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 of a Whole and Part of a Set


Understanding fractions is a fundamental part of math that allows us to express parts of a whole or parts of a set. In grade 3 math, students begin to explore the concept of fractions in a very concrete way. By learning about fractions, students begin to see how numbers can be divided into smaller segments and how this can help describe quantities.

Parts of a whole

The idea of a fraction is simple: it represents a part of something. When we talk about fractions of a whole, we are looking at how to divide an object or collection of objects into equal parts.

Imagine a pizza divided into equal slices. If a pizza is cut into 4 equal slices, each slice represents a fraction of the whole pizza. The whole pizza is 1 and each slice is a part of that whole. If you take one slice, the fraction is represented as: 

1/4
Here, 1 is the number of slices you have, and 4 is the total number of equal slices the pizza will be cut into.

In this picture, the orange shaded portion represents 1/4 of the whole circle (pizza). If we take two slices, the fraction will be: 

2/4
which can be simplified to 1/2. Simplifying fractions involves dividing the numerator (top number) and the denominator (bottom number) by the same number.

Fractions as part of a group

Now, let's understand fractions as part of a group. This concept is about determining how many items in a collection make up a fraction. Consider a group of 12 apples. If 3 of them are red and the rest are green, then the fraction representing the red apples is: 

3/12
Which simplifies to 1/4. This means that one-fourth of the apples are red.

In this picture, the red circles represent the part of the collection that is red. Notice the visual aspect here: it helps us see and understand what 3/12 means for a set.

Similarly, if we want to know the fraction of green apples, we will take the number of green apples (9) and write it above the total number of apples (12): 

9/12
This can be further simplified to 3/4.

To imagine and understand

The use of visuals is vital to understanding fractions. It can be helpful to use number lines or bar models to represent fractions, along with real-life examples such as pizza and apples.

Number line example

The number line is a straight line with numbers placed at even intervals. Fractions can be represented on the number line by dividing each part into equal parts. Let's see how this works with 1/2.

0 1/2 1

On the number line, 1/2 is represented exactly between 0 and 1. This representation helps in understanding the value of fractions compared to whole numbers.

Bar model example

Bar models provide another way to look at fractions. Imagine a chocolate bar that can be divided into equal parts. Here's what one-third would look like on the bar model:

1/3

In the bar model, 1/3 is shaded, showing part of the whole bar. Such visual models make it easier to understand how fractions are divided into parts.

Constructing and comparing fractions

We can make a fraction by breaking any whole into as many equal parts as we want. For example, if we divide 5 oranges equally among 3 people, we start by writing the fraction for each person's share:

Each person receives: 

1 2/3
Oranges. Here: 1 is the whole orange each gets, and 2/3 is the share of the other orange.

Additionally, comparing fractions can be made easier by using these concepts. For example, which is bigger, 1/3 or 1/4? We can compare these by using visualization or by thinking:

It is clear from the bar model that 1/3 has a larger portion shaded than 1/4. Therefore, 1/3 is larger than 1/4.

Applications in everyday life

Fractions are not just a part of math classes, but they are also an essential part of everyday life. We use fractions whenever we cook and divide portions. For example, a recipe may call for two-thirds of a cup of sugar.

While shopping, we may face a situation where there are many fruits and vegetables, but we want to take only half a dozen or a third of the fruits and vegetables.

Fractions are used to report statistics in sporting events. A player may hit two-fifths of shots successfully. To understand these situations, it is important to have a good grasp on fractions.

Finally, the importance of fractions can be seen in work and partnerships, as evidenced by sharing tasks and dividing responsibilities, making it easier for children to understand the importance and practical use of fractions.

Conclusion

Understanding fractions is very important for young students as it forms the basis for more advanced mathematical concepts. Although this concept may seem abstract at first, it can be made more relevant and understandable by relating it to everyday activities such as cutting a pizza or sharing sweets among friends.

Using visual models like number lines and bar graphs helps students better visualize complex ideas and simplify them into smaller, understandable parts. Recognizing parts of a whole and parts of a set can keep fractions concrete and meaningful, helping young learners apply these concepts outside of academic environments.


Grade 3 → 2.1.2


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Identifying and Representing Fractions
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Comparing and Ordering Fractions with Like Denominators

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Fractions of a Whole and Part of a Set

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