Grade 3 · Measurement & Data · MAT-03-MD-008
Read Scaled Bar Graphs
Represent read scaled bar graphs with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent read scaled bar graphs with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving read scaled bar graphs accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Read Scaled Bar Graphs
A scaled bar graph represents category values with bar lengths measured against a numbered scale.
A reliable reasoning strategy
Read axis labels and interval values first, then match each bar endpoint to the scale.
Representations that should agree
Scaled bars support comparison, difference, and total questions using the four operations. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
Interactive math lab
Change it. See what stays true.
Data & Graph Lab
Adjust category values and read the graph numerically.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
A bar ends at tick 3 on a scale increasing by 5. What value does the bar represent?
3 × 5 = 15Multiply the number of scale intervals by the value per interval.
A bar ends at tick 4 on a scale increasing by 10. What value does the bar represent?
4 × 10 = 40Multiply the number of scale intervals by the value per interval.
A bar ends at tick 5 on a scale increasing by 2. What value does the bar represent?
5 × 2 = 10Multiply the number of scale intervals by the value per interval.
A bar ends at tick 6 on a scale increasing by 5. What value does the bar represent?
6 × 5 = 30Multiply the number of scale intervals by the value per interval.
A bar ends at tick 7 on a scale increasing by 10. What value does the bar represent?
7 × 10 = 70Multiply the number of scale intervals by the value per interval.
A bar ends at tick 8 on a scale increasing by 2. What value does the bar represent?
8 × 2 = 16Multiply the number of scale intervals by the value per interval.
A bar ends at tick 2 on a scale increasing by 5. What value does the bar represent?
2 × 5 = 10Multiply the number of scale intervals by the value per interval.
A bar ends at tick 3 on a scale increasing by 10. What value does the bar represent?
3 × 10 = 30Multiply the number of scale intervals by the value per interval.
A bar ends at tick 4 on a scale increasing by 2. What value does the bar represent?
4 × 2 = 8Multiply the number of scale intervals by the value per interval.
A bar ends at tick 5 on a scale increasing by 5. What value does the bar represent?
5 × 5 = 25Multiply the number of scale intervals by the value per interval.
A bar ends at tick 6 on a scale increasing by 10. What value does the bar represent?
6 × 10 = 60Multiply the number of scale intervals by the value per interval.
A bar ends at tick 7 on a scale increasing by 2. What value does the bar represent?
7 × 2 = 14Multiply the number of scale intervals by the value per interval.
A bar ends at tick 8 on a scale increasing by 5. What value does the bar represent?
8 × 5 = 40Multiply the number of scale intervals by the value per interval.
A bar ends at tick 2 on a scale increasing by 10. What value does the bar represent?
2 × 10 = 20Multiply the number of scale intervals by the value per interval.
A bar ends at tick 3 on a scale increasing by 2. What value does the bar represent?
3 × 2 = 6Multiply the number of scale intervals by the value per interval.
A bar ends at tick 4 on a scale increasing by 5. What value does the bar represent?
4 × 5 = 20Multiply the number of scale intervals by the value per interval.
A bar ends at tick 5 on a scale increasing by 10. What value does the bar represent?
5 × 10 = 50Multiply the number of scale intervals by the value per interval.
A bar ends at tick 6 on a scale increasing by 2. What value does the bar represent?
6 × 2 = 12Multiply the number of scale intervals by the value per interval.
A bar ends at tick 7 on a scale increasing by 5. What value does the bar represent?
7 × 5 = 35Multiply the number of scale intervals by the value per interval.
A bar ends at tick 8 on a scale increasing by 10. What value does the bar represent?
8 × 10 = 80Multiply the number of scale intervals by the value per interval.
Practice
Guided practice with hints
01A bar ends at tick 5 on a scale increasing by 5. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 25
02A bar ends at tick 6 on a scale increasing by 10. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 60
03A bar ends at tick 7 on a scale increasing by 2. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 14
04A bar ends at tick 8 on a scale increasing by 5. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 40
05A bar ends at tick 2 on a scale increasing by 10. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 20
06A bar ends at tick 3 on a scale increasing by 2. What value does the bar represent?
Hint: Read axis labels and interval values first, then match each bar endpoint to the scale.
Answer: 6
Practice
Independent practice
01A bar ends at tick 4 on a scale increasing by 2. What value does the bar represent?
Answer: 8
02A bar ends at tick 5 on a scale increasing by 5. What value does the bar represent?
Answer: 25
03A bar ends at tick 6 on a scale increasing by 10. What value does the bar represent?
Answer: 60
04A bar ends at tick 7 on a scale increasing by 2. What value does the bar represent?
Answer: 14
05A bar ends at tick 8 on a scale increasing by 5. What value does the bar represent?
Answer: 40
06A bar ends at tick 2 on a scale increasing by 10. What value does the bar represent?
Answer: 20
07A bar ends at tick 3 on a scale increasing by 2. What value does the bar represent?
Answer: 6
08A bar ends at tick 4 on a scale increasing by 5. What value does the bar represent?
Answer: 20
Common mistakes
Learn to catch the error, not just the answer.
Determine the scale interval from labeled values before reading bar heights.
Reconnect the answer to read scaled bar graphs and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare category totals from surveys and observations.
- Use read scaled bar graphs to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
A bar ends at tick 3 on a scale increasing by 10. What value does the bar represent?
30
A bar ends at tick 4 on a scale increasing by 2. What value does the bar represent?
8
A bar ends at tick 5 on a scale increasing by 5. What value does the bar represent?
25
A bar ends at tick 6 on a scale increasing by 10. What value does the bar represent?
60
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Read Scaled Bar Graphs Challenge
Solve and explain Grade 3 problems involving read scaled bar graphs without relying on answer guessing.
Practice
Mastery check
01A bar ends at tick 2 on a scale increasing by 5. What value does the bar represent?
Answer: 10
02A bar ends at tick 3 on a scale increasing by 10. What value does the bar represent?
Answer: 30
03A bar ends at tick 4 on a scale increasing by 2. What value does the bar represent?
Answer: 8
04A bar ends at tick 5 on a scale increasing by 5. What value does the bar represent?
Answer: 25
05A bar ends at tick 6 on a scale increasing by 10. What value does the bar represent?
Answer: 60
06A bar ends at tick 7 on a scale increasing by 2. What value does the bar represent?
Answer: 14
07A bar ends at tick 8 on a scale increasing by 5. What value does the bar represent?
Answer: 40
08A bar ends at tick 2 on a scale increasing by 10. What value does the bar represent?
Answer: 20
Terminology
Words to know
- bar graph
- A graph using bar length to represent category value.
- axis scale
- The numerical values assigned to positions along an axis.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.MD.3
Primary standards alignment for Read Scaled Bar Graphs.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.