INTRODUCTION TO MULTIPLICATION BY 2, 3, 4, 5, AND 10

The Relevance of the Topic

• Basis for Future Operations: Multiplying is like adding the same number several times. Knowing multiplication opens the door to advanced mathematics.
• Everyday Tool: We use multiplication to count items in groups, calculate prices, understand schedules, and much more.
• Develops Logical Reasoning: Learning to multiply helps to think in an organized and fast way.

Contextualization

• Foundation of Mathematics: After learning to add and subtract, multiplication is the next step in building mathematical knowledge.
• Connection with Daily Life: When dealing with money, dividing tasks, or even in the kitchen, we apply multiplication frequently without realizing it.
• Preparation for Future Concepts: Understanding multiplication helps to deal with fractions, division, and proportions that will come in the following years.
• Integration with Other Themes: Multiplication is linked to geometry (area of figures), science (cell counting), and many other fields.

THEORETICAL DEVELOPMENT

Components

• Multiplicand and Multiplier: These are the numbers involved in the multiplication. The multiplicand is the number that will be "added" several times, and the multiplier is the number of times it will be added.
• Product: Result of the multiplication. The new number we discover after multiplying.
• Multiplication Table: Visual tool that helps to remember the results of the most common multiplications.
• Double (Multiplication by 2): Multiplying by 2 is simply adding a number to itself.
• Triple (Multiplication by 3): Multiplying by 3 means adding the number three times.
• Quadruple (Multiplication by 4): Multiplying by 4 is like adding the number four times in a row.
• Quintuple (Multiplication by 5): When we multiply a number by 5, it is the same as adding it five times.
• Decuple (Multiplication by 10): Multiplying by 10 adds a zero to the end of the number if it is an integer.

Key Terms

• "Times": Keyword in a multiplication sentence. For example, "2 times 3" means 2 multiplied by 3.
• "Double", "Triple", "Quadruple", "Quintuple": Expressions that indicate multiplication by 2, 3, 4, and 5, respectively.

Examples and Cases

• Multiplying by 2: If we have 4 dolls and want double, we do the calculation 4 times 2. We take the number 4 and add it to itself: 4 + 4 = 8. We then have 8 dolls in total.
• Multiplying by 3: If we plant 3 seeds in each pot and have 3 pots, how many seeds did we plant? We do 3 times 3. We count like this: 3 + 3 + 3 = 9. We planted 9 seeds.
• Multiplying by 4: We have 4 boxes with 4 oranges each. How many oranges do we have in total? We multiply 4 by 4: 4 + 4 + 4 + 4 = 16 oranges.
• Multiplying by 5: If a duck has 5 ducklings and each duckling has 5 friends, how many ducklings are there? We multiply 5 by 5: 5 + 5 + 5 + 5 + 5 = 25 ducklings.
• Multiplying by 10: When we multiply any number by 10, for example 6, we simply add a zero to the right of the number: 6 times 10 is the same as 60.

Each example shown is designed to reinforce the understanding of the multiplication operation and its practical application in everyday life.

DETAILED SUMMARY

Relevant Points

• Multiplication Concept: Understanding multiplication as adding a number several times.
• Identification of Components: Differentiating the multiplicand (number to be added) and the multiplier (how many times we add).
• Use of the Multiplication Table: Using the table as a resource for memorization and speed in calculation.
• Multiplication by 2 (Double): Recognizing that multiplying by 2 is the same as doubling the number.
• Multiplication by 3 (Triple): Understanding that multiplying by 3 is tripling, adding the number three times.
• Multiplication by 4 (Quadruple): Understanding that multiplying by 4 is quadrupling, that is, adding the number to itself four times.
• Multiplication by 5 (Quintuple): Knowing that multiplying by 5 is quintupling, that is, adding the number five times.
• Multiplication by 10 (Decuple): Learning that multiplying by 10 adds a zero to the end of an integer number.

Conclusions

• Importance of Practice: Continuous practice aids in memorizing multiplication tables and in the ability to perform operations mentally.
• Variety of Applications: Multiplication is a versatile operation applicable in various everyday situations.
• Mathematical Reasoning: Developing skills in multiplication strengthens logical reasoning and problem-solving abilities.

Exercises

1. Doubling Numbers: João has 7 toy cars. How many toy cars will he have if he doubles the quantity? (Tip: Multiply 7 by 2).
2. Groups of Three: A mother distributed 3 apples to each of her 3 children. How many apples did she distribute in total? (Tip: Multiply 3 by 3).
3. Varied Multiplication: If each box contains 4 balls and we have 5 boxes, how many balls do we have in total? (Tip: Multiply 4 by 5).

Each proposed exercise aims to consolidate the understanding of the multiplication operation through practical and everyday situations that encourage the student to apply the acquired knowledge.