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 ↓


Describing Attributes of 2D and 3D Shapes


Geometry is an essential part of mathematics that deals with shapes. These shapes can be two-dimensional (2D) or three-dimensional (3D). In this article, we will explore the fundamental properties of these shapes to strengthen our understanding of basic geometry. We will start by looking at the properties of 2D shapes, and then move on to 3D shapes.

Understanding 2D shapes

Two-dimensional shapes are flat and can be drawn on a piece of paper. These shapes have length and width, but no depth. Common examples of 2D shapes include squares, rectangles, triangles, and circles.

Common 2D shapes and their properties

Let's explore some common 2D shapes:

1. Square

A square is a four-sided polygon, known as a quadrilateral. The four sides of a square are of equal length and all four angles are right angles, meaning they are 90 degrees.

Visual example of the class:

Class characteristics:

  • four equal sides
  • Four right angles
  • opposite sides are parallel

2. Rectangle

A rectangle is similar to a square, but its opposite sides are of equal length, not all four. A rectangle also has four right angles.

Visual example of a rectangle:

Characteristics of rectangle:

  • opposite sides are equal and parallel
  • Four right angles

3. Triangle

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

Visual example of a triangle:

Characteristics of triangle:

  • Three sides
  • Three angles
  • The sum of all angles is 180 degrees

4. Circle

A circle is a simple closed figure. It is the set of all points in the plane that are at a fixed distance from a fixed point, called the centre.

Visual example of a circle:

Characteristics of a circle:

  • There is no side to it
  • Every point on the circumference is the same distance from the center
  • Infinite lines of symmetry

Understanding 3D shapes

Three-dimensional shapes have length, width, and depth or height. They can be seen all around us in real life. 3D shapes are also called solid shapes. Common examples include cubes, spheres, cylinders, and pyramids.

Common 3D shapes and their properties

1. Cube

The cube is the 3D version of a square. It has six square faces, all of equal size.

Visual example of a cube:

Characteristics of the cube:

  • Six equal square faces
  • 12 equal edges
  • Eight vertices (corners)

2. Sphere

A sphere is a perfectly round 3D shape, such as a basketball. Every point on the surface of the sphere is the same distance from its center.

Visual example of spheres:

Characteristics of a sphere:

  • No face
  • a curved surface
  • No edges or vertices

3. Cylinder

A cylinder has two parallel circular bases connected by a curved surface at a fixed distance from each other.

Visual example of a cylinder:

Cylinder features:

  • two circular faces
  • a curved surface
  • No top

4. Pyramid

Pyramids have polygonal bases and triangular faces that connect the bases to a common point (the apex).

Visual example of a pyramid:

Characteristics of the pyramid

  • has a base and a vertex
  • The base can be any polygon
  • Triangular faces

Comparison of 2D and 3D shapes

2D and 3D shapes have their own characteristics that make them unique. Here are some comparisons:

  • Dimensions:
    • 2D shapes have two dimensions: length and width.
    • 3D shapes have three dimensions: length, width, and height.
  • Representation:
    • 2D shapes can be drawn on paper because they are flat.
    • 3D shapes can be represented using models or images that show depth.
  • Appearance in real life:
    • Examples of 2D shapes include images such as triangles and circles.
    • Examples of 3D shapes include balls (spheres), boxes (cubes), and cans (cylinders).

Exploration and activities

Let us look at some activities to understand these shapes better:

Activity 1: Shape search

Look around your home, school or playground. Identify different objects that resemble the 2D and 3D shapes we have discussed. For example:

  • Is the clock in your classroom circular?
  • Is a cereal box a rectangular prism (a type of 3D rectangle)?
  • Are the windows square?

Activity 2: Painting and construction

Use paper, scissors and glue to cut out 2D shapes. Try making these shapes by drawing them first and then cutting them out. When you have these shapes, create 3D shapes using objects like clay, building blocks or paper. This will not only be fun but will also give you a practical understanding of the dimensions and characteristics of these shapes.

Activity 3: Count and compare

Count the sides, edges and vertices (corners) of various shapes:

  • How many sides does a pentagon (2D shape with 5 sides) have?
  • Count the edges and vertices of the cube.

Use these calculations to compare different shapes. Which has more sides? Which has more vertices?

Conclusion

Understanding the properties of 2D and 3D shapes is a foundational skill in geometry. It helps us better understand the world around us, as everything can be broken down into these basic shapes, whether we're talking about artwork, architecture, or nature. By identifying and describing the properties of shapes, we lay the groundwork for more complex geometric concepts, such as symmetry, tessellations, and transformations.


Grade 3 → 4.1.3


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Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)
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Recognizing Parallel and Perpendicular Lines

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Describing Attributes of 2D and 3D Shapes

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