Grade 3 · Measurement & Data · MAT-03-MD-007
Read Scaled Picture Graphs
Represent read scaled picture graphs with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent read scaled picture graphs with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving read scaled picture 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 Picture Graphs
A scaled picture graph uses each symbol to represent more than one item.
A reliable reasoning strategy
Read the key before counting symbols, then multiply the symbol count by the scale value.
Representations that should agree
The graph is a multiplication model because equal-value symbols form equal groups. 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.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
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 picture graph shows 3 stars and the key says 1 star = 5 votes. How many votes?
3 × 5 = 15Multiply the number of symbols by the value of each symbol.
A graph shows 4 books and the key says 1 book = 2 students. How many students?
4 × 2 = 8Four symbols at two students each represent eight students.
A graph shows 6 apples and the key says 1 apple = 3 baskets. How many baskets?
6 × 3 = 18Scale the symbol count by the key value.
A graph shows 5 circles and the key says 1 circle = 10 points. How many points?
5 × 10 = 50Each of five symbols represents ten points.
A graph shows 7 trees and the key says 1 tree = 2 trees planted. How many trees were planted?
7 × 2 = 14Multiply the seven symbols by two.
Category A has 4 symbols and Category B has 6 symbols; each symbol = 5 items. How many more items does B represent?
(6 − 4) × 5 = 10Find the two-symbol difference, then apply the scale.
A graph has 3 symbols for Monday and 5 for Tuesday; each symbol = 4 customers. What is the total?
(3 + 5) × 4 = 32Combine the symbol counts and multiply by the key.
A key says 1 symbol = 3 books. How many symbols are needed to represent 12 books?
12 ÷ 3 = 4 symbolsDivide the data value by the amount represented by each symbol.
A key says 1 symbol = 5 miles. A row represents 25 miles. How many symbols should appear?
25 ÷ 5 = 5 symbolsFive groups of five miles make 25 miles.
A graph shows 8 symbols with a key of 2 each. What value is represented?
8 × 2 = 16The scale changes each symbol from one item to two.
Two categories each have 5 symbols and the key is 4. Are their data values equal?
Yes; both represent 20.Equal symbol counts under the same key represent equal values.
A graph shows 2 symbols in one category and 7 in another; key = 3. What is the difference?
(7 − 2) × 3 = 15Five more symbols at three units each represent a difference of 15.
A graph has 9 symbols; key = 2. If one symbol is removed, what value remains?
8 × 2 = 16Removing one symbol removes two represented items.
A graph has 4 symbols; key = 5. If the key changed to 10 without changing the symbols, what would the represented total be?
4 × 10 = 40Changing the scale changes the value represented by every symbol.
A graph shows 6 symbols for red and 3 for blue; key = 4. How many items are shown altogether?
(6 + 3) × 4 = 36Nine total symbols at four items each represent 36.
A picture graph shows 1 symbol for a category; key = 8. What value does that category have?
8One full symbol represents the key value.
A graph represents 30 items with 6 symbols. What must each symbol represent?
30 ÷ 6 = 5 itemsThe scale equals total value divided by symbol count.
A category has 0 symbols and the key is 5. What value is represented?
0No symbols means no represented items.
A graph uses different symbol sizes in different rows but claims the same key. Why is that risky?
Symbol size can visually distort comparisons.Scaled picture graphs should use consistent symbols so the key is interpreted fairly.
Why must you read the key before comparing categories in a picture graph?
The key tells how much each symbol represents.Counting symbols alone can give the wrong numerical value when one symbol represents more than one item.
Practice
Guided practice with hints
01A picture graph shows 3 symbols and the key says each symbol represents 5 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 15
02A picture graph shows 4 symbols and the key says each symbol represents 2 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 8
03A picture graph shows 5 symbols and the key says each symbol represents 5 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 25
04A picture graph shows 6 symbols and the key says each symbol represents 2 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 12
05A picture graph shows 7 symbols and the key says each symbol represents 5 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 35
06A picture graph shows 2 symbols and the key says each symbol represents 2 items. How many items?
Hint: Read the key before counting symbols, then multiply the symbol count by the scale value.
Answer: 4
Practice
Independent practice
01A picture graph shows 5 symbols and the key says each symbol represents 5 items. How many items?
Answer: 25
02A picture graph shows 6 symbols and the key says each symbol represents 2 items. How many items?
Answer: 12
03A picture graph shows 7 symbols and the key says each symbol represents 5 items. How many items?
Answer: 35
04A picture graph shows 2 symbols and the key says each symbol represents 2 items. How many items?
Answer: 4
05A picture graph shows 3 symbols and the key says each symbol represents 5 items. How many items?
Answer: 15
06A picture graph shows 4 symbols and the key says each symbol represents 2 items. How many items?
Answer: 8
07A picture graph shows 5 symbols and the key says each symbol represents 5 items. How many items?
Answer: 25
08A picture graph shows 6 symbols and the key says each symbol represents 2 items. How many items?
Answer: 12
Common mistakes
Learn to catch the error, not just the answer.
Translate one symbol into its numerical value before answering questions.
Reconnect the answer to read scaled picture graphs and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Interpret survey and category data compactly.
- Use read scaled picture graphs to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
A picture graph shows 7 symbols and the key says each symbol represents 5 items. How many items?
35
A picture graph shows 2 symbols and the key says each symbol represents 2 items. How many items?
4
A picture graph shows 3 symbols and the key says each symbol represents 5 items. How many items?
15
A picture graph shows 4 symbols and the key says each symbol represents 2 items. How many items?
8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Read Scaled Picture Graphs Challenge
Solve and explain Grade 3 problems involving read scaled picture graphs without relying on answer guessing.
Practice
Mastery check
01A picture graph shows 3 symbols and the key says each symbol represents 5 items. How many items?
Answer: 15
02A picture graph shows 4 symbols and the key says each symbol represents 2 items. How many items?
Answer: 8
03A picture graph shows 5 symbols and the key says each symbol represents 5 items. How many items?
Answer: 25
04A picture graph shows 6 symbols and the key says each symbol represents 2 items. How many items?
Answer: 12
05A picture graph shows 7 symbols and the key says each symbol represents 5 items. How many items?
Answer: 35
06A picture graph shows 2 symbols and the key says each symbol represents 2 items. How many items?
Answer: 4
07A picture graph shows 3 symbols and the key says each symbol represents 5 items. How many items?
Answer: 15
08A picture graph shows 4 symbols and the key says each symbol represents 2 items. How many items?
Answer: 8
Terminology
Words to know
- scale
- The amount represented by one symbol or interval.
- key
- A statement explaining what a graph symbol represents.
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 Picture Graphs.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.