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 ↓


Comparing Angles (Acute, Right, Obtuse)


An angle is a way to measure how two lines come together at a point. In geometry, angles are an important part of understanding shapes, figures, and how they fit together. Today, we'll learn about three special types of angles you can find: acute angles, right angles, and obtuse angles. Let's learn about each of these in detail!

What is the angle?

Before we discuss specific types of angles, let's understand what an angle actually is. An angle is formed when two rays (or lines) start from the same point. This point is called the vertex. Each ray is called a side of the angle.

The size of an angle is measured in degrees. A complete circle around a point is 360 degrees. A semicircle, or a straight line through the point, is 180 degrees. Angles are simply a fraction of a circle.

Acute angle

An acute angle is an angle that is less than 90 degrees. These are small angles that appear sharp or narrow. Think of the tip of a slice of pizza or the hands of a clock when it shows 1 o'clock.

Intense

Right angles

A right angle is exactly 90 degrees. It's the angle you see when you have a perfect "L" shape. If you look around, you'll see right angles everywhere - the corners of a book, the edges of a piece of paper, even in the letter "L." Right angles are a great way for people to understand why squares and rectangles look square or rectangular.

Correct

Obtuse angle

An obtuse angle is one that is more than 90 degrees but less than 180 degrees. It looks wide or spacious. Imagine a book opened from the middle, the pages form an angle larger than a right angle. This wide difference is an example of an obtuse angle.

Frustrated

Comparing angles with real-world examples

Let's explore real-life scenarios where we might see these angles. Understanding them can make it easier to identify these angles around you:

  • Acute angle: Think of the blades of scissors, which often form an acute angle when partially closed. Another example is a slice of pizza—especially small slices.
  • Right angles: Check the corners of windows, doors and floor tiles. These often have right angles.
  • Obtuse angle: When the fans open or close, or when the clock shows 8 o’clock, it forms an obtuse angle.

To identify these angles on paper, you can use a protractor, which is a useful tool for measuring the size of an angle. When using a protractor:

  1. Place the midpoint of the protractor at the vertex of the angle.
  2. Align one side of the angle with the zero line of the protractor.
  3. The number that comes on the other side is the measure of the angle.

Following are simple ways to remember these angles:

  • Think "a cutie" for acute angles because they are short and narrow.
  • Remember "right is right" The perfect L shape is easy to visualize.
  • "Moreover” means broader or more extensive than necessary.

Simple exercises

Here are some simple exercises to reinforce our understanding of angles:

Exercise 1: Sort the angles

Look at the following descriptions and determine whether each description describes an acute angle, a right angle, or an obtuse angle:

  1. 45 degree angle.
  2. 90 degree angle.
  3. Angle of 120 degrees.

Answer:

  • 45 degrees - acute angle
  • 90 degrees - right angle
  • 120 degrees - obtuse angle

Exercise 2: Find the angle

Imagine the different hands of a clock at the following times. Determine whether the angle formed is an acute angle, a right angle, or an obtuse angle:

  1. 3 o'clock
  2. at 5 o'clock
  3. at 2 o'clock

Answer:

  • 3 o'clock - right angle
  • 5 o'clock - obtuse angle
  • 2 o'clock - acute angle

Conclusion

Understanding angles is one step closer to knowing how the world fits together geometrically. Every shape, every object in your surroundings, can tell you what place and purpose angles have. Remember, acute angles are small, right angles fit perfectly like a corner, and obtuse angles are wide and spacious.

With practice, you'll easily recognize and calculate these angles in your math problems and identify them in everyday life, too!


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Comparing Angles (Acute, Right, Obtuse)

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