D. Data · Data and Probability

Showing Data: Pictographs, Line Plots and Bar Graphs

D1.3About 40 minutes

Learning goals

I can show data in a concrete graph, a pictograph, a line plot, and a bar graph.
I can use one-to-one correspondence: one object, picture, X or square for each piece of data.
I can make vertical and horizontal bar graphs.
I can give every graph a title, labels, and a source.

Words to know

one-to-one correspondence
Each object, picture, X or square stands for exactly ONE piece of data.

pictograph
A graph that uses pictures. In Grade 2, each picture stands for 1.

bar graph
A graph that uses bars. A bar can go up (vertical) or across (horizontal).

line plot
A number line with an X above a number for each piece of data. It is good for data that are numbers.

title
The name of the graph. It tells what the graph is about.

labels
Words on the graph that tell what the categories and the numbers mean.

source
Where the data came from, like "survey of Mr. Lee's class".

scale
The numbers along the side or bottom of a bar graph. It starts at 0 and counts by 1s.

Let's get started!

Mr. Lee's Grade 2 class asked: "What is your favourite winter treat?" Here is their data:

Hot chocolate: 8
Maple taffy (maple syrup poured on snow): 6
Soup: 3
Popcorn: 5

Numbers in a list are useful. But a graph turns data into a picture, so we can compare groups at a glance!

Remember from Grade 1

In Grade 1 you made concrete graphs, pictographs, line plots and bar graphs. In every one, one thing stands for one piece of data. This is called one-to-one correspondence. In Grade 2, you will make bigger graphs, sideways bar graphs, and check that every graph has all its parts.

Concrete graph

A concrete graph uses real things. Each child could put one cube above their favourite treat. Lining up the cubes from the same starting line makes it fair to compare.

☕☕☕☕☕☕☕☕🍁🍁🍁🍁🍁🍁🥣🥣🥣🍿🍿🍿🍿🍿

Like a concrete graph: one object for each child. Hot chocolate 8, maple taffy 6, soup 3, popcorn 5.

Pictograph

A pictograph uses pictures. Each picture stands for 1 child. All the pictures should be the same size and lined up in neat rows.

Winter treat	Number of children (each ☕ = 1 child)
Hot chocolate	☕☕☕☕☕☕☕☕
Maple taffy	☕☕☕☕☕☕
Soup	☕☕☕
Popcorn	☕☕☕☕☕

Pictograph: Our Favourite Winter Treat. Source: survey of Mr. Lee's Grade 2 class.

Bar graph

A bar graph uses bars. Each square of a bar stands for 1 child. The scale starts at 0 and counts by 1s.

A bar graph can stand up (a vertical bar graph):

Vertical bar graph. The hot chocolate bar reaches 8.

Or it can lie sideways (a horizontal bar graph). It shows the same data! Read the length of each bar using the numbers along the bottom.

Horizontal bar graph of the same data.

The parts of a graph

Every graph needs:

A title that tells what the graph is about: Our Favourite Winter Treat.
Labels that tell what the categories are (Winter treat) and what the numbers count (Number of children). Each category gets its own label too, like Soup.
A source that tells where the data came from: survey of Mr. Lee's Grade 2 class.

Without these parts, a reader can't tell what the graph means!

A mystery graph with no title, no labels and no source. What is it about? We can't tell!

Line plot

A line plot is great when the data are numbers. Mr. Lee's class asked, "How many teeth have you lost?" For each child, we draw one X above their number on a number line.

Worked example

Making a line plot

20 children answered "How many teeth have you lost?"

0, 2, 1, 3, 2, 0, 1, 2, 4, 3, 2, 1, 5, 2, 3, 0, 2, 1, 3, 4

Make a line plot.

Find the smallest and largest numbers: 0 and 5. Draw a number line from 0 to 5.
Take each answer in order. Draw one X above its number. Cross the answer off the list.
Stack the Xs neatly, one above the other, the same size.
Count the Xs: 0 has 3, 1 has 4, 2 has 6, 3 has 4, 4 has 2, 5 has 1.
Check: 3 + 4 + 6 + 4 + 2 + 1 = 20. There were 20 children, so every answer is shown.
Add a title, a label under the number line, and a source.

The line plot has the most Xs above 2. Six children have lost 2 teeth.

Line plot: Teeth Lost in Our Class. Source: survey of Mr. Lee's Grade 2 class.

Worked example

From a tally table to a bar graph

Make a bar graph from this tally table: Favourite Sport — hockey: one bundle of 5 and 2 more; soccer: one bundle of 5 and 4 more; basketball: 4 lines; swimming: 3 lines.

Count each row: hockey 7, soccer 9, basketball 4, swimming 3.
The biggest number is 9, so the scale should go from 0 to at least 9.
Draw one bar for each sport. Colour one square for each child: hockey up to 7, soccer up to 9, basketball up to 4, swimming up to 3.
Leave a space between bars. Make every bar the same width.
Add the title Our Favourite Sport, labels (Sport, Number of children) and the source.

A bar graph with bars of 7, 9, 4 and 3. The soccer bar is the tallest.

Which graph should I use?

Pictograph or bar graph: good for categories, like treats, sports or colours.
Line plot: good when the answers are numbers, like how many teeth lost or how many pets.
Concrete graph: great for making a graph quickly in class with real things.

Just for fun

What is a bar graph's favourite snack?

A granola bar! 📊

Hands-on activity

Make a graph at home

Choose a question, like "What is your favourite fruit: apples, oranges, bananas or grapes?" Ask at least 10 people (family, friends, neighbours, or by phone).
Make a concrete graph first: put one spoon (or block) in a row for each answer.
Then draw a pictograph or bar graph on paper. Grid paper helps make the squares the same size.
Write a title, labels and the source (for example, "Asked by me, my family and neighbours, January").
Bonus: Ask "How many people live in your home?" and make a line plot.

Your turn

In a Grade 2 pictograph, how many children does one picture stand for?

Look at the winter treat bar graph. How many children chose popcorn?

Look at the line plot. How many children lost 3 teeth?

Look at the line plot. How many children lost 0 teeth?

What 3 parts must every graph have?

Which graph is best for showing "How many pets do you have?" when the answers are numbers like 0, 1, 2, 3?

Why should all the pictures in a pictograph be the same size?

More practice: warm-up

🍎🍎🍎🍎

🍌🍌🍌🍌🍌🍌

Each picture = 1 child. How many chose bananas?

Same pictograph. How many chose apples?

On a line plot, what does one X stand for?

What number does the scale on a bar graph start at?

What is a source?

More practice: on your own

Look at the horizontal bar graph. Which treat has the shortest bar? What does that tell you?

Data: red 4, blue 6, green 2. How tall should each bar be in a bar graph?

Look at the mystery graph with no title or labels. Write a title and labels that could fit it.

Make a line plot for these ages of kids at a party: 6, 7, 7, 8, 7, 6, 9, 7. How many Xs go above 7?

Look at the line plot of teeth lost. How many children lost more than 3 teeth?

Challenge

Kai made a pictograph. Hockey has 5 big pictures and soccer has 6 small pictures. The hockey row looks longer. Which sport did more children choose? What should Kai fix?

A bar graph is missing the soccer bar. The title says 20 children answered. Hockey 7, basketball 4, swimming 3. How tall should the soccer bar be?

Look at the line plot. Together, how many teeth did the 4 children who lost 3 teeth each lose?

Check your understanding

Quiz

In a Grade 2 pictograph, each picture stands for...

Which graph puts an X above a number for each piece of data?

Which part of a graph tells where the data came from?

In the winter treat bar graph, which treat did 6 children choose?

Answers to "How many people live in your home?" are numbers. Which graph fits best?

A horizontal bar graph and a vertical bar graph show the same data. What is different?

For parents and teachers

What your child is learning: to display data using one-to-one correspondence (one object, picture, X or square per piece of data) in concrete graphs, pictographs, line plots and bar graphs (vertical and horizontal), with a title, labels and source (Ontario expectation D1.3). Pictographs where one picture stands for more than one come in later grades.

Common difficulties:

Pictures or squares of different sizes, so lengths are not fair to compare. Grid paper helps a lot.
Starting a bar graph scale at 1 instead of 0, or skipping numbers on the scale.
Forgetting the title, labels or source. Use a checklist: Title? Labels? Source?
On a line plot, writing the number of Xs instead of drawing them, or leaving out numbers that have no Xs (every number in the range should be on the line).

At home: graph something real together: the colours of cars in a parking lot, family members' favourite fruit, or how many books each person read this week. Ask, "What does your graph tell us?"