# ALEX Lesson Plan

## Solar Angles and the Unequal Heating of the Earth

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This lesson provided by:
 Author: Virginia Hall System: Mobile County School: Mary G Montgomery High School
General Lesson Information
 Lesson Plan ID: 35792 Title: Solar Angles and the Unequal Heating of the Earth Overview/Annotation: In this activity, students will model how the directness of sunlight affects the heating of Earth’s atmosphere at the equator. Students will demonstrate that Earth’s shape has a direct effect on the unequal heating of the atmosphere. The students will discover how the tilt of Earth’s axis affects the amount of sunlight that reaches different regions of the earth’s surface thus causing different seasons.This lesson results from the ALEX Resource Gap Project.
Associated Standards and Objectives
Content Standard(s):
 Science SC2015 (2015) Grade: 9-12 Earth and Space Science 5 ) Use mathematics to explain the relationship of the seasons to the tilt of Earth's axis (e.g., zenith angle, solar angle, surface area) and its revolution about the sun, addressing intensity and distribution of sunlight on Earth's surface. Insight Unpacked Content Scientific And Engineering Practices:Using Mathematics and Computational ThinkingCrosscutting Concepts: Scale, Proportion, and QuantityDisciplinary Core Idea: Earth's Place in the UniverseEvidence Of Student Attainment:Students: Explain that seasons are not due to the Earth's proximity to the sun Show that sunlight concentrated in a small area will produce warmer temperatures than when spread out over a larger area. Explain that the northern hemisphere and southern hemisphere have opposite seasons due to the axial tilt. Mathematically compute the sun angle for a given day of the year at a given latitude. Create a data set and graph that can be used to determine the solar energy expected at a specified location and date on the Earth's surface. Graphically display the variations over one year of seasons of the sunlight received on the Earth's surface.Teacher Vocabulary:zenith solar angle surface area horizon north/ south pole axis revolution rotation hemisphereKnowledge:Students know: Earth's spin axis is fixed in direction over the short term but tilted relative to its orbit around the sun.Skills:Students are able to: Use mathematical representations to describe cyclic patterns of the seasons.Understanding:Students understand that: The seasons are a result of Earth's tilt relative to its orbit around the sun and are caused by the differential intensity of sunlight on different areas of Earth across the year. Patterns can be used to identify cause-and-effect relationships.

Local/National Standards:

During this activity, the students will demonstrate the following Scientific and Engineering Practices (from the Next Generation Science Standards):

Developing and using models

Planning and carrying out investigations

Analyzing and interpreting data

Engaging in argument from evidence

Obtaining, evaluating and communicating information

During this activity, the students will demonstrate the following Crosscutting Concepts (from the Next Generation Science Standards):

Systems and system models

Structure and function

Stability and change

During this activity, its pre-reading, and its extension, students will utilize the following Reading Standard (CCSS.ELA.LITERACY.RST.11-12.3):

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.

During this activity, its pre-reading, and its extension, students will utilize the following Writing Standard(s) (CCSS.ELA.LITERACY.WHST.9-10.2 and WHST.9-10.2F):

Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes.

Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic).

Primary Learning Objective(s):

Students will model how the directness of sunlight affects the heating of Earth’s atmosphere at the equator.

Students will demonstrate that Earth’s shape has a direct effect on the unequal heating of the atmosphere.

Students will discover how the tilt of Earth’s axis affects the amount of sunlight that reaches different regions of the earth’s surface thus causing different seasons.

Students will discover a mathematical relationship between the solar angle and solar radiation.

During this activity, the student will demonstrate knowledge at the following Bloom's Levels of Taxonomy (1-6 depending on what part of the activity being taught):

Blooms 1: Observe and recall information; know dates, events, places; know major ideas; master basic subject matter. Student recalls or recognizes information, ideas, and principles in the approximate form in which they were learned.

Blooms 2: Understand information; grasp meaning; translate knowledge to a new context; interpret facts; compare; contrast; order; group; infer causes; predict consequences Student translates, comprehends, or interprets information based on prior learning.

Blooms 3: Use information; use methods, concepts, theories in new situations; solve problems; use required skills or knowledge Student selects, transfers, and uses data and principles to complete a problem or task with a minimum of direction.

Blooms 4:  See patterns; organize the parts; recognize hidden meanings; identify components Student distinguishes, classifies, and relates the assumptions, hypotheses, evidence, or structure of a statement or question.

Blooms 5:  Compare/discriminate between ideas; assess value of theories; make choices based on argument; verify value of evidence; recognize subjectivity Student appraises, assesses, or critiques on a basis of specific standards and criteria.

Blooms 6: Use old ideas to create new ones; generalize from given facts; relate knowledge from several areas; predict; draw conclusions Student originates, integrates, and combines ideas into a product, plan or proposal that is new to him or her.

During this activity, the students will demonstrate knowledge at the following Depth of Knowledge Levels (1,2,3,4 depending on what part of the activity being taught):

DOK 1: Recall elements and details of story structure, such as sequence of events, character, plot and setting. Conduct basic mathematical calculations. Label locations on a map. Represent in words or diagrams a scientific concept or relationship. Perform routine procedures like measuring length or using punctuation marks correctly. Describe the features of a place or people.

DOK 2: Identify and summarize the major events in a narrative. Use context cues to identify the meaning of unfamiliar words. Solve routine multiple-step problems. Describe the cause/effect of a particular event. Identify patterns in events or behavior. Formulate a routine problem given data and conditions.

DOK 3: Support ideas with details and examples. Use voice appropriate to the purpose and audience. Identify research questions and design investigations for a scientific problem. Develop a scientific model for a complex situation. Determine the author’s purpose and describe how it affects the interpretation of a reading selection. Apply a concept in other contexts.

DOK 4: Conduct a project that requires specifying a problem, designing and conducting an experiment, analyzing its data, and reporting results/solutions. Apply mathematical model to illuminate a problem or situation. Analyze and synthesize information from multiple sources. Describe and illustrate how common themes are found across texts from different cultures. Design a mathematical model to inform and solve a practical or abstract situation.

During this activity and its extension, the students will demonstrate knowledge of the following Writing Standards (CCSS.ELA.LITERACY.WHST.9-10.1):

• Write arguments focused on discipline-specific content.

During this activity, its pre-reading, and its extension, students will utilize the following Reading Standard (CCSS.ELA.LITERACY.RST.11-12.3):

• Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.
Preparation Information
Procedures/Activities:

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Assessment

Assessment Strategies

Assess/Evaluate:

The following Formative Assessment questions are the last step of the lab activity. This should be completed by the students in groups and turned in with their lab activity.

Formative Assessment Questions:
1. At this point, your group should be able to postulate a theory as to why, when roughly the same amount of light from the flashlight struck the paper each time, more blocks were illuminated when the light came in from an angle.
2. Why is the atmosphere warmer near the equator? (Use data from your investigation to support your theory.)

3. The number of daylight hour’s changes during the year. The more daylight hours during the day, the more radiant energy the Earth's surface receives. The day with the most daylight hours in the Northern Hemisphere is the first day of summer, which is on or about June 21. This day is the summer solstice. Find out more about the changing number of daylight hours during the year. (a) What and when are the spring and fall equinoxes, and the winter solstice? (b) How does the Earth's tilt cause different seasons? (c) What is the difference between the angle of the Sun's rays in the Northern and Southern Hemispheres on these dates (listed in a)? (d) What is the general difference in their atmospheric temperatures (use your cities data for the dates listed in Part A)?

TABLE   page 5

1. At this point, your group should be able to postulate a theory as to why, when roughly the same amount of light from the flashlight struck the paper each time, more blocks were illuminated when the light came in from an angle. “If the Sun is directly overhead (the angle of incidence of the Sun’s rays to the surface is 90°), the shadow has a smaller surface area of coverage.  If the Sun is lower in the sky (e.g., 30° angle of incidence), the shadow length increases and covers a larger surface area.”
2. Why is the atmosphere warmer near the equator? (Use data from your investigation to support your theory.) “If the Sun is directly overhead (the angle of incidence of the Sun’s rays to the surface is 90°), the shadow is of minimum size, and the sunlight is concentrated into a small area, the maximum amount of heating takes place, and higher temperatures result.”
3. The number of daylight hours changes during the year. The more daylight hours during the day, the more radiant energy the Earth's surface receives. The day with the most daylight hours in the Northern Hemisphere is the first day of summer, which is on or about June 21. This day is the summer solstice. Find out more about the changing number of daylight hours during the year. (a) What and when are the spring and fall equinoxes, and the winter solstice? (b) How does the Earth's tilt cause different seasons? (c) What is the difference between the angle of the Sun's rays in the Northern and Southern Hemispheres on these dates (listed in a)? (d) What is the general difference in their atmospheric temperatures?

Part A:                                                                                              Part C:

 Season Definition Approximate date range General Sun’s angle Spring equinox “AKA vernal equinoxAn equinox is the moment in which the plane of Earth's equator passes through the center of the Sun's disk, which occurs twice each year, around 20 March and 23 September The equinox in spring, on about March 20 in the northern hemisphere and September 22 in the southern hemisphere. The equinoxes are the only times when the solar terminator (the "edge" between night and day) is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated. Fall equinox AKA Autumnal EquinoxOne of two points at which the ecliptic intersects the celestial equator. At the autumnal equinox, the sun is moving along the ecliptic in a southeasterly direction. The equinox in fall, on about September 22 in the northern hemisphere and March 20 in the southern hemisphere. The equinoxes are the only times when the solar terminator (the "edge" between night and day) is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated. Summer solstice The summer solstice occurs at the moment the earth's tilt toward from the sun is at a maximum. The solstice in summer, on or about June 20 - June 22 in the northern hemisphere and December 20 - December 23    in the southern hemisphere The Sun’s rays become more acute north of the equator, bringing summer and vice versa in the southern hemisphere. Winter solstice The winter solstice marks the shortest day and longest night of the year. The solstice in winter, on or about   December 20 - December 23   in the northern hemisphere and June 20 - June 22 in the southern hemisphere The Sun’s rays become more oblique north of the equator, bringing winter and vice versa in the northern hemisphere.”

Part B:       23.5o tilt angle.

“Many people believe that Earth is closer to the sun in the summer and that is why it is hotter. And, likewise, they think Earth is farthest from the sun in the winter. Although this idea makes sense, it is incorrect.  It is true that Earth’s orbit is not a perfect circle. It is a bit lop-sided. During part of the year, Earth is closer to the sun than at other times. However, in the Northern Hemisphere, we are having winter when Earth is closest to the sun and summer when it is farthest away! Compared with how far away the sun is, this change in Earth's distance throughout the year does not make much difference to our weather.  There is a different reason for Earth's seasons.  Earth's axis is an imaginary pole going right through the center of Earth from "top" to "bottom." Earth spins around this pole, making one complete turn each day. That is why we have day and night, and why every part of Earth's surface gets some of each. Earth has seasons because its axis doesn't stand up straight.”

Part D:

Season                        General Atmospheric Temperatures (Alabama - Mobile) degrees F

2016 data                High                                                     Low                            Average

Spring equinox        72.2                                                     49.8                                  61

Fall equinox            85.7                                                     71.3                                 78.5

Summer solstice     89.7                                                     66.2                                 77.95

Winter solstice       61.7                                                      41.5                                51.6

Part A and C: https://www.wikipedia.org/

Part A and C: http://www.dictionary.com/

For a more Summative Assessment, the following questions can be incorporated into a quiz or into the COS 5 Unit test.

• Earth's tilt in combination with its orbit around the Sun causes the ____. ”seasons”

• Different seasons occur because of ____________________ and Earth’s orbital motion around the Sun. “earth’s tilt”

• If the tilt of Earth’s axis were increased from 23.5° to 30°, summers in New York State would become _____. “warmer, and winters would become cooler”

Base your answers to the following questions on the diagram below and on your knowledge of Earth science. The diagrams, labeled A, B, and C, represent equal-sized portions of the Sun’s rays striking Earth’s surface at 23.5° N latitude at noon at three different times of the year. The angle at which the Sun’s rays hit Earth’s surface and the relative areas of Earth’s surface receiving the rays at the three different angles of insolation are shown.

PICTURE   page 1

• As viewed in sequence from A (90o) to B (66.5o) to C (43o), these solar path angles in the figure above represent which months and which change in the intensity of insolation? “June → September → December; and decreasing intensity”

• As the angle of the Sun’s rays striking Earth’s surface at noon changes from 90° to 43°, the length of a shadow cast by an object will ______. “ increase”

• What is Earth's axis?  “Earth's axis is the imaginary line around which Earth spins.”

• Why doesn't Earth's orbit cause seasonal temperature changes on Earth?  “The change in distance is actually minimal. Earth's tilted axis is the real cause of seasons on Earth.”

• Predict which season this following scenario describes: The sun is directly above an object, at a right angle, the temperature is hot, and the sun spends more time in the sky due to its higher trajectory thus more heating occurs.  “Summer”

• What is the mathematical relationship between the sun’s angle (surface sunlight) and intensity and distribution? “As the angle increases the intensity decreases (inverse relationship) and the distribution increases (direct relationship)”

 Acceleration: Acceleration/Elaborate/Extend:    Switch your design with another groups design and evaluate each other’s design with the criteria below:1. Following their procedure, would you be able to replicate their design? Please cite specifics on how to improve their procedures.2. Evaluate their drawing of their design.  Does it adequately represent what they said to do in their procedures?  Please cite specifics on how to improve their drawing.  Please keep in mind not everyone is an artist. Intervention: Intervention: Here are some suggestions for students who need extra assistance:Introduce the assignment in sequential stepsCheck for student understanding of instructionsCheck on progress often in the first few minutes of workProvide time suggestions for each taskProvide a checklist for long detailed tasksAssign a peer helper to check understanding of directionsAssign a peer helper to read important directions and essential informationAssign a peer tutor to record material dictated by the student Allow small group work

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

 Presentation of Material Environment Time Demands Materials Attention Using Groups and Peers Assisting the Reluctant Starter Dealing with Inappropriate Behavior
Be sure to check the student's IEP for specific accommodations.