Common Mistakes with Graphs
Learn
Everyone makes mistakes when learning! Knowing about common mistakes helps you avoid them. Let us look at errors students often make with graphs.
Mistake 1: Forgetting the Key in Picture Graphs
Wrong: Counting 5 star pictures and saying "5 items"
Right: If each star = 2 items, then 5 stars = 10 items
Fix: ALWAYS check the key first! Multiply the number of pictures by what each picture represents.
Mistake 2: Misreading Bar Heights
Wrong: Looking at the bar but not checking the number scale
Right: Follow the bar to the number line to find the exact value
Fix: Use your finger or a ruler to trace from the top of the bar to the numbers on the side.
Mistake 3: Confusing "More" and "Total"
Wrong: Adding when the question asks "how many more"
Right: "How many more" means SUBTRACT to find the difference
Fix: Circle the key words in the problem. "More than" or "fewer than" = subtract. "In all" or "total" = add.
Mistake 4: Skipping the Scale
Wrong: Assuming each line on the graph means 1
Right: The scale might count by 2s, 5s, or 10s
Fix: Look at the numbers on the side. What is the difference between them? That is how the graph counts!
Mistake 5: Not Reading the Title and Labels
Wrong: Jumping straight to the data without understanding what the graph shows
Right: Read the title first to know what the graph is about
Fix: Start at the top! Read the title, then the labels, then look at the data.
Examples
Example 1: Spot the Error
A picture graph shows cookies baked. Each cookie picture = 3 cookies.
Monday: 4 pictures, Tuesday: 5 pictures
Student Answer: "Monday had 4 cookies and Tuesday had 5 cookies. Tuesday had 1 more cookie."
What went wrong? The student forgot to use the key!
Correct Answer: Monday: 4 x 3 = 12 cookies. Tuesday: 5 x 3 = 15 cookies. Tuesday had 15 - 12 = 3 more cookies.
Example 2: Spot the Error
A bar graph shows: Apples = 8, Oranges = 5. Question: How many fruits in all?
Student Answer: "8 - 5 = 3 fruits"
What went wrong? The student subtracted instead of adding!
Correct Answer: "In all" means add: 8 + 5 = 13 fruits.
Example 3: Spot the Error
A bar graph counts by 2s. A bar reaches to the 4th line.
Student Answer: "The bar shows 4."
What went wrong? The student did not notice the scale counts by 2s!
Correct Answer: Counting by 2s: 2, 4, 6, 8. The 4th line = 8.
Practice
Find and fix the mistakes in these problems.
Problem 1
Picture graph: Each smiley face = 2 students. Reading shows 6 smiley faces. Math shows 4 smiley faces.
Student says: "6 + 4 = 10 students total."
What is the mistake? What is the correct answer?
Problem 2
Bar graph shows: Dogs = 15, Cats = 9. Question: How many more dogs than cats?
Student says: "15 + 9 = 24 more dogs."
What is the mistake? What is the correct answer?
Problem 3
A bar graph has a scale that counts by 5s. A bar reaches to the 3rd line.
Student says: "The bar shows 3."
What is the mistake? What is the correct answer?
Problem 4
Picture graph: Each star = 5 points. Week 1: 3 stars. Week 2: 4 stars.
Student says: "Week 2 had 4 - 3 = 1 more point than Week 1."
What is the mistake? What is the correct answer?
Problem 5
A bar graph shows favorite sports. The student did not read the title and thought it showed favorite foods.
Why is reading the title important?
Problem 6
Bar graph: Red = 12, Blue = 8, Green = 10. Question: Which color has the fewest?
Student says: "Green has the fewest because 10 is in the middle."
What is the mistake? What is the correct answer?
Problem 7
Picture graph: Each book = 2 books read. Amy: 7 books, Ben: 5 books.
Student says: "Amy read 7 x 2 = 14 books. Ben read 5 books."
What is the mistake? What is the correct answer for Ben?
Problem 8
Bar graph counts by 10s. Bars show: Class A at line 3, Class B at line 5.
Student says: "Class A has 3 and Class B has 5."
What is the mistake? What are the correct values?
Problem 9
A student makes a bar graph but forgets to add labels on the bottom.
Why is this a problem? What labels are needed?
Problem 10
Picture graph shows apples picked. Key says each apple = 4 real apples. Monday: 6 pictures. Tuesday: 6 pictures.
Student says: "Both days are equal, so 6 + 6 = 12 apples total."
What is the mistake? What is the correct total?
Check Your Understanding
- What should you always check first in a picture graph?
- What is the difference between "how many more" and "how many in all"?
- How do you know what each line on a bar graph represents?
- Name three things you should read before looking at the data in a graph.
Next Steps
- Keep a checklist of things to check when reading graphs
- Practice slowly and carefully to avoid mistakes
- Take the Unit Quiz when you feel ready!