Circles

Edward Knote, Melissa Gouthro, Jun 22, 2016

circle investigations

Table of Contents

  1. 6th grade areaof Polygons
    1. Area of a Rectangle
    2. Area Of A Triangle
    3. Area of A Parallelogram
    4. Area of a Trapezoid
  2. Circle Area and Circumference
    1. Circumference and Pi
    2. Archimedes Doubling Method (Square)
    3. Archimedes Doubling Method (triangle)
    4. Circle Area Dissection
    5. Area of a Circle
  3. Composite Shapes
    1. Area of a composite shape
    2. Circle in a Square
  4. Extra Stuff
    1. Rolling Quarter Puzzle

1.

6th grade areaof Polygons

  • 1. Area of a Rectangle
  • 2. Area Of A Triangle
  • 3. Area of A Parallelogram
  • 4. Area of a Trapezoid

1.1.

Area of a Rectangle

In this worksheet you will investigate the area of a rectangle.
Investigation:[br]1) Move the sliders Base and Height and describe what happens to the image.[br] 2) What relationship does the number of squares have with the area of the rectangle?[br] 3) Is there a way to find the number of square with out counting them?[br] 4) What conjecture can you make about the formula for area of a rectangle?
– Edward Knote

1.2.

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1.3.

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1.4.

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2.

Circle Area and Circumference

  • 1. Circumference and Pi
  • 2. Archimedes Doubling Method (Square)
  • 3. Archimedes Doubling Method (triangle)
  • 4. Circle Area Dissection
  • 5. Area of a Circle

2.1.

Circumference and Pi

– Edward Knote

2.2.

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2.3.

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2.4.

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2.5.

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3.

Composite Shapes

  • 1. Area of a composite shape
  • 2. Circle in a Square

3.1.

Area of a composite shape

The image below is of a local basketball teams court. The basketball key is in red and its perimeter is in blue. Assuming the units are in yards answer the questions below.
1) Describe any observations you make when moving the slider above the key.[br]2) How many square feet of paint were used to paint the red area (the key)?[br]2) How many inches of tape are needed to wrap around the key (the blue)?
– Edward Knote

3.2.

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4.

Extra Stuff

  • 1. Rolling Quarter Puzzle

4.1.

Rolling Quarter Puzzle

As the quarter on the right rolls completely around the quarter on the left one time, how many times will the rolling quarter rotate fully around its own center during its journey? Visualize the quarter rolling without moving the slider and make a conjecture. Use two real quarters to test your conjecture and then use the model below to explain your observations.
Rolling Quarter Puzzle
– Duke

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