Multi-Step Word Problems

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Concept Review

Multi-Step Word Problems: The Hidden Question Detective

You're at the grocery store with $20. You buy 3 bags of apples for $2 each, then want to buy as many granola bars as possible for letter: 'O', title: 'Multi-Step Word Problems', concept: each. How many granola bars can you buy? Wait—there's a secret question hiding inside this problem!

Multi-step word problems are like mystery stories. They don't give you all the information you need right away. Instead, you have to become a detective and find the hidden question—the question you must answer first before you can solve the main problem.

The Two-Step Dance

Let's solve our grocery store mystery step by step:

🔍 Step 1: Find the Hidden Question

Main Question: How many granola bars can you buy?

Hidden Question: How much money is left after buying apples?

The hidden question is the information you need but don't have yet!

⚡ Step 2: Solve Both Questions

Hidden Question: 3 bags × $2 each = $6 spent on apples

Money left: $20 - $6 = letter: 'O', title: 'Multi-Step Word Problems', concept: 4

Main Question: letter: 'O', title: 'Multi-Step Word Problems', concept: 4 ÷ letter: 'O', title: 'Multi-Step Word Problems', concept: per granola bar = 14 granola bars

💡 The Detective's Secret

Here's what's amazing: The hidden question is usually the opposite operation of what you see first! If the problem mentions multiplication (3 bags × $2), your hidden question often involves that multiplication. Then your main question uses a different operation entirely (division). It's like the problem is testing two math skills at once!

Spotting Hidden Questions Like a Pro

Look for these clues in word problems:

"How many more..." or "How many left..." — You probably need to find a total first
Multiple groups or rates — Find the total amount before dividing or comparing
Words like "remaining" or "change" — Calculate what was used or spent first

🔑 Key Takeaway

Just like our grocery store adventure, every multi-step word problem has a hidden question waiting to be discovered. Once you find it and solve it, the main question becomes as easy as counting your granola bars. Be the detective—find the hidden question first!

Sample questions

1. Abe buys 3 packs of 10 sensors. He gives 5 sensors to Pluto. To find how many sensors are left, what is the hidden question you must answer first?

○ How many sensors did Pluto get?

○ What color are the sensors?

○ How many are left?

✓ How many total sensors did Abe buy?

Answer: How many total sensors did Abe buy? — You cannot subtract the 5 until you know the starting total ($3 imes 10$).

2. Pluto earns $5 for every lawn he mows. He mows 4 lawns and then spends $7 on a book. What is the hidden question?

✓ How much total money did Pluto earn?

○ How many lawns did he mow?

○ What was the name of the book?

○ How much money is left?

Answer: How much total money did Pluto earn? — First find the total earnings ($5 imes 4$) before you can subtract the $7.

3. A crate has 48 apples. 10 are rotten and the rest are split into 2 equal bags. What is the hidden question?

○ How many apples are in each bag?

✓ How many good apples are there?

○ How many bags are there?

○ How many total apples?

Answer: How many good apples are there? — You must find the number of "good" apples ($48 - 10$) before you can divide them.

Skills in this topic

Identify the hidden question in a two-step word problem
Solve two-step addition and subtraction word problems
Solve two-step multiplication and addition word problems
Solve two-step division and subtraction word problems
Represent two-step word problems using equations with a letter

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