Measurement & Data · Grade 3

Bar Graphs and Picture Graphs

Quick answer

A bar graph shows amounts as bar heights, and a picture graph shows them as symbols. Both can be scaled, so one square or one symbol stands for more than one thing. Checking the scale or key before reading anything is the whole skill, because a bar of four squares can mean four, twenty or forty.

What you'll learn

  • Read a scaled bar graph and a picture graph
  • Use a key to figure out what a symbol stands for
  • Measure lengths and record them as data

Bar graphs show amounts as heights

A bar graph draws one bar per group. The taller the bar, the bigger the amount.

Reading one is quick. The tallest bar is the most, the shortest is the least, and two bars of the same height are equal.

But the height only means something once you know the scale.

Check the scale first

The numbers up the side tell you what one square is worth.

If one square isA bar 44 squares tall means
1144
552020
10104040

The same bar, three different answers. That is why the scale is the first thing to look at, before reading any bar.

amount=squares×what one square is worth\text{amount} = \text{squares} \times \text{what one square is worth}

Why graphs use a scale

Without one, a graph of 100100 people would need 100100 squares. That is a very tall graph.

Letting each square stand for 1010 brings it down to 1010 squares, which fits on a page and is quicker to read. The scale is what keeps a graph a sensible size.

The cost is that you have to check it. That is the trade every scaled graph makes.

Picture graphs use a key

A picture graph uses a symbol instead of a bar. The key says what one symbol stands for.

Key: one apple picture = 1010 apples

ClassPicturesApples
Red333030
Blue555050
Green222020

Multiply the pictures by the key, exactly as you multiply squares by the scale.

A half symbol means half of what the key says:

212 pictures×10=25 apples2\tfrac{1}{2} \text{ pictures} \times 10 = 25 \text{ apples}

Questions these graphs answer

QuestionHow to answer
Which is most?the tallest bar or most symbols
How many in this group?height times scale
How many more than?subtract the two amounts
How many altogether?add every amount

Using the apple table: how many more apples did Blue collect than Green?

50−20=30 apples50 - 20 = 30 \text{ apples}

Find the amounts first, then compare. Comparing symbols directly gives 5−2=35 - 2 = 3, which is the difference in pictures, not in apples.

Making your own data

To build a graph you need data, and one way to get it is to measure.

Measure things with a ruler. A ruler marked in halves and quarters of an inch lets you record lengths like 4124\tfrac{1}{2} inches.

Then count how many fall at each length, and that count is your bar height.

LengthHow many pencils
44 in22
4124\tfrac{1}{2} in55
55 in33

That table becomes a bar graph directly, and it is also a line plot if you draw one dot per pencil instead of a bar.

Worked examples

Common mistakes

Practice problems

  1. Each square is 22. A bar is 55 squares tall. What amount?

    Answer

    1010

    Full solution

    5×2=105 \times 2 = 10.

  2. Each square is 1010. A bar is 33 squares tall. What amount?

    Answer

    3030

    Full solution

    3×10=303 \times 10 = 30.

  3. Key: one star = 55. A row has 44 stars. How many?

    Answer

    2020

    Full solution

    4×5=204 \times 5 = 20.

  4. Key: one circle = 22. A row has 99 circles. How many?

    Answer

    1818

    Full solution

    9×2=189 \times 2 = 18.

  5. Each square is 55. One bar is 88 squares, another is 33. How many more?

    Answer

    2525

    Full solution

    40−15=2540 - 15 = 25.

  6. Key: one square = 44. A row has 2122\tfrac{1}{2} squares. How many?

    Answer

    1010

    Full solution

    2×4=82 \times 4 = 8, and half of 44 is 22, so 8+2=108 + 2 = 10.

  7. You need to show amounts up to 4040 using 88 squares. What scale?

    Answer

    Each square is 55

    Full solution

    40÷8=540 \div 8 = 5.

  8. Two bars are 66 and 22 squares tall, each square worth 1010. What is the total?

    Hint

    Add the squares, then scale.

    Answer

    8080

    Full solution

    (6+2)×10=8×10=80(6 + 2) \times 10 = 8 \times 10 = 80.

  9. Why do graphs use a scale instead of one square per item?

    Answer

    So large amounts fit on the page.

    Full solution

    One square per item would need 100100 squares to show 100100 things.

    With each square worth 1010, the same amount takes 1010 squares and still fits.

  10. On a graph where each square is 55, one bar is 99 squares and another is 44. Asked how many more, Tom answers 55. Find his error.

    Hint

    Did he compare squares or amounts?

    Answer

    He subtracted the squares. The answer is 2525.

    Full solution

    Tom found 9−4=59 - 4 = 5, which is the difference in squares, not in the amounts.

    Each square is worth 55, so find both amounts first:

    9×5=459 \times 5 = 45 and 4×5=204 \times 5 = 20.

    45−20=2545 - 20 = 25.

    His difference of 55 squares is right, and each of those squares is worth 55 — so 5×5=255 \times 5 = 25 gets there too.

Frequently asked questions

What is a scaled bar graph?

One where each square on the axis stands for more than one. If each square is 5, a bar four squares tall means 20.

What is a key on a picture graph?

A note saying what one symbol stands for. If one apple picture means 10 apples, three pictures mean 30.

What does half a symbol mean?

Half of whatever the key says. If one symbol is 10, half a symbol is 5.

Why check the scale first?

Because the same bar means different amounts on different graphs. Four squares could be 4, 20 or 40.

Why use a scale at all?

So large amounts fit on the page. Drawing 100 squares for 100 people would need a very tall graph.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.3.MD.B.3Measurement and DataDraw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
  • CCSS.MATH.CONTENT.3.MD.B.4Measurement and DataGenerate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.