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Grade 4 (age 9-10)

grade 4 Angles

An angle is formed by two rays that start at the same point, and its size tells how far apart the rays are opened. You meet angles of different sizes every day, for example when you open scissors or a door. Angles are measured with a protractor in degrees (°): a right angle is 90°, a smaller angle is acute, and one bigger than a right angle but less than 180° is obtuse. Move the slider to open the angle; the protractor and the clock hand turn through the same number of degrees together.

What Is an Angle?

📐 Two Rays Make an Angle
①Like the two blades of scissors, two rays from one point make an angle
②The wider you open the rays, the bigger the angle
③The length of the rays has nothing to do with the size of the angle
④Angles are measured with a protractor in degrees (°)

Measuring with a Protractor

45°
💡 Kinds of Angles
①Acute: more than 0° and less than 90°
②Right: exactly 90°, like the corner of a notebook
③Obtuse: more than 90° and less than 180°
④When the two rays form a straight line, the angle is 180° and is called a straight angle
⑤0° is not acute: the rays lie on top of each other and have not opened yet

Angles as Turns

🔄 Angles and Turns
①A full turn of a clock hand is 360°
②A half turn is 180°, and a quarter turn is 90°
③The minute hand turns 6° every minute, so it turns 90° in 15 minutes and 180° in 30 minutes
④The angle the hand turns from 12 in the picture is the same size as the angle on the protractor above

Summary

Right Angle
Right angle = 90°
The angle you get by folding a sheet of paper neatly twice
Comparing Angles
acute < 90° < obtuse < 180°
Smaller than a right angle is acute; bigger than a right angle but less than 180° is obtuse
Full Turn
Full turn = 360°
A half turn is 180° and a quarter turn is 90°
🎯 Summary
①The size of an angle is how far apart its two rays open, measured in degrees (°)
②A right angle is 90°, and a straight line is 180°
③An acute angle is smaller than a right angle; an obtuse angle is bigger than a right angle but less than 180°
④A full turn is 360°, and a half turn is 180°
⑤The minute hand turns 6° each minute

Examples and Unit Test

Example 1
Is a 70° angle acute, right or obtuse?
1
An acute angle is more than 0° and less than 90°.
2
70° is more than 0° and less than 90°, so it is acute.
▸ Acute
Less than 90° is acute, exactly 90° is right, and between 90° and 180° is obtuse.
Example 2
How many degrees does a clock hand turn in a half turn?
1
A full turn is 360°.
2
A half turn is half of 360°, so it is 180°.
▸ 180°
The minute hand turns exactly 180° in 30 minutes.
Unit Test
How many degrees does a clock hand turn in one full turn?
①90°
②180°
③270°
④360°
▸ ④ 360°
1
A full turn means going all the way around back to the start.
2
A half turn is 180°, and a full turn is twice that, 360°.
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Estimation — Number Range
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Types of Triangles

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