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Lesson plan of Probable and Improbable

Mathematics

Original Teachy

Probable and Improbable

Objectives (5 - 7 minutes)

  1. Understand the concept of probability: Students should be able to understand what probability is and how it applies to everyday situations. They should learn that probability is the chance of an event happening.

  2. Differentiate likely and unlikely events: Students should be able to distinguish between likely and unlikely events. They should learn that likely events have a high chance of happening, while unlikely events have a low chance of happening.

  3. Identify likely and unlikely events in practical situations: Students should be able to apply the concept of probability to identify likely and unlikely events in everyday situations. This may include things like the weather, the outcome of a game, or the color of a candy taken from a bag (if time allows, the teacher can bring concrete examples to the classroom or encourage students to bring their own examples).

Introduction (10 - 12 minutes)

  1. Review of previous content: The teacher starts the lesson by reminding students about the concepts of 'chance' and 'possibility' that were covered in previous classes. This can be done through simple questions and everyday situations so that students can connect the new content with what they have already learned.

  2. Problem Situation 1: The Even or Odd Game: The teacher proposes a simple game to the class. He divides the students into two groups and asks each group to choose a number: even or odd. Then, the teacher rolls a die and if the sum of the die points is even, the group that chose even wins, if it is odd, the group that chose odd wins. This activity serves to introduce the concept of a likely event (the sum being even) and an unlikely event (the sum being odd).

  3. Problem Situation 2: Weather Forecast: The teacher, through images or graphics, presents different weather forecasts for the day. He asks students to discuss in small groups which forecast they consider most likely and why. The goal is to make students think about the concept of probability in real situations, such as weather forecasting.

  4. Contextualization of the importance of the subject: The teacher explains to students that understanding probability and being able to distinguish likely and unlikely events is important because it helps them make informed decisions. For example, if they know there is a high probability of rain, they can decide to take an umbrella to school. Additionally, the teacher can mention how probability is used in gambling games, such as flipping a coin or choosing a card from a deck.

  5. Introduction to the topic: Curiosity about probability: To spark students' interest, the teacher can share some curiosities about probability. For example, the teacher can say that the probability of winning the lottery is very low, but someone always ends up winning. Or that the probability of being born identical twins is 1 in 250. These curiosities can stimulate students' curiosity and motivate them to learn more about the subject.

Development (20 - 25 minutes)

The teacher should choose one of the following options to develop the lesson topic in a more in-depth and engaging way. Both options are structured to allow students to apply what they have learned about likely and unlikely events in everyday situations.

Option 1: 'The Game of Colored Boxes'

  1. Game Preparation: The teacher prepares five boxes of different sizes and colors (two red, one green, one blue, and one yellow). Inside each box, the teacher places different items (for example: small balls of different colors, toy cars, dolls, etc.). The teacher must ensure that there is a different quantity of items inside each box, ranging from 1 to 5.

  2. Group Division: Students are divided into groups of up to five members. Each group receives a sheet of paper with the following table drawn:

    Box ColorQuantity of ItemsProbability (Likely/Unlikely)
  3. Objective: The objective of the game is for the groups, collectively, to analyze the boxes, make predictions about the color of the balls and the quantity inside each box, and classify these predictions according to the categories 'Likely' and 'Unlikely'.

  4. Game Resolution: A representative from each group must announce the color and quantity they believe to be inside each box. The teacher then opens the boxes and confirms whether the predictions are correct or not. Students should mark on the table whether the prediction was likely or unlikely.

  5. Discussion: After all groups have made their predictions and the teacher has confirmed the answers, the teacher should lead a discussion in the classroom. The teacher should ask students which boxes were easier or more difficult to predict and why. This discussion will help students better understand the concept of probability.

Option 2: 'The Game of Magic Colors'

  1. Game Preparation: The teacher prepares five transparent plastic cups and five different colored liquids (for example: water with food coloring - red, green, blue, yellow, and orange). The colored liquids should be placed in cups in a way that the quantity varies unevenly in each cup.

  2. Group Division: Students are divided into groups of up to five members. Each group receives a sheet of paper with the following table drawn:

    Liquid ColorQuantity of LiquidProbability (Likely/Unlikely)
  3. Objective: The objective of the game is for the groups, collectively, to analyze the cups, make predictions about the color and quantity of liquid inside each cup, and classify these predictions according to the categories 'Likely' and 'Unlikely'.

  4. Game Resolution: A representative from each group must announce the color and quantity they believe to be inside each cup. The teacher then lifts the cups one by one and confirms whether the predictions are correct or not. Students should mark on the table whether the prediction was likely or unlikely.

  5. Discussion: After all groups have made their predictions and the teacher has confirmed the answers, the teacher should lead a discussion in the classroom. The teacher should ask students which cups were easier or more difficult to predict and why. This discussion will help students better understand the concept of probability.

The teacher should choose the option that best suits the class dynamics and the available resources. Always remembering that the goal of the development is to allow students to apply what they have learned about likely and unlikely events in everyday situations in a playful and fun way.

Return (8 - 10 minutes)

  1. Group Discussion (3 - 4 minutes): The teacher gathers all students and promotes a group discussion about the solutions or conclusions found by different groups. Each group has the opportunity to share their answers and explain the reasoning behind them. During the discussion, the teacher should ask questions to encourage students to think critically about the solutions of other groups and to compare their answers. For example: 'Why do you think Group A considered the red box more likely and Group B considered it more unlikely?' or 'What do you think Group C could have done differently to arrive at a more accurate answer?'.

  2. Connection to Theory (2 - 3 minutes): After the discussion, the teacher makes the connection between the practical activities and the theory presented at the beginning of the lesson. He emphasizes how probability is used to determine the chance of an event happening and how the concepts of likely and unlikely events apply to the discussed situations. For example, the teacher can say, 'Do you remember when we discussed the weather forecast? This is an example of how we use probability in our daily lives. Meteorologists analyze different factors, such as temperature and atmospheric pressure, to make their predictions. They use probability to determine the chance of rain or sunshine.'

  3. Individual Reflection (3 - 4 minutes): Finally, the teacher proposes that students reflect individually on what they learned in the lesson. He asks two simple questions and gives a minute for students to think about the answers. The questions are:

    • What did you learn today about likely and unlikely events?
    • How can you use what you learned today in situations in your daily life?
  4. Sharing Reflections (1 minute): After a minute of reflection, the teacher invites some students to share their reflections with the class. Students can simply say their answers to the proposed questions out loud. The goal of this moment is to allow students to consolidate what they have learned and realize the relevance of the subject to their lives.

Throughout the return, the teacher should maintain a welcoming and respectful environment, encouraging all students to participate actively and valuing each one's contributions. The teacher should also be attentive to correct any misunderstandings and reinforce the most important concepts.

Conclusion (5 - 7 minutes)

  1. Lesson Summary (2 - 3 minutes): The teacher begins the conclusion phase by summarizing the main points of the lesson. He reiterates the definition of probability, explaining that it is the chance of an event happening. Additionally, the teacher emphasizes the difference between likely and unlikely events, highlighting that likely events have a high chance of occurring, while unlikely events have a low chance. Finally, the teacher recalls the practical activities carried out in the classroom, emphasizing how they helped illustrate the presented theory.

  2. Connection between Theory and Practice (1 - 2 minutes): The teacher then explains how the lesson connected theory to practice. He mentions the playful activities, such as 'The Game of Colored Boxes' or 'The Game of Magic Colors', which allowed students to apply the concept of probability concretely. The teacher also highlights how problem situations, such as the weather forecast, helped contextualize the theory, showing students how probability is used in everyday life.

  3. Extra Materials (1 minute): The teacher suggests some extra materials for students who wish to deepen their knowledge on the subject. This may include textbooks, educational websites, online games, or explanatory videos. For example, the teacher may recommend the website 'Fun Mathematics' (www.funmathematics.com), which has a section dedicated to probability with games and interactive activities.

  4. Importance of the Subject (1 minute): Finally, the teacher emphasizes the importance of the subject taught. He explains that understanding probability and being able to distinguish likely and unlikely events is useful in many everyday situations. For example, it can help make informed decisions, such as whether to take an umbrella or not, based on the weather forecast. Additionally, the teacher may mention how probability is used in many games, such as flipping a coin or drawing a card from a deck.

Throughout the conclusion, the teacher should ensure that students have space to ask questions and clarify doubts. He should encourage curiosity and students' interest in the subject, reinforcing that mathematics can be fun and applied in daily life.

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