Angles

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= Teaching Outlines =

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

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
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" /> Developmental Questions:
 * 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
 * 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.

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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 <ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" /> *Process: Linear pair of angles - adjacent and supplementary *Developmental Questions :(What discussion questions) *Evaluation: *Question Corner:
 * 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.
 * 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.

Activity No #

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

= Hints for difficult problems =

= Project Ideas =

= Math Fun =

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