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


Fractions are a way of representing parts of a whole. When we divide something into equal parts, each part is a fraction of the whole. Fractions are used in everyday life, from cutting pizza into slices to measuring ingredients for a recipe.

What is fraction?

A fraction is made up of two numbers, one above the other, separated by a line. The number on top is called the numerator, and the number on the bottom is called the denominator.

  meter
  ,
  Divisor

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

Example 1:

Suppose we have a pizza that is divided into 4 equal slices. We are left with 1 slice. How can we express this as a fraction?

Numerator = 1 (number of slices we have)

Denominator = 4 (total number of slices)

Fraction: 1/4

Types of fractions

There are different types. Here are some:

Proper fractions

In proper fractions the numerator is smaller than the denominator. They are less than 1.

Example: 
  1/4, 2/5, 3/8

Improper fractions

Improper fractions have a numerator greater than or equal to the denominator. They are equal to or greater than 1.

Example: 
  5/4, 6/5, 8/8

Mixed number

Mixed numbers are a combination of a whole number and a proper fraction.

Example: 
  1 1/2, 3 3/4, 5 2/3

Example 2:

Convert the improper fraction 9/4 to a mixed number.

Divide 9 by 4. The quotient is 2 and the remainder is 1.

So, 9/4 = 2 1/4

Equivalent fractions

Equivalent fractions have different numerators and denominators but they represent the same value.

Example 3:

Let's consider the fraction 1/2.

If we multiply the numerator and denominator by 2 we get 2/4.

If we multiply the numerator and denominator by 3 we get 3/6.

Therefore, 1/2, 2/4 and 3/6 are like fractions.

Adding fractions

When adding fractions, the denominators must be the same. If this is not the case, find the same denominators by finding the least common multiple.

Example 4:

Let's add 1/4 and 1/2.

The least common multiple of 4 and 2 is 4.

Convert 1/2 to 2/4.

Now add: 1/4 + 2/4 = 3/4

Subtracting fractions

As with addition, make sure the denominators are the same before subtracting fractions.

Example 5:

Let's subtract 1/3 from 3/4.

The least common multiple of 4 and 3 is 12.

Convert 3/4 to 9/12.

Convert 1/3 to 4/12.

Now subtract: 9/12 - 4/12 = 5/12

Multiplication of fractions

To multiply fractions, multiply the numerators together and the denominators together.

Example 6:

Let's multiply 1/2 by 2/3.

Multiply the fractions: 1 * 2 = 2

Multiply the denominators: 2 * 3 = 6

Product: 2/6, which simplifies to 1/3

Division of fractions

To divide fractions, multiply by the reciprocal of the fraction you're dividing by.

Example 7:

Let's divide 3/4 by 1/2.

The reciprocal of 1/2 is 2/1.

Multiply: 3/4 * 2/1 = 6/4, which simplifies to 1 1/2

Understanding fractions on the number line

Fractions can also be represented on the number line, which helps in understanding the size of fractions.

Example 8:

Let's locate 1/4, 1/2 and 3/4 on the number line.

    0 |---|---|---|---|---| 1
      0 1/4 1/2 3/4 1

Uses of fractions in real life

Fractions are used in many real-life situations:

  • Cooking: Recipes often call for fractions to measure ingredients, such as 1/2 cup sugar.
  • Time: A quarter of an hour represents 1/4 of an hour.
  • Purchases: Sometimes discounts are given in fractions, such as 1/3 off.
  • Construction: The measurement may involve different parts, such as cutting a piece of wood 3/8 meter long.

By understanding fractions we can solve many real-life problems more easily and with confidence.

Review of fractions

Fractions are a fundamental concept in math that helps us understand parts of a whole. Whether it's understanding pizza slices or scaled models, fractions are everywhere, and the more comfortable we are with them, the better!

Practice working with fractions regularly through exercises, and try to recognize the fractions around you. With time and practice, understanding fractions can become as natural as counting whole numbers.


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Understanding Fractions

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