GeoGebra - CAS Workshop: Part 1

Mathías Tejera, 15 mai 2025

Table des matières

  1. Before going into CAS: A sample of GeoGebra
    1. Exploring limits
  2. First Explorations
    1. Objectives
    2. Try It – Expanding and Factoring
    3. Solve Linear Equations
    4. Solve Quadratic Equations
    5. More Links Between Algebra and Graphs
    6. Pattern Generalization
    7. First Reflections
  3. Rational Expressions in CAS
    1. Objectives
    2. Simplifications
    3. Multiply and Divide Rational Expressions
    4. Add and Subtract Rational Expressions
    5. What Gets Lost? Exploring Rational Expressions and Domain
    6. A task with CAS
    7. Reflection
  4. Inequalities and Expressions with GeoGebra
    1. Objectives
    2. Mastering CAS Workflows
    3. Linear Inequalities & Properties
    4. Solve a compound inequality
    5. Explore Roots and Sign
    6. Rational Inequalities
    7. Exploration
    8. Teacher Reflection
  5. Trigonometric Explorations
    1. Objectives
    2. Identity Playground
    3. Expression Investigation
    4. Pattern Discovery & Generalization
    5. Open Task
    6. Considering our work today

1.

Before going into CAS: A sample of GeoGebra

  • 1. Exploring limits

1.1.

Exploring limits

Limit of a function: exploration
– Mathías Tejera, Fabián Vitabar

2.

First Explorations

[b]Welcome![/b] In this guided exploration, you’ll get to know the CAS View in GeoGebra and reflect on how it might support your students’ algebraic thinking.

  • 1. Objectives
  • 2. Try It – Expanding and Factoring
  • 3. Solve Linear Equations
  • 4. Solve Quadratic Equations
  • 5. More Links Between Algebra and Graphs
  • 6. Pattern Generalization
  • 7. First Reflections

2.1.

Objectives

[list][*][b]Explore how CAS handles symbolic expressions.[/b][/*][*][b]Solve equations with CAS.[/b][/*][*][b]Link algebraic and graphical representations.[/b][/*][*][b]Reflect on how this tool supports teaching.[/b][/*][/list]
– Mathías Tejera

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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3.

Rational Expressions in CAS

Rational Expressions: Simplify, Operate, and Reason Algebra Week 4 – R7: Algebraic Operations on Rational Expressions

  • 1. Objectives
  • 2. Simplifications
  • 3. Multiply and Divide Rational Expressions
  • 4. Add and Subtract Rational Expressions
  • 5. What Gets Lost? Exploring Rational Expressions and Domain
  • 6. A task with CAS
  • 7. Reflection

3.1.

Objectives

[list][*][b][/b][b]Use GeoGebra CAS to simplify, add, subtract, multiply, and divide rational expressions.[/b][br][/*][*][b]Explore and verify algebraic equivalence.[/b][br][/*][*][b]Reflect on domain restrictions and the meaning of simplification.[/b][br][/*][*][b]Design classroom questions that use CAS to foster conceptual reasoning.[/b][br][/*][/list]
– Mathías Tejera

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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4.

Inequalities and Expressions with GeoGebra

  • 1. Objectives
  • 2. Mastering CAS Workflows
  • 3. Linear Inequalities & Properties
  • 4. Solve a compound inequality
  • 5. Explore Roots and Sign
  • 6. Rational Inequalities
  • 7. Exploration
  • 8. Teacher Reflection

4.1.

Objectives

[list][*]Use dynamic and static line referencing in CAS ($n and #n)[br][/*][*]Use assignments (:=) and symbolic equation manipulation[br][/*][*]Solve and visualize [b]quadratic, polynomial[/b], and [b]rational inequalities[/b][br][/*][*]Connect [b]algebraic results to graphical representations[/b][br][/*][*]Reflect on how to scaffold this in the classroom[/*][/list]
– Mathías Tejera

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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5.

Trigonometric Explorations

  • 1. Objectives
  • 2. Identity Playground
  • 3. Expression Investigation
  • 4. Pattern Discovery & Generalization
  • 5. Open Task
  • 6. Considering our work today

5.1.

Objectives

[list][*][b]Investigate[/b] relationships between trigonometric expressions,[/*][*][b]Choose[/b] and apply appropriate identities,[/*][*][b]Compare[/b] multiple equivalent forms,[/*][*][b]Reflect[/b] on strategies for open-ended student exploration.[/*][/list]
– Mathías Tejera

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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Information