12th Grade Modelling With Differential Equations Lesson Plan (Math)

Topic: Modelling with differential equations

Subtopic: Differential equations are used to model and investigate phenomena in physics, chemistry and biology. In this module, we will learn how to model and solve problems involving differential equations using the method of separation of variables. Material required: A basic understanding of calculus and a calculator will be required for this module. Methodology outcomes: At the end of this module, the learner will be able to: -Solve problems involving differential equations using the method of separation of variables -Interpret and use the solutions obtained in practice.

• Apply the method of separation of variables to model and solve problems in physics, chemistry and biology.

Differentiation-based activity

 

Learners will be given a problem involving a differential equation and be required to solve it using the method of differentia

on. After submitting their solutions, mentors will provide feedback on the correctness and effectiveness of their solutions.

21st century skill-based activity

 

Learners will be given a problem involving a differential equation and be required to solve it using the method of differentia

on. After submitting their solutions, mentors will provide feedback on the correctness and effectiveness of their solutions. They will also be encouraged to explore and experiment with different approaches and strategies to find the solution.Probing questions based on blooms taxonomy

 

Understand: What is a differential equation and what is it used for?

Mentor will explain the concept of differential equations and demonstrate how they are used to model real-world phenomena.

Resear

h: What are the different methods of solving differential equations?

Mentor will introduce the various methods of solving differential equations and demonstrate how to use them.

Resear

h: What are the limitations of differential equations?

Mentor will discuss the limitations of differential equations, such as the occurrence of singularities and non-linearity.

Differentiation-based activity

 

Mentor will give the learners a problem involving a differential equation and ask them to solve it using one of the methods introduced earlier. The learners will work in pairs or small groups to solve the problem and present their solutions to the mentor. The mentor will provide feedback on their solutions and may ask them to justify why a certain step is taken.

Hots questions, probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which is a way of categorising the learners' responses.

Differentiation-based activity

The learners will be given a problem-solving task that involves solving a differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods. These multiple choice questions will be based on the solution methods taught in class. The learners will work individually or in small groups to solve the problem-solving task and answer the multiple choice questions. The results will be collected and the mentor will provide feedback on the answers. The mentor will also ask the learners to justify their answers if needed.

Differentiation-based activity

The learners will be given a problem-solving task that involves solving a differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods. These multiple choice questions will be based on the solution methods taught in class. The learners will work individually or in small groups to solve the problem-solving task and answer the multiple choice questions. The results will be collected and the mentor will provide feedback on the answers. The mentor will also ask the learners to justify their answers if needed.

Differentiation-based activity

The learners will be given a problem-solving task that involves solving a differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods. These multiple choice questions will be based on the solution methods taught in class. The learners will work individually or in small groups to solve the problem-solving task and answer the multiple choice questions. The results will be collected and the mentor will provide feedback on the answers. The mentor will also ask the learners to justify their answers if needed.

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Hots questions and probing questions based on blooms taxonomy and sustainability

 

Hots questions are used to check the understanding of the learners at the end of each topic. Probing questions are used to check the understanding of the learners at a deeper level. Both hots questions and probing questions are based on blooms taxonomy, which

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods. These multiple choice questions will be based on the solution methods taught in class. The learners will work individually or in small groups to solve the problem-solving task and answer the multiple choice questions. The results will be collected and the mentor will provide feedback on the answers. The mentor will also ask the learners to justify their answers if needed.

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given differential equation and asked to solve for the unknown variable(s). They will be given a set of multiple choice questions testing their understanding of the solution methods

Integration-based activity

The learners will be given a problem-solving task that involves solving an ordinary differential equation in one or more independent variables. They will be given a set of basic initial conditions for a given