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Sigma Notation Visualizer

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About This MicroSim

This interactive visualization helps students understand sigma notation (summation notation) by:

  • Displaying the sigma notation with adjustable parameters
  • Expanding sums term by term through step-through controls
  • Showing visual blocks representing each term value
  • Calculating running totals as terms are added

Iframe Code

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<iframe src="https://dmccreary.github.io/calculus/sims/sigma-notation-visualizer/main.html" height="482px" scrolling="no" style="width: 100%;"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Interpret sigma notation and identify its components (upper limit, lower limit, index, general term)
  2. Expand a summation into its individual terms
  3. Calculate the value of finite sums
  4. Connect the compact notation to the expanded form

Activities

  1. Exploration (5 min): Have students adjust the upper limit and observe how the sum grows
  2. Pattern Recognition (5 min): Switch between different formula types and predict the sum before stepping through
  3. Practice (10 min): Given sigma notation on the board, use the MicroSim to verify calculations

Assessment

Ask students to: - Write the expansion of \(\sum_{i=1}^{4} i^2\) - Calculate \(\sum_{k=0}^{3} 2^k\) without the MicroSim, then verify

References