Grade by Grade
D. Data · Data and Probability

Pictographs Where One Picture Stands for Many

D1.3About 40 minutes
Learning goals
  • I can read a pictograph where one picture stands for more than one thing.
  • I can use the key, including half pictures.
  • I can choose a good key and make a pictograph with a title, labels, a key and a source.

Words to know

pictograph
A graph that uses pictures or symbols to show data.
key
The part of a pictograph that tells how many each picture stands for, like ● = 2 children.
many-to-one correspondence
When one picture stands for more than one thing, like one picture for 5 books.
source
Where the data came from, like "survey of Room 12".
title
The name of the graph. It tells what the data is about.

Remember from Grade 2

In Grade 2 your pictographs used one picture for one thing. That is called one-to-one correspondence. If 8 children chose hot chocolate, you drew 8 pictures.

Too many pictures!

The whole school took a survey, and 40 children chose skating. Drawing 40 pictures in one row would take a long time and would not fit on the page!

Here is a smart idea: let one picture stand for more than one child. If one picture stands for 5 children, then 40 children need only 8 pictures. This is called many-to-one correspondence.

The key is the key!

A pictograph with many-to-one correspondence must have a key. The key tells how many each picture stands for.

  • Key: ● = 2 children. Then ●●● means 2 + 2 + 2 = 6 children.
  • A half picture stands for half of the key. Half of 2 is 1, so a half circle means 1 child.
How We Get to SchoolWalkBusCarBike= 2 children= 1 child
Pictograph: How We Get to School. Key: each circle = 2 children, a half circle = 1 child. Source: survey of the Grade 3 classes at Maple Ridge School.
Worked example

Example 1: Read the pictograph

Use the pictograph How We Get to School. How many children take the bus?

  1. Find the Bus row. It has 4 whole circles and a half circle.
  2. Each whole circle means 2 children. Skip count: 2, 4, 6, 8.
  3. The half circle means half of 2, which is 1 child.
  4. 8 + 1 = 9.

9 children take the bus.

How we get to schoolPicturesNumber of children
Walk6 circles2, 4, 6, 8, 10, 12 → 12
Bus4 circles and a half8 + 1 = 9
Car3 circles and a half6 + 1 = 7
Bike2 circles2, 4 → 4
Reading every row of the pictograph. 12 + 9 + 7 + 4 = 32 children in all.
Worked example

Example 2: Make a pictograph with a key of 5

The Grade 3 classes read books for Reading Month. Week 1: 15 books, Week 2: 20, Week 3: 25, Week 4: 10. Make a pictograph where each 📚 = 5 books.

  1. Count by 5s to find how many pictures each week needs.
  2. Week 1: 5, 10, 15. That's 3 pictures.
  3. Week 2: 5, 10, 15, 20. That's 4 pictures.
  4. Week 3: 5, 10, 15, 20, 25. That's 5 pictures.
  5. Week 4: 5, 10. That's 2 pictures.
  6. Add a title, labels, the key and the source.

See the pictograph below: 3, 4, 5 and 2 pictures.

WeekBooks read (each 📚 = 5 books)
Week 1📚📚📚
Week 2📚📚📚📚
Week 3📚📚📚📚📚
Week 4📚📚
Pictograph: Books Read in Reading Month. Key: 📚 = 5 books. Source: Grade 3 reading logs.

Choosing a good key

Look at your biggest number and the numbers you have.

  • If all your numbers are in the 2s count (2, 4, 6...), a key of 2 works well.
  • If all your numbers are in the 5s count (5, 10, 15...), a key of 5 works well.
  • If your numbers are big, like 30, 40, 50, try a key of 10.

A key of 2 or 10 lets you use half pictures for the numbers in between, because half of 2 is 1 and half of 10 is 5.

Cans for the Food DriveRoom 1Room 2Room 3Room 4= 10 cans= 5 cans
Pictograph: Cans for the Food Drive. Key: each circle = 10 cans, a half circle = 5 cans. Source: school food drive count, December.
Worked example

Example 3: A key of 10 with halves

Use Cans for the Food Drive. How many cans did Room 2 collect?

  1. Room 2 has 4 whole circles and a half circle.
  2. Each whole circle is 10 cans: 10, 20, 30, 40.
  3. Half of 10 is 5.
  4. 40 + 5 = 45.

Room 2 collected 45 cans.

Every good pictograph has

  • a title (what the graph is about)
  • labels for each row
  • pictures that are all the same size, lined up evenly
  • a key (how many each picture stands for)
  • a source (where the data came from)
Just for fun

In a pictograph, one 🍪 stands for 10 cookies. What does half a 🍪 stand for?

5 cookies... or the cookie you nibbled while making the graph!

Hands-on activity

Make a many-to-one pictograph

You need: paper, a pencil, and some small stickers or a stamp (or just draw circles).

  1. Ask 10 to 20 family members, friends or neighbours a question with 3 or 4 choices, like "What is your favourite fall fruit: apple, pear, grapes or pumpkin?" Make a frequency table.
  2. Choose a key. A key of 2 is good for these numbers. Use a half picture for 1.
  3. Draw the pictograph. Line the pictures up neatly.
  4. Add the title, labels, key and source.
  5. Ask someone to read your graph. Can they tell how many chose each fruit?

Math talk: "Why did I choose this key?"

Your turn

1

Use How We Get to School. How many children walk?

2

How many children come by car?

3

How many more children walk than ride a bike?

4

How many children are in the survey in all?

5

Key: ● = 2 children. How many circles do you draw to show 16 children?

6

Key: ● = 2 children. How do you show 11 children?

More practice: warm-up

1

Key: ⭐ = 2 stickers. A row has 3 ⭐. How many stickers?

2

Key: 📚 = 5 books. A row has 4 📚. How many books?

3

Key: ● = 10 cans. What does a half circle mean?

4

What does the key of a pictograph tell you?

5

Key: 📚 = 5 books. How many 📚 show 10 books?

More practice: on your own

1

Use Cans for the Food Drive. How many cans did Room 4 collect?

2

How many cans did Room 1 and Room 3 collect together?

3

How many more cans did Room 4 collect than Room 3?

4

Room 5 collected 25 cans. How would you show this on the food drive pictograph?

5

Ali drew a pictograph with a key of ● = 5. For a row of 12, he drew 2 circles and a half circle. Why is that not right?

Challenge

1

Votes for a class trip: Museum 40, Farm 25, Zoo 35, Science centre 50. Which key is best: ● = 1, ● = 2, or ● = 5? Explain.

2

Jo looks at a row with 3 pictures and says, "3 kids chose soccer." The key says ● = 5 kids. Explain Jo's mistake and give the right answer.

3

A pictograph has the key ● = 4 children. How many children does a half circle stand for? How would you show 10 children?

Check your understanding

Quiz

1.

Key: ● = 2 children. A row has 5 ●. How many children?

2.

Key: ● = 10 cans. What does a half circle stand for?

3.

Key: ● = 2 children. How many ● show 14 children?

4.

Why do we sometimes let one picture stand for many things?

5.

A pictograph uses one picture for 5 books. What must it have?

6.

Key: 📚 = 5 books. Tia read 20 books. How many 📚 does her row have?

For parents and teachers

What your child is learning: to read and make pictographs using many-to-one correspondence (one picture stands for 2, 5 or 10 things), with a proper title, labels, key and source (Ontario expectation D1.3). In Grade 2, each picture stood for one thing.

Common difficulties:

  • Counting pictures instead of using the key (saying "3" when 3 pictures × 5 = 15). Always ask, "What does one picture stand for?"
  • Half pictures. A half picture stands for half of the key, so it only works neatly with an even key like 2, 4 or 10.
  • Pictures of different sizes or spacing, which make rows look longer or shorter than they are.
  • Forgetting the key or source.

At home: practise skip counting by 2s, 5s and 10s; it is the engine of this lesson. Look for pictographs in children's magazines or flyers and ask your child to read them.