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Connected Experience: Polygon Poetry

Abstract

In this interdisciplinary problem-solving activity, students use themed poems to hunt for exhibit elements, connecting these points to form a simple shape. After recording distances between corners, they will convert measurements to solve a design problem.

Objectives

In this interdisciplinary problem-solving activity conducted both in the classroom and the museum gallery, students will:

  1. review the attributes of simple shapes.
  2. use themed poems to hunt for exhibit elements, connecting these points to form a particular polygon.
  3. estimate and record distances between their secret locations using non-standard units.
  4. learn to convert their measurements to standard units to solve a design problem.

Materials

  • ball of yarn
  • dictionary
  • Polygon Poetry Worksheets (1 riddle per group)
  • pencils
  • metric rulers
  • calculators

Vocabulary

  • polygon: a closed figure of three or more sides, lying on one flat plane
  • perimeter: the length of the border of a closed figure
  • convert: to find an equal value using a different unit of measurement

Activity

Before your Visit

Preparation

  1. Print copies of polygon riddle worksheets as convenient for your class (many versions are available). Students will work cooperatively in polygon groups to solve their riddle, but each is required to record their own data in the gallery (by repeating measurements in science, you can recognize mistakes!).

Procedure

  1. Select two students to stand up, each representing points. What forms when two points are connected? How about three? Have students toss a ball of yarn between points to create a visual triangle in the horizontal plane of the classroom. Continue using student ‘points’ to form a variety of closed polygons, discussing the number of corners, sides, and angles, and perhaps introducing terms such as parallel and perpendicular.
  2. Define perimeter and ask students to think of ways the class could measure the distance around the border of, for example, a triangle constructed by three student vertices. What if the class lacked rulers? Model how to measure distance in the units of a textbook, pencil, or hand, by having students trace the perimeter using these ‘tools’. Draw the simple shape on the board, and record the length of each side as the students go around. Calculate the final perimeter as a class.
  3. Tell students that the class will visit the African Hall while at the museum. The walls of this exhibit are made of life-size displays representing scenes from habitats in Africa, but the center of the hall is a wide, empty area.
  4. Explain that students will work in groups to solve a riddle. Riddle poems will contain clues directing them to specific displays, locations that form the ‘points’ of a mystery polygon. Each student will then use their own feet as a measuring device to record the perimeter of the groups’ shape.
  5. Distribute the worksheets to student groups. Have students read the text aloud to each other to develop an idea of what they might discover in the exhibit. Instruct them to look up any unknown words. Feign ignorance of diorama content.
  6. Have students label their ‘data sheet’ with their name, and record a guess as to what kind of shape they will be forming. Collect the worksheets.

At the Academy

Procedure

  1. Distribute worksheets to pre-arranged student groups.
  2. Instruct students to follow the clues to find the exhibit elements that represent the points of their polygon, marking these secret locations with an X. Students should then ‘connect the dots’ on their map to form the shape’s perimeter (no need to walk along diagonals!).
  3. Have students measure the length of each side of their polygon by counting their own footsteps, walking from one point to the next by placing one foot directly in front of the other. Students should record the distance along the appropriate side of the shape.
  4. Once data has been collected, students are free to explore the hall.

Riddle Answers

  • Isosceles Triangle: Oryx, Roan, Sable
  • Right Triangle: Cheetah, Tortoise, Zebra
  • Pentagon: Penguin, Lechwe, Bushbuck, Bongo, Hartebeest
  • Parallelogram: Steinbok, Klipspringer, Duiker, Dikdik
  • Equilateral Triangle: Klipspringer, Baboon, Leopard
  • Scalene Triangle*: Chameleon, Tortoise, Monitor

*As live displays, subject to change

Back at School

Procedure

  1. Have each student calculate the perimeter of their own polygon.
  2. Have students compare values among members of their own group. Why do values for the same shape differ? Explain how society has created standard units for convenient, comparable measurement. Cite everyday examples. (The metric system is the universal standard for measuring distance. The United States is exceptionally stubborn. In 1999, NASA lost a $125 million Mars orbiter because the ground crews forgot to convert from English to metric!).
  3. Using a metric ruler, introduce students to the relationship between meter, centimeter, and millimeter. What unit is most appropriate to measure one’s footstep? Have students measure and record the length of their shoe from toe to heel in centimeters.
  4. Lead students through the conversion of their estimated polygon perimeter from units of ‘my footsteps’ to ‘centimeters’ and then from ‘centimeters’ to ‘meters’.
  5. How do students’ results compare within their group now? Explain the importance of repetitive trials when conducting scientific experiments to validate the reproducibility of data and reduce error.
  6. Presume that the museum is building a new giraffe display in this space, but that the builders are limited by the amount of railing left from construction. Assuming the builders have 20 m of railing, where could they construct the giraffe diorama? In groups or as a class, discuss how to best include a display that is large enough for giraffes, but will leave room for guests to walk and stand around the scene. Students should use their recorded data to help estimate an appropriate shape or area. Have students present ideas and give reasons in support of their proposal.

How to convert measurements into a unit of length that others will understand:
‘My footsteps’ (varies with student) → centimeters (too small) → meters (just right!)

  • Step 1:
    My polygon’s perimeter = ________ of my footsteps.
    If each footstep = ________ centimeters,
    Then the perimeter = ________ × ________ = _______ cm. Wow! Seems like a lot…
  • Step 2:
    I calculated my polygon’s perimeter to be ________ cm.
    If there are 100 centimeters on one meter stick,
    Then, my polygon’s perimeter = _______ cm ÷ 100 = ________ meters.

Extensions

For older grades, consider:

  • calculating the area enclosed by the polygons.
  • discussing more complex geometry.
  • computing modes and medians for data of student groups.

California Content Standards

Grade Three

Mathematics: Measurement and Geometry

  • 1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.
  • 1.3 Find the perimeter of a polygon with integer sides.
  • 1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).
  • 2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
  • 2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).
  • 2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

Mathematics: Mathematical Reasoning

  • 2.1 Use estimation to verify the reasonableness of calculated results.
  • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Investigation and Experimentation

  • 5a. Repeat observations to improve accuracy and know that the results of similar scientific investigations seldom turn out exactly the same because of differences in the things being investigated, methods being used, or uncertainty in the observation.
  • 5c. Use numerical data in describing and comparing objects, events, and measurements.

English-language Arts: Reading

  • 1.6 Use sentence and word context to find the meaning of unknown words.
  • 1.7 Use a dictionary to learn the meaning and other features of unknown words.

Grade Four

Mathematics: Mathematical Reasoning

  • 2.1 Use estimation to verify the reasonableness of calculated results.
  • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Investigation and Experimentation

  • 6b. Measure and estimate the weight, length, or volume of objects.

Grade Five

Mathematics: Mathematical Reasoning

  • 2.1 Use estimation to verify the reasonableness of calculated results.
  • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Investigation and Experimentation

  • 6f. Select appropriate tools (e.g., thermometers, meter sticks, balances, and graduated cylinders) and make quantitative observations.

English-language Arts: Reading

  • 2.3 Discern main ideas and concepts presented in texts, identifying and assessing evidence that supports those ideas.
  • 2.4 Draw inferences, conclusions, or generalizations about text and support them with textual evidence and prior knowledge.

Grade Six

Mathematics: Algebra and Functions

  • 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

Mathematics: Mathematical Reasoning

  • 2.1 Use estimation to verify the reasonableness of calculated results.
  • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

English-language Arts: Reading

  • 1.4 Monitor expository text for unknown words or words with novel meanings by using word, sentence, and paragraph clues to determine meaning.

Grade Seven

Mathematics: Algebra and Functions

  • 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

Mathematics: Mathematical Reasoning

  • 2.1 Use estimation to verify the reasonableness of calculated results.
  • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

 

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