Comparison of Natural Numbers Less than 20

Introduction

The Relevance of the Topic

In the magical world of numbers, knowing how they relate to each other is like learning the dance of the stars in the night sky. The ability to compare natural numbers less than 20 is a powerful tool in the toolkit of young explorers in mathematics. It is essential to understand that each number has a unique value and can be measured against another. This is not only part of the foundation of mathematics but also a pillar in many everyday situations, such as counting objects, evaluating quantities, and even deciding who has more candies at recess!

Contextualization

The journey through the universe of numbers begins with small and safe steps. Before we reach the distant planets of more complex operations, it is vital to master the art of comparing the little ones - natural numbers less than 20. This skill is located at the beginning of the mathematical treasure map of the 1st year of Elementary School, where learning to recognize, count, and now compare numbers is one of the first great adventures. By mastering this technique, our young adventurers will be ready to advance along the winding path of mathematics with confidence and enthusiasm.

Theoretical Development

• Natural Numbers:

  • They are like steps of a staircase that always go up, one after the other, starting from zero.
  • Each step has a number that indicates its position.
  • There are no broken steps or numbers 'halfway' here, all are integers and follow in a row.

• Comparison:

  • Imagine a balloon race. Each balloon has a number, and we want to know which one flies higher.
  • To compare, we look at two balloons at a time, seeing which number is larger or smaller.
  • The balloon with the larger number flies higher in the race!

• Smaller and Larger:

  • These are like the siblings 'Mini' and 'Max'. 'Mini' is the younger sibling, and 'Max' is the older sibling.
  • When we compare two numbers, we ask: Who is 'Mini'? And who is 'Max'?
  • 'Mini' is the number with fewer balloons, and 'Max' is the one with more balloons.

• Ascending and Descending Order:

  • Similar to arranging toys by size, from smallest to largest, this is ascending order.
  • And from largest to smallest? That is descending order, like stacking blocks that decrease in size.

• Comparison Symbols:

  • The symbols '<', '>', '=' are the tools we use to say who is 'Mini' and who is 'Max'.
  • '<' looks like an arrow pointing to the smaller number, and '>' to the larger one.
  • '=' is like a balance that is in equilibrium, showing that the numbers are equal.

• Key Terms:

  • Natural number: a positive integer that we usually use for counting.
  • Compare: look at two numbers and decide which has a greater value.
  • Smaller: the number with less value in a comparison.
  • Larger: the number with more value in a comparison.
  • Ascending order: arrange numbers from smallest to largest.
  • Descending order: arrange numbers from largest to smallest.
  • Less than symbol: '<', used when one number is less than another.
  • Greater than symbol: '>', used when one number is greater than another.
  • Equal symbol: '=', used when two numbers have the same value.

• Examples and Cases:

  • Simple comparison: 3 and 5 are racing, and we want to know who wins.
    • 3 < 5, so 5 is our 'Max' and wins the race.
  • Ascending order: We have the numbers 6, 2, and 9 and want to arrange them to climb the stairs.
    • The stairs look like this: 2, 6, 9. We start with 'Mini' (2) and end with 'Max' (9).
  • Descending order: We have the numbers 1, 4, and 3 and want to stack blocks from largest to smallest.
    • Our blocks are stacked like this: 4, 3, 1. 'Max' (4) is at the top and 'Mini' (1) at the base.

Detailed Summary

Key Points

• Steps of the Staircase: Each natural number is a step in the climb of knowledge, starting from 0 and going to infinity. In this lesson, we focus up to step number 20.
• Balloon Race: We use the image of balloons in a race to understand that some numbers 'fly' higher (are larger) than others.
• Siblings 'Mini' and 'Max': To facilitate the comparison process, we personify the concepts of smaller and larger into characters, making them more friendly and understandable.
• Arranging Toys and Blocks: The analogy of arranging toys and blocks simplifies the idea of ascending and descending orders, making spatial logic an ally in learning mathematical concepts.
• Comparison Tools: The arrows and the balance ('<', '>', '=') are visualized as tools that help determine quickly the relationship between numbers.

Conclusions

• Each Number Has Its Place: We conclude that in the dance of numbers, each one has its specific place and a value that can be measured in relation to others.
• Simplified Comparisons: With the right tools and analogies, comparing numbers becomes a simple and intuitive task.
• Organization: The ability to organize numbers in ascending or descending order is essential for various activities, from solving mathematical problems to organizing objects in real life.

Exercises

1. Identify the 'Mini' and 'Max': Look at pairs of numbers and use the symbols '<' or '>'. For example: 7 ___ 10; 16 ___ 3; 19 ___ 19.
2. Climbing the Stairs: Arrange the numbers 4, 18, 9, 14, and 1 in ascending order. Then, organize the same numbers in descending order.
3. Balloons in the Race: Draw five balloons and write a different number, less than 20, on each one. Now, draw them according to the height they fly, from the smallest to the largest number.