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  1. 3rd Grade Math
  2. Scaled Bar Graphs: Read, Draw, and Compare Data

3RD GRADE MATH • MATHEMATICS

Scaled Bar Graphs: Read, Draw, and Compare Data

Learn to read and create bar graphs where each square stands for more than one item.

SECTION 1

When Did People Start Using Bar Graphs?

Long ago, people needed ways to show numbers and compare amounts. Imagine you run a lemonade stand and want to show how many cups you sold each day. You could write numbers, but pictures make it much easier to see which days were best!

1786
First Bar Graph
A man named William Playfair made the first bar graph to show trade between countries.
1850s
School Reports
Schools started using bar graphs to show test scores and attendance.
1900s
Business Uses
Companies began using bar graphs to track sales and make business decisions.
Today
Everywhere!
We see bar graphs in newspapers, on websites, and in schools to compare all kinds of data.

But what happens when the numbers get really big? If your lemonade stand sold 50 cups on Monday, would you draw 50 tiny squares? That would take forever! This is why people invented scaled bar graphs where each square or unit can represent more than one item.

SECTION 2

What Makes a Bar Graph "Scaled"?

A scaled bar graph is special because each square or unit stands for more than one thing. Instead of drawing 20 tiny squares for 20 apples, you might draw 4 squares where each square equals 5 apples.

1

Scale

The scale tells you what each square represents. If the scale is 1 square = 5 items, then 3 squares = 15 items.
2

Key or Legend

This shows what the scale means. It might say "Each ⬜ = 10 books" so you know how to read the graph.
3

Bars

The rectangles that show data. Taller bars mean bigger numbers, and shorter bars mean smaller numbers.
4

Labels

Words that tell you what each bar represents, like "Monday," "Tuesday," or "Apples," "Oranges."
✦ KEY TAKEAWAY
Think of scaled bar graphs like money! One dollar bill represents 100 pennies. You don't need to carry 100 pennies—one bill does the job. In the same way, one square on a scaled bar graph can represent many items, making big numbers easier to show and understand.
SECTION 3

See How Scaled Bar Graphs Work

Fruits Sold at School StoreNumber of FruitsType of Fruit010203040506070ApplesOrangesBananasGrapesStrawberriesEach square = 4 fruits
This bar graph shows how many fruits were sold at the school store. Notice the scale at the bottom: each small square equals 4 fruits. The banana bar reaches 60 on the scale, so 60 bananas were sold. Can you figure out how many apples were sold by looking at where the blue bar ends?

Look at the graph above carefully. The scale shows "Each square = 4 fruits." This means every line on the left side represents 4 more fruits. The apple bar goes up to the "40" line, so 40 apples were sold. The banana bar is the tallest—it reaches 60, so 60 bananas were sold!

SECTION 4

The Math Behind Scaled Bar Graphs

Reading a scaled bar graph is like solving a multiplication problem. You need to figure out how many units high the bar is, then multiply by the scale number.

READING SCALED BAR GRAPHS
Total Amount = Height of Bar × Scale Number
Height of Bar = how many units tall the bar is Scale Number = what each unit represents Total Amount = the actual number of items

When you want to draw a scaled bar graph, you work backwards. You know the total amount, and you know the scale, so you divide to find how tall to make the bar.

DRAWING SCALED BAR GRAPHS
Height of Bar = Total Amount ÷ Scale Number
Total Amount = the number of items you want to show Scale Number = what each unit represents Height of Bar = how many units tall to draw the bar

For example, if you sold 24 cookies and your scale is 1 unit = 6 cookies, then your bar should be 24 ÷ 6 = 4 units tall.

SECTION 5

Different Ways to Show Scales

There are different ways to show the scale on a bar graph. Each way helps you understand what the numbers mean.

Three Ways to Show ScaleSymbol ScaleABC= 5 itemsNumber Scale010203040ABCPicture ScaleDogsCatsBirds🐕 = 3 petsHow to Read Each Type:Symbol Scale:• Count squares in the bar• Multiply by what each square equals• Bar A has 12 squares × 5 = 60 itemsNumber Scale:• Look where the bar top ends• Read the number on the left side• Bar A reaches 20, so 20 itemsPicture Scale:• Count pictures in the bar• Multiply by what each picture equals• Bar has 4 pictures × 3 = 12 pets
These three examples show different ways to display scales on bar graphs. Symbol scales use squares or rectangles, number scales show actual values on the side, and picture scales use small images. Each method helps you understand the data, but the math is the same: multiply the count by what each unit represents.
Comparison of different scale types used in bar graphs
Scale TypeBest ForExample
Symbol ScaleSmaller numbers, easier countingEach ⬜ = 2 cookies
Number ScaleBigger numbers, quick readingY-axis shows 0, 10, 20, 30...
Picture ScaleFun topics, easy to understandEach 🍎 = 5 apples
SECTION 6

Step-by-Step: Creating a Scaled Bar Graph

Let's create a bar graph together! The school cafeteria wants to show how many lunches they served this week. Here's their data: Monday = 36 lunches, Tuesday = 48 lunches, Wednesday = 24 lunches, Thursday = 60 lunches, Friday = 42 lunches.

Creating Our Lunch Data Bar Graph

Step 1 — Choose the Scale

Look at our biggest number: 60 lunches. If we made each square equal 1 lunch, we'd need to draw 60 tiny squares! Instead, let's choose a scale where each square equals 6 lunches. This way, our tallest bar will be 60 ÷ 6 = 10 squares tall, which is much easier to draw and read.
Scale: 1 square = 6 lunches

Step 2 — Calculate Bar Heights

Now we divide each day's lunches by 6 to find how many squares tall each bar should be. Monday: 36 ÷ 6 = 6 squares. Tuesday: 48 ÷ 6 = 8 squares. Wednesday: 24 ÷ 6 = 4 squares. Thursday: 60 ÷ 6 = 10 squares. Friday: 42 ÷ 6 = 7 squares.
Mon=6, Tue=8, Wed=4, Thu=10, Fri=7

Step 3 — Draw the Graph

Start with a title at the top. Draw two lines that meet at the bottom left corner—one going right (for days) and one going up (for number of lunches). Mark the left side with numbers: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. Then draw rectangles for each day with the heights we calculated.
Complete bar graph with all elements

Step 4 — Add Labels and Scale

Write the day names under each bar: Monday, Tuesday, Wednesday, Thursday, Friday. Add a note at the bottom showing our scale: "Each square = 6 lunches." Don't forget to label the axes: "Days of the Week" on the bottom and "Number of Lunches" on the left side.
Finished, labeled bar graph

Great job! Now anyone can look at your graph and quickly see that Thursday was the busiest lunch day with 60 lunches served, and Wednesday was the quietest with only 24 lunches.

SECTION 7

Comparing Data with Scaled Bar Graphs

One of the best things about bar graphs is how easy they make it to compare data. Your eyes can quickly see which bars are taller or shorter, and you can ask interesting questions about the information.

Different ways to analyze and compare data in bar graphs
Type of ComparisonWhat to Look ForExample Question
Biggest vs. SmallestThe tallest and shortest barsWhich fruit sold the most? The least?
DifferencesHow much bigger one bar is than anotherHow many more apples than oranges were sold?
PatternsBars that go up, down, or stay the sameDid sales go up or down during the week?
TotalsAdding up all the barsHow many total fruits were sold all week?
✦ KEY TAKEAWAY
Think of bar graphs like a race! The tallest bars are like the fastest runners—they "won" by having the biggest numbers. Just like you can see who came in 1st, 2nd, and 3rd place by looking at runners, you can see which data came in 1st, 2nd, and 3rd by looking at bar heights. The scale is like a measuring tape that tells you exactly how much each runner accomplished.
SECTION 8

Getting Ready for Double Bar Graphs

Once you master scaled bar graphs, you'll be ready for even cooler graphs! Double bar graphs let you compare two different things side by side, like comparing how many books boys and girls read each month.

Single Bar Graphs (What You Know)Double Bar Graphs (Coming Next!)
One bar for each categoryTwo bars for each category
Shows one set of dataCompares two sets of data
Example: Fruits sold this weekExample: Fruits sold this week vs. last week
One color for all barsTwo colors to tell the data sets apart
Simple scale applies to all barsSame scale works for both sets of bars

The skills you're learning now—reading scales, calculating bar heights, and comparing data—are the building blocks for all kinds of graphs you'll see in 4th grade and beyond. You're becoming a data detective!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL
Look at a bar graph where the scale shows "Each ⬜ = 3 stickers." If the red bar is 4 squares tall, how many red stickers are there?
PROBLEM 2 — BASIC CALCULATION
Maria collected 18 shells at the beach. If she wants to show this on a bar graph where each square equals 6 shells, how many squares tall should her bar be?
PROBLEM 3 — INTERMEDIATE
A pet store graph shows: Dogs = 5 squares, Cats = 7 squares, Birds = 3 squares. The scale is 1 square = 4 pets. How many more cats than birds does the store have?
PROBLEM 4 — APPLIED
The school library tracks books borrowed each day: Monday = 24, Tuesday = 36, Wednesday = 12, Thursday = 30. Create a scale that would work well for a bar graph, and find the height of each bar.
PROBLEM 5 — CRITICAL THINKING
Two students made bar graphs of the same cookie data, but one used the scale "1 square = 2 cookies" and the other used "1 square = 4 cookies." If both graphs show 16 cookies sold, how will the bar heights be different? Which scale would be better for showing 50 cookies, and why?
SUMMARY

Scaled Bar Graphs: What You've Learned

You've mastered scaled bar graphs—a powerful tool for showing big numbers in small spaces! You learned that the scale tells you what each unit represents, and you can read graphs by multiplying the bar height by the scale number. When creating graphs, you divide the data by the scale to find the right bar height.

Most importantly, you can now compare data quickly by looking at bar heights, find differences between categories, and spot patterns in numbers. Whether you're tracking your reading progress, comparing sports scores, or helping with a school survey, scaled bar graphs make data easy to understand and share with others!

Varsity Tutors • 3rd Grade Math • Scaled Bar Graphs: Read, Draw, and Compare Data