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


In grade 3 math, students learn about fractions and decimals. These are fundamental concepts in math that help us understand parts of a whole and represent numbers that are not whole.

Introduction to fractions

A fraction is a way of representing a part of a whole. Fractions are written with two numbers separated by a line called the fraction bar. The number above the line is the numerator, and the number below the line is the denominator. For example:

1/2

In this fraction, 1 is the numerator and 2 is the denominator.

1/2

The fraction 1/2 means that we have one part of two equal parts of a whole.

Understanding the numerator and denominator

The numerator tells us how many parts we have. The denominator tells us how many equal parts the whole is divided into. In our example:

  • Fraction: 1 (we have one part)
  • Denominator: 2 (the whole is divided into two equal parts)

Types of fractions

Proper fractions

A proper fraction is when the numerator is smaller than the denominator. For example, 3/4 is a proper fraction because 3 is smaller than 4.

3/4

Improper fractions

An improper fraction is when the numerator is greater than or equal to the denominator. For example, 5/4 is an improper fraction because 5 is greater than 4.

Mixed number

Mixed numbers include a whole number and a fraction, such as 1 1/4 which means one whole and one-fourth of the other.

Introduction to decimals

Decimals are another way of representing parts of a whole. Decimal numbers are based on 10.

In decimals a decimal point is used to separate the whole number part from the fractional part. For example:

0.5

The number 0.5 means five-tenths or half.

Understanding place value in decimals

Tenth place

When a number has one digit after the decimal point, that number is in the tenths place. For example:

0.7

Here 7 is in the tenth place, that is, seven-tenth part.

Hundredths place

When a number has two digits after the decimal point, the second digit is in the hundredths place. For example:

0.25

In this number, 2 is in the tenth place, and 5 is in the hundredth place.

Adding fractions to decimals

Both fractions and decimals represent parts of a whole. Let's see how they are related:

  • 1/2 = 0.5
  • 1/4 = 0.25
  • 3/4 = 0.75

Practice exercises

Converting fractions to decimals

  1. Convert 1/5 to decimal: 
    1/5 = 0.2
  2. Convert 3/5 to decimal: 
    3/5 = 0.6

Converting decimals to fractions

  1. Convert 0.4 to a fraction: 
    0.4 = 4/10 = 2/5
  2. Convert 0.8 to a fraction: 
    0.8 = 8/10 = 4/5

Adding and subtracting fractions

Same denominator

When adding or subtracting fractions with the same denominators, we add or subtract the numerators:

Example: 1/4 + 2/4 = 3/4

Different denominators

To add fractions with different denominators, first convert them to fractions with the same denominator:

Example: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

Adding and subtracting decimals

Adding and subtracting decimals is just like working with whole numbers, but we need to line up the decimal points:

1.2 + 0.8 ----- 2.0
1.2 + 0.8 ----- 2.0

Subtracting decimals works the same way:

2.5 - 1.3 ----- 1.2
2.5 - 1.3 ----- 1.2

Visual example of fractions and decimals

1/4 and 0.25 visualizations:

Part

1/4

Decimal

The decimal 0.25 is equal to the fraction 1/4. If we look at this on the number line, 0.25 represents one-quarter of the way from 0 to 1.

00.250.50.751

Comparing fractions and decimals

Comparing fractions

To compare fractions with the same denominators, compare numerators:

2/5 is less than 3/5 because 2 is less than 3.

Comparing decimals

To compare decimals, line up their decimal points. The larger decimal is the one with the higher value first, where they differ:

0.4 is less than 0.5.

Conclusion

Understanding fractions and decimals helps us understand numbers that aren't whole. With practice, you'll be able to use these concepts in everyday life, for things like cooking, shopping, and measuring. Keep practicing, and these will become second nature!


Grade 3 → 2


U
username
0%
completed in Grade 3

← Prev (1.4)
Understanding Even and Odd Numbers
Next (2.1) →
Understanding Fractions

Comments 



Fractions and Decimals

https://www.buddymath.com/g3/2?bmal=en