## Task Teacher Guide

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### In This Purposeful Practice…

Students will continue exploring the graphical representation of relative frequency tables through stacked bar graphs. Students will analyze stack bar graphs in order to draw conclusions and construct graphs based on relative frequency tables.

### Intentionality…

The purpose of the Day 4 activities is to reinforce key concepts from Day 3. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

- 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.

## Visual Math Talk

### Overview of This Math Talk

Present the following stacked bar graph. Tell students that the information represented in this graph are the results of a survey. Ask students to draw conclusions about this survey. Some questions you might consider asking include:

- How many people were surveyed?
- What was the most popular flavour?
- What was the least popular flavour?

Encourage relative thinking through questioning.

For example:

- What percent or fraction of the total people surveyed chose cherry chip as their favourite cupcake flavour?

Rather than simply sharing the following stacked bar graphs, you might consider leveraging the visual math talk prompts below to guide you through this routine.

### Visual Number Talk Prompt #1

Begin playing the following silent visual number talk prompt video:

After the initial context is set up, be prepared to pause the video where students are prompted with a question to struggle with.

**Prompt:**

**Create a stacked bar graph and determine the relative frequency of each flavour to determine which is most preferred.**

By this point in the unit, the hope is that students are able to begin constructing a stacked bar graph by using their understanding that each part of the whole (i.e.: different cupcake flavours) must be represented proportionally to one another. This means students will need to consider how many cupcakes there are in total and then use their fractional thinking skills to partition the whole into appropriately sized parts.

While different students may apply different strategies to partition the whole of 50 cupcakes into 5 parts, one of the big ideas we would like to highlight is that if each part is sized appropriately relative to the whole, we can visually approximate the relative frequency as a fraction or a percent.

Although earlier in the unit, we often “moved” different parts of the whole to the leftmost part of the stacked bar graph, this is not easy for students to do when drawing on paper or whiteboards. Therefore, a strategy you may observe students employing to determine the relative frequency for each part may include finding the range (i.e.: the difference between the start and end of each part).

Students may choose to add a relative frequency column to a frequency table or they may simply indicate the relative frequency of each cupcake flavour under the stacked bar graph.

### Visual Number Talk Prompt #2

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## Purposeful Practice

### While Students Are Practicing…

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### Questions: Shrinking Linear Patterns

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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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## Resources and Downloads

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## Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.

### Visual Math Talk Prompt #1

### Visual Math Talk Prompt #2

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### Question #1

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### Question #2

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### Question #3

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### Question #4

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**Download Editable/Printable Handout**

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