Technical Card in Mathematics
Technical Card in Mathematics
Title: A little math helps know better about satellites
Grade: 5 (or 6 ) Duration: 2 periods
| Competence |
based on proper input )texts, tables, given data….(, the student is able to solve a problem situation involving knowledge of all operations on numbers greater than 100 000, decimals and fractions, and the properties of geometric plane figures. |
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| General objective | Student will be able to integrate (invest) different learning objectives involving calculations, construction, and imagination skills | |
| Calculation skills | Geometric/measurements skills | |
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Prior knowledge: The student is supposed to have already learned how to: |
• Calculate the L.C.M. of 3 numbers. • Multiply 2 several-digit numbers or • Use calculator to calculate and verify products. • Read and write great numbers. |
• Draw circles. • Use axial symmetry. • Measure using a protractor. • Construct angles having certain measures. • Relate time and distance in a motion |
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Specific objectives / learning outcomes: |
• Recognize the meaning of L.C.M. • Identify the L.C.M. in real life situation. • Express parts as fractions • Calculate length of circles (perimeter of a circle). |
• Visualize periodicity on a cyclic trajectory. • Use protractor to measure angles. • Use math rules to make a graduated circle. |
Introduction:
This session is conceived in the new perspective of the teaching/learning perspective, aiming to give teachers and students an example of a real usage of math concepts as well as their related rules and principles. Thus, even if a little bit new, this situation can enhance student’s capacity to solve problems having new contexts or stories, while giving sense to many math concepts not frequently met in real life (such as L.C.M. and circumference). By choosing the most relevant context: Satellites, with a very short introduction about the new era of telecommunication and the role of artificial satellites, student’s interest will instantly be captured. You also can start with a video clip on the first artificial satellite launched by the Soviet Union in 1957 at:http://www.encyclopedia.com/video/hJpLgxY7wes-sputnik1.aspx
Suggested procedures:
- Teacher may begin with a short introduction about satellites )he may use document 1( or start with simple questions: What about artificial satellites? Does anyone know any? What is your favorite TV channel? Where is
it broadcasting on which satellite? (5 min.) - Distribute “student’s document”. Allow time for individual reading and exploration. 7 min
- Let a student read aloud. Ask questions to make sure they all understand. Involve the whole class in the discussion (any comment is welcome). Ask students to form groups of 4. (7 min)
- Allow 20 min. for groups to achieve the 1st two questions. Check with the whole class the answers and let the groups post and explain their work. 30 min.
- In a second session: Explain how protractors can help in determining the directions. And give them a hint about the graduation on the clock, and how they can divide a circle into 12 parts, using the protractor and measuring the angle at the center.
Teachers’ documents:
Teachers’ supplementary reading:
that may be useful to start the session, not to be given to students
“The artificial satellites are made to specific tasks. One of the most significant applications of artificial satellite is its use in telecast around the world (such as Nilesat, Badrsat, Eurobird.). In recent time, advancements in communication have brought about astounding change in the way we live. The backbone of this communication wonder is variety of satellite systems orbiting around Earth. The most common kinds are:
- Communication satellites: They facilitate communication around the world. The geostationary satellite covers ground locations, which are close to equator.
- Astronomical satellites: They are designed for studying celestial bodies.
- Navigational satellites: They are used to specify location on Earth and develop services based on navigation (like GPS services).
- Earth observation satellites: They are designed for studying Earth system, environment and disaster management.
- Weather satellites: They facilitate to monitor weather and related services.
- Space station: It is an artificial structure in space for human beings to stay and do assigned experiments/works.
As a matter of fact, there are varieties of satellite systems, including reconnaissance satellites, to meet military requirement”. Cnx.org. (dynamic digital educational ecosystem).
Answer keys of student’s questions:
When a mobile turns around a circle in 3 hours, then it can be found at the end of every hour on one third further from the initial position. Assimilating the circle to a clock then starting at 12, it can be found at 4, 8 and 12 resp. When the period is 4, in one hour, the mobile will travel only a quarter of the circle, then its endpoints are: 12, 3, 6, 9 and 12 again on the clock circle. When the period is 6, it divides the circle to 6 equal parts at the end of every hour, hence its ends are on 12, 2, 4, 6, 8, 10 and 12 again. The next alignment of the 3 satellites, will be after 12 hours (which corresponds to the L.C.M. of the numbers 3, 4 and 6) therefore at 7:00 AM.
The respective distances are: 2×3.14×(6000 + 300) = 39 564 km = 39 564 000m.
2×3.14×(6000 + 600) = 41448 km = 41 448 000 m.
2×3.14×(6000 + 1000) = 43960 km = 43 960 000 m.
Student’s documents:
Document 1. Problem- Situation:
“wow, I can see 3 satellites lining up” Marwan was very excited to look at the space through the telescope Mum bought him for his birthday. He run to telephone and invited his friend Farida to come over and see it. One hour later when Farida came,
none of the 3 satellites was in sight! Both kids started their inquiry to find out why. They wanted to know when and why will the 3 satellites line up again? They keep looking through the telescope, and found that:
a- The first satellite, the closer one is seen 3 hours later.
b- The 2nd satellite, the intermediate one is seen 4 hours later.
c- The 3rd satellite is seen with the 1st one 6 hours later.
Using the different documents below, you will help Marwan and Farida to:
- Complete the diagram “A”, showing at the end of every hour where each of the three satellites could be find.
- If Marwan saw the satellites lining up at 7:00 PM, then when will he see the next lining up?
- Marwan read on the telescope the altitudes of 3 satellites respectively: 300 km, 600 km and 1000km. What are distances travelled by each of 3 satellites in each round?
- Marwan needs an instrument, to help him track the motion of the satellites. What do you suggest?
Document 2: Orbit of a satellite
the circle on which a satellite moves around the Earth is called “orbit” its radius is the sum of its altitude h or heights and the radius R = 6000 km of the Eart.
