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 → Number Sense and Numeration → Operations with Whole Numbers ↓


Division as Equal Sharing


Division in math is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. In grade 3 math, one of the fundamental concepts students learn is "division as equal distribution." This concept helps students understand how to divide numbers by breaking groups into equal parts. In this lengthy explanation, we will understand division as equal distribution in detail, including examples and visual aids to help enhance understanding.

Understanding partitioning

Before we dive into dividing equally, let us first understand what division really means. Division is the process of dividing a number into equal parts. For example, if you have 8 apples and you want to divide them equally among 4 friends, each friend will get 2 apples. Dividing into equal parts is the essence of division.

8 ÷ 4 = 2

In this example, 8 is called the quotient, 4 is called the divisor, and 2 is called the quotient.

Partition as equal sharing

Division as equal sharing is a simple but powerful way to understand division. It helps students visualize division as distributing items into equal groups. Let's explore this concept further with examples and illustrations.

Example 1: Handing out candies

Imagine you have 12 candies and you want to divide them equally among 3 friends. How many candies will each friend get?

12 ÷ 3 = ?

Step-by-step solution:

  1. Start by understanding the problem: You have 12 candies that you need to divide equally among three friends.
  2. Think of the candies as one large group of 12.
  3. Begin dividing the candies into equal groups of three.
  4. Continue distributing until all the candies have been distributed:
    Each group will get 4 candies.

The calculation to find out how many candies each friend will get is as follows:

12 ÷ 3 = 4
4 4 4 group 1 Group 2 Group 3

Each friend gets 4 candies, and the candies are distributed equally.

More text examples: Division in daily life

Equal sharing can be applied to many everyday situations. Here are some more examples:

Example 2: Baking cupcakes

Let's say you've made 24 cupcakes for a party and you want to arrange them equally on 4 plates. How many cupcakes will be on each plate?

24 ÷ 4 = ?
  1. Total cupcakes: 24
  2. Available Plates: 4
  3. Begin dividing the cupcakes evenly onto each plate.
  4. Each plate gets:
    24 ÷ 4 = 6

So, each plate will have 6 cupcakes.

Exploring further: The concept of residues

When dividing, sometimes the numbers do not divide evenly. This leftover part is called the remainder. Let's look at an example.

Example 3: Dividing marbles

You have 10 marbles and you want to share them with 3 friends. How many marbles will each friend get and are there any marbles left?

10 ÷ 3 = ?
  1. Total marbles: 10
  2. Friends: 3
  3. Begin dividing the marbles into equal groups of three.
  4. Each group may have 3 marbles, but one will be left over, because 9 marbles will be evenly distributed and 1 marble will be left over.

This can be expressed as:

10 ÷ 3 = 3 remainder 1

This means that each friend will get 3 marbles, and 1 marble will be left over.

3 3 3 1 left

Visualizing partitions with tables

Arrays are another great way to represent partitions. They give a concrete representation of the distribution.

Example 4: Image table

To solve 15 ÷ 5 using an array, imagine 15 objects placed in a grid that has 5 rows. How many columns will there be?

Since the grid of objects is made up of equal rows of objects, each column contains 3 objects. So:

15 ÷ 5 = 3

The object array demonstrates that we can distribute evenly into groups of 5.

Interactive exercises with division

At home or in the classroom, students can practice division as equal sharing with simple activities. For example:

Practice activity 1: Sharing pebbles

Take 18 pebbles and divide them equally into 6 containers. Find how many pebbles will go into each container?

18 ÷ 6 = ?

Practice activity 2: Toy cars

You have 16 toy cars, and you want to give an equal number of toy cars to each child at the party. If there are 4 children, how many cars will each child get?

16 ÷ 4 = ?

Conclusion

Division as equal sharing is a fundamental skill in math. It helps students understand how to solve real-life problems that involve sharing equally. By using visual examples, step-by-step methods, and practical exercises, students can develop a strong understanding of this essential mathematical concept. Understanding division through the lens of equal sharing not only simplifies the subject but also makes math more accessible and enjoyable.


Grade 3 → 1.2.5


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Division as Equal Sharing

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