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 ↓


Symmetry and Transformations


In geometry, symmetry and transformations are important concepts that help us understand the shapes and patterns we see around us. These topics are introduced in Grade 3 and help develop spatial reasoning and the ability to observe transformations. Let's dive into the details, starting with the concept of symmetry.

Symmetry

Symmetry is when one part of a shape or object is the same as another part when you flip, slide, or rotate it. A shape is symmetrical if you can divide it into two equal parts that are mirror images of each other.

Types of symmetry

You can see different types of symmetry in shapes:

  • Line symmetry (or mirror symmetry): This is the most common type of symmetry. A figure has line symmetry when a line can be drawn through it, and the two parts are mirror images of each other.
  • Rotational symmetry: A figure has rotational symmetry when it can be rotated (less than a full rotation) and still look the same.

Examples of Line Symmetry

Let's look at some simple examples of line symmetry.

Example 1: Symmetrical Shapes

Consider a simple geometric shape: a square. A square has 4 lines of symmetry. It can be divided along the following axes:

In this instance:

  • The red line divides the square horizontally into two equal parts.
  • The blue line divides the square vertically into two equal parts.
  • The green line divides the square diagonally from the bottom left to the top right.
  • The orange line divides the square diagonally from the top left to the bottom right.

Example 2: Alphabet isomorphism

Some letters of the alphabet also have a line of symmetry. For example, the letter "A" has a vertical line of symmetry.

A

In this illustration, the blue line divides the letter "A" into two equal parts that are mirror images of each other.

Exploring rotational symmetry

It might be a little more fun to explore rotational symmetry. Let's take a look at a simple shape to understand this concept better.

Example: Rotational symmetry in a triangle

A shape like an equilateral triangle has rotational symmetry. This means that if you rotate the triangle 120 degrees, it will still look exactly the same.

  Rotate 120°
  ,
 , 
,
,
 ,
   The original was rotated

In this example, after rotating the triangle 120 degrees twice, the triangle looks the same as its original state.

Transformations

Transformations are movements of shapes. They help to understand how a shape can change its state without changing its actual shape. There are four basic types of transformations in geometry:

  • Translation: Moving a shape without rotating or flipping it. This is like sliding the shape along a path.
  • Reflection: Flipping a figure on a line, creating a mirror image.
  • Rotation: Rotating a shape around a point or center.
  • Scaling (usually not included in Grade 3): Making a shape larger or smaller while maintaining its proportions.

Translation

During the move, every point in the shape travels the same distance in the same direction. Think of it as sliding a piece of paper smoothly across a table.

Example: Translating a rectangular shape

In this example, the rectangle on the left is moved to the right without changing its orientation or size.

Reflection

Reflection involves flipping a figure about a specific line, known as the line of reflection.

Example: Reflection at a vertical line

Here, the figure on the left is reflected across the vertical blue line, creating its mirror image on the right.

Rotation

Rotation means moving a figure around a fixed point. This point can be the center of the figure or any other point.

Example: Rotating a shape 90 degrees

Notice in this picture that the triangle rotates 90 degrees around the red dot.

Understanding through activities

Activities are a great way to deepen understanding of symmetry and transformations. Here are some activities to explore these concepts:

Activity 1: Finding symmetry

Materials: Paper, pencil and scissors.

  • Fold a piece of paper in half.
  • Draw a simple half-shape with a twist, such as a half heart.
  • Cut it and open both the halves to make a symmetrical shape.

Discuss where the line of symmetry is and explore other shapes using different bends.

Activity 2: Mirrors and reflections

Materials: Small mirror, paper, and objects like letters or shapes drawn on the paper.

  • Place the mirror at the edge of the drawn shape.
  • Observe the complete shape formed by the image.

Try drawing different shapes and letters to see their reflections.

Activity 3: Shapeshifting

Contents: Tangram Set.

  • Use tangrams to make shapes.
  • Slide, flip and rotate the different pieces to create new shapes.

Discover how many different shapes can be made by simply switching around tangram pieces.

Conclusion

Understanding symmetry and transformation helps build strong foundational geometry skills. These concepts are important not only in mathematics but also in everyday observation of the world around us. From art and design to nature, symmetry and transformation exist everywhere. Exploring through visual examples and activities can make learning these concepts interesting and enjoyable.

Remember, whether you're looking at butterfly wings or designs on a carpet, symmetry plays a fascinating role in the beauty and structure of the things around us. Transformations allow us to see how objects can change and still retain their original characteristics.


Grade 3 → 4.2


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Recognizing Parallel and Perpendicular Lines
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Recognizing Lines of Symmetry

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Symmetry and Transformations

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