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Picture Graphs with Scales

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Reading and Creating Picture GraphsReading and Interpreting Scaled Graphs
data picture-graphs scale

Core Idea

Picture graphs use symbols (pictures) to represent data. A scale explains what each symbol represents—for example, one apple picture = 2 real apples. Scales are necessary when data quantities are large, making one-symbol-per-item impractical.

Explainer

You already know how to read and create picture graphs where each symbol stands for exactly one item — a 1-to-1 picture graph. That works great when the numbers are small. But what if a school survey asked 120 students about their favorite subject, and you had to draw 120 symbols? The graph would be enormous. Scaled picture graphs solve this by letting each symbol represent more than one item, so the graph stays a manageable size.

The scale is the rule that tells you how many real items each symbol counts for. The scale is always shown in a key (also called a legend) somewhere on the graph, usually written like: "Each 🍎 = 5 apples." Once you know the scale, you can read the graph by multiplying: if the "Apples" row has 6 symbols and each symbol = 5, then 6 × 5 = 30 apples total. If a row has 4 symbols, that row represents 4 × 5 = 20 items. Reading a scaled picture graph is really a multiplication problem in disguise.

Sometimes a row will have a partial symbol — like half a picture. If the scale is "each symbol = 4," then half a symbol means 2. Partial symbols are just a visual way of representing amounts that fall between multiples of the scale. When you see a half symbol, divide the scale value in half to find what it represents.

Choosing the right scale when you create a graph is a decision that requires judgment. If your largest value is 30 and you use a scale of 1, you draw 30 symbols — too many. If you use a scale of 10, you draw 3 symbols — clean and readable. A good scale divides evenly into most of the data values, so you avoid awkward fractions. Thinking about scale is your first taste of the kind of design decisions that make data displays clear and useful.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Making 10 as an Addition StrategyAddition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts Through 10Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersLength ComparisonMeasuring Length with Non-Standard UnitsMeasuring Length With a RulerMeasuring with Feet and MetersEstimating LengthsLine Plots with Measurement DataOrganizing and Representing DataCollecting and Displaying Categorical DataCollecting and Organizing DataReading and Creating Picture GraphsPicture Graphs with Scales

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