Students will analyze and create stacked bar graphs. 

In this task, students will be introduced to the stacked bar graph. Stacked bar graphs can be created horizontally or vertically to display the relative frequency of a data set. Students will look at the flavours in assorted boxes of chocolate. They will compare the relative frequency of each flavour in three different boxes. Some of the big ideas that may emerge in today’s task include: 

• Frequency is the number of times a category or event occurs within a data set. 
• A relative frequency table shows each category expressed as a fraction of the total quantity or frequency.
• Relative frequency can be represented using fractions, decimals, or percents. 
•  Fractions, decimals, and percents can all represent relationships to a whole.
• The sum of the relative frequencies is 1 or 100%.
• Stacked-bar graphs display the data proportionally, relative to the whole.
• Stacked-bar graphs relative frequency. 
• Each bar in the graph represents a whole, and each of the segments in a bar represents a different category. 
• Different colours are used within each bar to represent each category.

Show students this video:

Then, ask students:

What do you notice?

What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group.

Some of the noticing and wondering that came up in a class recently included:

• I notice a box of chocolates.
• I notice it says “assorted”.
• I notice they are arranged in an array. 
• I notice the box is square.
• I notice there are different flavours.
• I wonder why there are different flavours. 
• I wonder why there is only one hazelnut. 
• I wonder if all the boxes are the same. 
• I wonder how much the box costs. 

At this point, you can answer any notices and wonders that you can cross off the list right away.

Prompt students with:

What is the frequency of each type of chocolate?

Make an estimate.

Give students the opportunity to make estimates with their elbow partners before sharing out to the group.

You might also extend this prompt by asking: 

Use your estimates to determine the relative frequency of each type of chocolate.

Share the following animation with students: 

After the frequency of each chocolate flavour is revealed, construct or share the animation (or screenshot) of the stacked bar graph being created.

Ask students to consider what this graph can tell us about the flavours of chocolates in the box. Tell students that this particular type of graph is called a stacked bar graph. A stacked bar graph is another way to display the relative frequency of a data set. 

Highlight the following characteristics:

• The bar represents the whole. In this case, all the chocolate in the box.
• Each colour represents a different category. In this case, the different flavours of chocolate.

Since you have already taken some time to set the context for this problem and student curiosity is already sparked, we can now push their thinking further by fuelling sense making.
Share the following silent animation.

You can verbally share the following prompt with students:

Create stacked bar graphs to represent the flavours found in the second and third boxes of chocolate. 

Ask students to answer the following question:

Relative to the total number of chocolates in each box, which of the three boxes has the greatest frequency of hazelnut chocolates? Justify your answer.

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Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.

Consolidation Prompt #1:

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Consolidation Prompt #2:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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