Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Geometry and Spatial Reasoning → Shapes and Their Attributes ↓


Identifying basic shapes (circle, triangle, square, rectangle)


Understanding basic shapes is an essential foundation in geometry and spatial reasoning. In this explanation, we'll explore the characteristics and examples of the four fundamental shapes: circle, triangle, square, and rectangle. These shapes are everywhere around us, and recognizing them helps solve problems and better understand the world.

Understanding the circle

A circle is a circular figure, every point on the edge of which is at the same distance from its center. This distance is called the radius. The entire distance around the circle is called the circumference or perimeter.

It's a circle. It's perfectly round!

Circles are everywhere. Here are some examples to consider:

  • Clock face.
  • A plate of food.
  • Wheels of a car.

The formula to calculate the circumference of a circle is:

Circumference = 2 × π × radius

Where π (pi) is approximately 3.14159. If the radius of a circle is 5 units, then the circumference will be:

2 × 3.14159 × 5 = 31.4159 units

Understanding the triangle

A triangle is a shape with three sides and three corners. Triangles can vary depending on the length of their sides and the size of their angles:

  • Equilateral triangle: All sides are the same length, and all angles are equal.
  • Isosceles triangle: Two sides are the same length, and two angles are equal.
  • Scalene triangle: All sides and angles are different.

This is an equilateral triangle. All sides are equal!

Triangles are strong shapes used in many real-world structures such as bridges and roofs. Here are some common places you might find them:

  • Trusses in roofs.
  • Supporting beams in bridges.
  • Designs in some jewellery.

Understanding square

A square is a four-sided shape in which all sides are the same length, and each angle is a right angle (90 degrees).

It's a square. All sides are equal, and so are the angles!

Squares are often found on tiles, game boards, and in various patterns. Here are some examples of where squares appear:

  • Chess board.
  • Floor tiles.
  • Some buildings have windows.

The formula for finding the area of a square is:

Area = side × side

If one side of a square is 4 units, then its area will be:

4 × 4 = 16 square units

Understanding the rectangle

A rectangle is a four-sided shape in which opposite sides are of equal length and each angle is a right angle.

This is a rectangle. Opposite sides are equal.

Rectangles are commonly used in everyday objects such as books, screens, and doors. You may recognize them in the following:

  • Smartphone screen.
  • Doors.
  • Books and notebooks.

The formula for finding the area of a rectangle is:

Area = length × width

If the length is 5 units and the breadth is 3 units, then the area is:

5 × 3 = 15 square units

Recognizing shapes in our environment

Recognizing these basic shapes helps us understand the environment. These shapes form the basis of countless designs, from the architectural structures we live in to the tools we use every day. To identify these shapes, consider the following:

  • Wheels of vehicles (circles).
  • Triangles in bridge design.
  • Paved paths using square tiles.
  • Rectangular doors and windows.

The importance of shape recognition

Understanding shapes is crucial for a variety of mathematical and practical applications. Mastering the ability to recognize shape features and reason with them is foundational to further study in geometry, algebra, and even fields such as architecture, engineering, and computer graphics.

In short, the skills to distinguish and work with these shapes are crucial not only for academic success, but also for efficiently understanding and interacting with the world.

Practicing with real-world examples and exercises significantly improves spatial reasoning and geometric understanding. To further improve these skills, one can consider the following activities:

  • Create a shape collage.
  • Solving puzzles with different shapes.
  • Drawing and tracing shapes for art projects.

As learners progress in their educational journey, the abilities gained from understanding these basic shapes will provide a strong framework for tackling more complex geometric concepts and problems.


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Identifying basic shapes (circle, triangle, square, rectangle)

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