Multiplication by 2, 3, 4, 5, and 10 | Active Summary

Objectives

1. Master multiplication techniques for the numbers 2, 3, 4, 5, and 10, applying these concepts in practical and everyday situations.

2. Develop logical reasoning and problem-solving skills through contextualized problems involving multiplication.

Contextualization

Did you know that multiplication is one of the oldest mathematical operations used by humanity? Ancient civilizations like the Egyptians and Babylonians already used multiplication techniques to facilitate trade and the construction of large monuments! Today, multiplication is an essential tool in many daily activities, from calculating change at the market to dividing tasks equally. Mastering multiplication by 2, 3, 4, 5, and 10 not only makes these tasks easier, but also opens doors to understanding more complex mathematical concepts in the future. Let's dive into this world of mathematical challenges and discover how we can use multiplication in a fun and practical way!

Important Topics

Multiplication by 2, 3, 4, 5, and 10

Multiplication is a fundamental mathematical operation that combines groups of equal quantities. Multiplying by 2, 3, 4, 5, or 10 means adding the number to itself that many times, which is essential for solving problems of scale, repetition, and proportion.

• Multiplying by 2 is the same as doubling the number. For example, 4 x 2 = 8.

• Multiplying by 3 is tripling the number. For example, 3 x 4 = 12.

• Multiplying by 4 is quadrupling the number. For example, 6 x 4 = 24.

• Multiplying by 5 is adding the number to itself five times. For example, 7 x 5 = 35.

• Multiplying by 10 is easy, just add a zero to the number multiplied. For example, 9 x 10 = 90.

Contextualized Problems

Solving multiplication problems in real or everyday contexts helps students understand the practical applicability of these operations. This includes situations like calculating prices in a store (for example, 5 t-shirts at R$ 8 each), or dividing resources equally among a number of people or tasks.

• Identify the problem: understand what is given and what is being asked in the practical situation.

• Choose the operation: determine which multiplication to use based on the situation (for example, multiplication by 2 to double a recipe).

• Execute the operation: perform the multiplication calculation and arrive at the correct answer.

• Check the answer: ensure that the answer makes sense in the context of the problem.

Calculation Strategies

There are various strategies that can be employed to facilitate mental calculation or with paper and pencil. Some of these strategies include using properties of multiplication, such as commutativity and distributivity, or breaking down numbers to make more complex calculations easier.

• Commutativity: The order of factors does not change the product. For example, 2 x 3 is the same as 3 x 2.

• Distributivity: Multiplying the sum of numbers by another number is the same as multiplying each term of the sum by that number and then adding. Example: 2 x (3 + 4) = 2 x 3 + 2 x 4.

• Breaking down: Dividing a number into known parts to make calculation easier. For example, 7 x 8 can be broken down into (5 x 8) + (2 x 8).

• Use of friendly numbers: Utilizing numbers that add or multiply more easily to facilitate calculation. For example, 6 x 8 can be seen as 6 x 10 - 6 x 2.

Key Terms

• Multiplication: A mathematical operation that represents increasing an original quantity by a specific number of times.

• Commutativity: Property of multiplication stating that the order of numbers does not change the product.

• Distributivity: Property that allows for distributing multiplication over the addition or subtraction of numbers.

• Breaking down: A strategy that involves dividing a number into easier-to-calculate parts and then adding the results.

To Reflect

• How can understanding multiplication by 2, 3, 4, 5, and 10 help in your daily life? Think of practical examples.

• Why is it important to understand the properties of multiplication, such as commutativity and distributivity, to solve problems more quickly?

• In what ways can strategies like breaking down and using friendly numbers simplify the calculation of larger multiplications? Try creating your own examples to explore these strategies.

Important Conclusions

• We reviewed the importance and function of multiplication by 2, 3, 4, 5, and 10, which is essential for various situations in our daily lives.

• We explored how multiplication is used in different practical contexts, from calculating prices to dividing tasks equally.

• We learned calculation strategies that make multiplication more efficient and faster, such as using commutativity and distributivity.

• We discussed the application of properties of multiplication and how they facilitate solving complex mathematical problems.

To Exercise Knowledge

Create a multiplication journal for a week. Each day, note three different examples of situations where you used multiplication, such as calculating the price of items in a store or dividing a number of tasks equally. Try to use different numbers each day to practice multiplication by 2, 3, 4, 5, and 10.

Challenge

Supermarket Challenge: With the help of an adult, plan a meal for the family and calculate the total cost of the ingredients. Use multiplication to adjust quantities based on the number of people the meal should serve, ensuring that each item is bought in the correct amount for the recipe.

Study Tips

• Practice multiplication tables regularly to develop fluency and speed in multiplication. Apps and online games can be great tools to make this process more fun.

• Try teaching a friend or family member the multiplication strategies you learned. Teaching is one of the best ways to reinforce what you have learned.

• Use what you learned about the distributive property of multiplication to help simplify other mathematical operations, such as division and subtraction, in more complex problems.