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


Geometry is an exciting and fun part of mathematics. It helps us understand the shapes and spaces that we see around us. In Grade 3, children learn the basics of geometry, including shapes, lines, angles, and more. Let us explore these concepts in detail.

What is geometry?

Geometry is the branch of mathematics that deals with shapes and their properties. It involves the study of points, lines, surfaces, solids, and their relationship to one another. In our daily lives, everything around us has a shape, and that is why geometry is important.

Basic Shapes

There are many shapes in geometry, but some are basic and form the building blocks of more complex shapes. Let's take a look at these shapes:

Circle

A circle is a round shape. It is perfectly round and every point on its edge is the same distance from the center.

<svg width="100" height="100"> <circle cx="50" cy="50" r="40" stroke="black" stroke-width="2" fill="none" /> </svg>

The above figure shows a circle.

Square

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

<svg width="100" height="100"> <rect width="80" height="80" x="10" y="10" stroke="black" stroke-width="2" fill="none" /> </svg>

Now look further and see that all the sides are equal.

Rectangle

A rectangle has equal opposite sides and four right angles. It is longer than it is wide or vice versa.

<svg width="150" height="100"> <rect width="120" height="60" x="15" y="20" stroke="black" stroke-width="2" fill="none" /> </svg>

It represents a rectangle with unequal adjacent sides.

Triangle

A triangle has three sides and three angles. There are different types of triangles depending upon the angles and sides.

<svg width="120" height="100"> <polygon points="60,10 10,90 110,90" stroke="black" stroke-width="2" fill="none"/> </svg>

Above is a simple triangle. Notice that this shape has three sides.

Understanding the lines

Lines are straight paths that extend somewhat endlessly in both directions. Lines can be straight or curved, but here we're focusing on straight lines.

Types of lines

Straight line

This is how it looks:

<svg width="200" height="20"> <line x1="10" y1="10" x2="190" y2="10" stroke="black" stroke-width="2" /> </svg>

Straight lines never bend. They go on endlessly in both directions.

Horizontal line

It goes from left to right:

<svg width="200" height="20"> <line x1="10" y1="10" x2="190" y2="10" stroke="black" stroke-width="2" /> </svg>

It is a horizontal line, similar to the horizon.

Vertical line

It goes up and down:

<svg width="20" height="200"> <line x1="10" y1="10" x2="10" y2="190" stroke="black" stroke-width="2" /> </svg>

A vertical line looks like this.

Parallel lines

Parallel lines are equidistant from each other and never meet:

<svg width="200" height="50"> <line x1="10" y1="10" x2="190" y2="10" stroke="black" stroke-width="2" /> <line x1="10" y1="40" x2="190" y2="40" stroke="black" stroke-width="2" /> </svg>

The lines above are parallel.

Intersected lines

Intersecting lines cross each other:

<svg width="200" height="200"> <line x1="10" y1="10" x2="190" y2="190" stroke="black" stroke-width="2" /> <line x1="190" y1="10" x2="10" y2="190" stroke="black" stroke-width="2" /> </svg>

Where they meet is called the point of intersection.

Finding angles

Angles are formed when two lines meet at a point. The space between the two lines forms an angle.

Types of angles

Right angle

Right angles look like this:

<svg width="100" height="100"> <line x1="50" y1="50" x2="50" y2="10" stroke="black" stroke-width="2"/> <line x1="50" y1="50" x2="90" y2="50" stroke="black" stroke-width="2"/> </svg>

This angle is 90 degrees.

Acute angle

Acute angles are smaller than right angles:

<svg width="100" height="100"> <line x1="50" y1="50" x2="80" y2="30" stroke="black" stroke-width="2"/> <line x1="50" y1="50" x2="90" y2="50" stroke="black" stroke-width="2"/> </svg>

The angles are less than 90 degrees.

Obtuse angle

Obtuse angles are larger than right angles:

<svg width="100" height="100"> <line x1="50" y1="50" x2="30" y2="70" stroke="black" stroke-width="2"/> <line x1="50" y1="50" x2="90" y2="50" stroke="black" stroke-width="2"/> </svg>

The angle is greater than 90 degrees.

Polygons and their properties

Polygons are shapes with three or more straight sides. They are named based on the number of sides:

Triangle (3 sides)

As we saw earlier, triangles are simple polygons with three sides.

<svg width="120" height="100"> <polygon points="60,10 10,90 110,90" stroke="black" stroke-width="2" fill="none"/> </svg>

Quadrilateral (4 sides)

A quadrilateral has four sides. For example, square and rectangle.

<svg width="120" height="100"> <polygon points="30,10 90,10 110,70 10,70" stroke="black" stroke-width="2" fill="none"/> </svg>

Pentagon (5 sides)

<svg width="150" height="150"> <polygon points="75,20 30,80 50,140 100,140 120,80" stroke="black" stroke-width="2" fill="none"/> </svg>

A pentagon has five sides.

Hexagon (6 sides)

<svg width="150" height="150"> <polygon points="75,10 20,50 20,100 75,140 130,100 130,50" stroke="black" stroke-width="2" fill="none"/> </svg>

Six-sided hexagons are often seen in nature, such as beehives.

More examples of shapes

Discover more shapes, like heptagons (7 sides), octagons (8 sides), and keep adding sides to discover more complex polygons.

Identical and equal size

If the shapes are the same they are congruent. If the shapes are the same but have different sizes they are similar.

Symmetry in geometry

A figure is symmetrical if it can be divided into two equal parts. The line dividing these parts is called the line of symmetry.

Examples of line of symmetry

Square symmetry

<svg width="100" height="100"> <rect width="80" height="80" x="10" y="10" stroke="black" stroke-width="2" fill="none" /> <line x1="50" y1="10" x2="50" y2="90" stroke="red" stroke-width="2"/> </svg>

A square has four lines of symmetry.

Circle symmetry

<svg width="120" height="120"> <circle cx="60" cy="60" r="50" stroke="black" stroke-width="2" fill="none"/> <line x1="60" y1="10" x2="60" y2="110" stroke="red" stroke-width="2"/> </svg>

A circle has infinite symmetry lines.

Perimeter and area

Perimeter

The perimeter is the distance around a shape. To find it, add up the lengths of all sides.

Example of a square, if each side is 4 units:

Perimeter = 4 + 4 + 4 + 4 = 16 units

Area

Area is the space inside a shape. Calculate area differently for different shapes.

Example of a square, if the sides are 4 units:

Area = 4 * 4 = 16 square units

Transformations

Transformations involve changing the position or size of a shape. There are three main types of transformations:

Translation

Moves a shape from one location to another.

Rotation

Rotates a shape around a point without changing its shape.

Reflection

Flips the shape over a line like a mirror image.

Conclusion

Geometry means understanding shapes, lines, angles and how they relate. It is everywhere around us and helps us understand the world better. By learning geometry we not only improve math skills but also enhance problem-solving and critical thinking abilities.

Keep exploring and trying new shapes and concepts in geometry. You will find that it is like unraveling the mysteries of both mathematics and nature.


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