Lesson plan of Algorithms and Problems: Medium

Objectives (5 - 7 minutes)

1. Understand the concept of algorithms and their application in problem solving: Students should be able to define and understand what algorithms are, as well as recognize their importance in solving mathematical problems. This includes being able to identify algorithms in everyday actions and problem-solving situations.

2. Develop problem-solving skills using algorithms: Students should be able to apply the concepts of algorithms to solve mathematical problems of medium difficulty. This includes the ability to identify the problem, break it down into smaller steps, and then create and execute an algorithm to solve it.

3. Promote logical and analytical thinking: Through the use of algorithms to solve mathematical problems, students will be encouraged to develop and refine their logical and analytical thinking skills. This includes the ability to analyze a problem, identify patterns, and apply effective strategies to solve it.

Secondary Objectives:

• Encourage group collaboration: During the hands-on activities, students should be encouraged to work in groups, fostering collaboration and the development of social skills.
• Nurture curiosity and interest in mathematics: Through hands-on and interactive activities, students should be encouraged to develop a positive attitude towards mathematics, seeing it as a useful and engaging tool for solving everyday problems.

Introduction (10 - 15 minutes)

1. Review of prior concepts: The teacher begins the lesson by reviewing the basic concepts of algorithms and their application in problem solving. This can be done through a quick oral or written review, asking students to share what they recall about the topic. The teacher can then clarify any misconceptions or questions students may have before proceeding with the new material.

2. Problem situation 1: "The Robot's Journey": The teacher describes a situation in which a robot needs to navigate a maze to reach a goal. However, the robot can only move forward or backward and can only turn in one direction. Students are challenged to think about how they could create an algorithm to guide the robot to the goal, taking into account the movement restrictions.

3. Problem situation 2: "The Memory Game": The teacher introduces a second problem, this time involving a memory game. Students are challenged to create an algorithm that can "memorize" the location of pairs of cards and then "recall" that location to match the pairs. The teacher can use actual playing cards to make the problem more concrete.

4. Contextualization: The teacher explains that these are examples of problems that can be solved using algorithms. He/she emphasizes that algorithms are a powerful tool for problem solving in many fields, including mathematics, computer science, and engineering. The teacher can share examples of how algorithms are used in the real world, such as in GPS navigation, classifying emails as spam or non-spam, and weather forecasting.

5. Grabbing students' attention: To capture students' attention and pique their interest in the topic, the teacher can share some fun facts about algorithms. For example, he/she could mention that the term "algorithm" comes from the name of the Persian mathematician Al-Khwarizmi, who lived in the 9th century. Or, he/she could share the story of the "Chinese Postman Problem", a famous mathematical problem that involves creating an algorithm to find the shortest route for a postman who needs to deliver letters to every house on a street, even if the street is a closed loop.

By the end of the Introduction, students should have a clear understanding of what algorithms are, how they can be used to solve problems, and why they are a valuable and interesting tool.

Development (20 - 25 minutes)

1. Activity 1: "Solving the Maze": The teacher divides the class into groups of 4-5 students. Each group receives a copy of the maze and a "robot" (a small object, such as a coin, that can be moved around the maze). The challenge is to create an algorithm that will allow the robot to navigate the maze back to the starting point. The algorithm should be written step-by-step and should take into account the robot's movement restrictions. Students are encouraged to test their algorithm on the maze and make adjustments as needed. At the end of the activity, each group should present their algorithm to the class and explain how it works.

   • Steps for the activity:
     1. Divide the class into groups.
     2. Distribute copies of the maze and "robots" to each group.
     3. Explain the challenge and rules of the activity.
     4. Allow students to work on their algorithms.
     5. Encourage students to test their algorithms on the maze.
     6. Have each group present their algorithm to the class.

2. Activity 2: "The Memory Game": The teacher continues with the "Memory Game" activity, but this time students should work individually. Each student receives a set of playing cards and the challenge is to create an algorithm that can "memorize" the location of pairs of cards and then "recall" that location to match the pairs. The algorithm should be written step-by-step and should take into account the structure of the game (i.e., the number of cards and how they are arranged). Students are encouraged to test their algorithm with a partner and make adjustments as needed. At the end of the activity, students should have an effective algorithm for the "Memory Game".

   • Steps for the activity:
     1. Distribute playing cards to each student.
     2. Explain the challenge and rules of the activity.
     3. Allow students to work on their algorithms.
     4. Encourage students to test their algorithms with a partner.
     5. Have students share their algorithms with the class.

3. Discussion and Reflection: After the completion of the activities, the teacher should lead a class discussion to reflect on what was learned. He/she can ask questions such as "What was the most challenging part of creating an algorithm?" or "How could you apply these concepts and skills in other contexts?" The teacher should also highlight the importance of teamwork, effective communication, and critical thinking when creating and testing algorithms.

   • Steps for the discussion:
     1. Lead a class discussion.
     2. Ask questions to encourage student reflection.
     3. Highlight the importance of teamwork, effective communication, and critical thinking when creating and testing algorithms.
     4. Conclude the lesson by reinforcing the main points learned and how they apply to the real world.

Debrief (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should bring the whole class together and facilitate a group discussion. Each group should briefly share the algorithm they created for solving the maze and the memory game. Students should be encouraged to ask questions and provide feedback on the algorithms of other groups.

   • Steps for the group discussion:
     1. Bring the whole class together.
     2. Have each group briefly share their algorithm.
     3. Encourage students to ask questions and provide feedback on the algorithms of other groups.
     4. Facilitate the discussion, ensuring that all students have an opportunity to speak.

2. Connecting to Theory (2 - 3 minutes): The teacher should then connect the hands-on activities to the theory presented in the lesson. He/she can do this by emphasizing how the algorithms created by the students reflect the theoretical concepts of algorithms and how these can be applied to problem solving. For example, the teacher could point out how the steps of the algorithm correspond to the concepts of sequence, selection, and repetition.

   • Steps for connecting to theory:
     1. Briefly recap the theoretical concepts of algorithms.
     2. Connect the algorithms created by the students to these concepts.
     3. Explain how the algorithms can be applied to problem solving.

3. Individual Reflection (3 - 4 minutes): Finally, the teacher should have the students reflect individually on what they learned in the lesson. He/she can do this by asking questions such as "What was the most important concept you learned today?" and "What questions do you still have?" Students should have a minute to think about their answers and then they will be invited to share their reflections with the class.

   • Steps for individual reflection:
     1. Have students reflect individually on what they learned.
     2. Ask questions to guide student reflection.
     3. Give students a minute to think about their answers.
     4. Have students share their reflections with the class.

4. Conclusion and Closure: The teacher should conclude the lesson by reinforcing the main points learned and how they apply to the real world. He/she should also encourage students to continue exploring the topic on their own and to bring any questions or concerns to the next class.

   • Steps for Conclusion:
     1. Recap the main points learned in the lesson.
     2. Encourage students to continue exploring the topic on their own.
     3. Close the lesson, thanking students for their participation and reinforcing the importance of continued learning.

Conclusion (5 - 7 minutes)

1. Summary and Recap (2 - 3 minutes): The teacher should begin the Conclusion of the lesson by summarizing and recapping the main points covered during the lesson. This includes the definition of algorithms, their importance in problem solving, and how they were applied in the hands-on activities of the maze and the memory game. The teacher can highlight the most creative or effective algorithms created by students during the activities to reinforce the understanding of the concept.

   • Steps for summary and recap:
     1. Recall the definition of algorithms and their importance in problem solving.
     2. Recap the hands-on activities of the maze and the memory game and how the algorithms were applied.
     3. Highlight the most creative or effective algorithms created by students.

2. Theory-Practice Connection (1 - 2 minutes): The teacher should explain how the lesson connected the theory of algorithms with the practice of problem solving. He/she can, for example, mention how the hands-on activities allowed students to apply the theoretical concepts of algorithms in a concrete and meaningful way. The teacher should emphasize that the ability to create and execute algorithms is a valuable skill that can be applied in many aspects of everyday life and in various careers.

   • Steps for theory-practice connection:
     1. Explain how the lesson connected the theory of algorithms with the practice of problem solving.
     2. Mention how the hands-on activities allowed students to apply the theoretical concepts in a concrete and meaningful way.
     3. Emphasize the importance of algorithms and their application in various careers.

3. Supplemental Materials (1 - 2 minutes): The teacher should suggest some supplemental materials for students who want to further explore algorithms and problem solving. This could include math and computer science books, educational websites, logic games and puzzles, and free online courses. The teacher should encourage students to explore these resources on their own and to bring any questions or concerns to the next class.

   • Steps for suggesting supplemental materials:
     1. Suggest some books, websites, games, and online courses that cover algorithms and problem solving.
     2. Encourage students to explore these resources on their own.
     3. Remind students to bring any questions or concerns to the next class.

4. Relevance of the Topic (1 minute): Finally, the teacher should conclude the lesson by reinforcing the relevance of the topic presented. He/she can do this by mentioning examples of how algorithms are used in everyday life, such as in GPS navigation, classifying emails, and weather forecasting. The teacher should emphasize that, although the lesson focused on mathematical algorithms, the skill of creating and executing algorithms is a valuable tool in many aspects of life and work.

   • Steps for relevance of the topic:
     1. Relate the concepts of algorithms to real-life examples.
     2. Emphasize that the skill of creating and executing algorithms is a valuable tool in many aspects of life and work.
     3. Close the lesson, reinforcing the importance of continued learning and the application of the concepts learned.