so $40 + 40 = 80$, then $80 \div 4 = 20$. Expect about 20.

Exact answer: $38 + 41 = 79$, then... $79$ isn't a clean divide, but our estimate of $20$ tells us the real per-box number should be close to $20$. If you got $200$ or $5$, you'd know something went wrong!

💡 An estimate won't give the exact answer — it gives you a target zone. If your real answer lands far from the estimate, recheck your steps.

Concept Check 🎯

Is the Answer Reasonable?

Besides estimating, ask common-sense questions:

⚠️ Reasonableness trap: If a problem says "Jon shares 12 candies with 3 friends," each friend can't get more than 12. An answer of $36$ would be unreasonable — division should make the number smaller: $12 \div 3 = 4$.

Reasonable or Not? 🔽

For each, decide whether the answer is reasonable or not reasonable.

Estimate, Then Solve 🧮

For each, enter the EXACT final answer.

1) A store sells 19 toy cars on Saturday and 22 on Sunday. They split the weekend total into 3 equal display cases left over... actually, find just the weekend total: how many cars in all? 2) There are 4 tables with 12 chairs each. 7 chairs are broken and removed. How many chairs are usable?

🧩 Multi-Step Word Problems

Part 5 of 5 — Putting It All Together & Mastery Check

You can now (1) spot a multi-step problem, (2) choose the right operation for each step, (3) handle money, time, and measurement, and (4) estimate to check. Time to put it all together!

Quick Reference

🔑 The 4-Step Plan never changes: Read → Plan → Solve → Check. Always re-read the final question so you answer what was actually asked — not the hidden number.

One Big Worked Example

A class of 24 students goes on a field trip. Tickets cost $5 each. The teacher has $150. How much money is left after buying everyone a ticket?

Step 1 — Read: We need the money left after buying 24 tickets.

Step 2 & 3 — Plan & Solve: Total cost: $24 \times 5 = 120$, i.e. $120 Money left: $150 - 120 = 30$, i.e. $30

Step 4 — Check: Estimate $25 \times 5 = 125$, i.e. $125, and $150 - 125 = 25$, i.e. $25. Our answer $30 is close to $25, so it's reasonable. ✓

💡 The hidden answer was $120 (the total cost). The real answer is $30 (money left). Always finish the last step!

Mixed Practice 🎯

Mastery Drill 🧮

Enter the final number only.

1) A baker makes 5 batches of 12 cookies. She sells 48 cookies. How many cookies are left? 2) 7 kids each bring 6 stickers to school. They put them into 3 equal piles. How many stickers are in each pile? (decimal is fine)

Exit Quiz ✅

Answer all three to finish the lesson.