D. Data · Data and Probability

Bar Graphs with Scales

D1.3About 40 minutes

Learning goals

I can read a bar graph whose scale counts by 2s, 5s or 10s.
I can read a bar that ends halfway between two lines.
I can choose a good scale for my data.
I can make a bar graph with a title, labels, a scale and a source.

Words to know

bar graph
A graph that uses bars to show how many are in each category.

scale
The numbers along the side of a bar graph. They start at 0 and go up by the same amount each time.

interval
The amount the scale goes up by each time, like 2 or 5 or 10.

axis
One of the two lines along the edge of a graph. One shows the categories and one shows the scale. (More than one are called axes.)

label
Words that tell what each axis or bar shows.

Remember from Grade 2

In Grade 2 your bar graphs had a scale that counted by 1s: 0, 1, 2, 3... Each square or line stood for 1. In Grade 3, the scale can count by 2s, 5s or 10s. This is many-to-one again: one space on the scale stands for more than one.

Reading the scale

The scale is the column of numbers up the side of a bar graph. A good scale:

starts at 0
goes up by the same amount every time (this amount is the interval)
goes a little higher than the biggest number in the data

To read a bar, look at the top of the bar and follow it across to the scale.

Bar graph: Our Favourite Fall Activity. The scale counts by 2s. Source: survey of Ms. Okafor's Grade 3 class.

Worked example

Example 1: A bar on a line

How many children chose jumping in leaves?

Find the Leaves bar.
Follow the top of the bar across to the scale.
It lines up exactly with 14.

14 children chose jumping in leaves.

Worked example

Example 2: A bar between two lines

How many children chose apple picking?

Follow the top of the Apples bar across to the scale.
It is halfway between 8 and 10.
The scale counts by 2s, so halfway between 8 and 10 is the number in the middle: 9.

9 children chose apple picking. The data: leaves 14, apples 9, pumpkins 12, soccer 6.

Halfway between lines

Scale of 2: halfway between two lines is 1 more than the lower line. Halfway between 8 and 10 is 9.
Scale of 10: halfway is 5 more. Halfway between 30 and 40 is 35.
Scale of 5: halfway between 10 and 15 is not a whole number, so a scale of 5 works best when your numbers are in the 5s count.

Choosing a scale

Look at your biggest number.

Small numbers (up to about 10): count by 1s.
Up to about 20: count by 2s.
Up to about 50: count by 5s or 10s.
Bigger numbers: count by 10s (or more).

Also look at all your numbers. With a scale of 5 or 10, it's easiest if your numbers land on a line or exactly halfway.

Worked example

Example 3: Make a bar graph from a table

The food drive collected: Room 1: 30 cans, Room 2: 45, Room 3: 20, Room 4: 35. Make a bar graph.

The biggest number is 45. A scale of 10 up to 50 works: 0, 10, 20, 30, 40, 50.
Room 1: draw the bar up to the 30 line.
Room 2: 45 is halfway between 40 and 50. Draw the bar halfway between those lines.
Room 3: up to 20. Room 4: halfway between 30 and 40.
Make all the bars the same width, with equal spaces between them.
Add a title, labels on both axes, and the source.

See the bar graph below. It shows the same data as the food drive pictograph from the last lesson.

Bar graph: Cans for the Food Drive. The scale counts by 10s. Source: school food drive count, December.

Every good bar graph has

a title
a label on each axis
a scale that starts at 0 with equal intervals
bars of the same width, with equal spaces
a source (where the data came from)

Just for fun

Why did the bar graph bring a ladder to school?

It wanted to reach the top of its scale!

Hands-on activity

Build a bar graph

You need: grid paper (or paper with lines you draw with a ruler), a pencil and crayons.

Collect data: count how many of each kind of thing you have, for example books on a shelf by type, or toy cars by colour. Or use data from your frequency table in the earlier lesson.
Look at your biggest number and choose a scale: 1s, 2s, 5s or 10s.
Draw the two axes with a ruler. Write the scale up the side, starting at 0.
Draw each bar. Use halfway for numbers between lines.
Add the title, labels and source.

Math talk: "Why did I choose this scale? What would my graph look like with a different one?"

Your turn

Use Our Favourite Fall Activity. What is the interval of the scale?

How many children chose carving pumpkins?

How many children chose soccer?

How many more children chose pumpkins than soccer?

How many children were surveyed in all?

Using a scale of 2, where would the top of a bar for 7 go?

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

More practice: warm-up

A scale goes 0, 2, 4, 6. What comes next?

A scale counts by 5s. A bar ends exactly at the 20 line. What number does it show?

A scale counts by 10s. A bar ends halfway between 30 and 40. What number does it show?

What number should every bar graph scale start at?

Name the parts every good bar graph needs.

More practice: on your own

Your data is 3, 8, 6, 5. What scale would you use? Why?

Your data is 40, 70, 25, 55. What scale would you use? Why?

Use the food drive bar graph. How many cans did Room 1 and Room 3 collect together?

How many more cans does Room 4 need to reach 50?

Pia's scale goes 0, 2, 4, 7, 10. What is wrong?

Challenge

Your data is 18, 24, 11, 15. Would a scale of 2 or a scale of 5 work better? Explain.

On a graph with a scale of 5, one bar ends at 35 and another at 50. How many intervals (spaces) apart are the tops of the bars? What is the difference?

Kai and Mia graph the same data (the biggest number is 10) on the same size paper. Kai's scale counts by 1s up to 10. Mia's counts by 5s up to 50. Whose bars look taller? Do the numbers change?

Check your understanding

Quiz

A scale counts 0, 5, 10, 15, 20, 25, 30. A bar ends exactly at the 25 line. What number does it show?

A scale counts by 2s. A bar ends halfway between 6 and 8. What number does it show?

Which of these does a good bar graph need?

The data is 10, 40, 30, 50. Which scale is best?

Which scale is correct?

Fall activity graph: 14 children chose leaves and 9 chose apples. How many more chose leaves?

For parents and teachers

What your child is learning: to read and make bar graphs with scales that count by 2s, 5s or 10s (many-to-one correspondence), with proper titles, labels and sources (Ontario expectation D1.3). In Grade 2, scales counted by 1s.

Common difficulties:

Counting the grid lines instead of reading the scale numbers (saying a bar at the 3rd line is "3" when the scale counts by 5s).
Bars between lines. Show that halfway between 8 and 10 is 9, using a number line.
Scales that don't start at 0 or that skip unevenly.
Choosing a scale. Encourage your child to look at the biggest number first.

At home: look at bar graphs in news stories, sports pages or weather reports together and ask, "What does the scale count by? What is this bar's number?"