The purpose of this Warm-up is to encourage students to recognize that in some situations it is helpful to think about an increase in terms of what fraction or percentage it is of the original value. This will be useful when students interpret statements about percent increase in a later activity. While students may notice and wonder many things about this table, the important discussion points are that each team’s increase is the same when viewed additively and that the increases are very different when viewed multiplicatively.. For example, an increase of 8 points from 100 to 108 is not as significant as an increase from 4 points to 12 points, because the first increase is only 8% of the original value, while the second is 200% of the original value.
As students share things they notice, listen for language students use to discuss the significance of the different increases. For example, students may say that the baseball team tripled their score, which would be like the basketball team going from 100 to 300 points in the next game. 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.
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. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner.
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. If no students wonder which team improved the most, direct them to the second question, and give them 1 minute to work with a partner.
Here are the scores from three different sports teams from their last two games.
| sports team | total points in Game 1 | total points in Game 2 |
|---|---|---|
| football team | 22 | 30 |
| basketball team | 100 | 108 |
| baseball team | 4 | 12 |
Students may wonder:
Poll students on which team they think improved the most. First, ask a student who thinks they all improved by the same amount to share their reasoning. (Each team increased its score by 8 points.) Then, ask a few students who said the baseball team improved the most to share their reasoning.
There is no need to introduce the phrase “percent increase” at this time. The goal is to plant the idea that it sometimes makes sense to describe a change relative to a starting amount instead of just looking at absolute change. In the course of discussion, it may be natural to say things like:
Students may say that the football team improved the least because the 8 points could have been scored from only 1 touchdown in football, but it would have to be 3 or 4 baskets in basketball and 8 separate runs in baseball. Prompt students to look at the significance of the 8 additional points in the context of each team’s score in the Game 1 rather than the mechanics of scoring in each sport.
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The purpose of this Warm-up is to encourage students to recognize that in some situations it is helpful to think about an increase in terms of what fraction or percentage it is of the original value. This will be useful when students interpret statements about percent increase in a later activity. While students may notice and wonder many things about this table, the important discussion points are that each team’s increase is the same when viewed additively and that the increases are very different when viewed multiplicatively.. For example, an increase of 8 points from 100 to 108 is not as significant as an increase from 4 points to 12 points, because the first increase is only 8% of the original value, while the second is 200% of the original value.
As students share things they notice, listen for language students use to discuss the significance of the different increases. For example, students may say that the baseball team tripled their score, which would be like the basketball team going from 100 to 300 points in the next game. 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.
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. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner.
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. If no students wonder which team improved the most, direct them to the second question, and give them 1 minute to work with a partner.
Here are the scores from three different sports teams from their last two games.
| sports team | total points in Game 1 | total points in Game 2 |
|---|---|---|
| football team | 22 | 30 |
| basketball team | 100 | 108 |
| baseball team | 4 | 12 |
Students may wonder:
Poll students on which team they think improved the most. First, ask a student who thinks they all improved by the same amount to share their reasoning. (Each team increased its score by 8 points.) Then, ask a few students who said the baseball team improved the most to share their reasoning.
There is no need to introduce the phrase “percent increase” at this time. The goal is to plant the idea that it sometimes makes sense to describe a change relative to a starting amount instead of just looking at absolute change. In the course of discussion, it may be natural to say things like:
Students may say that the football team improved the least because the 8 points could have been scored from only 1 touchdown in football, but it would have to be 3 or 4 baskets in basketball and 8 separate runs in baseball. Prompt students to look at the significance of the 8 additional points in the context of each team’s score in the Game 1 rather than the mechanics of scoring in each sport.