Lesson plan of Sequences: Increasing and Decreasing

Objectives (5 – 7 minutes)

1. To introduce the concept of increasing and decreasing sequences of numbers to the students. This will be done through clear and simple explanations, along with the use of practical, real-world examples that the students can relate to.
2. To develop students’ skills in identifying and completing increasing and decreasing sequences. They will be challenged to complete a variety of sequences given by the teacher, using their mathematical logic and reasoning.
3. To foster students’ ability to create their own increasing and decreasing sequences. After understanding the concept and practicing with provided examples, they will be encouraged to create their own sequences, thus stimulating their logical thinking and creativity.

Introduction (10 – 12 minutes)

1. Review of Prior Knowledge: The teacher will begin the lesson by reviewing the concept of numbers and number sequences with the students. They will be encouraged to recite the number sequence from 0 to 100, for example, to refresh this skill.
2. Real-World Situations: The teacher will present two real-world situations that require the use of increasing and decreasing sequences. The first situation can be about the growth of a plant over time, and the second about the number of students in a classroom, which can vary from day to day.
3. Contextualization: The teacher will explain that in mathematics, as in life, many things can follow a predictable sequence. For example, when counting from 1 to 10, that is an increasing sequence. On the other hand, If counting from 10 to 1, that is a decreasing sequence. The teacher may also bring examples from everyday events, such as the passing of hours on a clock (an increasing sequence) or the countdown to a special event (a decreasing sequence).
4. Capturing Students’ Attention: To make the topic more interesting, the teacher can present two sequences that seem confusing at first glance. For example, the sequence 2, 4, 6, 8, 10, ..., may seem like an increasing sequence, but it is actually a sequence of even numbers. On the other hand, the sequence 20, 15, 10, 5, 0, ..., may seem like a decreasing sequence, but it is actually a sequence of multiples of 5. These examples can pique students’ curiosity and encourage them to learn more about sequences.

Development (20 – 25 minutes)

1. Increasing and Decreasing Number Sequence Game: The teacher will facilitate a game where students have to create increasing or decreasing number sequences. Each student will have a turn to create a sequence. The game will continue until all students have had a chance or until the time is up. The teacher can use number cards to help students visualize the sequences. The aim of the game is to have students practice creating increasing and decreasing number sequences in a fun and engaging way.
2. Sequence Completion Activity: The teacher will distribute a worksheet with several incomplete sequences to each student. The students will have to analyze the sequences and fill in the missing numbers. The teacher should make sure that the sequences vary in difficulty, so that all students can participate. The sequences can be of even numbers, odd numbers, multiples of 2, 3, or 5, for example. This activity allows students to practice pattern recognition and extending number sequences.
3. Sequence Surprise Box Game: The teacher will prepare a box with several cards inside beforehand. Each card will have a number sequence on it. The teacher will pick a card from the box and read the sequence to the class. The students will then have to guess whether the sequence is increasing or decreasing. To make the game more interactive, students can raise one hand if they think the sequence is increasing and the other hand if they think it is decreasing. The teacher will reveal the answer, and students who guess correctly will earn points for their team. This game will help students practice identifying increasing and decreasing sequences in a playful manner.

The teacher may choose to do one or more of these activities depending on the time available and the students’ level of engagement. The important thing is that they have the opportunity to practice creating and identifying increasing and decreasing sequences in an active and engaging way.

Debrief (8 – 10 minutes)

1. Group Discussion (3 – 4 minutes): The teacher will lead a group discussion with the whole class. Each group or individual student will get a chance to share the sequences they created during the “Increasing and Decreasing Number Sequence” game and explain the pattern they used. The teacher will encourage students to ask questions and give comments, and to provide constructive feedback. This will allow students to learn from one another and reinforce what they have learned in the activity.
2. Connecting to the Theory (2 – 3 minutes): The teacher will reinforce the concepts of increasing and decreasing sequences, connecting them to the practical activities that were done. For example, the teacher may ask: “Remember the sequence that John created? He started with the number 1 and added 3 each time. That is an increasing sequence of odd numbers! Can you think of other examples of increasing or decreasing sequences?”
3. Individual Reflection (3 – 4 minutes): To conclude the lesson, the teacher will ask the students to take a moment to reflect on what they have learned. They will be asked two simple questions:

• Question 1: “Which sequence did you enjoy creating or completing the most today? Why?”
• Question 2: “What have you learned about increasing and decreasing sequences today that you think you can use in the future?” The teacher will give the students a minute to think about their answers, then encourage them to share them with the class if they feel comfortable. This reflection stage gives students an opportunity to internalize what they have learned and to see how mathematics can be applied in real-world situations.

This debriefing stage is essential for consolidating students’ learning and for the teacher to assess the effectiveness of the lesson. The teacher will be able to observe whether the students were able to understand and apply the concept of increasing and decreasing sequences, and whether they were able to engage with the practical activities. Furthermore, the group discussion and individual reflection promote students’ critical thinking, verbal expression, and self-assessment.

Conclusion (5 – 7 minutes)

1. Summary of Content (2 – 3 minutes): The teacher will give a brief summary of the main points covered in the lesson. He or she will reinforce the definition of increasing and decreasing sequences, and remind students of the patterns that can be found in these sequences. Additionally, the teacher will highlight the importance of number sequences in everyday life, such as in counting, calendars, schedules, and so on.
2. Connection between Theory and Practice (1 – 2 minutes): The teacher will explain how the lesson connected mathematical theory with practice. He or she will emphasize that, by playing the “Increasing and Decreasing Number Sequence” game, the students had the opportunity to apply the concepts they had learned in a fun and engaging way. Furthermore, the sequence completion activities and the “Sequence Surprise Box” game allowed students to practice creating and identifying increasing and decreasing sequences.
3. Extension Materials (1 – 2 minutes): The teacher will suggest some extension materials for students who wish to explore the topic further. This could include educational videos, online games, and textbooks. For example, the teacher may recommend using interactive math apps, which offer games and activities related to number sequences.
4. Significance of the Topic (1 minute): Finally, the teacher will highlight the significance of the topic covered for the students’ everyday lives. He or she will explain that the ability to recognize and complete number sequences is useful in a variety of situations, from planning daily tasks to solving more complex math problems. Moreover, the teacher will encourage students to look for sequences in their environment, whether it be counting the steps of a staircase, organizing books on a shelf, or observing the passing of time on a clock, for example.

The conclusion is a crucial part of the lesson plan as it allows students to review and consolidate what they have learned, as well as encouraging them to continue exploring the topic on their own. Furthermore, by emphasizing the relevance of the topic to everyday life, the teacher helps students see the importance of mathematics in their lives.