Angles

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Concept Plan


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= Teaching Outlines =

Activities
Foramtion of

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #1.Crazy Angles using Geogebra

 * Estimated Time: 40 minutes
 * Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
 * Prerequisites/Instructions, if any:
 * 1) The students should have a basic understanding about  point, rays, line segments and vertex.
 * 2) They should know how angles are formed.
 * 3) They should know that angles are measured in units called degrees. 360 ° is a full rotation (a circle)
 * 4) They should know to use a protractor and measure the  angles.
 * 5) They should know the meaning of terms acute, obtuse, straight, reflex, and complete angles.
 * Multimedia resources; Laptop
 * Website interactives/ links/ / Geogebra Applets

Developmental Questions:
 * Process:
 * 1) The teacher should recaptulate the concept of a point, line segment, ray, vertex and angles.
 * 2) The teacher should show how angles are formed.
 * 3) Discuss the concept of  cartesian plane, X and Y axes, rotation, and how it relates to angles.
 * 4) Demonstrate how to measure angles using a protractor.
 * 5) Define and illustrate the classification of the types of angles—acute, obtuse, right, straight zero and complete angles.
 * 6) In the succeeding class give the students protractors and let them have enough practise measuring  and classifying angles.
 * 1) What is a point ?
 * 2) A minimum of how many points are needed to define a line segment ?
 * 3) A minimum of how many points are needed to form an angle ?
 * 4) Name the line segments from the figure.
 * 5) What is a vertex ?
 * 6) How many rays /line segments are needed to form an angle ?
 * 7) Name the vertex at which the angle is formed
 * 8) Name the angle.
 * 9) Name the type of angle formed.
 * Evaluation:
 * 1) Assess the students knowledge of angles by projecting different types of angles and asking     them to name
 * 2) What are the characteristics of an acute angle ?
 * 3) What are the characteristics of an obtuse angle?
 * 4) What are the characteristics of a right angle
 * 5) Evaluate if the students have understood that :
 * An angle is formed where 2 lines meet at a point.
 * A right angle looks like a corner of a square or a rectangle.
 * An acute angle is narrower than a right angle.
 * An obtuse angle is wider than a right angle.
 * Question Corner:
 * 1) What is an angle ?
 * 2) Where do you name an angle ?
 * 3) How do you identify different types of angles in 2-dimensional figures?
 * 4) How do angles help to classify 2-dimensional figures?
 * 5) Are angles <ABA' and <A'BA the same ? Justify
 * 6) Differentiate between the zero angle and a complete angle.

Notes for teachers
Activity - Construction of angle with measure 22.5∘

This activity helps to illustrate the 'angle bisector' construction three times since we construct ∡22.5 by constructing ∡90∘ (bisecting a segment / straight angle ∡180∘, then bisect ∡90∘ to get ∡45∘ and finally bisect ∡45∘ to get ∡22.5∘).

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Notes for teachers
Activity No # 1.Angles formed when a transversal intersects parallel lines  *Estimated Time : 40 minutes *Materials/ Resources needed :Laptop, geogebra file, projector and pointer. *Prerequisites/Instructions, if any : *Multimedia resources: Laptop *Website interactives/ links/ / Geogebra Applets
 * 1) The students should have prior knowledge of parallel lines, transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
 * 2) They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
 * 3) Students should know the definition of complementary angles, supplementary angles, and congruent angles.


 * This is a resource file on 'vertically opposite angles'

It has been created by Sucheta, Mathematics teacher, GHS Thyamangondlu

*Process: Linear pair of angles - adjacent and supplementary *Developmental Questions :(What discussion questions) *Evaluation: *Question Corner:
 * 1) Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
 * 2) Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
 * 3) The teacher can next project the GeoGebra worksheet and discuss about types of angles and their relationships with the class.
 * 4) Finally the teacher and students can summarize together the angle relationshipsalong with their characteristics.
 * Vertical angles - congruent
 * Corresponding angles -congruent
 * Alternate interior angles - congruent
 * Same side interior angles - supplementary
 * Alternate exterior angles - congruent
 * Same side exterior angles - supplementary
 * 1) How many pairs of corresponding angles are there ?
 * 2) What is true about corresponding angles formed when parallel lines are cut by a transversal?
 * 3) Compare different pairs of alternate interior angles. What do you notice?
 * 4) <EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
 * 5) Compare different pairs of same-side interior angles. What do you notice?
 * 6) Compare different pairs of same-side exterior angles. What do you notice?
 * 1) What are the characteristics of linear angles (adjacent and supplementary) ?
 * 2) What do you observe about the angle measures of the linear angles?
 * 1) What do adjacent, alternate, linear , corresponding and consecutive mean individually
 * 2) What are complementary angles?
 * 3) What are supplementary angles ?
 * 4) What does it mean if two angles are congruent?
 * 5) What is the complement of 65 degrees
 * 6) What is the supplement of 70 degrees?
 * 7) Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.

Activity No 2 Angles formed when a transversal intersects parallel lines
Laptop, geogebra file, projector and pointer. Laptop Linear pair of angles - adjacent and supplementary Vertical angles - congruent Corresponding angles -congruent Alternate interior angles - congruent Same side interior angles - supplementary Alternate exterior angles - congruent Same side exterior angles - supplementary
 * Estimated Time : 90 minutes
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * 1) The students should have prior knowledge of parallel lines, transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
 * 2) They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
 * 3) Students should know the definition of complementary angles, supplementary angles, and congruent angles.
 * Multimedia resources:
 * Website interactives/ links/ / Geogebra Applets
 * Process
 * 1) Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
 * 2) Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
 * 3) The teacher can next project the GeoGebra worksheet and discuss about types of angles and their relationships with the class.
 * 4) Finally the teacher and students can summarize together the angle relationships.


 * Developmental Questions
 * 1) How many pairs of corresponding angles are there ?
 * 2) What is true about corresponding angles formed when parallel lines are cut by a transversal?
 * 3) Compare different pairs of alternate interior angles. What do you notice?
 * 4) <EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
 * 5) Compare different pairs of same-side interior angles. What do you notice?
 * 6) Compare different pairs of same-side exterior angles. What do you notice?

Evaluation
 * 1) What are the characteristics of linear angles (adjacent and supplementary) ?
 * 2) What do you observe about the angle measures of the linear angles?


 * Question Corner
 * 1) What do adjacent, alternate, linear , corresponding and consecutive mean individually
 * 2) What are complementary angles?
 * 3) What are supplementary angles ?
 * 4) What does it mean if two angles are congruent?
 * 5) What is the complement of 65 degrees
 * 6) What is the supplement of 70 degrees?
 * 7) Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.

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