Lesson Plan

Solar Angles and the Unequal Heating of the Earth

Subject Area

Science

Grade(s)

9, 10, 11, 12

Overview

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.

Content Standards

Science (2015) Grade(s): 09-12 - Earth and Space Science

SC15.ESS.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.

Unpacked Content

Vocabulary

zenith
solar angle
surface area
horizon
north/ south pole
axis
revolution
rotation
hemisphere

Knowledge

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.

Scientific and Engineering Practices

Using Mathematics and Computational Thinking

Crosscutting Concepts

Scale, Proportion, and Quantity

Interdisciplinary Connections

Learning Objectives

Primary Learning Objectives

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.

Additional Learning Objective(s)

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.

Procedures/Activities

Before Strategy/ Engage:

Group students by 2 or 3 to do the lab activity – in class.

Have students create flash cards of vocabulary and the essential questions. (This can be used to prepare for an assessment later.) I have students do the Vocabulary and Essential Questions the night before the lab activity so they are “pre-loaded” with some information prior to the activity.

Vocabulary:

Climate

Concentrated

Cosine Projection Effect

Fall equinox

Infrared rays

Perpendicular

Radiant energy

Radio waves

Spring equinox

Summer solstice

Troposphere

Ultraviolet rays

Visible light.

Weather

Winter solstice

X rays

During Strategy/Explore/Explain

1. Tape the ruler along the side of the flashlight so that a 6-inch (15-cm) section of the ruler extends past the lamp end of the flashlight.

2. Lay the graph paper on a table.

3. Hold the flashlight perpendicular to the paper so that the free end of the ruler is on the edge of the paper and the flashlight is over the paper.

4. Darken the room and turn on the flashlight.

5. Place the thermometer in the brightest part of the light. Wait 2 minutes and then start recording the temperature (record the initial temperature and then record every minute for 5 minutes) on the data chart.

6. Observe the number of squares covered on the paper by the inner bright circle of light. Record the number of squares on the data chart.

7. Tilt the ruler down so the back end of the flashlight is about 6 inches (15 cm) above the table. Use the other ruler to help gauge distance and stabilize flashlight.

8. Place the thermometer in the brightest part of the light. Wait 2 minutes then start recording the temperature (record the initial temperature and then record every minute for 5 minutes) on the data chart.

9. Again, observe the number of squares covered by the light. Record the number of squares on the data chart.

Try New Approaches How does the curvature of the Earth affect the Sun's light rays?

10. Use the flashlight from the experiment; lay it on a table with the attached flashlight/ruler (the 6 inches are on the table) extending over the table edge.

11. Make a large cylinder out of the graph paper by overlapping the short ends.

12. Hold the cylinder vertically at the end of the ruler.

13. Place the thermometer in the brightest part of the light. Wait 2 minutes and then start recording the temperature (record the initial temperature and then record every minute for 5 minutes) on the data chart.

14. Observe the number of squares that are lit on the curved paper. Record the number of squares on the data chart.

15. Then move the cylinder slightly to the left or right so that the light grazes the edge of the cylinder. Again, observe the number of lit squares. Record the number of squares on the data chart.

Design Your Own Experiment

16. At this point, your group should discuss a good experimental design to answer the question as to why the atmosphere above the equator is warmest. Record your design procedures in the space below.

17. Using the materials that you have been provided, test your design procedure.

18. Sketch a simple illustration of your procedural setup (example: Figure 1 as an example)

19. Place the thermometer in the brightest part of the light. Wait 2 minutes and then start recording the temperature (record the initial temperature and then record every minute for 5 minutes) on the data chart.

20. Observe the number of illuminated squares on the paper. Record the number of squares on the data chart.

Student Data Chart

After Strategy/Explain, Elaborate:

Graphing:

1. Using the data that was collected on the student data sheet, please create a line graph the time (x-axis) versus temperature (y-axis) for each of the 6 designs on the graph paper below. Use a different color to represent each design. *Create a KEY to indicate which design is which color. Also, ensure that you label the graph's axes and title correctly.

2. Using the data from the student data chart, create a bar graph of the 6 designs (x-axis) vs temperature at 5 min (y-axis). Ensure that you label the graph's axes and title correctly.

3. Review the student data chart again, is there any other way to classify the data into a single graph? When your group has decided on the data and graph type, use the graph paper below to graph your information. Ensure that you label the graph's axes and title correctly.

Laboratory Activity with graphing section page 4

Before Strategy/ Engage:

Group students by 2 or 3 to do the lab activity – in class.

Vocabulary:

Climate

Concentrated

Cosine Projection Effect

Fall equinox

Infrared rays

Perpendicular

Radiant energy

Radio waves

Spring equinox

Summer solstice

Troposphere

Ultraviolet rays

Visible light.

Weather

Winter solstice

X rays

During Strategy/Explore/Explain

1. Tape the ruler along the side of the flashlight so that a 6-inch (15-cm) section of the ruler extends past the lamp end of the flashlight.

2. Lay the graph paper on a table.

3. Hold the flashlight perpendicular to the paper so that the free end of the ruler is on the edge of the paper and the flashlight is over the paper.

4. Darken the room and turn on the flashlight.

6. Observe the number of squares covered on the paper by the inner bright circle of light. Record the number of squares on the data chart.

7. Tilt the ruler down so the back end of the flashlight is about 6 inches (15 cm) above the table. Use the other ruler to help gauge distance and stabilize flashlight.

9. Again, observe the number of squares covered by the light. Record the number of squares on the data chart.

Try New Approaches How does the curvature of the Earth affect the Sun's light rays?

10. Use the flashlight from the experiment; lay it on a table with the attached flashlight/ruler (the 6 inches are on the table) extending over the table edge.

11. Make a large cylinder out of the graph paper by overlapping the short ends.

12. Hold the cylinder vertically at the end of the ruler.

14. Observe the number of squares that are lit on the curved paper. Record the number of squares on the data chart.

15. Then move the cylinder slightly to the left or right so that the light grazes the edge of the cylinder. Again, observe the number of lit squares. Record the number of squares on the data chart.

Design Your Own Experiment

16. At this point, your group should discuss a good experimental design to answer the question as to why the atmosphere above the equator is warmest. Record your design procedures in the space below.

17. Using the materials that you have been provided, test your design procedure.

18. Sketch a simple illustration of your procedural setup (example: Figure 1 as an example)

20. Observe the number of illuminated squares on the paper. Record the number of squares on the data chart.

Student Data Chart

After Strategy/Explain, Elaborate:

Graphing:

2. Using the data from the student data chart, create a bar graph of the 6 designs (x-axis) vs temperature at 5 min (y-axis). Ensure that you label the graph's axes and title correctly.

Laboratory Activity with graphing section page 4

Learning Activity (Before)

Learning Activity (During)

Learning Activity (After)

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

Questions with Answers:

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.”
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.”
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 equinox An 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 Equinox One 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: 23.5^otilt 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 B: https://spaceplace.nasa.gov/seasons/en/

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

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

Questions 1 and 2: https://www.nasa.gov/centers/langley/pdf/245895main_MeteorologyTeacherRes-Ch4.r3.pdf

Part D: http://www.usclimatedata.com/climate/mobile/alabama/united-states/usal0899

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 (90^o) to B (66.5^o) to C (43^o), 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 and Intervention

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 steps

Check for student understanding of instructions

Check on progress often in the first few minutes of work

Provide time suggestions for each task

Provide a checklist for long detailed tasks

Assign a peer helper to check understanding of directions

Assign a peer helper to read important directions and essential information

Assign a peer tutor to record material dictated by the student

Allow small group work

Approximate Duration

Total Duration

91 to 120 Minutes

Background and Preparation

Background/Preparation

Background Information:

“The temperature of the Earth's atmosphere comes from the Sun's radiant energy warming the Earth's surface. The weather, climate, and seasons of a given area of the Earth depend on the temperature, which measures the atmospheric energy."

In this activity, you will model how the directness of sunlight affects the heating of the earth’s atmosphere (at the equator). You will demonstrate that the earth’s shape has a direct effect on the unequal heating of the atmosphere. You will discover how the tilt of the earth’s axis affects the amount of sunlight that reaches different regions of the earth’s surface thus causing different seasons.”

Explain: Background Information

The Background Information above links to Chapter 4: Angle of Light Rays and Surface Distribution: A Structured-Inquiry Activity

Page 19: Probing Further: would be a good Formative Assessment Activity to gauge student awareness prior to the lesson.

Page 22: Background Information for Teacher is an excellent resource for information prior to planning lesson.

Prior to lab:

The teacher should set up each station or area with ~3 feet of masking tape, 2 rulers, 1 flashlight, 1 sheet of graph paper, 1 thermometer, stopwatch, and 6 different colors of pencils/markers/crayons.

Skills students should know:

Students should be able to correctly use a ruler, be able to read a thermometer, use a stopwatch, be able to correctly set up a graph (including creating scales for the x- and y-axis as well as all labels and title), plot a graph (line and bar), be able to use a search engine such as Google.

Knowledge the students should understand:

Students should have a basic understanding of seasons relationship to the 23.5^o tilt of the Earth’s axis, solar angles and solar radiation, a basic understanding of the Cosine Projection Effect.

The picture (PICTURE page 1) represents the solar angels at noon, 2 o’clock, and 4 o’clock. Notice the solar shadow on the paper is elongating. Use this information to explain the Cosine Projection Effect. (Cosine Projection Effect:

When you tilt a surface away from a beam of light, you spread the same density of light across a larger area.) Also use this information to explain the mathematical relationship (inverse) of the sun’s angle (surface sunlight) to intensity and distribution.

Oblique (obtuse/acute) angles: less light (less solar energy– heat); greater surface area
Right angles: more light (more solar energy– heat); less surface area

This lab is designed to be performed before a detailed explanation is provided to students. The gathering of the data, as well as graphing of the data, is key prior to teacher explanation. After graphing has occurred (teacher may have to assist in scaling) on all 3 graphs, then the teaching moment can occur. It is recommended that the teacher perform the lab in advance. This will allow the teacher to gather a data set that can be graphed in advance to use as the teaching template. NOTE: not all students will get the optimal data sets so having one ready to display on smart board or projector is easier than trying to find student ones that meet the criteria.

What should be seen: line graphs will vary but there should be an increase or constant line over time. With the perpendicular increasing, the most (90^o angle) and the horizontal increasing the least (180^o angle) and the 6in above table (~45^o angle) being in the middle. The curvature should be similar to the perpendicular with their choice being in between. The bar graph of the temperature should be similar in height. This graph shows the perpendicular the highest with the horizontal being the lowest. The perpendicular temperature represents summer with the 6in being fall/spring and the horizontal representing winter. Fall/Spring being similar in average temperature range can be shown as the same graph plot. You can also use this to represent times of day with 90^o being noon and 6in above table being ~ 4 PM and 180^o being dusk. Explain to students that the solar radiation decreases as the solar angle decreases. The third graph is the illuminated boxes vs angle. This should show the angle increases as the number of boxes illuminated increases. Explain that this means that as the solar angle increases the surface illumination increases. Together these two data sets show the Cosine Projection Effect as solar radiation increases the surface are affected decreases and as the solar radiation decreases the surface increases. This mathematical relationship is known as an inverse relationship (see definition of Cosine Projection Effect above).

Materials and Resources

Materials

Masking tape (1 roll)
Ruler (2 per student or group)
Flashlight (not LED) – old-fashioned ones with C or D batteries work well (looking for heat to be produced) (1 per student or group)
Graph paper (1 sheet per student or group)
Thermometer (the bulb – colored with a Sharpie black or dark green +120 to -20 F) one per student or group)
Clock/stopwatch/something to measure time (1 per student or group) timer on phone may be used
Colored Pencils/markers (6 different colors per student or group)
Copy of the laboratory procedures, charts, graphs, and questions. Solar Angles and the Unequal Heating of the Earth (1 per group)

Technology Resources Needed

Technology is not required for this activity; however, a search engine could be utilized to access information pertaining to the activity.

Approved Date

2018-02-08

Learning Resource Type

Solar Angles and the Unequal Heating of the Earth

Subject Area

Grade(s)

Overview

SC15.ESS.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.

Unpacked Content

Vocabulary

Knowledge

Skills

Understanding

Scientific and Engineering Practices

Crosscutting Concepts

Primary Learning Objectives

Additional Learning Objective(s)

Procedures/Activities

Assessment Strategies

Acceleration

Intervention

Approximate Duration

Total Duration

Background and Preparation

Background/Preparation

Materials and Resources

Materials and Resources

Technology Resources Needed

Approved Date

SC15.ESS.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.