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


In geometry, we learn about different shapes and their properties. Understanding shapes is an important aspect of math in grade 2. Let's learn about some common shapes and what makes them special.

Basic 2D shapes

2D shapes, also called two-dimensional shapes, are flat. They have length and width but no depth.

Circle

A circle is a circular figure in which every point on its edge is the same distance from the center. It has no sides or corners.

Area = π × radius²
Circumference = 2 × π × radius

Social class

A square has four equal sides and four right angles. All sides are of equal length.

Area = side × side
Perimeter = 4 × side

Rectangle

A rectangle has four sides and four right angles. Opposite sides are of equal length.

Area = length × width
Perimeter = 2 × (length + width)

Triangle

A triangle has three sides and three angles. The sum of the angles of a triangle is always 180 degrees.

Area = 1/2 × base × height
Perimeter = side1 + side2 + side3

3D shapes

3D shapes, also called three-dimensional shapes, have length, width, and depth (or height).

Cuboid

A cuboid has six rectangular faces, and its opposite faces are equal. It is like a box.

Volume = length × width × height
Surface Area = 2(lw + lh + wh)

Cube

A cube is a special type of cuboid in which all sides are equal. All faces are squares.

Volume = side³
Surface Area = 6 × side²

Cylinder

A cylinder has two parallel circular bases and a curved surface joining them.

Volume = π × radius² × height
Surface Area = 2 × π × radius × (radius + height)

Circle

A sphere is round like a ball. Every point on its surface is the same distance from its center.

Volume = 4/3 × π × radius³
Surface Area = 4 × π × radius²

Characteristics of shapes

Shapes have different characteristics that help us recognize and describe them.

Sides and corners (vertices)

  • A square has 4 sides and 4 corners.
  • A triangle has 3 sides and 3 corners.
  • A rectangle has 4 sides and 4 corners.
  • A circle has 0 sides and 0 corners.

Angle type

Angles are formed where two sides meet.

  • Right Angle: An angle of 90 degrees.
  • Acute Angle: An angle less than 90 degrees.
  • Obtuse Angle: An angle more than 90 degrees but less than 180 degrees.

Classification of shapes

Shapes can be classified based on their characteristics, such as number of sides, types of angles, or symmetry.

Symmetry

Symmetry means that a shape can be divided into two equal parts.

  • A square has 4 lines of symmetry.
  • A rectangle has two lines of symmetry.
  • A circle has infinite symmetry lines.

Examples and exercises

Let's practice recognizing and naming shapes.

Example 1

Look at the figure below:

What is its shape? It is a circle.

Example 2

Look at this figure:

How many sides does it have? It has 3 sides. Its shape is a triangle.

Practice

  1. Draw a shape with four equal sides. What is it called?
  2. Name a shape which has no sides or corners.
  3. Find a shape that has four sides but is not a square.

Conclusion

Understanding shapes and their properties is very important in math. It helps us describe the world around us. Practice recognizing different shapes and remember their special properties. Have fun learning!


Grade 2 → 4.1


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Shapes and Their Attributes

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