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. Explore 1
    2. Explore 2
    3. Explore New 3
    4. Explore New 4
    5. Explore New 5
    6. Explore New 6
    7. Explore New 7
    8. Explore New 8
  2. Imagining Angles
    1. The Tower Bridge
    2. Windshield wipers
    3. Bike
    4. Seesaw
    5. Fan
  3. Comparing Angles
    1. Multiplicative 1.1
    2. Multiplicative 1.2
    3. Multiplicative 2
    4. Multiplicative 3
    5. Multiplicative 4
    6. Multiplicative 5
  4. Measuring Angles
    1. Numeric 1 (unlimited)
    2. Numeric 2 (360 degrees)
    3. Numeric 3 (split a circle)
    4. Numeric 4 (make your angle)
    5. Numeric 5 (make your angle)
    6. Numeric 6 (make your angle)
    7. Numeric 7 (How is this model different?)
    8. Numeric 8 (Make your angle)
    9. Numeric 9

1.

Exploration of Angles

  • 1. Explore 1
  • 2. Explore 2
  • 3. Explore New 3
  • 4. Explore New 4
  • 5. Explore New 5
  • 6. Explore New 6
  • 7. Explore New 7
  • 8. Explore New 8

1.1.

Explore 1

[list=1][*]What is an angle?[/*][*]Describe the shapes. [/*][*]Where are the angles in these shapes? Please trace them.[/*][/list]
– Erell Germia

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

2.

Imagining Angles

  • 1. The Tower Bridge
  • 2. Windshield wipers
  • 3. Bike
  • 4. Seesaw
  • 5. Fan

2.1.

The Tower Bridge

1. Help the cruise ship cross the tower bridge. Drag the slider to open the leaves of the bridge. [br]2. How can you make the cruise ship cross the bridge?[br]3. How much turn do you have to make to lift the leaves of the bridge? Make an estimate first and check your answer.[br]
– Erell Germia

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Comparing Angles

  • 1. Multiplicative 1.1
  • 2. Multiplicative 1.2
  • 3. Multiplicative 2
  • 4. Multiplicative 3
  • 5. Multiplicative 4
  • 6. Multiplicative 5

3.1.

Multiplicative 1.1

Explore the Ferris wheel.
– Erell Germia

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

4.

Measuring Angles

  • 1. Numeric 1 (unlimited)
  • 2. Numeric 2 (360 degrees)
  • 3. Numeric 3 (split a circle)
  • 4. Numeric 4 (make your angle)
  • 5. Numeric 5 (make your angle)
  • 6. Numeric 6 (make your angle)
  • 7. Numeric 7 (How is this model different?)
  • 8. Numeric 8 (Make your angle)
  • 9. Numeric 9

4.1.

Numeric 1 (unlimited)

[list=1][*]Drag the blue ray. [/*][*]What are you creating?[/*][*]How are you creating it?[/*][*]How many of these are there?[/*][/list]
– Erell Germia

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

4.8.

–

4.9.

–

Information