NCTM Dynamic Angle Project

Erell Germia, Apr 29, 2024

This module includes interactive tools for elementary students to explore and make mathematical meanings about dynamic angles. Dynamic angles integrates multiple natures of mathematics of angles such as its qualitative nature (an angle as a union of two rays), quantitative nature (an angle with measurable attribute illustrated by a wedge), and multiplicative nature (an angle as an iterative amount of rotation).

Table of Contents

  1. Exploration of Angles
    1. Angles Everywhere
    2. Explore 1: Angles in Shapes
    3. Explore 2: Creating Angles
    4. Explore 3: Changing Angles
    5. Explore 4: A Different Angle?
    6. Imagine: Double, Triple, Half of an Angle
  2. Imagining Angles
    1. Imagine: How Many Angles Are There?
    2. Imagine: Angles in a Whole Circle
    3. Imagine: Splitting a Circle
    4. Imagine: The Biggest Angle
    5. Imagine: The Fish Angle
    6. Imagine: Ferriswheel
    7. Imagine: Tower Bridge
    8. Imagine: Windshield wipers
    9. Imagine: Seesaw
    10. Imagine: Angles Fan
    11. Imagine: Angle Detective
  3. Comparing Angles
    1. Multiplicative 2
    2. Multiplicative 3
    3. Multiplicative 4
    4. Imagine: Ferriswheel
  4. Measuring Angles
    1. Numeric 4 (make your angle)
    2. Numeric 5 (make your angle)
    3. Numeric 6 (make your angle)
    4. Numeric 7 (How is this model different?)
    5. Numeric 8 (Make your angle)

1.

Exploration of Angles

  • 1. Angles Everywhere
  • 2. Explore 1: Angles in Shapes
  • 3. Explore 2: Creating Angles
  • 4. Explore 3: Changing Angles
  • 5. Explore 4: A Different Angle?
  • 6. Imagine: Double, Triple, Half of an Angle

1.1.

Angles Everywhere

Search and point at the angles that you find on the objects.
– Erell Germia

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Imagining Angles

  • 1. Imagine: How Many Angles Are There?
  • 2. Imagine: Angles in a Whole Circle
  • 3. Imagine: Splitting a Circle
  • 4. Imagine: The Biggest Angle
  • 5. Imagine: The Fish Angle
  • 6. Imagine: Ferriswheel
  • 7. Imagine: Tower Bridge
  • 8. Imagine: Windshield wipers
  • 9. Imagine: Seesaw
  • 10. Imagine: Angles Fan
  • 11. Imagine: Angle Detective

2.1.

Imagine: How Many Angles Are There?

[list=1][*]Drag the blue ray. [/*][*]What are you creating?[/*][*]How many angles are there?[/*][*]Can you count them?[/*][/list]
– Erell Germia

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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3.

Comparing Angles

  • 1. Multiplicative 2
  • 2. Multiplicative 3
  • 3. Multiplicative 4
  • 4. Imagine: Ferriswheel

3.1.

Multiplicative 2

Compare the openness of the blue angle and the red angle.
– Erell Germia

3.2.

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3.3.

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3.4.

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4.

Measuring Angles

  • 1. Numeric 4 (make your angle)
  • 2. Numeric 5 (make your angle)
  • 3. Numeric 6 (make your angle)
  • 4. Numeric 7 (How is this model different?)
  • 5. Numeric 8 (Make your angle)

4.1.

Numeric 4 (make your angle)

[list=1][*]Create an angle that you can measure.[/*][*]What is the measure of the angle you made?[/*][/list]
– Erell Germia

4.2.

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4.3.

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4.4.

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4.5.

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