Activity Title: 'Up Slope'

Subject Area: Math

Theme: Sacred Sites

Grade Level: 4th - 6th

 

Have you ever wondered how high a hill is? Students will investigate how early geologists made accurate estimates of the height of mountains. They will learn the skill of ‘leveling’ to determine slope.

Colorado Standard(s) and/or Benchmark(s) addressed in this activity:

Grade	Content Area	Standard	Benchmark
4th - 6th	Math	1-use of number sense in problem solving	1.6-number sense to estimate, justify reasonable solutions
4th - 6th	Math	3-data analysis in problem solving	3.6-making predictions/comparing results
4th - 6th	Math	4-geometric concepts in problem solving	4.4-use of coordinate geometry

 

National Standard(s) and/or Benchmark(s) addressed in this activity:

Grade	Content Area	Standard	Benchmark
4th - 6th	Math	1-number sense in problem solving	1.1-number sense to justify reasonable solutions
4th - 6th	Math	3-data collection in problem solving	3.1-make predictions and compare results
4th - 6th	Math	5-use a variety of tools to measure results	5.1-communicate reasoning

 

Introduction:

In the background for this lesson, we learned how far one has to travel to measure the circumference of the base (8.8 km) of the monolith Uluru. We also learned the percent of the steepness of the sides. (Compare that to a 7% grade a highway travels over a mountain pass!) The height of Uluru is approximate to that of the Eiffel Tower.

How do scientists and mathematicians figure out the height of a mountain? Experiment with the ancient art of ‘leveling’ to figure the height of a slope.

 

Vocabulary:

• kilomometres
• Geological
• monolith
• summit
• traverse
• circumference

 

Materials:

• quart size (946 ml) glass jar with lid, half full of water
• wide rubber band
• pointed stick about 2 feet (61 cm) long
• journal, pencil, tape measure

 

Preparation:

 

Procedure:

• Place the jar of water on a level table or level ground. When the water is still, place the rubber band around the exact level of the water.
• Stand at the bottom of the slope you wish to measure. Hold the jar directly in front of your eyes and look straight across the water. (Make sure the water level and rubber band are in the same place)
• As you look through the water level, find a place on the slope and ask your friend to place the stick there as a mark.
• Record ‘1’ in your journal.
• Climb the slope and stand where the stick is touching the ground. Place your feet on either side of the spot, look through the jar until the water is level for the next place on the slope to mark. Your friend should move to the new spot and mark it. Record ‘2’ in your journal.
• Repeat the previous step until you are at the top of the hill or as far as you wish to measure.
• Add all of your marks and record the sum in your notebook.
• Use the tape measure to find the distance between your eyes and the ground. Multiply the number of marks you recorded by the distance between your eyes and the ground. The answer is the height of the slope you measured.

 

Analyze and Conclude:

Assessment Rubric:

Advanced proficient 4	Proficient 3	Partially proficient 2	Unsatisfactory 1
Student and the partner accurately measure the slope; they devise a plan to measure using a different strategy.	Student works effectively with a partner to measure a slope.	Student assumes a dominant role in the measurement instead of working compatibly with a partner.	Student and partner are unable to measure the slope accurately.
Student journal reflects comprehension of slope measurement; journal offers insight as to alternative ways to measure a slope.	Recordings in student journal reflect understanding of the process of ‘leveling’.	Journal entries lack details, but the main idea of slope measurement is accurate.	Journal entries are incomplete and do not reflect student understanding of ‘leveling’.
Journal entries provide details that reflect the meaning of rock art to the various clans.	Journal entries are stated in complete sentences and reflect meaning to the author	Journal entries are incomplete sentences, but reflect some meaning	Journal entries do not describe the author’s discoveries of rock art
Student and partner gathered the materials to conduct the experiment; they checked for accuracy at each measurement point; they devised an alternate plan and developed a materials list needed.	Student gathered materials needed to measure the slope; measurements were accurate.	Student did not have all of the materials needed to conduct the measurement; measuring was not completely accurate.	Student did not have the correct materials necessary to conduct the experiment.

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