Addition and Subtraction of Natural Numbers Less than 100 | Active Summary

Objectives

1. Develop the ability to add and subtract two-digit numbers, using or not using specific algorithms.

2. Enhance problem-solving skills involving addition and subtraction of numbers up to two digits, promoting the practical application of these operations.

3. Encourage the development of analytical skills and logical reasoning through practical and interactive activities.

4. Encourage collaboration and communication among students during group activities, promoting a cooperative learning environment.

Contextualization

Did you know that the ability to add and subtract numbers is one of the oldest forms of calculation used by humanity? Since antiquity, peoples around the world have developed ways to add and subtract quantities to solve everyday problems, such as measuring land or calculating food production. Today, these basic operations continue to be the basis for many other mathematical operations and are fundamental in countless situations in our daily lives, from shopping to budgeting. Mastering addition and subtraction is not only essential for success in mathematics but also for being more efficient and accurate in our daily tasks. Let's explore how these simple operations can lead us to significant mathematical discoveries and solve complex problems!

Important Topics

Addition

Addition is the basic mathematical operation that consists of putting together two or more quantities to find a total quantity. It is represented by the plus sign (+) and is essential for adding numbers and quantities in our daily lives. For example, when buying several items in a store, you are adding the prices to calculate the total to pay.

• The addition sign (+) is used to indicate that two or more numbers should be summed.

• The commutative property of addition states that the order of numbers does not change the result, that is, a + b = b + a.

• Adding zero does not change the value of the number, which is known as the additive property of zero.

• Addition is the inverse operation of subtraction, meaning that when you add a number and the result of a subtraction, you get the initial number.

Subtraction

Subtraction is the process of taking one quantity away from another or finding the difference between two quantities. It is represented by the minus sign (-). Subtraction is used daily in situations such as calculating the change from a purchase or determining the distance traveled by subtracting the initial position from the final position.

• The subtraction sign (-) is used to indicate that one number should be subtracted from another.

• The order of numbers in subtraction is important and the result is not commutative, that is, a - b is not the same as b - a.

• Subtracting zero does not change the value of the initial number, maintaining its identity, which is the property of subtraction by zero.

• Subtraction is the inverse operation of addition; by subtracting a number and the result of an addition, we arrive at the initial number.

Calculation Strategies

Calculation strategies refer to methods and techniques that can be used to facilitate the process of addition and subtraction, especially when dealing with larger numbers or multiple operations simultaneously. Some examples include using grouping, compensations, and decompositions, which help simplify the calculation and understanding of the operations.

• Decomposition: Breaking numbers into smaller parts to facilitate addition or subtraction, especially numbers close to tens or hundreds.

• Grouping: Putting together or grouping numbers in a way that makes the calculation simpler, for example, grouping all numbers with tens, hundreds, etc.

• Compensation: Adding or subtracting a convenient quantity to make the calculation easier, such as subtracting 3 from both numbers in a subtraction to make the calculations easier.

• Use of algorithms: Learning and applying formal methods of addition and subtraction, such as the column method, which is essential for handling larger numbers and ensuring accuracy in calculations.

Key Terms

• Addition: Mathematical operation of combining two or more numbers to obtain a total.

• Subtraction: Mathematical operation of taking one number from another.

• Ten: Grouping of 10 items, fundamental for understanding addition and subtraction of numbers greater than 10.

• Hundred: Grouping of 100 items, important for calculations with numbers greater than 100.

To Reflect

• Why is it important to understand and practice both addition and subtraction? How do these operations relate to everyday situations?

• What is the importance of developing effective calculation strategies? How can they help improve your ability to solve mathematical problems?

• How do the properties of addition and subtraction, such as commutativity and the additive property of zero, facilitate calculation and mathematical understanding?

Important Conclusions

• In this lesson, we explored the fascinating mathematics of addition and subtraction, fundamental skills that we use daily in various situations.

• We learned to add and subtract two-digit numbers, developing calculation strategies that help us tackle mathematical challenges more efficiently and accurately.

• We discussed how mathematical properties, such as commutativity and the additive property of zero, are essential for understanding and correctly applying these operations, both in practical and theoretical problems.

To Exercise Knowledge

1. Create your own addition and subtraction problem involving two-digit numbers. Exchange it with a colleague to solve. 2. Use cards or papers to practice the addition and subtraction of tens and units. 3. Draw a bar graph to represent different sums and subtractions that you find in a book or magazine.

Challenge

Change Challenge: Simulate being in a store and calculate the change for different purchases. Use the largest number of items possible, including hundreds, so that you have to perform multiple additions and subtractions. Try to do this quickly, as if you were a supermarket cashier!

Study Tips

• Practice addition and subtraction regularly with online games, such as 'Math Playground' or 'Cool Math Games', to keep your skills sharp.

• Use concrete materials, such as base 10 blocks or colored beads, to visualize and solve addition and subtraction problems, which helps better understand concepts.

• Try to teach your friends or family the strategies you've learned; the act of teaching is a great way to consolidate your own understanding.