Grade by Grade
D. Data · Data and Probability

Stacked-Bar Graphs

D1.3 D1.6About 45 minutes
Learning goals
  • I can read a stacked-bar graph using its legend and scale.
  • I can find the size of each part of a stacked bar and the total of the whole bar.
  • I can read a stacked-bar graph that shows relative frequencies, where every bar is one whole.
  • I can explain when a stacked-bar graph is a good choice.

Words to know

stacked-bar graph
A bar graph where each bar is split into parts stacked on top of each other (or end to end). Each part shows one category.
legend
The key that tells which colour or pattern stands for which category.
segment
One part of a stacked bar.
scale
The numbers along the axis, counting up by equal steps (the interval).

Remember from Grade 4

You read and made multiple-bar graphs, where bars for different groups stand side by side. A stacked-bar graph uses the same data in a new way: the bars are piled on top of each other.

Building a bar out of parts

Three junior classes chose what to play at recess on a snowy day: sliding, building snow forts, or tag.

In a stacked-bar graph, each grade gets one bar. The bar is cut into parts, one part for each choice. The parts are stacked on top of each other.

  • The height of the whole bar shows the total for that grade.
  • Each part (segment) shows one category. The legend tells you which is which.
A snowy schoolyard where children slide down a hill, build a snow fort and play tag.
Sliding, building snow forts and playing tag on a snowy day. Each choice becomes one part of a stacked bar. AI-generated image
Snowy-Day Recess ChoicesSlidingSnow fortsTag0510152025301086Grade 38612Grade 46915Grade 5GradeNumber of studentsSource: junior class surveys, January 2026
Each bar is stacked from the bottom: sliding (green), then snow forts (yellow), then tag (blue). The number in each part is how many students chose it. Grade 3: 10, 8, 6. Grade 4: 8, 6, 12. Grade 5: 6, 9, 15.

How to read it

  1. Read the title and the legend.
  2. To find a total, read the top of the whole bar on the scale. The Grade 5 bar reaches 30, so 30 Grade 5 students answered.
  3. To find a part, read where the part starts and where it ends, then subtract. The Grade 4 tag part starts at 14 and ends at 26. 26 − 14 = 12 students.
  4. The bottom part starts at 0, so you can read it straight from the scale.
Worked example

Example 1: Read a part of a stacked bar

Use the recess graph. How many Grade 5 students built snow forts?

  1. Find the Grade 5 bar and the yellow part (snow forts).
  2. The sliding part goes from 0 to 6. So the snow fort part starts at 6.
  3. The snow fort part ends at 15, where the tag part begins.
  4. Subtract: 15 − 6 = 9.

9 Grade 5 students built snow forts.

Every bar is one whole: relative frequencies

Room 5 has 20 students and Room 6 has 25. Both rooms had 10 students choose an apple at snack time. Is apple equally popular in both rooms?

This kind of stacked-bar graph shows relative frequencies. Every bar is the same length, because every bar is 1 whole class. Each part shows the share of the class.

Snack Fruit ChoicesAppleOrangeBanana00.20.40.60.810.50.250.25Room 50.40.40.2Room 6Relative frequencySource: snack program records, one day in March
Room 5: apple 10 of 20 = 0.5, orange 5 of 20 = 0.25, banana 5 of 20 = 0.25. Room 6: apple 10 of 25 = 0.4, orange 10 of 25 = 0.4, banana 5 of 25 = 0.2. Apple is green, orange is yellow, banana is blue.

Now we can see it: apple fills half of Room 5's bar (0.50) but less than half of Room 6's bar (0.40). The same count (10) is a bigger share of the smaller class.

Worked example

Example 2: Compare shares

In the snack graph, which room had the greater share choosing orange?

  1. Room 5's orange part (yellow) goes from 0.5 to 0.75. That's 0.25.
  2. Room 6's orange part goes from 0.4 to 0.8. That's 0.40.
  3. 0.40 is greater than 0.25.

Room 6 had the greater share choosing orange.

Stacked or multiple-bar?

  • Use a stacked-bar graph when you want to see the total for each group and how it is split into parts.
  • Use a stacked-bar graph with relative frequencies (every bar = 1 whole) when you want to compare the shares of groups of different sizes.
  • Use a multiple-bar graph when you mostly want to compare one category across groups, because all the bars start at 0 and are easy to compare.
Just for fun

Why don't stacked-bar graphs ever fall over?

They always start on a solid base: 0!

Hands-on activity

Build a stacked bar

You need: building bricks or blocks in three colours (or paper squares coloured with three crayons), and some tape.

  1. Ask everyone at home (or on a video call) what they want for a weekend breakfast: pancakes, eggs or cereal. Ask the question on two different days, Saturday and Sunday.
  2. Make one tower for each day. Use one colour for each food and put the same colour together: pancakes on the bottom, then eggs, then cereal.
  3. Stand the towers side by side. Which day has the taller tower? Which food has the biggest part?
  4. Draw your towers on grid paper as a stacked-bar graph. Add a title, a scale that starts at 0, a legend and a source.
Library Books Borrowed by Room 9FictionNon-fictionGraphic0510152025303540MonTueWedThuDayNumber of booksSource: Room 9 library sign-out sheet
Use this graph for the Your turn questions. Each bar is stacked from the bottom: fiction (green), non-fiction (yellow), graphic novels (blue). The scale counts by 5s.

Your turn

1

How many books did Room 9 borrow on Monday altogether?

2

How many graphic novels were borrowed on Tuesday?

3

On which day were the most fiction books borrowed?

4

How many non-fiction books were borrowed over the four days?

5

On which day were the most books borrowed in all?

6

On which day was fiction exactly half of all the books borrowed?

More practice: warm-up

1

In a stacked-bar graph, what does the height of the whole bar show?

2

Recess graph: how many Grade 3 students answered?

3

Recess graph: which part of each bar shows tag?

4

Recess graph: how many Grade 5 students chose tag?

5

True or false: a stacked-bar graph needs a legend.

More practice: on your own

1

Recess graph: how many students chose sliding in all three grades?

2

Recess graph: which grade had the most students choose tag? What fraction of that grade is it?

3

Library graph: how many more books were borrowed on Thursday than on Monday?

4

Snack graph: which room had the greater share choosing banana?

5

When is a stacked-bar graph a better choice than a multiple-bar graph?

Challenge

1

On Saturday, 6 friends went skating and 4 went sledding. On Sunday, 3 went skating and 9 went sledding. Describe how to draw a stacked-bar graph of this data, including the scale.

2

Library graph: what fraction of Thursday's books were graphic novels? Write it as a decimal too.

3

The snack graph shows Room 5's apple share is 0.50. If you saw only this graph, with no counts, could you tell how many Room 5 students chose apple? Explain.

Check your understanding

Quiz

1.

In a stacked-bar graph, what does the whole bar show?

2.

A stacked bar has parts from 0 to 12, from 12 to 20 and from 20 to 27. How big is the middle part?

3.

What does the legend of a stacked-bar graph tell you?

4.

In a stacked-bar graph that shows relative frequencies, every bar is:

5.

Library graph: how many non-fiction books were borrowed on Wednesday?

6.

Which graph best shows each class's total and the parts that make it up?

For parents and teachers

What this lesson teaches: reading and interpreting stacked-bar graphs (new in Grade 5), including ones that show relative frequencies, where every bar is one whole (D1.3, D1.6).

How to help at home:

  • Point out stacked bars in flyers, reports or apps (for example, a phone's storage bar is a single stacked bar).
  • When reading a part of a bar, ask your child to say where it starts and where it ends, then subtract.
  • Build towers of coloured blocks to make the idea concrete.

Common difficulties:

  • Reading the top of a middle segment as its value (saying Grade 4 tag is 26 instead of 26 − 14 = 12). Only the bottom segment starts at 0.
  • Forgetting to check the legend.
  • Comparing counts in a relative-frequency bar graph. Those bars show shares, not how many.