Review and Mistakes
Learn
In this lesson, you'll learn about common mistakes students make on multi-step word problems and how to avoid them. Understanding these errors will help you improve your problem-solving skills!
Common Mistakes
- Skipping steps: Forgetting to do all parts of a multi-step problem.
- Wrong operation: Adding when you should subtract, or multiplying when you should divide.
- Not reading carefully: Missing important information or misunderstanding what the question asks.
- Calculation errors: Making simple math mistakes.
- Forgetting to check: Not verifying that your answer makes sense.
- Using the wrong numbers: Grabbing numbers without understanding what they represent.
Examples
Example: Finding the Mistake
Problem: A store has 84 toys. They sell 36 toys, then get a shipment of 48 more toys. How many toys does the store have now?
Wrong Solution: 84 + 36 + 48 = 168 toys
The Mistake: The student added 36 instead of subtracting it. They "sell" 36 toys, which means those toys leave the store.
Correct Solution:
Step 1: 84 - 36 = 48 toys (after selling)
Step 2: 48 + 48 = 96 toys (after shipment)
Answer: 96 toys
Practice Quiz
For each problem, find the mistake in the student's work and solve it correctly.
1. Problem: Josh had 56 baseball cards. He gave 18 to his brother and bought 25 more. How many does he have now?
Student's work: 56 + 18 + 25 = 99 cards
What mistake did the student make? What is the correct answer?
Show Answer
Mistake: The student added 18 instead of subtracting. Josh GAVE away cards.
Correct: 56 - 18 = 38, then 38 + 25 = 63 cards
2. Problem: A recipe needs 3 cups of flour for one batch of cookies. How many cups are needed for 4 batches?
Student's work: 3 + 4 = 7 cups
What mistake did the student make?
Show Answer
Mistake: The student added instead of multiplying. Each batch needs 3 cups, so 4 batches need 4 times as much.
Correct: 3 x 4 = 12 cups
3. Problem: Maria read 45 pages on Monday and 38 pages on Tuesday. Her book has 120 pages. How many pages are left?
Student's work: 120 - 45 = 75 pages left
What did the student forget?
Show Answer
Mistake: The student forgot to include Tuesday's reading - they only subtracted Monday.
Correct: 45 + 38 = 83 pages read, then 120 - 83 = 37 pages left
4. Problem: 24 students need to be divided into teams of 4. How many teams will there be?
Student's work: 24 x 4 = 96 teams
What is the correct operation and answer?
Show Answer
Mistake: The student multiplied instead of dividing. "Divided into" means division!
Correct: 24 / 4 = 6 teams
5. Problem: A box holds 12 donuts. A bakery made 7 boxes of donuts and sold 50 donuts. How many donuts are left?
Student's work: 12 + 7 = 19, then 19 - 50 = can't do it (negative)
What went wrong?
Show Answer
Mistake: The student added 12 + 7 instead of multiplying to find total donuts.
Correct: 12 x 7 = 84 donuts, then 84 - 50 = 34 donuts left
6. Problem: Sam earns $9 per hour. He worked 5 hours on Saturday and 3 hours on Sunday. How much did he earn?
Student's work: $9 x 5 = $45
What did the student forget?
Show Answer
Mistake: The student forgot about Sunday's work.
Correct: 5 + 3 = 8 hours total, then 8 x $9 = $72
7. Problem: There are 35 students. 8 students are absent. The rest are divided equally into 3 groups. How many in each group?
Student's work: 35 / 3 = about 11 or 12
What step did the student skip?
Show Answer
Mistake: The student forgot to subtract the absent students first.
Correct: 35 - 8 = 27 present, then 27 / 3 = 9 students per group
8. Problem: A bus holds 48 passengers. How many buses are needed for 200 passengers?
Student's work: 200 / 48 = 4.16, so 4 buses
Why is this answer wrong? What is the correct answer?
Show Answer
Mistake: 4 buses only hold 192 passengers (4 x 48 = 192). The remaining 8 people still need a bus!
Correct: You need 5 buses (4 full buses + 1 partially filled bus)
9. Problem: Anna had $50. She bought 3 books that cost $8 each. How much money does she have left?
Student's work: $50 - $8 = $42
What did the student do wrong?
Show Answer
Mistake: The student only subtracted the cost of ONE book, not all 3.
Correct: 3 x $8 = $24 spent, then $50 - $24 = $26 left
10. Problem: A farmer has 72 eggs. He puts 6 eggs in each carton. Then he sells 8 cartons. How many eggs does he have left?
Student's work: 72 - 8 = 64 eggs
Find all the mistakes and solve correctly.
Show Answer
Mistakes: The student subtracted 8 cartons as if they were 8 eggs. They forgot that each carton has 6 eggs, so 8 cartons = 48 eggs.
Correct: 8 cartons x 6 eggs = 48 eggs sold
72 - 48 = 24 eggs left
Check Your Understanding
Were you able to spot the mistakes? Creating a checklist of common errors can help you avoid them in your own work!
Next Steps
- Always re-read the problem to check you found all the steps
- Ask yourself: "Does my answer make sense?"
- Move on to Lesson 6: Mixed Practice Set