# Linear Programming for Gifted Students

- Algebra

- ISCED 1 = Lower Secondary Education

- English

## Introduction

The purpose of this learning plan is to help pupils understand some of the differences between linear algebra and linear programming, using graphs of first-degree functions and solving inequalities. Then they practice by considering exercises, including ones with real life applications.

This activity is most adequate for students between 12 and 14 years old. In most of the countries this age range corresponds to ISCED 2 = Lower Secondary Education, but in others can also include the first year of ISCED 3 = Upper Secondary Education.

## Learning Outcomes

This Learning plan provides activities that lead/ enable/ support a pupil (mainly a gifted one)

- To identify the best connections between the first-degree function and the graphical representation of the function
- To identify the real solution to a minimum or maximum problem
- To identify the graphical solution of a minimum or maximum problem.
- To calculate the intersections of the graph with the coordinate axes. To calculate the representation in the axis system (xOy) of the graph of the linear function.
- To solve real world problems.
- To state and demonstrate minimum and maximum problems with the help of linear programming notions
- To develop skills for problem solving.
- To identify/ develop/ create applications of the related concepts and processes in the real world.
- To develop critical thinking skills.
- To adopt various strategies for problem solving.
- To develop motives and positive affective tendencies for mathematics.

## How Does It Work

The learning plan suggests that pupils use the Internet to find similar or more advanced real-world problems and attempt to solve them using linear programming.

This emphasis on real world problems adds value to the organisation of the INNOMATH project for the Mathematics Meets Industry Day, which reflects the expected impact of this activity, as well as for the other activities proposed in the project

The learning plans provides ideas for activities that suggest to the pupils:

- To explore the lines of connection between the field of definition of the function and the graphic representation.
- To look for the shortest connections.
- To specify what conditions are expected.
- To clarify whether the graph provides solutions for determining the required minimum or maximum (optimized) quantities.
- To graphically represent the conditions in the hypothesis of the problem.
- To use their newly acquired knowledge to determine the maximum or minimum value of the function.
- To explore how to determine the requirements of the problem with the help of a graph

## Why Is It A Good Practice?

It encourages critical thinking, creativity and communication, and the content is connected to the real world.

## Assessment

The learning plan suggests that the students, using the Internet, find similar or more advanced problems in the real world and try to solve them using linear programming.

This emphasis on real world problems provides an added value which is reflected in the organization, through the INNOMATH project of the activity Mathematics meets Industry day which reflects the expected impact of this activity, in particular, as well as for the other activities that are suggested in the project.

## Inclusion

The approach is addressed to the needs of gifted pupils.

When including students with learning disabilities in linear programming activities, it’s important to provide appropriate adaptations and accommodations to ensure their full participation and learning. Some ideas are:

**Clear Instructions:** Provide clear and concise instructions for each activity, using simple language and visual aids if necessary. Break down complex problems into smaller, more manageable steps to facilitate understanding.

**Visual Representations:** Utilize visual aids, such as charts, graphs, or diagrams, to present linear programming problems. Visual representations can help students with learning disabilities better understand the problem and make connections between the mathematical concepts and real-life situations.

**Collaborative Learning:** Encourage collaborative learning opportunities where students with learning disabilities can work in pairs or small groups. This allows them to learn from their peers, engage in discussions, and receive support from others while practicing linear programming concepts.

**Flexible Assessment Methods:** Consider alternative assessment methods that align with the needs and abilities of students with learning disabilities. This may include verbal assessments, project-based assessments, or using assistive technology tools during assessments.