Contextualization

Theoretical Introduction

Multiplication is one of the four basic operations of arithmetic, along with addition, subtraction, and division. It can be seen as repeated addition; For example, multiplying 5 (multiplicand) by 4 (multiplier) is equivalent to adding four times 5 (5 + 5 + 5 + 5) and the result is 20 (product). This is redefined when one of the terms is unknown, where the known terms (multiplicand, multiplier, or product) are used to determine the unknown term.

In addition, multiplication has some important properties that help solve mathematical problems: the commutative property (the order of the factors does not change the product), the associative property (the way we group the terms does not change the result), and the distributive property (multiplication over addition), all of these properties help in solving problems involving missing values.

The concept of solving an equation where one of the terms is unknown is fundamental for the development of algebraic thinking, which is an essential skill in advanced mathematics studies.

Contextualization

The ability to solve multiplication problems with unknown terms is very useful in everyday situations. For example, when we go to the supermarket and want to buy several items of the same type, but the price is given per unit, we need to multiply to find the total price. However, if we know the total price and the price per unit, but not the number of items, we have a situation where one term is unknown, which can be solved with the skills that will be developed in this project.

Furthermore, this skill is also crucial in various professions. Engineers, economists, data scientists, programmers, among many others, often need to solve problems with unknown terms.

Practical Activity

Activity Title: "Math Mission: Discovering Missing Values"

Project Objective

Build a didactic and interactive board game where students will need to solve multiplication problems with unknown terms to advance on the board.

Detailed Project Description

Students, divided into groups of 3 to 5, will create a board game whose objective is to solve problems involving multiplication with unknown terms. Each square on the board will have a mathematical challenge that needs to be solved for the player to advance. The game ends when a player reaches the end of the board.

Required Materials

1. Cardboard or cardstock for the base of the board.
2. Colored pens, colored pencils, or paints for customizing the board.
3. Small paper or cards to write the questions and answers.
4. One die.
5. Game pieces (can be anything small, such as buttons, bottle caps, stones, etc.)

Step-by-Step

1. Each group should draw a board on the cardboard or cardstock, the board should be divided into squares, in the way they prefer (for example, like a path, or in a circle, etc.).

2. On each square, students should write a multiplication problem with an unknown value.

3. On the back of each card with problems, write the corresponding answers. These cards should be shuffled and placed face down next to the board.

4. Each student chooses a game piece.

5. Students roll the die to determine who starts. The student with the highest roll starts.

6. Each player, on their turn, rolls the die and advances the corresponding squares.

7. When landing on a square, the player must pick a card with a problem, solve the problem, and check the answer on the back. If correct, they stay on the square, if wrong, they go back to the square they came from.

8. The game ends when all players reach the end of the game.

Upon completing the practical activity, each group must write a report describing the experience. The report should include:

1. Introduction: Here students should discuss the project's objective, its relevance, and real-world applications.
2. Development: The activity should be explained in detail, including the creation of the board, the elaboration of the problems, and the game dynamics. Additionally, they should discuss the results, how the problems were solved, the difficulties encountered, and how they were overcome.
3. Conclusion: Students should summarize the main points of the report, what they learned from the experience, both in terms of mathematical skills and socio-emotional aspects, and the importance of teamwork.
4. Bibliography used: Here students should indicate the sources consulted for the elaboration of the problems and for the study of the topic.

The reports will be evaluated considering both teamwork and the correct application of mathematical content.