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 ↓


Angles


Angles are a fundamental concept in geometry. They are everywhere in our daily lives, from the corners of a book to the hands of a watch. Understanding angles can be both fun and educational, and it helps us view the world mathematically.

What is the angle?

An angle is formed when two lines meet at the same end point. This end point is called the vertex of the angle, and the two lines are called the sides or arms of the angle.

    A
     ,
      ,
       ,
        C -------- B

Here, in this view, the angle is formed at point C, which is the vertex. The sides are lines AC and CB.

How to measure angles?

Angles are measured in degrees, which is a unit of measurement in circles. A full circle is 360 degrees. When you open your arms to make a circle, you create 360 degrees!

Right angle

The right angle forms a square corner. It is always 90 degrees.

      A
      , 
      , 
      C -------- B

In this diagram, angle ACB is a right angle because it forms a 90 degree corner.

Acute angle

An acute angle is an angle that is less than 90 degrees. It looks sharp or narrow.

       B
      ,
     ,
    ,
   A -------- C

In this diagram, angle BAC is an acute angle because it is less than 90 degrees.

Obtuse angle

An obtuse angle is an angle that is more than 90 degrees but less than 180 degrees. It looks wide.

  C
   ,
    ,
     ,
      A -------- B

In this diagram, angle ACB is an obtuse angle because it is wide and more than 90 degrees.

Straight angle

A straight angle looks like a straight line and is exactly 180 degrees.

A ------------- B ------------- C

Here, angle ABC is a straight angle as it forms a straight line.

Naming angles

An angle is named by its vertex, which is the point where the two sides meet. Sometimes, angles can also be named by three points: the point where one side begins, the vertex, and the point where the other side ends.

For example, consider:

  A
 ,
,
BC
  • Here, the angle can be called ∠A if A is the vertex.
  • It can also be called ∠BAC or ∠CAB.

Types of angles in everyday life

Angles play an important role in our everyday lives, often in ways we don't consciously recognize. Let's look at where we see different types of angles:

Right angles in everyday life

  • The corner of your notebook or book forms a right angle.
  • Doors and windows usually form right angles with the floor.

Acute angles in daily life

  • The beak of a bird makes an acute angle.
  • The hands of a clock make an acute angle at 10:10.

Obtuse angles in daily life

  • At 8:00 o'clock the angle between the minute and hour hands of a clock makes an obtuse angle.
  • If one keeps his arms fully open, he forms an obtuse angle.

Straight angles in everyday life

  • The horizon looks like a straight angle.
  • When the clock hands are at 6:00, they form a right angle.

How to build an angle?

You can use a variety of tools to draw and measure angles, such as a protractor. Here's a simple way to draw an angle on paper:

  1. Draw a straight line using the ruler. This is the base of your angle.
  2. Place the focal point of the protractor at one end of the line.
  3. Find the degrees you want on the protractor and mark a point on the paper.
  4. Use the ruler to connect the end point to the marked point to create an angle.

Practice identifying angles

Let's practice identifying angles in some examples. Look at these diagrams and try to name the angles:

1.
      P
     ,
    ,
   QR

Identify angle ∠QPR.

2.
X--------Y--------Z

What type of angle does XYZ make?

3.
     M
      ,
       ,
        No

Identify angle ∠MNO.

Practical activity

Try making your own angle checking tool out of cardboard or paper. You can cut out different angle shapes and sort them to practice identifying each type.

Why learn about angles?

Learning about angles is important because they are a fundamental component of mathematics that appear in almost every aspect of life. Knowing how to measure and identify angles helps us solve problems, whether it's in education, engineering, or personal projects like crafts and art.

Understanding angles is foundational to later math lessons such as trigonometry, calculus, and a variety of fields such as architecture, physics, and even art.

Conclusion

Angles aren't just mathematical terms - they're a way of looking at and organizing the world. When you understand angles, you can understand the shapes, patterns, and mechanisms that govern both natural and artificial objects. So the next time you look at a corner, a clock, or your bare arms, remember that you're looking at angles in action. Keep exploring and discovering angles in everything around you!

Understanding the different types of angles and practicing observing and measuring them can help you gain insight into both geometry and the environment around you.


Grade 3 → 4.3


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Angles

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