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 → Introduction to Decimals ↓


Relationship between Fractions and Decimals


Introduction

Understanding the relationship between fractions and decimals is a basic skill in math. Fractions and decimals are two different ways to represent numbers that are not whole numbers. They can express parts of a whole or parts of a set. In this lesson, we will explore their differences, similarities, and how to convert one form to another using simple methods suitable for third grade students.

Basic concepts

What are the fractions?

A fraction is a way of dividing a whole into equal parts. It is represented using two numbers separated by a line. The number on top is called the numerator, and the number on the bottom is called the denominator. For example, the fraction 1/2 means a part of a whole that is divided into two equal parts.

Example of fraction

1/2 1/2

What are decimals?

Decimals are another way to represent numbers that are less than whole numbers. They use a decimal point to separate the whole number from the fractional part. For example, 0.5 is a decimal that represents the same value as the fraction 1/2.

Example of decimals

0.5 0.5

Understanding the connection

Converting fractions to decimals

To convert fractions to decimals, the numerator has to be divided by the denominator. For example, the fraction 1/4 can be converted to a decimal by dividing 1 by 4.

1 ÷ 4 = 0.25

Here, 0.25 is the decimal equivalent of the fraction 1/4.

Visual representation

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

Different from decimal

Converting a decimal to a fraction is like reversing the process. Take the decimal and write it as a fraction with a denominator of a power of 10, depending on how many decimal places it has. Then, simplify the fraction if necessary.

Example

Convert 0.75 to a fraction:

0.75 = 75/100
= 3/4 (after simplification)

Therefore, 0.75 as a fraction is 3/4.

Practice with examples

Convert fraction to decimal

Convert 3/5 to decimal:

3 ÷ 5 = 0.6

Therefore, 3/5 as a decimal is 0.6.

3/5 3/5

Convert decimal to fraction

Convert 0.40 to a fraction:

0.40 = 40/100
= 2/5 (after simplification)

Therefore, 0.40 as a fraction is 2/5.

0.40

Summary

Fractions and decimals provide different ways to express the same values. Understanding how to convert between them is useful in many areas of life, from measuring ingredients in a recipe to calculating distance. Practice these conversions to get comfortable with both forms of numbers. Remember, fractions use two numbers to show parts of a whole, while decimals use a decimal point.


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Relationship between Fractions and Decimals

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