Scaled graphs

A scaled graph uses a number on the scale that stands for more than one thing, so big amounts can fit on one neat chart.

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Definition

A scaled graph is a bar graph or picture graph where each mark, bar, or picture symbol stands for more than 1. The scale tells you how much each unit or symbol is worth. You use the scale to figure out the real amount by counting marks or symbols and multiplying by the scale number.

Remember the rule

Value = Number of units (or symbols) × Scale number. For example, 3 symbols × 5 = 15.

Key words

Scale: The number that tells you how much each bar unit or picture symbol stands for, like each square = 2 apples.
Bar graph: A chart that uses bars of different lengths to show amounts.
Picture graph (pictograph): A chart that uses small pictures or symbols to show amounts.
Key: The little box on a picture graph that tells you what one symbol stands for, for example one star = 5 votes.
Interval: The equal jump between numbers on a scale, like 0, 2, 4, 6 all jump by 2.
Axis: The line along the bottom or side of a graph where the scale numbers are written.
Data: Information collected by counting or measuring, like how many students picked each favorite fruit.
Value: The real number an amount stands for after you use the scale to figure it out.

Worked examples

A picture graph shows favorite pets. The key says 1 paw print = 2 votes. Dogs got 4 paw prints. How many students voted for dogs?

→ 4 paw prints × 2 = 8 students voted for dogs. · Always multiply the number of symbols by the scale number in the key.

A bar graph has a scale that goes 0, 5, 10, 15, 20. The bar for soccer reaches up to 15. How many students picked soccer?

→ 15 students picked soccer. You just read the number where the bar stops. · When the bar lands exactly on a line, just read that number off the scale.

A picture graph shows books read. Each book symbol = 3 books. Maria has 5 symbols. How many books did Maria read?

→ 5 × 3 = 15 books.

A bar graph scale goes by 2s: 0, 2, 4, 6, 8, 10. The bar for apples ends halfway between 4 and 6. How many apples?

→ Halfway between 4 and 6 is 5, so there are 5 apples. · When a bar stops between two lines, find the middle value between those two numbers.

You want to make a picture graph for data showing 30, 25, and 15 stickers. Which key makes sense: 1 star = 1 sticker or 1 star = 5 stickers?

→ 1 star = 5 stickers makes more sense. With scale 5, you only need 6, 5, and 3 stars. Using scale 1 would need 30 stars and be way too crowded. · Pick a scale that keeps your graph a manageable size.

A bar graph shows rainfall. Scale goes by 10s. January bar is at 30, February bar is at 50. How much more rain fell in February than January?

→ 50 − 30 = 20 more units of rain in February.

Common mistakes

Forgetting to use the scale — reading the number of symbols or bar units as the final answer instead of multiplying by the scale number.
Adding the scale number instead of multiplying. For example, seeing 3 symbols with scale 5 and writing 3 + 5 = 8 instead of 3 × 5 = 15.
Not reading the key before starting, so they use the wrong scale for the whole problem.
Misreading bars that stop between two lines by guessing randomly instead of finding the halfway value.
Skipping the key when building their own graph and leaving readers no way to know what each symbol stands for.

FAQs

Why do graphs use a scale instead of just showing every single number?

If you had 200 apples, you would need 200 squares or symbols and the graph would be huge. A scale like 1 square = 10 lets you show 200 with just 20 squares — much easier to read.

How do I know what scale to pick when I make my own graph?

Look at your biggest number. Pick a scale number that divides into it evenly and keeps the graph to about 10 bars or symbols. Common choices are 2, 5, or 10.

What if the bar stops between two lines and it is not exactly in the middle?

In 3rd grade, bars usually land on a line or right in the middle. If it seems in between, look carefully — most of the time the bar does hit a line or the exact midpoint.

Is the key the same thing as the scale?

They are closely related. The key is the little box that explains what one symbol stands for in a picture graph. The scale is the set of numbers along the axis of a bar graph. Both tell you the worth of each unit.

Can the scale start at a number other than zero?

In 3rd grade, scales almost always start at zero. Starting at zero makes sure the bars show the true comparison between amounts.

What is the difference between a scaled bar graph and a regular bar graph?

A regular bar graph has a scale of 1, so every unit equals exactly 1. A scaled bar graph has each unit equal to 2, 5, 10, or another number greater than 1, which lets bigger data fit neatly on the page.

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