The purpose of this warm-up is to familiarize students with data in a context that they will be using in a later activity. While students may notice and wonder many things about these data, estimates of average rate of change and curiosity about models for the populations are the important discussion points.
This Warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved (MP1).
Arrange students in groups of 2. Display the table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder about. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Here are the populations of three cities during different years.
What do you notice? What do you wonder?
| City | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
|---|---|---|---|---|---|---|
| Paris | 6,300,000 | 7,400,000 | 8,200,000 | 8,700,000 | 9,300,000 | 9,700,000 |
| Austin | 132,000 | 187,000 | 254,000 | 346,000 | 466,000 | 657,000 |
| Chicago | 3,600,000 | 3,550,000 | 3,400,000 | 3,000,000 | 2,800,000 | 2,900,000 |
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered about. Record and display, for all to see, their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If a general description of the trends in population and possible models for population do not come up during the conversation, ask students to discuss this idea.
For example:
All skills for this lesson
No KCs tagged for this lesson
The purpose of this warm-up is to familiarize students with data in a context that they will be using in a later activity. While students may notice and wonder many things about these data, estimates of average rate of change and curiosity about models for the populations are the important discussion points.
This Warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved (MP1).
Arrange students in groups of 2. Display the table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder about. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Here are the populations of three cities during different years.
What do you notice? What do you wonder?
| City | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
|---|---|---|---|---|---|---|
| Paris | 6,300,000 | 7,400,000 | 8,200,000 | 8,700,000 | 9,300,000 | 9,700,000 |
| Austin | 132,000 | 187,000 | 254,000 | 346,000 | 466,000 | 657,000 |
| Chicago | 3,600,000 | 3,550,000 | 3,400,000 | 3,000,000 | 2,800,000 | 2,900,000 |
Students may notice:
Students may wonder:
Ask students to share the things they noticed and wondered about. Record and display, for all to see, their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If a general description of the trends in population and possible models for population do not come up during the conversation, ask students to discuss this idea.
For example: