Lesson Plan | Active Learning | Counting Principle

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is crucial for directing the focus of students and the teacher toward the specific learning goals of the lesson. By clearly establishing what is expected to be achieved, this section lays the groundwork for subsequent activities, ensuring that both preparation and execution are aligned with the competencies that students need to develop.

Main Objectives:

1. Empower students to solve simple counting problems using the multiplicative principle, applying it in practical and everyday situations.

2. Develop the skill to create tree diagrams and tables to represent and solve combination and counting problems.

Side Objectives:

1. Encourage critical thinking and mathematical logic among students when dealing with combination and grouping situations.

Introduction

Duration: (15 - 20 minutes)

The Introduction serves to engage students and activate the prior knowledge they have acquired at home. By working with problem situations, the teacher stimulates the practical application of the Counting Principle, making learning more dynamic and meaningful. The contextualization demonstrates the relevance of the theme in daily life, increasing students' interest and motivation to learn and apply mathematical content in real situations.

Problem-Based Situations

1. Imagine you have 3 t-shirts (blue, red, and green) and 2 pairs of pants (jeans and black). What are the different combinations of outfits you can create using one t-shirt and one pair of pants?

2. At a birthday party, the organizer has 4 types of cakes (chocolate, strawberry, carrot, and vanilla) and 3 types of soft drinks (cola, lemon, and guarana). He needs to decide how many options of cake and soft drink combinations to offer the guests. How can he do that?

Contextualization

The Counting Principle is not just a mathematical tool, but something we use daily in various situations, such as planning meals, choosing clothes to wear, or determining possibilities in games. For example, when deciding how many pizza flavors and different sizes to order for a party, we are applying the multiplicative principle to calculate all possible combinations. Furthermore, understanding this concept helps us to value organization and logic in everyday tasks.

Development

Duration: (75 - 80 minutes)

The Development stage is designed to put students in practical and challenging situations where they can apply the theoretical knowledge of the Counting Principle in a creative and playful manner. Through the proposed activities, students will reinforce their understanding of combinations and the use of the multiplicative principle, as well as develop teamwork, critical thinking, and problem-solving skills. Each activity is carefully planned to be interactive and engaging, ensuring that learning is meaningful and fun.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Mixing Fair

> Duration: (60 - 70 minutes)

- Objective: Apply the counting principle to solve a practical and playful problem, reinforcing the understanding of the concepts of combinations and multiplication.

- Description: Students will plan a 'Mixing Fair' where they must create juice combinations from different types of fruits and sizes of cups. Each group will receive cards representing fruits and cups of various sizes. They must use the multiplicative principle to calculate how many different juice combinations they can create, considering that each cup must have at least one fruit and all juices must be different.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the cards representing the fruits and cups to each group.

• Guide students to use the multiplicative principle to calculate the possible combinations.

• Each group should present at the end a list of all the combinations they managed to create and how many there were in total.

• Encourage creativity in naming the juices!

Activity 2 - The Dress and Shoe Challenge

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to apply the counting principle in combination situations, while also stimulating teamwork and creativity in problem-solving.

- Description: In this activity, students will have to help a clothing store organize its showcase outfits. They will receive cards representing different dresses and types of shoes. The task will be to combine each dress with a pair of shoes, using the counting principle to calculate the total number of possible combinations.

- Instructions:

• Organize students into groups of up to 5 people.

• Hand out the cards representing the dresses and shoes to each group.

• Instruct students to apply the multiplicative principle to find all possible combinations.

• Each group should present a report with the combinations found and the total number of possibilities.

• Encourage a discussion about the strategies used by each group.

Activity 3 - Special Ice Cream Builders

> Duration: (60 - 70 minutes)

- Objective: Utilize the counting principle to solve a practical and fun problem, stimulating students' imagination and calculation skills.

- Description: Students will be divided into groups to create special ice creams by combining different flavors, toppings, and cone sizes. Using cards that represent each element, they must calculate the number of unique combinations possible and describe each one.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the cards representing ice cream flavors, toppings, and cone sizes to each group.

• Students should use the multiplicative principle to determine the total number of unique combinations.

• Each group should present their combinations and explain how they arrived at the result.

• Encourage a discussion about which combinations were the most creative and why.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback stage is to consolidate learning, allowing students to articulate what they have learned and reflect on the problem-solving process. Group discussion helps reinforce concepts and identify any points that may still generate doubts. Additionally, by sharing their experiences, students can learn from each other, developing a deeper and more collaborative understanding of the topic.

Group Discussion

To start the group discussion, the teacher can ask each group to share a situation they faced during the activity and how they managed to overcome the challenge. Then, it can proceed to discuss the different strategies used by each group and which were more effective. The teacher can also encourage students to reflect on how the Counting Principle can be applied in other areas of their lives or in everyday situations.

Key Questions

1. What were the main challenges you faced when applying the Counting Principle in the activities?

2. How did the use of tree diagrams or tables facilitate the resolution of combination problems?

3. Can you think of other everyday situations where the Counting Principle could be applied?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to consolidate learning, ensuring that students have a clear understanding of the concepts covered and how they apply in the real world. Summarizing and connecting theory with the practices carried out during the lesson helps students recognize the utility and relevance of what they have learned, in addition to preparing them for future applications of the Counting Principle in various contexts.

Summary

In the final stage of the lesson, the teacher should summarize the main concepts covered regarding the Counting Principle, reinforcing the understanding of the multiplicative principle and how it is applied to calculate combinations. The practical activities carried out, such as 'Mixing Fair', 'The Dress and Shoe Challenge', and 'Special Ice Cream Builders', should be recapped, highlighting the solutions found and the calculation methods used.

Theory Connection

Today's lesson was structured to connect theory with practice in an integrated manner, making learning more significant for students. The proposed activities, based on real and playful situations, allowed for the direct application of the Counting Principle, reinforcing mathematical understanding through everyday contexts. This practical method aimed to solidify the theoretical knowledge previously studied by students.

Closing

At the end of the lesson, it is important to highlight the relevance of the Counting Principle in everyday life, emphasizing how it is used in various practical situations, such as event organization, meal planning, and even game solving. Understanding and applying this principle helps students develop logical and mathematical reasoning skills that are fundamental in their lives.