Grade 3
  1. Number Sense and Numeration  1.1. Understanding Numbers  1.1.1. Reading and Writing Numbers up to 10,000  1.1.2. Place Value up to Thousands  1.1.3. Comparing and Ordering Numbers  1.1.4. Rounding Numbers to the Nearest Ten and Hundred  1.1.5. Skip Counting by 2s, 5s, 10s, and 100s up to 1,000  1.2. Operations with Whole Numbers  1.2.1. Addition and Subtraction up to 1,000  1.2.2. Multiplication Facts (up to 10 x 10)  1.2.3. Division Facts (up to 100)  1.2.4. Multiplication as Repeated Addition  1.2.5. Division as Equal Sharing  1.2.6. Word Problems with Addition, Subtraction, Multiplication, and Division  1.3. Estimation  1.3.1. Estimating Sums and Differences  1.3.2. Estimating Products and Quotients  1.4. Understanding Even and Odd Numbers
  2. Fractions and Decimals  2.1. Understanding Fractions  2.1.1. Identifying and Representing Fractions  2.1.2. Fractions of a Whole and Part of a Set  2.1.3. Comparing and Ordering Fractions with Like Denominators  2.1.4. Equivalent Fractions  2.1.5. Simple Fraction Word Problems  2.2. Introduction to Decimals  2.2.1. Tenths and Hundredths as Decimals  2.2.2. Relationship between Fractions and Decimals
  3. Measurement  3.1. Length  3.1.1. Measuring in Centimeters and Meters  3.1.2. Comparing and Ordering Lengths  3.1.3. Estimating Lengths  3.1.4. Converting Between Centimeters and Meters  3.2. Mass  3.2.1. Measuring in Grams and Kilograms  3.2.2. Estimating and Comparing Mass  3.3. Capacity  3.3.1. Measuring in Milliliters and Liters  3.3.2. Estimating and Comparing Capacity  3.4. Time  3.4.1. Telling Time to the Nearest Minute  3.4.2. Calculating Elapsed Time  3.4.3. Using a Calendar  3.4.4. Understanding A.M. and P.M.  3.5. Area and Perimeter  3.5.1. Calculating Perimeter of Simple Shapes  3.5.2. Estimating and Measuring Area of Shapes  3.5.3. Finding Area by Counting Squares
  4. Geometry  4.1. Properties of Shapes  4.1.1. Identifying 2D Shapes (Triangles, Quadrilaterals, Circles, etc.)  4.1.2. Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)  4.1.3. Describing Attributes of 2D and 3D Shapes  4.1.4. Recognizing Parallel and Perpendicular Lines  4.2. Symmetry and Transformations  4.2.1. Recognizing Lines of Symmetry  4.2.2. Identifying Flips, Slides, and Turns  4.3. Angles  4.3.1. Understanding Right Angles  4.3.2. Comparing Angles (Acute, Right, Obtuse)
  5. Data Management and Probability  5.1. Data Collection and Organization  5.1.1. Collecting Data using Surveys and Experiments  5.1.2. Organizing Data using Tally Charts and Tables  5.2.1. Creating and Interpreting Pictographs  5.2.2. Creating and Interpreting Bar Graphs  5.2.3. Reading Simple Line Graphs  5.3. Probability  5.3.1. Understanding Basic Probability Terms (Certain, Possible, Impossible)  5.3.2. Predicting Outcomes  5.3.3. Simple Probability Experiments
  6. Patterns and Algebra  6.1. Patterns  6.1.1. Identifying and Extending Numeric Patterns  6.1.2. Identifying and Extending Shape Patterns  6.1.3. Creating Patterns Using Rules  6.2. Introduction to Algebra  6.2.1. Understanding Variables as Unknowns  6.2.2. Solving Simple Addition and Subtraction Equations  6.2.3. Using Patterns to Solve Problems
  7. Problem-Solving Skills  7.1. Strategies for Problem-Solving  7.1.1. Using Pictures or Diagrams  7.1.2. Identifying Patterns in Problems  7.1.3. Making Organized Lists  7.1.4. Guessing and Checking  7.1.5. Using Logical Reasoning  7.1.6. Breaking Down Problems into Steps

Grade 3 → Number Sense and Numeration ↓


Understanding Even and Odd Numbers


Introduction

In math, understanding the difference between even and odd numbers is fundamental. Children begin to recognize and classify numbers from an early age, and being able to distinguish between even and odd numbers forms a fundamental skill in number sense and arithmetic.

The concepts of even and odd numbers are simple yet important because they lay the foundation for more advanced concepts in math. In this explanation, we will explore what even and odd numbers are, why they are important, and how they are identified. Additionally, we will discuss patterns, the reasons behind these classifications, and examples in both text and simple illustrations.

What are even numbers?

Even numbers are numbers that can be divided into two equal groups without any remainder. In mathematical terms, a number is considered even if it is divisible by 2. This means that when you divide an even number by 2, you will get a perfect number as the result, with no remainder.

Examples of even numbers

  • 2 is an even number because 2 ÷ 2 = 1 no remainder.
  • 4 is even because 4 ÷ 2 = 2 without remainder.
  • 6, 8, and 10 are even numbers for the same reason: they are all divisible by 2.

Illustrating even numbers

2 2

The number 4 is represented as two equal parts (2 and 2), which shows that it is even.

What are the odd numbers?

Odd numbers are numbers that cannot be divided into two equal groups. When you divide an odd number by 2, you get a remainder of 1.

Examples of odd numbers

  • 1 is odd because 1 ÷ 2 = 0 remainder 1.
  • 3 is odd because 3 ÷ 2 = 1 remainder 1.
  • This is why 5, 7 and 9 are odd numbers.

Drawing of odd numbers

2 1

The number 3 is represented by two parts: 2 parts and 1 remainder, which shows that it is odd.

Recognizing even and odd numbers

The simplest way to identify whether a number is even or odd is to look at the last digit. This specific rule makes it quick and easy to classify numbers without any full calculations.

Last digit rule

- A number is even if its last digit is one of: 0, 2, 4, 6, 8.
- A number is odd if its last digit is one of: 1, 3, 5, 7, 9.

Example using the last digit rule

  • 24 ends with 4, so it is even.
  • 37 ends in a 7, so it is odd.
  • 128 ends with 8, so it is even.

Visual example using the last digit rule

Number: 256 Last digit: 6 (even)

Patterns in even and odd numbers

When you look at a sequence of numbers or continue counting, you will notice that even and odd numbers follow a regular alternating pattern. Understanding these patterns can help reinforce concepts and make it easier to quickly identify numbers.

Counting patterns

Let's count from 1 to 10 to see the pattern:
1 (Odd), 2 (Even), 3 (Odd), 4 (Even), 5 (Odd), 6 (Even), 7 (Odd), 8 (Even), 9 (Odd), 10 (Even)

Mathematical patterns

  • even + even = even
  • odd + odd = even
  • even + odd = odd
  • odd + even = odd
Example:
4 + 6 = 10 (even)
3 + 5 = 8 (even)
2 + 3 = 5 (odd)
7 + 2 = 9 (odd)

Visual representation of the pattern

I Hey I Hey I

The pattern shows how the even (E) and odd (O) numbers vary with each other.

Importance in real life

Understanding even and odd numbers is not only essential for school math, but also important for practical, everyday situations. Many real-life applications benefit from this understanding:

  • Sharing items: When items need to be distributed equally, knowing the difference between odd and even can determine if this is possible.
  • Patterns and designs: Even numbers are often used to create symmetrical designs.
  • Game rules: Many games use even or odd numbers as rules.

Conclusion

Understanding the idea of even and odd numbers is an essential step in mathematics. Whether through simple calculations, pattern recognition or real-world applications, understanding these concepts enhances our interaction with numbers. By practicing with examples and visual illustrations, students can easily become proficient at identifying and using even and odd numbers, thus fostering a strong mathematical foundation.


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Understanding Even and Odd Numbers

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