# Learn functions and discuss how equations and inequations can be solved using GeoGebra representation

- Algebra, Functions

- ISCED 2 = Upper Secondary Education

- English

## Introduction

Solving inequations, especially non-linear ones, can result in a long and difficult process. Using GeoGebra pupils can represent non-linear functions and they can easily interpret the regions where the functions are positive or negative and consequently, they can solve the inequation.

## Learning Outcomes

At the end of the lesson, the learner will be able to:

- Understand the concept of equations and inequalities.
- Learn to represent equations and inequalities using GeoGebra.
- Solve linear equations and inequalities using GeoGebra.
- Solve quadratic equations using GeoGebra.
- Analyse and interpret the solutions of equations and inequalities in the context of real-world problems.
- Use GeoGebra to graphically represent and solve systems of equations.

## How Does It Work

Pupils start drawing non-linear functions in GeoGebra and they can discuss and find out how they change. Then the teacher gives an activity in which the pupils have to represent parables and they have to find a connection between the form and:

- The term of highest degree is positive or negative.
- Changing the independent term.

Teacher can help pupils asking:

- Do the branches of the parable go up or down? Is there any
- relation to the changes in the expression of the function?
- Do you notice any patterns?
- Can you find a general rule?

Next step is solving inequations using the representation of the parable and analysing where it is positive or negative.

Finally, they discuss the solutions obtained within the group and with other groups

## Why Is It A Good Practice?

Using GeoGebra to graphically represent and solve systems of equations offers several benefits and is considered a good practice for learning. Here are some reasons why:

Visual Representation: GeoGebra provides a visual representation of equations and their solutions through graphs. This visual representation helps students understand the relationship between equations, variables, and solutions more intuitively.

Geometric Interpretation: GeoGebra allows students to interpret the solutions of a system of equations geometrically. The students can relate the solutions to real-world scenarios or geometric situations, making the learning more meaningful and applicable.

## Assessment

- Provide each student with a computer or tablet with access to the GeoGebra online platform.
- Share a system of equations with the students:
- Ask students to open GeoGebra and graphically represent the system of equations on the coordinate plane.
- Once students have found the solution, ask them to verify it algebraically by solving the system of equations using traditional methods.
- Encourage students to write a brief explanation of how they used GeoGebra to solve the system and how they verified the solution algebraically.
- Collect the GeoGebra files or screenshots from each student for assessment purposes.
- Evaluate students based on the following criteria:

- Correct representation of the graphs of the two equations on GeoGebra.
- Accurate determination of the point of intersection and correct interpretation of the solution.
- Correct algebraic verification of the solution using traditional methods.
- Clarity and coherence in the explanation of the solution process.

## Inclusion

For students who finish early or need an additional challenge, you can provide a more complex system of equations and ask them to solve it using GeoGebra. Alternatively, you can introduce a system of three equations and ask them to find the points of intersection of the three graphs.

For students with learning disabilities provide:

- Scaffolded Practice: Offer guided practice activities with step-by-step instructions and gradually release responsibility to the students as they gain confidence. Break complex tasks into smaller, manageable parts, and provide support as needed.
- Collaborative Learning: Encourage peer collaboration and group work. Pair students with learning disabilities with classmates who can provide support, guidance, or explanations when needed. Promote a positive and inclusive classroom environment where students feel comfortable asking for help.