STUDY OF THE LINE: THE PERPENDICULR ISECTOR Study of the Line, Second Series: The Perpendicular isector (4: 20) Material Geometry Classified Nomenclature 4 (20) Paper Pencil Compass Ruler Presentation (See page 106 for detailed instructions.) 1. Lay out the geometry classified nomenclature card 4 (20) on the work area. 2. Read the definition and match it to the picture. (Latin: bi - two, sector - cutter) 20 The perpendicular bisector of a line segment is a perpendicular line drawn through the midpoint of a line segment. 3. Share the Second Series 4 booklet with the children. 4. Display the Second Series 4 wall chart. NOTE: It is suggested that the perpendicular bisector follow perpendicular lines. Montessori Research and Development 2010 105
20 Perpendicular isector Montessori Research and Development 2010 106
1 Objective: Copy Line Segment TO COPY LINE SEGMENT 3 C Draw a Segment longer than Place a compass tips on and. 2 4 C C D Establish a point ( C ) on the longer line that corresponds with ON. With metal tip at C, transfer length of to longer line. label D CD=. TO CONSTRUCT PERPENDICULR TO LINE FROM POINT OFF THE LINE 1 Objective: Construct a perpendicular to passing through C. c Draw a segment longer than. H c I Using C as center and any convenient length as radius, draw an rc which intersects at two points (H and I). 2 c H I xd 2 c H I xd Using points H and I as centers, draw arcs with equal radii that intersect at a point (D) below the line. Draw CD, CD Montessori Research and Development 2010 107
STUDY OF THE LINE: THE RELTIONSHIP OF THREE STRIGHT LINES Study of the Line, Second Series: The Relationship of Three Straight Lines (5: 21-23) Material Geometry Stick ox Geometry Classified Nomenclature 5 (21-23) Paper Red and blue pencils Presentation 1. Place paper on the board. 2. Take two sticks and tack them to the board. Note that these lines are not parallel and that they actually go on to infinity at both ends. The sticks are only representations of the line. The paper is the plane and both straight lines are on the plane. 3. The plane is subdivided by these lines into three parts. Color the outer parts of the plane red and the part lying between the two straight lines blue. 4. Name the outer regions exterior and the inner regions interior. The colors help to point out the concept of interior and exterior regions. Exterior Region Interior Region Exterior Region Montessori Research and Development 2010 108
5. Take a third stick with holes all along its length. 6. Place this stick on the first two and give the term transversal. (Latin: traversare - to cross.) 7. Determine how many angles are formed: Place a yellow pen mark at each angle. 8. Establish which are the exterior angles and which are the interior angles. ) Those which lie on the external part are exterior angles. External means outside - in this case outside the two lines. Mark these angles with red tacks. ) Those which lie in the internal part are interior angles. Internal means inside - in this case, inside the two lines. Mark these angles with blue tacks. Montessori Research and Development 2010 109
9. Lay out the geometry classified nomenclature cards 5 (21-23) from left to right at the top of the work area. 10. Distribute the labels to the children. 11. Invite each child to read the label and to match it to the picture. 12. Distribute the definitions. Invite each child to read the definition and to match it to the picture. 21 Two straight lines divide the plane into three regions. The interior region is the region that lies between the straight lines. 22 Two straight lines divide the plane into three regions. The exterior regions are the two regions that do not lie between the straight lines. 23 The transversal line is a line that intersects two or more straight lines. 13. Share the Second Series 5 booklet with the children. 14. Display the Second Series 5 wall chart. Montessori Research and Development 2010 110
21 22 23 Interior Region Exterior Regions Transversal Line Montessori Research and Development 2010 111
STUDY OF THE NGLE: PRTS OF N NGLE Study of the ngle, Third Series: n ngle, Parts of an ngle (C1: 24-27) Material Geometry Stick ox Geometry Classified Nomenclature C1 (24-27) Two sticks with an arrow taped to one end of each Presentation 1. Recall that each stick with an arrow fastened to it is a ray. 2. Fix the two rays together on the plane by tacking their origins together. 3. Say, When two rays have the same origin, the figure they form is called an angle. 4. Invite the children to construct angles. 5. When two rays form an angle, we can call each of the rays a side of the angle. Their shared origin is the vertex of the angle. The space between the sides is called the size of the angle. Label each part as you define it. 6. Continue with a three-period lesson. 7. Lay out the geometry classified nomenclature C1 (24-27) at the top of the work area. 8. Distribute the labels to the children. 9. Invite the children to read the label and to match the label to the pictures: angle, sides, vertex, size. Montessori Research and Development 2010 112
10. Then distribute the definitions. Invite the children to read the definitions and to match the definitions to the pictures. C24 C25 C26 C27 n angle is a figure formed by two rays drawn from the same origin. The sides of an angle are two rays which form the angle. The vertex of the angle is the common origin of two rays. The size of the angle is the measurement of the opening between the two rays. The size of the opening is measured in degrees. 11. Share the Third Series C1 booklet with the children. 12. Display the Third Series C1 wall chart. NOTE: t this point the presentations on measuring angles and the use of the protractor may be introduced with the lesson on the Sumerians (pp. 187-188) or delayed. Montessori Research and Development 2010 113
14 15 ngle Sides of an ngle 16 17 Convergent Lines Size of the ngle Montessori Research and Development 2010 114
STUDY OF THE NGLE: TYPES OF NGLES Study of the ngle, Third Series: Types of ngles (C2: 28-33) Material Geometry Stick ox red pencil red tack Geometry Classified Nomenclature C2 (28-33) Presentation 1. Take two sticks of different lengths (a red stick and a tan stick - the tan stick having holes all along it.) 2. Superimpose the longer stick over the shorter stick. 3. ttach the two sticks to the plane with a red tack that represents the vertex of the angles that will be formed with the sticks. 4. Fix the tan stick at the other end also, but leave the red stick free. 5. Take a red pencil and place it in the last hole of the red stick. Montessori Research and Development 2010 115
6. Move the red stick saying, This is an angle. 7. Make the angle wider, saying, This is an angle. 8. Continue to move the red stick around the plane, naming the figure of the angle each time. 9. When the rotation is complete, say, This is a whole angle. Montessori Research and Development 2010 116
10. Illustrate acute angle. cute ngle 11. Illustrate right angle. Right ngle 12. Illustrate obtuse angle. Obtuse ngle 13. Illustrate straight angle. Straight ngle 14. Illustrate reflex angle. Reflex ngle 15. Illustrate whole angle. NOTE: The measuring angle is used to verify the right angle Reflex ngle and to establish acute and obtuse angles. Montessori Research and Development 2010 117
16. Use the measuring angle to illustrate the fact that the straight angle is two measuring angles. 17. Use the measuring angle to illustrate that the whole angle is four measuring angles. 18. sk the child to use the sticks to form a right angle, an acute angle, and an obtuse angle. 19. Lay out the geometry classified nomenclature cards C2 (28-33) from left to right at the top of the work area. 20. Distribute the labels to the children. 21. Invite each child to read the label and to match it to the picture. 22. Then distribute the definitions. llow each child to read the definition and to match it to the picture. C28 The whole angle is formed by one complete rotation of a ray around its origin. C29 The straight angle is an angle whose sides extend in opposite directions from its vertex. C30 C31 C32 The right angle is an angle that is exactly half of a straight angle. The acute angle is an angle that is smaller than a right angle. The obtuse angle is an angle that is larger than a right angle and smaller than a straight angle. C33 The reflex angle is an angle that is larger than a straight angle and smaller than a whole angle. 23. Share the Third Series C2 booklet with the children. 24. Display the Third Series C2 wall chart. Montessori Research and Development 2010 118
STUDY OF THE NGLE: PRINCIPLE NGLES Study of the ngle, Third Series: Principle ngles Material Geometry Stick ox White paper Presentation - Length versus Size of an ngle 1. Place one sheet of paper on the geometry stick board. Take two sticks of different lengths, the longer with holes all along it. 2. Superimpose the longer one over the shorter. ttach the two sticks to the plane with a long pin, representing the vertex of the angle formed. Fasten the shorter stick at its other end also. 3. Place the red pencil through the third hole of the longer stick, and show the formation of the various angles. 4. Make an acute angle. Move the stick slowly, and ask the child to tell you when it forms a right angle. s each angle is formed, name it, mark it, and label it on the paper. 5. sk the child to tell you when it forms an obtuse angle. 6. sk the child to tell you when it forms a straight angle. 7. sk the child to tell you when it forms a reflex angle. 8. sk the child to tell you when it forms a whole angle. 9. Move it down two more holes and repeat the procedure. In this way, we demonstrate the fact that the size of the angle does not depend on the length of the sides. The sides become longer, but the size of the angle remains the same. Montessori Research and Development 2010 119