NCDPI – AIG Instructional Resource: Background Information
Resource Title: Earth’s RotationSubject Area/Grade Level (s): Math/Fourth Grade / Time Frame: One day
Common Core Standard Addressed:
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle
measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
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.
Additional Standards Addressed:
Science Essential Standard
4.E.1 Explain the causes of day and night and phases of the moon.
4.E.1.1 Explain the cause of day and night based on the rotation of Earth axis.
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).
Type of Differentiation for AIGs (include all that apply): Enrichment x Extension x Acceleration
Adaptations for AIGs: Content x Process x 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
Sources:
· North Carolina Science 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).
NCDPI AIG Curriculum Resource Outline
The teacher should set the stage for learning and assess student understanding of the Earth’s rotation.
1. 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.
2. Ask,
a. 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.)
b. 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.)
STAGE TWO: 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:
sun sun sun sun
0° 45° 90° 180°
midnight 3:00am 6:00am noon
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 THREE: 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 should 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.
TEACHER NOTES: NA
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project