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 → Fractions and Decimals → Introduction to Fractions ↓


Understanding halves and quarters


In our journey to learn fractions, we will start by understanding halves and quarters. Fractions are parts of a whole. When you divide something into parts, each part is a fraction of the whole. Let's dive deeper into understanding what halves and quarters mean and how we use them in our daily lives.

What are halves?

Half means when we divide something into two equal parts. We call one part "half". Let's look at some examples:

Example 1: Cutting a pizza

Imagine you have a round pizza. If you want to share it equally with a friend, you would cut the pizza into two equal halves. Each person would get half of the pizza.

In mathematical terms, if you cut the pizza into two equal pieces, each piece:

1/2

Example 2: Sharing an apple

If you have an apple and want to share it with a friend, you can cut it into two equal parts. Each part is half of the apple.

What are quarters?

Quarter means to divide something into 4 equal parts. Each part is a "fourth" of the whole.

Example 1: Cutting a sandwich

If you have a sandwich and you cut it into four equal parts, each piece will be a quarter of the sandwich.

Example 2: Sharing a chocolate bar

Suppose you have a chocolate bar with four equal pieces. If you eat one piece, you have eaten a quarter of the chocolate bar.

Writing halves and quarters as fractions

In fractions, we write halves and quarters using numbers. The top number of the fraction is called the numerator, and the bottom number is called the denominator.

  • is a fraction of half
    1/2
    It means 1 part out of 2 equal parts.
  • is a fraction of a quarter
    1/4
    This means 1 part out of 4 equal parts.

More examples

Using shapes

To understand these fractions better, we can divide the shapes into halves and quarters.

1/2

In the above verse it is divided into two parts. Each part

1/2
Of the whole.

1/4 1/4 1/4 1/4

Above, a square is divided into quarters. Each quarter is a square.

1/4
of the whole figure.

Real-life situations

Scenario 1: If you have $1 and you divide it equally between you and your friend, each of you will get:

1/2 dollar each

Scenario 2: If you decide to divide the same dollar among four friends, each will get:

1/4 dollar each

Advanced understanding of halves and quarters

Sometimes we need to think a little deeper when considering halves and quarters. Let's look at different examples and situations.

Combining fractions

If you eat two quarters of a chocolate bar, you are eating the equivalent of eating half of it. Therefore, two quarters make one half.

1/4 + 1/4 = 1/2

Disintegration of halves

Sometimes, it's helpful to see how to make a half from a quarter:

1/2 = 1/4 + 1/4

So, if you think of a sandwich that's cut into two halves, each half is made up of two quarters.

Understanding fractions on the number line

Another way to understand halves and quarters is to look at the number line. Let's divide the line between 0 and 1 into equal parts:

0 1/2 1

For quarters, the line looks like this:

0 1/4 1/2 3/4 1

Conclusion

Understanding halves and quarters helps us better understand the basics of fractions. It's important to know how to divide and share things equally. As we continue to learn fractions, these basic concepts will help us learn and understand more complex ideas in math. Remember, fractions are just another way to express parts of a whole, and knowing how to use them helps in making everyday decisions.


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Understanding halves and quarters

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