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 → Fractions and Decimals → Understanding Fractions ↓


Identifying and Representing Fractions


Fractions are an important part of math, especially in grade 3 where students begin to explore numbers less than whole numbers. Fractions help us document parts of a whole, express quantities that are not whole numbers, and gain an understanding of measurement concepts.

A fraction represents a part of a whole. It consists of two numbers, one written above the other, separated by a line. The number on top is called the numerator which tells us how many parts we have. The number below the line is the denominator which tells us how many parts there are in a whole.

Here's a simple representation of a fraction:

meter
,
Divisor

Understanding the concept of fractions

To begin understanding fractions, imagine a pizza cut into equal parts. If you have a pizza cut into 4 equal slices and you eat one, you have eaten 1 of the 4 slices of pizza. We can represent this as the fraction 1/4 (one-fourth).

Whole and parts

Suppose a rectangular chocolate bar is cut into several equal squares. If there are 8 squares and you eat 3, you have eaten a fraction of the chocolate.

3/8

Here, 3 is the numerator (the portions you ate) and 8 is the denominator (the total portions).

Types of fractions

Proper fractions

Proper fractions are fractions in which the numerator is smaller than the denominator. For example, in the fraction 3/8 the numerator 3 is smaller than the denominator 8.

Improper fractions

In improper fractions the numerator is greater than or equal to the denominator. For example, in the fraction 9/8 the numerator 9 is greater than the denominator 8.

Mixed number

Mixed numbers consist of a whole number and a proper fraction. For example, 1 1/4 represents 1 whole and 1-quarter.

Visualization of fractions

Using visual aids helps to understand how we divide a whole into equal parts. Let's look at some graphical representations of fractions using shapes.

Circle example

A circle is divided into four equal parts, out of which one part is shaded:

This image shows the fraction 1/4.

Rectangle example

A rectangle divided into 4 equal parts, of which 2 parts are colored:

This represents the fraction 2/4, which can be simplified to 1/2.

Finding equivalent fractions

Equivalent fractions are fractions that represent the same part of a whole. For example, 1/2 is equivalent to 2/4 and 4/8. They all represent the same quantity, even though they use different numbers.

Example of equivalent fractions

Cut a pizza into 8 slices. If 4 slices are eaten, we can write the fraction as follows:

4/8

This is equal to half of a pizza, and can be written as:

1/2

Uses of fractions in real life

Understanding fractions is very useful in everyday activities. Whether it's cutting an apple into pieces, dividing a cake between friends, or measuring ingredients in a recipe.

Example: sharing a sandwich

Imagine you have a sandwich and you want to share it equally with your friend. You cut it into two equal parts. You will both get half of the sandwich. In fractional form, each person will get 1/2 of the sandwich.

Baking with fractions

When baking, measurements often require fractions. For example, when a recipe calls for 3/4 cup of sugar, you need to be able to measure this portion of a whole cup.

Practice example

Let us try to identify fractions from the following examples. Look at the picture given below and try to write the fraction shown.

Example 1

The figure described shows the fraction 1/2.

Example 2

This is the representation of the fraction 1/4.

Example 3

Imagine that you divide a chocolate bar into 6 equal parts. You eat 4 parts. Write down the fraction of the chocolate bar you ate.

This represents the fraction 4/6, which simplifies to 2/3.

Conclusion

Mastering fractions is about understanding how to divide a whole item into parts and learning that these parts can be expressed using numbers. They are essential for understanding more complex mathematical concepts and are highly relevant in a variety of daily activities. Identifying and representing fractions with visual aids and real-life examples can be fun and engaging. Practice, visualization, and practical application will help build a strong foundation in fractions.


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Identifying and Representing Fractions

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