Construct & interpret picture graphs (many-to-one)
Theory
Many-to-one picture graphs are a Year 4 statistics skill: reading and making graphs where one picture stands for many things. This page shows how to use the key to find a value by multiplying, how to read half a picture, how to compare rows and find totals, how to work out how many pictures to draw, and how to choose a key that suits the data. Curriculum: VC2M4ST01 / AC9M4ST01.
A picture graph shows data using pictures. Each row is one group, and the pictures line up so the longer rows are easy to spot. It is also called a pictograph.
In a many-to-one picture graph, one picture stands for more than one thing. The key tells you how many, such as \(1\) picture \(=5\) cans. To find the value of a row you multiply the number of pictures by the key. To draw a row you divide the total by the key.
A picture does not have to be whole. Half a picture is worth half of the key. If \(1\) picture \(=10\), then half a picture is worth \(5\). A many-to-one key keeps a graph small when the counts are large, such as crowds of hundreds of people.
Every many-to-one picture graph works from its key. These facts turn pictures into totals and back again.
How to read a many-to-one picture graph
- Read the key. Find what one picture is worth before you count anything.
- Count the pictures. Count the whole pictures in the row, and check for a half picture at the end.
- Multiply, then add. Multiply the whole pictures by the key, add half the key for a half picture, and that is the row value.
- Answer the question. Compare row values for the most or fewest, subtract for how many more, and add row values for a total.
How to draw a row
- Divide by the key. Total \(\div\) key gives the number of whole pictures.
- Check the leftover. If half the key is left over, draw half a picture.
- Line them up. Use pictures of the same size with equal spacing, and show the key on the graph.
| \(\text{pictures}\) | \(=\) | \(7,\ \text{key}=5\) |
| \(7\times5\) | \(=\) | \(35\) |
The row shows \(35\) tickets.
| \(5\times4\) | \(=\) | \(20\) |
| \(\text{half of }4\) | \(=\) | \(2\) |
| \(20+2\) | \(=\) | \(22\) |
The row shows \(22\) stickers.
| \(\text{Tue}=7\times3\) | \(=\) | \(21\) |
| \(\text{Mon}=4\times3\) | \(=\) | \(12\) |
| \(21-12\) | \(=\) | \(9\) |
Tuesday sold \(9\) more cartons. (Quick check: Tuesday has \(3\) more pictures, and \(3\times3=9\).)
| \(\text{total}\) | \(=\) | \(18,\ \text{key}=3\) |
| \(18\div3\) | \(=\) | \(6\) |
Draw \(6\) pictures, lined up.
| \(6\times2\) | \(=\) | \(12\) |
| \(13-12\) | \(=\) | \(1 = \text{half of }2\) |
| \(\text{pictures}\) | \(=\) | \(6\text{ and a half}\) |
Draw \(6\) whole pictures and half a picture.
| \(35\div2\) | \(=\) | \(17\text{ and a half}\) |
| \(35\div10\) | \(=\) | \(3\text{ and a half}\) |
| \(35\div5,\ 20\div5,\ 50\div5\) | \(=\) | \(7,\ 4,\ 10\) |
Only \(1\) picture \(=5\) gives whole pictures for every row: \(7\), \(4\) and \(10\).
| \(\text{Fri}=2\times100\) | \(=\) | \(200\) |
| \(\text{Sat}=300+50\) | \(=\) | \(350\) |
| \(\text{Sun}=6\times100\) | \(=\) | \(600\) |
| \(200+350+600\) | \(=\) | \(1150\) |
\(1150\) people came. A key of \(100\) shows these big numbers with only a few pictures.
Common pitfalls
Frequently asked questions
What is a many-to-one picture graph?
A many-to-one picture graph shows data with pictures, where one picture stands for more than one thing. A key tells you how many, for example \(1\) picture \(=5\) cans.
How do you read a picture graph with a key?
Count the pictures in the row, then multiply by the key. If the key is \(1\) picture \(=5\) and a row has \(8\) pictures, the value is \(8\times5=40\).
What does half a picture mean on a picture graph?
Half a picture is worth half of the key. If one whole picture stands for \(10\), then half a picture stands for \(5\). Add the half to the whole pictures to find the value.
How do you work out how many pictures to draw?
Divide the total by the key. If a class read \(18\) books and the key is \(1\) picture \(=3\) books, draw \(18\div3=6\) pictures.
How do you choose a good key?
Pick a key that every number divides into easily, so the rows are whole pictures or halves. For \(60\), \(40\) and \(90\) trees, a key of \(1\) picture \(=10\) trees gives \(6\), \(4\) and \(9\) pictures.
When is a big key useful?
A big key is useful when the numbers are large, such as a crowd of \(400\) people. With \(1\) picture \(=50\) people you only need \(8\) pictures.