Geometry

UK Secondary (7-11)

Fishing for Polygons (Investigation)

Lesson

- To practice with estimating angles visually.
- To practice with measuring angles.
- To learn how to classify quadrilaterals.
- To become fluent with the properties of quadrilaterals.

- Construction paper
- 5 Printed out shapes
- Scissors
- Protractor
- Crayon or Marker
- Compass
- Glue
- Magnets
- Long stick (at least 1 foot long)
- String

Work in pairs or in small groups. Each person should collect the necessary materials and follow the procedure instructions for how to set up the game on their own.

- Cut out a circle with a 5 inch diameter from the construction paper using your compass.
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- Use your protractor to measure an angle between 10 and 100 degrees on the circle.
- Glue the angle you have just cut out to the other side of the circle to create your fish.
- Use your marker to draw an eye on your fish and decorate it however you would like.
- Glue one magnet to the fish you have just created.
- Cut out the 5 shapes provided at the bottom and color them in.
- Glue one magnet to each of the 5 shapes.
- Tie the string to the end of your stick. The string must be at least 2 feet long.
- Glue or tie a magnet to the end of the string to complete the fishing pole.

- Put all of the fish and all of the shapes in a pile on the floor with the side that has the magnet on it face up.
- Use your fishing pole to pick up an item from the pile.
- If you pick up a fish:
- Estimate the angle of the fish’s mouth.
- Measure the actual angle of the fish’s mouth.
- Write down this angle.
- Throw the fish back into the pile, magnet up.

- If you pick up a quadrilateral:
- Name it.
- State at least two properties it has.
- Do not put it back into the pile. Place it to the side.

- The game ends when one person gets ONE of the following:
- Two angles that are supplementary (do not need to be fished out consecutively)
- Two angles that are complementary (do not need to be fished out consecutively)
- Three quadrilaterals that have at least two common properties.

- When the game is over hold on to all the shapes you fished out. Divide up the quadrilaterals left in the pile among the players who fished out the least amount of quadrilaterals.

Examine your quadrilaterals and use them to answer the following questions.

- What do all of your quadrilaterals have in common? List as many commonalities as you can.
- What makes all of your quadrilaterals different? List some of the ways in which they differ.
- Find the interior angles for each shape. Do not use your protractor to measure all the angles. Use your knowledge about complementary and supplementary angles as well as properties of quadrilaterals to determine the angles. You are allowed to measure at most 2 angles in each shape.
- Draw all the diagonals in on each one of your quadrilaterals.
- Measure the interior angles formed by drawing in the diagonals. What do you notice? Compare with a friend! Did they notice anything different than you did?
- Identify each of the triangles created when the diagonals were drawn as isosceles, scalene, or right.
- What do the interior angles of each of the shapes add up to?

- Think of two characteristics of quadrilaterals. Use these characteristics to sort the shapes you have. How did you do it?
- Compare with a friend! What characteristics did they use to sort their shapes? Did they use different ones from you?