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 → Measurement → Area and Perimeter ↓


Finding Area by Counting Squares


In math, area is the amount of space inside a closed shape. It's an important concept, especially in measurement. When you think about the floor of your room, a football field, or a piece of land, what you're thinking about is area. Understanding how to find the area of different shapes is an essential skill. In grade 3, students learn one of the simplest ways to find area: counting squares.

Understanding the region

Area can be understood as the "space" that a shape covers. Imagine a flat object placed on a table. The surface of the table that is covered by the object is its area. We usually measure area using square units. A square unit is simply a square that is one unit long on each side. Depending on what you are measuring, the unit can be centimeters, meters, inches, feet, etc.

Square calculation method

The easiest way to find the area of a shape, especially for young learners, is to count how many square units it contains. This method is especially useful for calculating the areas of rectangles and squares drawn on a grid.

Examples: square

Let's start by finding the area of a simple square. Consider the square below on the grid:

___________________ | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | | | | | # | |---+---+---+---+---| | | | | | # | |---+---+---+---+---| | # | # | # | # | # | |___|___|___|___|___|
___________________ | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | | | | | # | |---+---+---+---+---| | | | | | # | |---+---+---+---+---| | # | # | # | # | # | |___|___|___|___|___|

The square above is filled with squares of 1 unit by 1 unit. If we count the number of small squares, we will find that it is a 5 by 5 grid. So we have a total of 25 (since there are 5 rows of 5 squares) small squares. Thus, the area of this square is 25 square units.

Examples: rectangle

Let's take another example with a rectangle:

___________________ | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | # | # | # | # | # | |---+---+---+---+---| | # | # | # | # | # | |---+---+---+---+---|
___________________ | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | | | | | | |---+---+---+---+---| | # | # | # | # | # | |---+---+---+---+---| | # | # | # | # | # | |---+---+---+---+---|

This rectangle is 5 units wide and 2 units high. To find the area, we again count the number of small squares. If we look at each row, there are 5 squares. We have 2 such rows. Therefore, the total number of small squares is 10 (5 squares per row times 2 rows). Thus, the area of this rectangle is 10 square units.

Using rectangular areas

To find the area of more complex rectangular areas, the method of calculating squares remains the same. You should always make sure that each row and each column is completely filled with unit squares.

Examples: irregular shapes

What if you have an irregular shape? Consider the shape on the grid below:

___________________ | | | # | # | | |---+---+---+---+---| | | # | # | | | |---+---+---+---+---| | # | # | | | | |---+---+---+---+---| | # | | | | | |___|___|___|___|___|
___________________ | | | # | # | | |---+---+---+---+---| | | # | # | | | |---+---+---+---+---| | # | # | | | | |---+---+---+---+---| | # | | | | | |___|___|___|___|___|

This shape does not cover a neat rectangle. To find its area, you count each square within the shape's boundary. You identify full squares and add up parts of square units when needed. In the grid above, the total number of full squares is 6.5 (6 full squares and 2 half squares combined into one). Therefore, the area is 6.5 square units.

Conceptual practice problems

Practice by considering the following figures and try to find their area:

1. ___________ | | | | |---+---+---| | | | # | |---+---+---| | | | # | |---+---+---| | | # | # | |___|___|___| 2. ________________ | | | | | |---+---+---+---| | | | | # | |---+---+---+---| | | # | # | # | |---+---+---+---| | # | # | # | # | |___|___|___|___| 3. ___________ | | | | |---+---+---| | | # | # | |---+---+---| | # | # | # | |---+---+---| | # | # | | |___|___|___|
1. ___________ | | | | |---+---+---| | | | # | |---+---+---| | | | # | |---+---+---| | | # | # | |___|___|___| 2. ________________ | | | | | |---+---+---+---| | | | | # | |---+---+---+---| | | # | # | # | |---+---+---+---| | # | # | # | # | |___|___|___|___| 3. ___________ | | | | |---+---+---| | | # | # | |---+---+---| | # | # | # | |---+---+---| | # | # | | |___|___|___|

Calculate their area using the square counting method.

Mathematical understanding behind area calculation

Understanding counting squares provides the basis for learning the formulas for calculating the area of rectangles and squares. The underlying formula when counting square units is:

Area = Length × Width

Since the length and width represent the number of unit squares in two directions of the rectangle, multiplying them gives the total number of small squares contained within the rectangle. This is why counting squares works so directly for rectangles.

Conclusion

The method of finding area by counting squares not only introduces young learners to measuring space from shape, but also grounds the understanding in concrete terms. As one counts and visualizes unit tiles, they gain a deeper understanding of what it means to measure area before moving to algebraic formulas in later grades. Hands-on practice through such counting, reinforcement through shape practice, and continued engagement for skill mastery are encouraged.


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Finding Area by Counting Squares

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