Looking for Associations
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to become familiar with a bar graph by noticing and wondering things about it. While reading a bar graph is a review of a previous grade's work, it is an important for students to look for patterns of association in categorical data.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the table and images for all to see. Ask students to think of at least 1 thing they notice and at least 1 thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Two-way table
| has cell phone |
does not have cell phone |
total | |
|---|---|---|---|
| 10 to 12 years old | 25 | 35 | 60 |
| 13 to 15 years old | 40 | 10 | 50 |
| 16 to 18 years old | 50 | 10 | 60 |
| total | 115 | 55 | 170 |
Bar graph
Segmented bar graph
Sample Response
Students may notice:
- 170 people are represented in the information from the table.
- A much greater percentage of 13–18 year olds have cell phones than 10–12 year olds.
- The graphs have a legend (or key) to show what the different bars (or parts of the bars) mean.
Students may wonder:
- Do all 3 representations show the same data?
- Why aren’t the vertical axes labeled?
- Why does the segmented bar graph go up to 100 for all of them when the table shows totals of 60 or 50?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the table and images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If a relationship between the 2 variables does not come up during the conversation, ask students to discuss this idea.
Tell students that, in this course, bar graphs are assumed to have a vertical axis representing the frequency of the categories and segmented bar graphs have a vertical axis representing percentage of the category.
Standards
- 8.SP.4·Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. <em>For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?</em>
- 8.SP.A.4·Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. <span>For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?</span>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Looking for Associations
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to become familiar with a bar graph by noticing and wondering things about it. While reading a bar graph is a review of a previous grade's work, it is an important for students to look for patterns of association in categorical data.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the table and images for all to see. Ask students to think of at least 1 thing they notice and at least 1 thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Two-way table
| has cell phone |
does not have cell phone |
total | |
|---|---|---|---|
| 10 to 12 years old | 25 | 35 | 60 |
| 13 to 15 years old | 40 | 10 | 50 |
| 16 to 18 years old | 50 | 10 | 60 |
| total | 115 | 55 | 170 |
Bar graph
Segmented bar graph
Sample Response
Students may notice:
- 170 people are represented in the information from the table.
- A much greater percentage of 13–18 year olds have cell phones than 10–12 year olds.
- The graphs have a legend (or key) to show what the different bars (or parts of the bars) mean.
Students may wonder:
- Do all 3 representations show the same data?
- Why aren’t the vertical axes labeled?
- Why does the segmented bar graph go up to 100 for all of them when the table shows totals of 60 or 50?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the table and images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If a relationship between the 2 variables does not come up during the conversation, ask students to discuss this idea.
Tell students that, in this course, bar graphs are assumed to have a vertical axis representing the frequency of the categories and segmented bar graphs have a vertical axis representing percentage of the category.
Standards
- 8.SP.4·Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. <em>For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?</em>
- 8.SP.A.4·Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. <span>For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?</span>