Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Number Sense and Operations → Odd and Even Numbers ↓


Simple operations with odd and even numbers


Introduction

In this lesson, we will explore what odd and even numbers are, and how to perform basic operations with them. It is important to understand these concepts because they form the basis for more complex mathematical ideas. This explanation will use simple language and examples to help you understand the basic ideas.

What are even numbers?

Even numbers are numbers that can be divided by 2 and leave no remainder. This means that any number that ends in 0, 2, 4, 6, or 8 is considered an even number. Here are some examples of even numbers:

  • 2
  • 4
  • 10
  • 38
6 (even number)

What are the odd numbers?

Odd numbers are numbers that cannot be divided evenly by 2. When you divide an odd number by 2, there is always a remainder of 1. Numbers ending in 1, 3, 5, 7, or 9 are considered odd numbers. Here are some examples of odd numbers:

  • 1
  • 3
  • 15
  • 29
7 (odd number)

Adding even and odd numbers

Let's see what happens when we add even and odd numbers:

Even + even

Adding two even numbers always gives an even number. Here's an example:

4 + 6 = 10

Both 4 and 6 are even numbers and their sum 10 is also even.

Odd + odd

Adding two odd numbers always gives an even number. Here's an example:

3 + 5 = 8

3 and 5 are both odd numbers, yet their sum 8 is even.

Even + odd

Adding an even number to an odd number will always give an odd number. Here's an example:

4 + 3 = 7

The number 4 is even and 3 is odd; together they make 7, which is odd.

Subtracting odd and even numbers

Now, let's see what happens when we subtract odd and even numbers from each other:

Even - even

Subtracting an even number from another even number gives an even result. Here's an example:

8 - 2 = 6

Both 8 and 2 are even numbers and the result 6 is also even.

Odd - odd

Subtracting an odd number from another odd number will give an even number. Here is an example:

9 - 5 = 4

9 and 5 are both odd numbers, and the result 4 is even.

Even - odd

Subtracting an odd number from an even number gives an odd number. Here is an example:

10 - 3 = 7

The number 10 is even, and 3 is odd, resulting in the number 7, which is odd.

Multiplication of even and odd numbers

Let's look at the multiplication of even and odd numbers:

Even x even

Multiplying two even numbers always gives an even number. For example:

4 x 6 = 24

The numbers 4 and 6 are both even, and 24 is also even.

Odd x odd

Multiplying two odd numbers gives an odd number. Here's an example:

3 x 5 = 15

3 and 5 are both odd numbers, and 15 is also odd.

Even x odd

Multiplying an even number and an odd number always gives an even number. For example:

4 x 3 = 12

The number 4 is even, 3 is odd, and the result 12 is even.

Division of even and odd numbers

When dividing numbers, the result depends on the specific values and is not as predictable as with addition, subtraction, and multiplication:

Even ÷ even

Dividing one even number by another can give an even or odd number or a fraction, depending on the numbers involved. For example:

8 ÷ 4 = 2

Here 8 and 4 are even, and the result is 2, which is even.

6 ÷ 4 = 1.5

Here 6 and 4 are even, but the result is different (1.5).

Odd ÷ odd

When dividing an odd number by another odd number, the result may be odd or even. For example:

9 ÷ 3 = 3

Here both the numbers are odd, and the result 3 is odd.

9 ÷ 5 = 1.8

Here, the division gives the fraction (1.8).

Even ÷ odd

Dividing an even number by an odd number can give an even number or a fraction. For example:

8 ÷ 2 = 4

The numbers 8 and 2 are even and odd respectively, and the result 4 is even.

8 ÷ 3 = 2.67

Here, division gives the fraction (2.67).

Odd ÷ even

In general, dividing an odd number by an even number gives a fraction. For example:

9 ÷ 2 = 4.5

9 and 2 are both odd and even, respectively, resulting in a fraction (4.5).

Conclusion

Learning how to add, subtract, multiply, and divide odd and even numbers helps you see patterns in math and make predictions. These principles are fundamental and can be applied to many areas of math and everyday life.

A good understanding of simple operations with odd and even numbers helps in the development of number sense and lays the foundation for tackling more complex concepts in the future.

Practice example

Let's put into practice what we've learned. Try these for yourself:

  • 6 + 7 = ? (odd or even)
  • 10 - 4 = ? (odd or even)
  • 3 x 2 = ? (odd or even)
  • 7 ÷ 2 = ? (odd, even or different)

Try making similar problems and predict whether the answer will be odd, even, or different.


Grade 2 → 1.4.3


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Simple operations with odd and even numbers

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