# Earth's Rotation (AIG IRP)

## Overview

Students will apply math concepts related to measuring angles to diagram the Earth’s rotation throughout a 24-hour period. This task allows for multiple entry points in that students can either use their knowledge of angle measures (e.g., the Earth would rotate 180° by noon) or knowledge of fractions (e.g., 1/2 of a complete rotation would occur by noon) to begin grappling with the task. By creating diagrams, students will also develop an understanding of using tools to measure angles, as well as apply the concept that angle measures are additive (e.g., I figured out that the Earth rotates 15° each hour. Therefore, I realize that the earth rotates 45° in three hours). This lesson was developed by NCDPI as part of the Academically and/or Intellectually Gifted Instructional Resources Project. This lesson plan has been vetted at the state level for standards alignment, AIG focus, and content accuracy.

# Lesson Overview

**Brief Description of Lesson/Task/Activity: **Students will apply math concepts related to measuring angles to diagram the Earth’s rotation throughout a 24-hour period. This task allows for multiple entry points in that students can either use their knowledge of angle measures (e.g., the Earth would rotate 180° by noon) or knowledge of fractions (e.g., 1/2 of a complete rotation would occur by noon) to begin grappling with the task. By creating diagrams, students will also develop an understanding of using tools to measure angles, as well as apply the concept that angle measures are additive (e.g., I figured out that the Earth rotates 15° each hour. Therefore, I realize that the earth rotates 45° in three hours).

**Time Frame: **One day

**Type of Differentiation for AIGs:**

- Extension
- Acceleration

**Adaptations for AIGs:**

- Process
- Product

**Explanation of How Resource is Appropriate for AIGs:** This task is appropriate for AIG students because it takes the abstract topic of the Earth’s rotation and requires students to create a concrete application. The task requires students to reason abstractly, explain thinking, construct viable arguments, and critique the reasoning of others. In addition, students must extend fourth grade concepts of angles to generate rules that others can use when examining the Earth’s rotation.

**Needed Resources/Materials: **

- Chart paper
- Protractors
- Rulers
- Markers or colored pencils

**Source:** North Carolina Essential Standards

**Teacher Notes: **This activity does not specifically address fractions. However, students should be able to make connections to fractions (e.g., a 90 degree turn is ¼ of an entire rotation).

**Mathematical Practices:**

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

4. Model with mathematics.

5. Use appropriate tools strategically.

# Stage 1: Engage

The teacher should set the stage for learning and assess student understanding of the Earth’s rotation.

- Explain to students that a long time ago people believed that Earth was flat and the sun moved around Earth. In fact, the Aztecs (an ancient civilization) believed that they must worship the sun and have special ceremonies in order to ensure that the sun would rise and set each day. Today we know that this is not actually true.
- Ask,
- Why do we see the sun rise in the morning and set in the evening every day?
*(Earth’s rotation and our position on Earth cause us to only see the sun during the day.)* - What do we know about the Earth’s rotation?
*(It rotates 360° each day. We are furthest from the sun at night and closest during the day.)*

- Why do we see the sun rise in the morning and set in the evening every day?

# Stage 2: Elaborate

In order to teach others about the Earth’s rotation and causes of day and night, your teacher has asked you to create a poster. On your poster, draw diagrams of the Earth’s rotation throughout the day, beginning at midnight. For each turn of the Earth that you illustrate, label the time of day, degrees rotated, and your position on the Earth in relation to the sun. Use mathematics to justify that all illustrations on your poster are correct. Lastly, create a rule, formula, or steps that others can use to determine the total number of degrees the Earth has rotated by any given time of day.

Examples:

Before students begin this task, ask them to silently think about the following questions:

- What is this task asking you to do?
- Where do you expect the sun to be in relation to your position on Earth at midnight? Noon?
- How can you determine the time of day for each turn that you draw?
*E.g., Students may generate a chart. The can decompose a full rotation into parts and decompose a full 24 hours into parts. For example half of a full rotation is 180° and halfway through the day is noon.*

Once students have completed their diagrams, share and justify work. As students share, the teacher may ask the following questions:

- How did you begin this task?
*Students may have started by decomposing the full rotation into smaller angles, and identified corresponding times. Students may have started with “friendly” angles (e.g., 0°, 90°, 180°).* - What strategies did you use for drawing your diagrams?
- How did each diagram on the poster show your position in relation to the sun at different times of the day?
- How did you use addition or subtraction to determine the angles in your diagram?
- How could you use the angle measured on your first illustration of the Earth to help create other illustrations?
*Students should realize that the earth rotates 15° per hour. Once they realize this, they can use the additive nature of angles to determine other angles (e.g., I figured out that the Earth rotates 15° each hour. Therefore, I knew that the earth rotates 45° in three hours).* - Explain the rule, formula, or steps that you generated to determine the degrees that the Earth has rotated by any time of day?
- Does the size of the Earth on the different students’ posters affect the size of the angle measures? Why or why not?
*E.g. A 90° angle should have the same angle measure on a large diagram and a small diagram.* - How is measuring the Earth’s rotation the same as measuring the angles of polygons? How is it different?

# Stage 3: Evaluate

Evaluation should focus on the student’s ability to measure angles using the midpoint of the Earth as the common endpoint of two rays. The student should be able to decompose the Earth’s full 360° rotation into smaller turns and generate the corresponding time of day for each turn. Students must develop rules for determining the degrees the Earth has rotated by any given time of day. Students should also understand that the size of a diagram does not affect the size of an angle. Precise use of vocabulary and appropriate use of tools should be evident.