Investigation Title: Angles

glossaryitem

Angle:
-the figure formed by two rays or two line segments with a common endpoint called the vertex.

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Acute Angle:
-an angle whose measure is less than 90°.

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Right Angle:
-an angle whose measure is 90°.

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Obtuse Angle:
-an angle whose measure is more than 90° but less than 180°.

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Straight Angle:
-an angle whose measure is 180°.

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Reflex Angle:
-an angle whose measure is more than180° but less than 360°.

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Complementary Angles:
-two angles whose
sum is 90°.

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Supplementary Angles:
-two angles whose
sum is 180°.

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Congruent:
-exactly the same size and shape
- the symbol for congruency is º

timesaver

math 6-8

learningobjects

Three - Four Lessons

Protractors
Two strips of cardboard about 12cm X 2cm per student
Brad (paper fastener) per student
Geoboards and elastics
Dot Paper
Angles
(Guided Practice Sheet)
Constructing Angles with a Protractor
(Transparency)
Rolling for 360°
(Game)

Whole class
Pairs

Throughout the lessons reinforce angle terminology and encourage students to use it often.
Some students may have trouble handling a protractor. Walk them through the steps:
Be sure to read the measure from the correct scale. On a double scale protractor, an angle that looks to be less than 90°, the number less than 90° will be the measure. Conversely if the angle looks larger, students should read the greater number on the protractor.

What is an Angle?

Learning Object: MIGHTY MEASUREMENT
Investigation Title: Angles
Developmental

Students will use their estimation skills to estimate angles.
Students will classify, identify, and draw acute, right, obtuse, straight, reflex, complementary and supplementary angles.
Students will measure and draw angles using a protractor.
Students will find angle measures by exploring relationships.
Students will recognize angles in their environment.

Draw several different types of angles on the board (right, acute obtuse straight and reflex).
Include angles that are congruent.
Discuss what is common and different.
Guide students to identify angles that are congruent even if the orientation is different.
Ask students if they recall the definitions for the angles represented.

Have students construct an angle measurer.
Students connect a pair of cardboard strips (using brads) to make two movable angle arms.

Invite volunteers to measure the angles on the board, identify them as right, acute obtuse, straight and reflex and the angles that are congruent, and label them.
Three methods are used for naming angles: Ð I or Ð HIJ or Ð JIH.
Continue by having students use their angle measurer to draw, name, label and measure angles that are less than 90°, are 90°, between 90° and 180°, are 180° and more than 180°.

Display the transparency Constructing Angles with a Protractor and work through the activity.

Have pairs of students find different angles in the class. Encourage students to estimate sizes by using known angles, and understand that checking an estimate with a protractor is a way of refining estimation skills, it is not a judgment of whether an estimate is correct or incorrect. The goal is to increase students’ ability to visualize the measure of angles. For each use the angle measurer to assist in drawing the angle and to show the object with a sketch. Have students name the angles with letters and label them. Then use a protractor to measure the angle and record it.

Distribute elastics, geoboards and dot paper to pairs. Tell students they will investigate the relationship of complementary and supplementary angles. Ask one student to make a right angle on the geoboard and place an elastic at the vertex so that the angle is divided. The other student draws it on the dot paper and measures the two angles with a protractor. Have the students add the measurements. Be sure that the students exchange roles so both have practice with the geoboard and dot paper. Have pairs explore with several different pairs of angles by moving the elastic to form new pairs of angles. Challenge students to arrive at a definition for complementary angles.
Instruct students to repeat the activity for supplementary angles by first constructing a straight angle.

Students use geoboards, elastics and dot paper to investigate the sum of the angles in any triangle. Have pairs take turns creating different sized and shaped triangles, reproducing them on dot paper and measuring the interior angles. When the activity is complete, ask the pairs to make a generalization about the angles in any triangle. Ask how students could find the measurement of a third angle if they knew the measurement of the other two?
Continue with pairs creating quadrilaterals and measuring the four angles. Then ask students how they could find the measurement of a fourth angle if they knew the measurements of the other three.

Students often confuse terms for the different angles. Have them write a plan to teach someone how to remember the terms.
Ask the students to write about the conclusions they can draw about the interior angles of triangles and quadrilaterals.

As the students work, circulate and ask students to explain what is meant by complementary and supplementary angles; by acute, right, obtuse and straight angles.
Encourage them to describe their activities and conclusions. Assess the student’s use of manipulatives, vocabulary and reasoning skills.

Work through theAngles Guided Practice Sheet.
Play the.Rolling for 360° Game.
Investigate the use of angles in the semaphore flag signaling system. Students may enjoy preparing a short message for the rest of the class to decipher.
Semaphore Flag Signaling System