TitleIII Technology Literacy Challenge Grant

Learning Unit

Overview | Content Knowledge | Essential Questions | Connection To Standards | Initiating Activity | Learning Experiences | Culminating Performance | Pre-Requisite Skills | Modifications | Schedual/Time Plan | Technology Use

OVERVIEW

This unit (The earth’s dimensions) is where we first learn tools for building a more complete earth model. The topics include: The apparent shape of the earth, the earth’s actual shape, Finding the size of the earth, Latitude and longitude, Using data points to draw isolines, and isoline appications including topographic maps. Because of the disjointed nature of this topic I split it into 2 smaller units. There is an interesting blend of declarative and procedural knowledge in this unit. I look at these units as a rather disjointed whole which can be separated without destroying meaning. I am presenting the first part of this unit here. (in red type above)

CONTENT KNOWLEDGE

P = procedural knowledge D = declarative knowledge

ESSENTIAL QUESTIONS

1.  Compare the apparent shape of the earth to the actual shape of the earth. Give evidence to support your ideas. D
2. Given the following information ( small arc distance, and angular measure of that arc) find the circumference of any sphere. P
3. Use information gotten by calculation of circumference to arrange spheres(planets) in order by size, or be able to identify individual planets from calculations and using reference table information. P
4. The student can reasonably locate a specific position on a map or globe using coordinates. P
5. Describe the relationship between the altitude of polaris, and a person’s latitude in the northern hemisphere. How is this related to the earth’s shape?D

CONNECTIONS TO NYS LEARNING STANDARDS
List Standard # and Key Idea #: Write out related Performance Indicator(s) or Benchmark(s)

 I used the Core Curriculum Draft based on M.S.T , The Physical Setting to do this part of this document.

Standard 1 Analysis,Inquiry,and Design- Mathematical analysis and design

key idea 1: Degrees and minutes are used to mathematically represent positions on the earth’s surface.

Key idea 2, : Students are to develop a logical method for determining circumference of a sphere given an interior angle, and the exterior distance covered by that angle.

Key idea 2 again : Students are to use their method to place the planets in our solar system in order by size. (Classifying)

Key idea 3: Students are to identify a specific planet by using calculations and comparison with data on their reference table.

Standard 1 Analysis,inquiry, and design- Scientific Inquiry

Key idea 1 How do observations show that the earth is basically spherical in shape, but that more precise measurements show its oblateness.

Standard 6 Interconnectedness: Common Themes

Key idea 2 models- Latitude and longitude systems can be used to find positions on any sphere.

Key idea 2 models again- The earth and other celestial bodies are basically spherical in shape.

Standard 4

Key idea 1- The Earth and celestial phenomena can be described by principles of relative motion and perspective.

Major understanding 1.1e - The earth’s coordinate system of latitude and longitude, with the Equator and Prime Meridian as reference lines, is based upon the Earth’s rotation, and our observations of stars such as Polaris.

Color code for highlighted areas is daily lessons:

Bright Red- Assignments or tasks for students

Blue- Specifice methods used during lessons for acquisition, storage, or extending concepts.

If terms are unfamiliar they are techniques taught during the B.O.C.E.S. workshops on Reading and writing in the content areas, or learning unit training.

Purple- Specific resources used during lessons.

INITIATING ACTIVITY

 Launch- (Day 1)

Introductory questions for launch

Teacher introduces movie with , " Many uneducated people in medieval times believed that the earth was a flat object. Even today some people still believe this to be true. The teacher also asks the following questions:

What is the shape of the earth? What are some evidences for your belief? How can we prove our ideas? (2-5 minutes)

To introduce a discrepant idea about the earth’s shape, the teacher shows the movie "In Search of the Edge". This movie presents the idea that the earth is a round but flat object, not a sphere, as is taught in public schools. Can be ordered through BOCES film service.

(30 min.)

Students Think about ideas produced in movie, students also are to use some source text, review book, etc. to to the following

Assignment- Have students state their belief of the shape of the earth, and come back to class with at least 4 reasons for us to believe their answer. ( in outline, note form, not a summary,yet)

This can be accomplished by having students go to their textbook, library sources, or review books which we use before exams. As long as it is a reliable source of the information you want to discuss in class.

LEARNING EXPERIENCES
In chronological order including acquisition experiences and extending/refining
experiences for all stated declarative and procedural knowledge.

 Day 2- (discussion of launch assignment) Acquisition

I give or - for completion of assignment

Noncompletion of assignment. (Students get a check if they have a statement , with 4 reasons from book or movie(some of the true reasons for spherical shape are denounced in movie), if they have a reason with no real evidence or with less than 4 reasons they receive a minus. 5 checks eventually equal a 100. Minuses represent a 15 to 20 point deduction. This becomes an assignment grade. It only takes about 5 minutes to walk around and scan 15 to 20 papers. I find this a useful tool to make sure students complete simple assignments which I intend to grade later as a summary or a quiz after a discussion of ideas. (5 min.)

Prediscussion

• In my introductory unit we have defined the term sphere and spherical so no prevocabulary work(key terms) is really needed. You may have to address this now!!
• We have described major spheres of the earth in lab #1 where we draw a scale model of the lithosphere,hydrosphere, atmosphere, and mantle,outer core, and inner core.
• Use some sort of pair grouping activity.

I use think,pair, share.

Think- The individual thinking portion has already taken place overnight in the original assignment!! (0 min.)

Pair-Have your students pair up and share ideas for their idea of the earth’s shape. They must come up with a statement of their belief of shape and at least 4 reasons for this belief. (This could be taken as a grade since there are fewer papers, and some real thought has gone into this task since they usually don’t want to let their partner down) These papers would be collected, along with original efforts and stapeled together at end of class.(10-15 min.)

Share- (20 to 25 minutes)

As a large class grouping students are to share ideas about earth’s shape. Have each group report out as to their belief in the earth’s shape. Keep track somewhere(board,overhead, chart paper)

The next part of the discussion is crucial and should be guided very carefully by you.

]

Guided, discussion, lecture.

1. I split the board into 2 parts and explain that there are 2 ways to look at the earth’s shape:

1. what it looks like from all angles including models, and
2. what its actual shape is.

1. I explain that there are 2 types of evidence that can be used: 1) indirect (logical but not proven by actual direct sight) and direct (seen by an observer to be true). So we classify evidence as to shape first under proofs for apparent shape and proofs for actual shape. We further classify these as Indirect(I) or as Direct(D)
2. You can elicit responses from students and place them in the correct categories. This is also a good time to explain some difficult concepts such as how latitude and north star altitude are related. I accomplish this with a series of questions:

1. where would the north star’s altitude be aat the north pole?
2. what is the latitude of the N. Pole?
3. Where would you see it at the equator?
4. What is the equator’s latitude?

Finally leading to this relationship. The earth acts like a protractor which is curved and measures angles.

• This is also where I use my flexible hoop demonstrator to show the bulge caused by rapid rotation, using a power drill.
• Some actual space photographs can be used for an example.
• A globe can be used to show the scientific model of apparent shape.
• A scene from the movie Christopher Columbus shows the ship sailing over the horizon. I also show a short clip from a science film: Earth,Moon, and sun showing a solar eclipse at this time.

4)Students are to copy notes from the board in chart form (chart becomes Graphic Organizer)

5) Hand out FWOL rubric for summaries

(FWOL is an acronym for a Fifty Words Or Less summary)

Assignment-

Write a 100 word or less summary on the earth’s apparent shape. Not the actual shape. Use at least 4 pieces of evidence. (position paper rubric)

Write a second summary 50 words or less on the earth’s actual shape. Support your belief. (FWOL rubric)

Day 3- Acquisition and Storage

Students to work on summaries in class in order to receive feedback. Peer editing, teacher commentary (30 minutes)

Near end of period Use Key terms sheet to define Oblate spheroid. I have a film about microgravity in space from NASA which shows the behavior of water drops in space which shows them recovering to a spherical shape after being shot into apparent weightlessness inside a spacecraft (see also Apollo 13.) You could also redemonstrate the effect on the hoop demonstrator when spun. (10 min.)

Assignment- Final copies of summaries due tomorrow.

Day 4,5 and possibly 6 The earth’s size- Lab activity- ( inductive )

(between 2 to 2 ½ periods) Procedural knowledge.

Instead of lecturing about Erastothenes calculation of the earth’s cirumference from sun altitudes on different dates at similar longitude, I have developed a lab activity which challenges students to find a method for finding circumference in groups of 2 to 4. I call this lab the GREAT PIZZA LAB from a cartoon the Wizard of Id where the king listens to both arguments about the earth’s shape and decides to call it the Pizza theory since it is both round and flat.

In this lab the teacher:

1. Produces 5 different colored circles. Each circle is larger than the next by a radius change of 1 inch. All the measurements are done in inches since my circles were originally done in inches. (I used a roller ruler to draw the circles.)
2. Cut the circles up into pieces measuring 2(90 degrees), 1(60), 2(30), 1(45),1(15) Make envelopes with the calculated circumferences written on the inside. (for reference later)
3. Cuts 5 lengths of string for measuring outside arcs.
4. Calculators for calculating
5. Clues at approximately 10 minute intervals (on board or overhead)
6. Provides 5 physically separate locations for each puzzle envelope
7. 5 rulers with inch measures( if you wish; make your system metric.)

In this lab students:

1. Calculate the circumference of 5 colored circles each with a specific diameter( since I used a roller ruler to draw the circles they are 2,4,6,8,and 10 inches in diameter.
2. Measure with a string to find a nonstraightline distance.
3. Use a ruler to find the straightline equivalent distance.
4. Use proportions to solve an unknown.

Prelab discussion

1. Explain to students that their purpose is to come up with a universal method for finding the circumference of any sphere.
2. The radius and diameter of a closed sphere cannot be measured so some other way must be found. They are invited to find the actual circumferences of their circles using C = p D. They can use this to verify whether their method works.

3. The lab-

4. Students are supplied with only 2 pieces of any one puzzle at a time. These 2 pieces can be proportionally related!! For Example:

90 and 45, or 60 and 30, 15 and 30, etc. If a group is really struggling maybe you can give them both 90 degree pieces at the same time.

• Every ten minutes give the group a clue. I usually give the following clues in this order

1. The circumference of a circle is the measurment around the outside.
2. The interior angle of a circle is 360 degrees.
3. 100 is 4 times larger than 25

4. The head of a barbie doll is perfectly proportioned to the head of a real life human

1. If a group thinks they have solved the problem, have them demonstrate the procedure.
2. Next show them the answer under the flap of the envelope.
3. They are to verify all of the other circles circumferences, and they must show their work.

Storage- This is where after learning this procedure they lock it into memory.

8)Finally they must write a 3 to 4 step description of their method.

9)They are to check their reference tables to find if there is something similar to their method.

10)They must make sure that every student in the class can solve the circumference using this method. ( In order to receive their reward all students must know this method, they become the teacher.)

Extend and Refine- They have extended practice and also have to use the method for a purpose other than for which it was originally intended!!

11) Students solve the "Planet Puzzle"

• Students have to solve a number of practice exercises
• Students use the astronomy information on their reference table to determine by size, which planet is which.
• Students can either compare their circumferences by size proportionately to the diameters given in the chart or solve for the circumferences by using p D. Than compare circumferences.
• Students identify planets by size
• Students show all work for calculating answers.

I will provide the worksheet as an appendix to this document!!

Rationale for 3 days of time- You may only see 1 or 2 questions on the regents based on any of this procedure, but the skills used and reinforced by this activity will be used many times in the future.

• Inductive and deductive reasoning skills (in solving the puzzle)
• Using proportional relationships (lab and planet puzzle)
• This gives a much higher percentage of students knowing this process cold, without reteaching. It took me the same amount of time when lecture,practice, reteaching, and more practice took place.
• It can be used to introduce the relative sizes of the planets for the astronomy extension for the syllabus.

Assignment- Be ready for quiz on method!! I have students pick 3 they want to count toward pizza reward, and I pick 3. All 6 must pass quiz. 5 out of 6 must score 90 or above to get pizza reward.

If successful I buy 1 pizza per class and 1 large bottle of soda for a christmas party and movie before christmas vacation. The movie I pick has earth science relationship: Jurassic Park, Dante’s peak, Twister, Deep Impact, Apollo 13, etc. I use this film as part of a launch for another unit!!

Quiz- in class The quiz consists of 4 examples in which students have to find circumferences using proportional methods. The bonus on quiz uses students understanding of planet puzzle to identify certain planets.

Day 7- Acquisition- Latitude and Longitude

Prelesson-

1. go over quiz results from previous day
2. any reteaching to be done on method done now in small group, as others start latitude and longitude exercise. (10min.)
3. My room has a tile floor that lends itself to making longitude and latitude grids at 10^o increments. I lay down tape over existing tile lines in strategic places, and label each 30^o increment. I end up with a flat world sized model of latitude and longitude which fits in my classroom.

Lesson-

1. Key terms- latitude,longitude, parallel, meridian

Most of my 9^th grade students have been introduced to latitude and longitude in 9^th Grade Global Studies. It is up to me to extend and refine their ability to use this system.

My key terms descriptions for latitude and longitude center around an image of a dome house with an attached ladder system. The ladder is able to rotate around the house when needed. The rungs come to a common point at the very top of the dome, and spread out at the bottom. I can rotate this ladder to any location around the dome (motorized system.) The ladder can shift position 24 widths around the dome. The rungs are all separated by 10 degrees of height.

Latitude is when I climb up and down the ladder. I try to get students to answer this by themselves with directed questions based on student opinions. I describe replacing a window at 90 degrees west from the ladder’s original position up at the midpoint of the dome (45 degrees) above the ground.

One of the apparent related terms becomes "ladder" for latitude.

Longitude represents the movement of the ladder around the house.

I can move the ladder westward, or eastward. I than describe that I want a second replacement window at 180 degrees from storage position. I than ask the class if there would be any problem if the workmen went East instead of west around the building, and then up the ladder.

Parallels become the "rungs" of the Ladder. The rungs are all parallel.

Meridians become the "long" rung supports. The only place the meridians are almost parallel is at ground level.

Other models of longitude are orange sections, or if you have a very sharp kitchen knife,cuttingboard, and apples you can make "hemispheres" and than smaller sections.

Latitude can be represented by making two hemispheres and than slices of apple. Dole pineapple rings can also be used to show parallel relations.

4. After showing them how to "walk latitude" and "walk longitude", I give them points(colored sticky dots with numbers) to find in the room which I have already located on a world globe. I also place the numbered positions on a world map for students who need extra help, or for absentees. After finding the latitude and longitude for the 20 to 22 pts. each student must place another colored dot on a position, locate it, and write a 100 words or less summary about a short vacation to that locality.

The description must include activities, climate, clothing, and other interesting information about their unique location.

Day 8(lab period)

Lab 11- In my textbook there is another group of latitude and longitude location exercises. I use this as more guided practice.

I suggest that you use pairs check, as the method for this activity. In pairs check, students check their answers after every 4 or 5 problems. If there is disagreement they discuss methods and rethink answer.

Day 9 & 10 Finding latitude and longitude using degrees and minutes.

In this class activity I teach students the procedure for using minutes on a smaller scale map. I use the N.Y.S. geologic map for this exercise, since it is the map used on the regents exam. I also use the seismic map used on the 1994 or 1995 modified regents as a quiz and exam map for this skill.

The teacher provides:

1. a blown up version of The N.Y.S. geologic map (page 3) of the reference table for a student practice document.
2. Rulers for drawing reference degree lines
3. The student copies "how to find and estimate minutes" procedure.
4. Pairings for work groups.
5. Some practice examples in a large group setting. (When I have smaller classes I do the actual practicing in a large group setting around a lab table, 12-15 students) If you have a larger group you can first introduce this on a blown up version on an overhead. I have found the more hands on large group approach to be much more successful.

The student :

1. Draws whole degree reference lines (in pencil) for latitude on the N.Y.S. maps.
2. Does all practice groupings with partner.
3. Does pairs check for all 3 practice groupings, than does the last grouping for a grade with partner. (Since there are more than 20 cities and villages on the N.Y.S. map I have set up a worksheet with 5 cities of my choice to be located for both latitude and longitude. Group 4 is for a grade and includes cities and villages of my choice from scattered positions around the state.

Procedure for finding minutes of latitude

1. Locate city on map
2. Locate the whole degree latitude lines above and below the city you are finding coordinates for.
3. Line up the degree lines across your map with a straight edge, and draw in pencil lines. Do this for both sets of degrees. You now have a section of the map outlined.
4. Find the line showing the halfway point on the map. (Split the degree in half)
5. Label the bottommost degree as 0 minutes
6. Label the topmost degree 60 minutes
7. Label the middle line 30 minutes.
8. Split each half section in half again.
9. Label them 15 minutes(bottom), and 45 minutes(above 30 line).
10. To get even smaller detail divide the smaller intervals into thirds and label them by 5 minute intervals. You only have to label the section closest to the city you are trying to label.

Procedure for finding minutes of longitude

• Locate city on map
• Locate the whole degree longitude lines left and right of the city you are finding coordinates for.
• Line up the degree lines across your map with a straight edge, and draw in pencil lines. Do this for both sets of degrees. You now have a section of the map outlined.
• Find the line showing the halfway point on the map. (Split the degree in half)
• Label the rightmost degree line as 0 minutes
• Label the leftmost degree 60 minutes
• Label the middle line 30 minutes.
• Split each half section in half again.
• Label them 15 minutes(bottom), and 45 minutes(above 30 line).
• To get even smaller detail divide the smaller intervals into thirds and label them by 5 minute intervals. You only have to label the section closest to the city you are trying to label.

Extending and Refining Experiences.

1. The lesson in finding latitude and longitude is an extension of the procedural skill of finding positions by using a coordinate system. This skill will be used again in other situations during the year: finding locations on the moon, in drainage systems, landforms on topographic maps, etc.
2. On the unit exam there is a support your position essay about the apparent shape of the earth. The student is to state what the earth appears to look like, and must explain 4 proofs completely from a list of 10 proofs which they have been supplied with ahead of the exam.
3. In the planet puzzle assignment students are asked to use their method for finding circumference to place all 9 planets in order by size using information from page 14 of the reference table. The diameters of the planets are given in this chart. On the planet puzzle angular measures and exterior arc measures are given for 9 planetary bodies. The student must calculate the circumferences and compare his or her results to this information. (Sequencing , by size.) There are also 3 circumference problems on the summative exam: One like they have seen many times with the interior angle and exterior arc measure given, one with the circumference given and the interior angle asking for the distance between the 2 points, the last with the circumference given and the arc distance given asking for the angular measure between the 2 points. (This question is based on the actual numbers used by Erastothenes which we have discussed in class.)
4. The second lab activity also extends and refines each student’s procedural ability to use coordinate systems for location purposes.

Summative Assessment

A unit exam which includes:

1. An essay asking students to state a position about the earth’s apparent shape, and to specifically defend this position using 4 of 10 acceptable proofs.
2. Opportunities to find locations using:

• Whole degrees of latitude and longitude.
• Minutes of latitude and longitude on a 1) california seismic map and 2) N.Y.S map

1. 3 more problems using proportional methods of finding circumferences in a little fashion than originally taught For example find : The distance between the cities, the shadow angle difference, given the other 3 quantities. Use the circumference answer to determine which planet it might be using reference table information.(planet puzzle)

CULMINATING PERFORMANCE
Include rubric(s)

1. The essay on exam(Essential Question), and any review questions on 6 week review exams!!
2. Finding latitude and longitude on other maps during the year. Landforms labs: mountains, valleys, plateaus, and plains, astronomy: the moon and mars, weathering and erosion features: rivers, drainage systems, deltas, etc.
3. Outside during star watching lab- Find altitude of polaris using astrolabe and constellations. Show altitude is latitude.
4. On review exams students would be expected to use circumference finding method.
5. On planet puzzle students are to use method to order planets by size!!

Rubric for essay(essential questions)

Rubric for FWOL(short summaries)

  4 3 2 1

Topic sentence

First sentence addresses main idea.

Intro sentence is close to main idea.

There is only one sentence.

Answer is completely off target.

Second and/or third sentence provide needed detail to support original idea.

Second or third sentence do not completely support main idea.

There is a second or third sentence but they are not directly related to first sentence.

Answer is completely off target.

Language is appropriate, uses correct scientific terminology and concepts correctly

Answer may be mostly correct but there is some minor flaw in the use of terms.

Answer is correct but some major flaw exists in use of scientific terminology

Answer is not correct, and use of terminology is flawed.

There are no spelling or grammatical errors.

There are only an average of 1 spelling or grammatical error per sentence.

There are only 3 grammatical or spelling errors.

More than 3 errors.

PRE-REQUISITE SKILLS

1.  The ability to recognize the difference between latitude and longitude.
2. The ability to measure distances fairly accurately with a ruler.
3. The ability to measure angles fairly accurately with a protractor.

4) The ability to set up and solve proportional relationships with some fluency. If this skill is not present you may have to do a proportions minilesson.

MODIFICATIONS

 This unit is very visually oriented, and I don’t really know what I would do if I had a visually impaired student in class.

UNIT SCHEDULE/TIME PLAN

1.  The unit takes 10 –11 (40 minute) periods of in class time.
2. It will also take a couple of lab periods to complete practice latitude and longitude exercises.
3. The teacher will have to spend at least a couple of hours ahead of the unit doing the following:

• Preparing the latitude and longitude grid on the classroom floor.(every year)
• Preparing the 5 colored circles, cutting out the circles into appropriate angles, producing an answer key for each one ( only once materials are laminated)
• Copying off pizza lab instructions, and planet puzzle extension.

1. The student will

Descriptions of student activities included in lesson descriptions!!

TECHNOLOGY USE

 I use a computer program called Redshift. Its main purpose is for Astronomy. Built into this program is a global latitude-longitude location system. Later in the year during Astronomy I use this function to discuss longitude and time zones. It could also be used to do city locations. It could also be used during Weather and climate along with climate data to show the relationship between latitude and climate. (Redshift can be purchased through______ at approximately

For a single copy or at ________ for a site license.