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Discrete vs Continuous Number Line

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Description

This MicroSim provides an interactive visualization that helps students understand the fundamental difference between discrete and continuous variables. The simulation displays two horizontal number lines stacked vertically:

Discrete Number Line (Top): Labeled "Number of Pets" with a range of 0-10. This line shows only integer values as clickable blue dots. When students click between integers, the marker automatically snaps to the nearest whole number with visual feedback, demonstrating that discrete variables can only take on specific, countable values.

Continuous Number Line (Bottom): Labeled "Height in Inches" with a range of 60-72 inches. This line displays a smooth gradient bar. When students click anywhere on this line, a marker is placed at the exact position, and the precise value (to two decimal places) is displayed, illustrating that continuous variables can take on any value within a range.

The key learning moment occurs when students try to click "between" values on the discrete line and observe the snap behavior, compared to clicking anywhere on the continuous line and seeing exact decimal values.

How to Use

  1. Click on the discrete line (top) to place markers. Notice how clicking between integers snaps to the nearest whole number.

  2. Click on the continuous line (bottom) to place markers. Notice how you can place markers at any position, and the exact decimal value is displayed.

  3. Toggle "Show Examples" to see pre-placed example values on each line.

  4. Click "Reset" to clear all markers and start fresh.

Lesson Plan

Learning Objective

Students will distinguish between discrete and continuous variables by visualizing how values can be plotted on a number line and observing the different behaviors when placing markers.

Bloom's Taxonomy Level

Understand (L2) - Students compare and contrast discrete and continuous variable behavior through direct interaction.

Duration

5-10 minutes for initial exploration; can be extended with discussion activities.

Warm-Up Activity (2 minutes)

Ask students: "If I asked you how many pets you have, could you answer '2.5 pets'? What about your height - could you be 66.5 inches tall?" Let students share their thinking.

Guided Exploration (5 minutes)

  1. Have students click on the discrete line first. Ask them to try clicking exactly between two numbers. What happens?

  2. Have students click on the continuous line. Ask them to try to place a marker at exactly 65.5 inches. Then 65.55 inches. Can they do it?

  3. Discuss: Why does the pet line snap to whole numbers? Why can the height line accept any value?

Discussion Questions

  • What are other examples of discrete variables in your life? (Number of siblings, number of classes, shoe sizes in US system)

  • What are other examples of continuous variables? (Temperature, time, weight, distance)

  • Could a variable that seems discrete sometimes be treated as continuous? (Think about age - we say "16 years old" but really we're 16.347... years old)

Assessment

Have students classify the following as discrete or continuous:

  1. Number of students in a class (discrete)
  2. Amount of water in a glass (continuous)
  3. Number of text messages sent (discrete)
  4. Speed of a car (continuous)
  5. Number of pages in a book (discrete)
  6. Room temperature (continuous)

Extension Activity

Challenge students to think of a variable that could be argued as either discrete or continuous depending on context (e.g., money - discrete at the cent level, but often treated as continuous in economics).

References