D. Data · Data and Likelihood

Showing Data: Concrete Graphs, Pictographs, Line Plots and Bar Graphs

D1.3About 35 minutes

Learning goals

I can make a concrete graph, a pictograph, and a bar graph using one-to-one correspondence.
I can make a line plot with an X for each piece of data.
I can give my graph a title, labels, and a source.

Words to know

graph
A picture that shows data so it is easy to compare.

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

concrete graph
A graph made with real objects, like shoes or blocks, lined up in rows or columns.

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

bar graph
A graph that uses bars. The longer the bar, the more there are.

line plot
A number line with an X above a number for each piece of data.

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

label
Words that tell what each part of the graph means.

source
Where the data came from, like "Survey of Ms. Roy's class".

Let's get started!

A tally table holds data. But a graph turns data into a picture! With a graph you can see at a glance which group is biggest.

Today we will use one set of data and show it four ways. Ms. Roy's class asked: "How do you get to school?"

Walk: 7
Bus: 5
Car: 4
Bike: 2

That is 18 children in all.

The big idea

In every graph we make today, one thing stands for one child. One shoe, one picture, one square, one X. This is called one-to-one correspondence.

1. Concrete graph

A concrete graph uses real objects. Each child could put one block in the column for how they get to school. Or children can stand in lines! The longest line is the biggest group.

Line up the objects neatly, starting at the same starting line, so you can compare fairly.

🚶🚶🚶🚶🚶🚶🚶🚌🚌🚌🚌🚌🚗🚗🚗🚗🚲🚲

A concrete graph is like this: one object for each child, lined up in rows. Walk 7, bus 5, car 4, bike 2.

2. Pictograph

A pictograph uses pictures instead of real objects. Each picture stands for 1 child. Every picture should be the same size and lined up, so the rows are fair to compare.

How we get to school	Number of children (each picture = 1 child)
Walk	🚶🚶🚶🚶🚶🚶🚶
Bus	🚌🚌🚌🚌🚌
Car	🚗🚗🚗🚗
Bike	🚲🚲

Pictograph: How We Get to School. Source: survey of Ms. Roy's Grade 1 class.

3. Bar graph

A bar graph uses bars. Each square of the bar stands for 1 child. The number line along the side, called the scale, helps you read how tall each bar is. Always start the scale at 0.

Bar graph: How We Get to School. Source: survey of Ms. Roy's Grade 1 class. Walk 7, bus 5, car 4, bike 2.

Parts of a graph

A complete graph has:

a title (what is it about?)
labels (what do the categories and the numbers mean?)
a source (where did the data come from?)

Without these, nobody knows what your graph is about!

Worked example

Turning a tally table into a bar graph

Liam's tally table shows birds at his feeder: chickadee 6, blue jay 2, cardinal 2. Make a bar graph.

Draw a line going across (the bottom) and a line going up (the side).
Write the categories along the bottom: Chickadee, Blue jay, Cardinal. Write a label underneath: Kind of bird.
Write numbers up the side, starting at 0: 0, 1, 2, 3, 4, 5, 6, 7. Write a label: Number of birds.
Colour the chickadee bar up to 6. Colour the blue jay bar up to 2. Colour the cardinal bar up to 2.
Write the title at the top: Birds at Our Feeder. Write the source: Liam's observation, Saturday morning.

A bar graph with bars of 6, 2 and 2, a title, labels, and a source.

Source: Liam's observation, Saturday morning.

4. Line plot

A line plot is good when the answers are numbers. Draw a number line. Then put one X above the number for each answer.

Mr. Singh's class asked: "How many teeth have you lost?" Here are 15 answers:

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

Line plot. Each X is one child. 0 teeth: 4 children, 1 tooth: 3, 2 teeth: 5, 3 teeth: 2, 4 teeth: 1, 5 teeth: 0. Source: survey of Mr. Singh's class.

Worked example

Reading the line plot

Use the line plot above. How many children lost 2 teeth? Did anyone lose 5 teeth?

Find 2 on the number line.
Count the X's above 2: 1, 2, 3, 4, 5.
Find 5 on the number line. There are no X's above it.

5 children lost 2 teeth. Nobody lost 5 teeth.

Just for fun

What if the pictures in a pictograph were not the same size? One giant bus picture could look bigger than seven tiny walking pictures. Silly! That is why every picture must be the same size.

Hands-on activity

Graphs at home

Concrete graph: Collect everyone's shoes by the door. Sort them by kind (boots, running shoes, slippers). Line each kind up in a row from a starting line. Which row is longest?
Building-block bar graph: Use LEGO or other blocks. Make a tower for each category of the data you collected last lesson. One block = one answer.
Pictograph or bar graph on paper: Draw your data from last lesson. Use grid paper if you have it, so every square is the same size.
Don't forget the title, labels and source!

Your turn

In a pictograph, each 🍎 stands for 1 child. The Apples row has 🍎🍎🍎🍎🍎🍎. How many children chose apples?

A bar for Hockey goes up to 9. What does that mean?

Your tally table says Red: 3, Blue: 5. How many squares tall should each bar be?

Why should every picture in a pictograph be the same size and lined up?

What three things should every graph have?

On a line plot about pets at home, there are 3 X's above the number 2. What does that mean?

Which graph uses real objects?

Be proud of your work

Making a graph takes time and care. If a bar is too tall, it's okay to erase and fix it. Checking your work is what real mathematicians do!

More practice: warm-up

Each ⛸️ stands for 1 child. The Skating row is ⛸️⛸️⛸️⛸️⛸️. How many children chose skating?

True or false? On a bar graph, a longer bar shows more.

Which part of a graph tells where the data came from: the title, a label, or the source?

On a line plot, how many does each X stand for?

Which graph uses pictures: a pictograph or a line plot?

More practice: on your own

Pictograph: Favourite Treat (each picture = 1 child).

Ice cream: 🍦🍦🍦🍦
Cookie: 🍪🍪🍪🍪🍪🍪
Apple: 🍎🍎

How many chose each treat? Which treat has the most?

Your tally table says: Rain boots 4, Running shoes 7, Sandals 1. How tall is each bar on your bar graph? Which bar is tallest?

Answers to "How many brothers and sisters do you have?": 1, 0, 2, 1, 1, 0. On a line plot, how many X's go above 0? Above 1? Above 2?

A graph has the title Our Favourite Seasons and the labels Season and Number of children. What is missing?

In a concrete graph, the red tower has 6 blocks and the blue tower has 6 blocks. What does that tell you?

Challenge

Find the mistake! Kai's tally table says Dogs 4, Cats 5. His pictograph shows:

Dogs: 🐶🐶🐶🐶
Cats: 🐱🐱🐱

What is wrong? How can he fix it?

Use the line plot about teeth from this lesson: 0 teeth: 4 children, 1 tooth: 3, 2 teeth: 5, 3 teeth: 2, 4 teeth: 1. How many children lost at least 1 tooth?

You asked "How many pets do you have?" and got answers like 0, 1, 2, 3. Which kind of graph is a good choice: a line plot or a pictograph of fruit? Explain.

Check your understanding

Quiz

In our Grade 1 pictographs, each picture stands for...

A bar goes up to 4 on the scale. How many does it show?

What tells you what a graph is about?

Which graph puts an X above numbers on a number line?

Where should the numbers on the side of a bar graph start?

In a pictograph, the Bus row shows 🚌🚌🚌🚌🚌🚌. Each picture = 1 child. How many children ride the bus?

What is the source of a graph?

For parents and teachers

What your child is learning: to display data using one-to-one correspondence in concrete graphs, pictographs, line plots and bar graphs, with a title, labels and source (D1.3).

Common mistakes:

Pictures of different sizes or unevenly spaced, so a shorter row looks longer. Grid paper helps a lot.
Starting the bar-graph scale at 1, or drawing a bar to the wrong line. Have your child point to the top of the bar and slide a finger across to the scale.
Forgetting the title, labels or source. Make a little checklist together.
On line plots, writing numbers instead of X's, or stacking X's unevenly.

How to help: Graph real family data: who likes which cereal, the weather each day this week, how many books each person read. A concrete graph with real objects (shoes, cans, toys) is the best starting point before moving to paper.