Reading Diagrams
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Sometimes tests and textbooks show you pictures, charts, or diagrams with important information. Learning to READ diagrams helps you find answers and understand data. Let's learn how!
What is a Diagram?
A diagram is a picture that shows information. It might be a chart, a graph, a map, or a drawing with labels. Diagrams help us see information quickly without reading lots of words.
Types of Diagrams You'll See
- Picture graphs: Use pictures to show amounts (like 5 apples = 5 apple pictures)
- Bar graphs: Use bars of different heights to compare amounts
- Tally charts: Use marks (||||) to count things
- Tables: Organize information in rows and columns
- Labeled pictures: Pictures with arrows and words pointing to parts
How to Read a Diagram
- Look at the title. What is the diagram about?
- Read the labels. What does each part mean?
- Look at the numbers. What amounts are shown?
- Study the key/legend. Does it explain what symbols mean?
- Answer the question. Find what you need in the diagram.
Test-Taking Tip
On the SAT and ACT, you will see many questions about graphs and charts. Always read the title and labels FIRST. Then look carefully at the data before answering. The answer is usually IN the diagram!
Examples
Let's practice reading different kinds of diagrams.
Example 1: Reading a Picture Graph
Favorite Fruit (Each picture = 1 student)
Apples: [apple][apple][apple][apple] = 4 students
Bananas: [banana][banana][banana] = 3 students
Oranges: [orange][orange][orange][orange][orange] = 5 students
Question: Which fruit is the most popular?
How to solve: Count the pictures. Oranges has 5 (the most).
Answer: Oranges is the most popular.
Example 2: Reading a Tally Chart
Animals at the Farm
Cows: |||| = 4
Pigs: ||| = 3
Chickens: |||| ||| = 8
Question: How many more chickens are there than cows?
How to solve: Chickens = 8, Cows = 4. 8 - 4 = 4
Answer: There are 4 more chickens than cows.
Example 3: Reading a Simple Table
Ice Cream Sales
| Day | Cones Sold |
|---|---|
| Monday | 10 |
| Tuesday | 15 |
| Wednesday | 8 |
Question: On which day were the most cones sold?
How to solve: Look at the "Cones Sold" column. Find the biggest number.
Answer: Tuesday (15 cones).
Example 4: Reading a Bar Graph
Books Read This Month
Tom: [====] 4 books
Sara: [======] 6 books
Max: [===] 3 books
(Imagine bars going to the right, where each = is one book)
Question: How many books did Sara and Max read together?
How to solve: Sara = 6, Max = 3. 6 + 3 = 9
Answer: Sara and Max read 9 books together.
Example 5: Reading a Labeled Diagram
Parts of a Flower
A diagram shows a flower with arrows pointing to: Petal, Stem, Leaf, Roots
Question: What part of the flower is underground?
How to solve: Look at the labels. Which part is below the ground?
Answer: The roots are underground.
Practice
Use the diagrams to answer each question.
Pet Survey (Each paw = 2 students)
Dogs: [paw][paw][paw] = ?
Cats: [paw][paw] = ?
Fish: [paw] = ?
1. How many students chose dogs?
Show Answer
3 paws x 2 students = 6 students chose dogs.
Using the same pet survey above:
2. How many students chose fish?
Show Answer
1 paw x 2 students = 2 students chose fish.
Weather This Week (Tally Chart)
Sunny: |||| || = 7 days
Cloudy: ||| = 3 days
Rainy: |||| = 4 days
3. How many days were rainy?
Show Answer
4 days were rainy (count the tally marks).
Using the same weather chart:
4. How many more sunny days were there than cloudy days?
Show Answer
Sunny = 7, Cloudy = 3. 7 - 3 = 4 more sunny days.
Toy Store Prices Table
Ball: $3 | Car: $5 | Doll: $8 | Puzzle: $4
5. What is the most expensive toy?
Show Answer
The Doll is the most expensive at $8.
Using the same toy price table:
6. How much would a ball and a car cost together?
Show Answer
$3 + $5 = $8
Snack Bar Graph
Cookies: ===== (5)
Chips: === (3)
Fruit: ======== (8)
7. Which snack did the most people choose?
Show Answer
Fruit - it has the longest bar (8).
Using the same snack bar graph:
8. How many people chose snacks in all?
Show Answer
5 + 3 + 8 = 16 people
Class Schedule Table
9:00 - Math | 10:00 - Reading | 11:00 - Science | 12:00 - Lunch
9. What subject is at 10:00?
Show Answer
Reading is at 10:00.
10. In a diagram of a bicycle, which part would help you stop?
Parts shown: wheel, pedal, handlebar, brake
Show Answer
The brake helps you stop.
Check Your Understanding
Question 1: What should you look at FIRST when you see a diagram?
Show Answer
Look at the title first. It tells you what the diagram is about. Then look at the labels and key.
Question 2: What is a key (or legend) in a graph?
Show Answer
A key or legend explains what the symbols or colors mean. For example, it might say "Each star = 5 people" or show what different colors represent.
Question 3: How do you find the total in a picture graph?
Show Answer
Count all the pictures. If each picture stands for more than 1 (like "each star = 2"), multiply the number of pictures by that amount.
Question 4: Why are diagrams helpful?
Show Answer
Diagrams are helpful because they show information visually. You can compare amounts quickly, see patterns, and find specific information without reading lots of text.
Next Steps
- Look for diagrams everywhere: You'll find graphs and charts in books, newspapers, and on cereal boxes!
- Practice reading keys: Always check what each picture or bar represents.
- Keep learning: You have completed the Word Problems with Diagrams unit! Keep building your test-taking skills by reviewing all SAT/ACT Skills lessons.