Picture Graphs Formula

Picture graphs are a way of displaying data using pictures or icons, where each picture represents one unit (or a set number of units), and the total for.

The Formula

total for category=number of pictures×value per picture (from the key)\text{total for category} = \text{number of pictures} \times \text{value per picture (from the key)}

When to use: Imagine voting for your favorite fruit by placing a sticker in a column. When you're done, the column with the most stickers is the winner—you can see the answer at a glance.

Quick Example

Favorite Pet: 🐕🐕🐕3 dogs,🐈🐈🐈🐈🐈5 cats,🐟🐟2 fish\text{Favorite Pet: } \underbrace{🐕🐕🐕}_{3 \text{ dogs}}, \quad \underbrace{🐈🐈🐈🐈🐈}_{5 \text{ cats}}, \quad \underbrace{🐟🐟}_{2 \text{ fish}}

Notation

A key (or legend) shows what each picture represents, e.g., '\bigstar = 2 votes' means each star icon stands for 2 units

What This Formula Means

A way of displaying data using pictures or icons, where each picture represents one unit (or a set number of units), and the total for each category is found by counting or multiplying the number of pictures by the scale value.

Imagine voting for your favorite fruit by placing a sticker in a column. When you're done, the column with the most stickers is the winner—you can see the answer at a glance.

Formal View

A picture graph maps categories {c1,,cn}\{c_1, \ldots, c_n\} to counts {v1,,vn}\{v_1, \ldots, v_n\} via icons, where vi=(number of icons for ci)×sv_i = (\text{number of icons for } c_i) \times s and ss is the scale factor from the key

Worked Examples

Example 1

easy
A picture graph shows: Cats = 🐱🐱🐱 (3 symbols), Dogs = 🐶🐶🐶🐶🐶 (5 symbols). Each symbol = 1 animal. How many more dogs than cats are there?

Answer

2 more dogs

First step

1
Read the graph: Cats = 3, Dogs = 5.

Full solution

  1. 2
    Find the difference: 53=25 - 3 = 2.
  2. 3
    There are 2 more dogs than cats.
In a picture graph, count the symbols for each category, then subtract to compare.

Example 2

medium
A picture graph shows favorite fruits. Apple = 4 symbols, Banana = 6 symbols, Orange = 3 symbols. Each symbol = 2 students. How many students chose banana?

Example 3

easy
A picture graph shows fish in the tank: 4 fish pictures. How many fish?

Common Mistakes

  • Ignoring the key and counting icons as 1 - multiply the picture count by the key's value per icon.
  • Missing half icons - a half icon counts as half the key value (e.g., half of 2 is 1).
  • Comparing categories without applying the key to each - apply the scale to every row before comparing.

Why This Formula Matters

It introduces the idea that one symbol can stand for many — the scale/key — which is the same scaling logic as bar-graph axes and, later, map scales and units. Students who ignore the key and count icons as one each read every scaled graph wrong. Recognizing it by "Are categories shown as icons with a key telling each icon's value?" — rather than by familiar numbers — is what lets a student tell it apart from bar graphs and tally charts and counting (icons as 1) in a mixed problem set.

Frequently Asked Questions

What is the Picture Graphs formula?

A way of displaying data using pictures or icons, where each picture represents one unit (or a set number of units), and the total for each category is found by counting or multiplying the number of pictures by the scale value.

How do you use the Picture Graphs formula?

Imagine voting for your favorite fruit by placing a sticker in a column. When you're done, the column with the most stickers is the winner—you can see the answer at a glance.

What do the symbols mean in the Picture Graphs formula?

A key (or legend) shows what each picture represents, e.g., '\bigstar = 2 votes' means each star icon stands for 2 units

Why is the Picture Graphs formula important in Math?

It introduces the idea that one symbol can stand for many — the scale/key — which is the same scaling logic as bar-graph axes and, later, map scales and units. Students who ignore the key and count icons as one each read every scaled graph wrong. Recognizing it by "Are categories shown as icons with a key telling each icon's value?" — rather than by familiar numbers — is what lets a student tell it apart from bar graphs and tally charts and counting (icons as 1) in a mixed problem set.

What do students get wrong about Picture Graphs?

The procedure for picture graphs is the easy part; the trap is ignoring the key and counting icons as 1. Asking "Are categories shown as icons with a key telling each icon's value?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

What should I learn before the Picture Graphs formula?

Before studying the Picture Graphs formula, you should understand: counting.