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 → Geometry ↓


Properties of Shapes


Geometry is an important part of mathematics that teaches us about the world of shapes. In Grade 3, students explore the properties and characteristics of different shapes. Understanding these fundamental concepts helps us identify and compare different shapes in our everyday surroundings.

What is the size?

A shape is a two-dimensional outline or surface that forms the boundary of an object. Shapes can be simple, such as circles, squares, and triangles, or complex, such as hexagons and octagons.

Basic properties of shapes

Let's look at some basic properties and characteristics of shapes:

1. Sides and corners (vertex)

- A side is a straight line that forms part of the boundary of a shape. - A corner, also known as a vertex, is the point where two sides meet.

2. Edge

Edges are the lines where two surfaces meet. In the context of 2D shapes, they are simply the sides of the shape.

3. Faces

A face is a flat surface that forms part of the boundary of a solid (three-dimensional) object.

4. Line segment

A line segment is a part of a line between two end points and includes all the points between the end points.

[Point A] -- [Point B]
[Point A] -- [Point B]

Types of basic shapes

Let us look at some basic shapes that are often taught in Class 3.

Circles

A circle is a circular shape with no sides or corners. Every point on a circle is the same distance from the center. The distance around the circle is called the circumference, and the distance from the center to the edge is called the radius.

radius

Triangle

A triangle has three sides and three corners. The sum of the angles in a triangle is always 180 degrees. Triangles can be of different types depending on the length of their sides.

Social class

A square is a polygon with four equal sides and four right angles. Each angle in a square is 90 degrees. Squares have lines of symmetry and rotational symmetry.

Rectangle

Like squares, rectangles also have four sides and four right angles. However, unlike squares, opposite sides are equal in length, and adjacent sides are not equal.

Polygon

A polygon is a closed shape with straight sides. Triangles, squares, and hexagons are examples of polygons. A polygon can have any number of sides.

Special properties of shapes

Shapes have several properties that make them unique and recognizable. Knowing these properties helps us understand the world better.

Symmetry

A figure is symmetrical if it can be divided into two equal halves. Symmetrical figures have at least one line of symmetry, also called a mirror line.

Congruence

Similar shapes are identical in shape and size. When two shapes are similar, they cover each other completely when placed on top of each other.

Circumference

The perimeter of a shape is the distance around it. For polygons, you can calculate the perimeter by adding up the lengths of all sides.

Math Formulas

Perimeter of a rectangle

Perimeter = 2 * (Length + Width)
Perimeter = 2 * (Length + Width)

Perimeter of a square

Perimeter = 4 * side
Perimeter = 4 * side

Area of a Rectangle

Area = Length * Width
Area = Length * Width

Area of a Square

Area = side * side
Area = side * side

Putting Everything Together with Examples

Let's apply what we've learned with some examples.

Example 1: Triangle

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then its perimeter is:

Perimeter = 3 cm + 4 cm + 5 cm = 12 cm
Perimeter = 3 cm + 4 cm + 5 cm = 12 cm

Example 2: Rectangle

For a rectangle of length 8 cm and width 3 cm, the perimeter and area are:

Perimeter = 2 * (8 cm + 3 cm) = 22 cm
Perimeter = 2 * (8 cm + 3 cm) = 22 cm

Area = 8 cm * 3 cm = 24 cm²
Area = 8 cm * 3 cm = 24 cm²

Example 3: Square

If the length of the side of a square is 5 cm, then the perimeter and area are:

Perimeter = 4 * 5 cm = 20 cm
Perimeter = 4 * 5 cm = 20 cm

Area = 5 cm * 5 cm = 25 cm²
Area = 5 cm * 5 cm = 25 cm²

Practice comparing shapes

Let's compare some different shapes. Look at their properties and see how they are alike and how they are different.

Figure A: Circle

  • No edges or corners
  • Constant radius
  • Perfectly round

Shape B: Square

  • 4 equal sides
  • 4 corners, each 90 degrees
  • Symmetrical

Figure C: Triangle

  • 3rd Party
  • 3 corners
  • The sum of the angles is 180 degrees

By comparison, you can see that the circle is different from the square and triangle because it has no sides or corners, while the square and triangle have straight sides and corners.

This detailed overview introduces grade 3 students to the fundamental properties and characteristics of different shapes. By recognizing and understanding these properties, students can apply them in practical situations and build a strong foundation for deeper mathematical study in the future.


Grade 3 → 4.1


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Properties of Shapes

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