CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS - SIMPLE CLOSED CURVE FIGURES AND POLYGONS Material: Geometry Stick Box and Board A piece of string Paper and scissors Paper labels and pencil Presentation: Formation of Regions 1. Have the children take two sticks and fasten them together. 2. Cut a closed curved figure from the piece of paper. 3. Have the children take a third stick to attach to the two sticks. 4. Place the string on the Board. 5. What does this string represent? A curved line. 6. What do your sticks represent? Broken straight lines. 7. Move the string to form a closed figure. 8. When we close this curved line, we have created a surface or region. 9. Close the broken lines to form a surface or region. 10. In geometry, we have two types of figures: simple closed curve regions and polygons. Montessori Research and Development 2004 21
Formation of Polygons 11. Take one of your sticks and form a region. Impossible. 12. Take two of your sticks and form a region. Impossible. 13. Take all three of the sticks that you have and form a region. Possible. A triangle is formed which is the simplest polygon. 14. Continue to have the children form polygons. Each child may have a different number of sticks to form a different polygon: 4 sticks quadrilateral 5 sticks pentagon 6 sticks hexagon 7 sticks heptagon 8 sticks octagon 9 sticks nonagon 10 sticks decagon 15. The ending gon means sides in Greek. Poly means many. 16. Allow the children to draw and label simple closed curved figures and polygons in their geometry notebook. Follow-Up Activities: 17. Allow the children to draw and label simple closed curved figures and polygons in their geometry notebook. 18. Individually and in pairs, the children review the nomenclature cards. Point of Interest/Discussion: Montessori Research and Development 2004 22
CLASSIFIED NOMENCLATURE: STUDY OF THE TRIANGLE Material: Triangles from the Geometry Cabinet Parts of the Triangle nomenclature Presentation: 1. Select a triangle from the Geometric Cabinet. 2. Indicate the surface or region of the triangle. 3. The internal part of the triangle limited by the three line segments is called the region or surface. Discuss. 4. These three line segments joined together are called the perimeter of the triangle. The word perimeter comes from the Greek meaning meter, to measure and peri, around. 5. Write this information on paper labels: meter: peri: to measure around 6. Indicate the line segments. 7. Each line segment represents a side of the triangle. How many sides are there? Three. Discuss. 8. Does the triangle have a base? Any of the sides of the triangle may serve as the base. Discuss. 9. What is the space at which the sides meet? Angle. Discuss. 10. What is the point at which the sides meet? Vertex. Discuss. Montessori Research and Development 2004 23
11. Allow several children to select each of the triangles in the Geometric Cabinet. Each group discusses the parts of the triangle. 12. Allow several children to draw and label triangles in their geometry notebook. Follow-Up Activites: 13. Allow the children to draw and label triangles in their geometry notebook. 14. Individually and in pairs, the children review the nomenclature cards. Point of Interest/Discussion: Montessori Research and Development 2004 24
CLASSIFIED NOMENCLATURE: STUDY OF TRIANGLES ACCORDING TO SIDES Material: Geometry Stick Box and Board Paper labels Presentation: 1. Allow each child to select three sticks of different lengths from the Geometry Stick Box. 2. Have the children form a triangle. 3. Allow each child to select another three sticks with two sticks of the same length. 4. Have the children form a triangle. 5. Allow each child to select another three sticks with all sticks of the same length. 6. Have the children form a triangle. 7. Discuss the names of triangles with: No sides the same length: Two sides the same length: Three sides the same length: scalene triangle isosceles triangle equilateral triangle Montessori Research and Development 2004 25
Lengths of the Sides of a Triangle: 8. Allow the children to experiment with the forming of triangles that are scalene and isosceles. 9. As the children make scalene and isosceles triangles categorize the triangles. Impossible: Limited: Possible: 10. Allow the children to generate rules: No triangle is formed: Impossible: Two sticks together are shorter than the third stick. No triangle is formed. An open figure is created. Limited: Two sticks together equal the length of the third stick. A degenerate triangle is formed. The superimposed sides create endpoints. Triangle is formed: Possible: Two sticks together are longer than the third stick. A triangle is formed. Follow-Up Activities: 11. Allow the children to draw, measure, and label triangles in their Geoemtry notebook. 12. Individually and in pairs, the children review the nomenclature cards. Point of Interest/Discussion: Montessori Research and Development 2004 26
Drawing: Type of Triangle: Scalene Isosceles Calculations: Long side Sum of two shorter sides cm. = cm. Conclusion: Impossible Case = Limited Case Possible Case Drawing: Type of Triangle: Scalene Isosceles Calculations: Long side Sum of two shorter sides cm. = cm. Conclusion: Impossible Case = Limited Case Possible Case Montessori Research and Development 2004 27
CLASSIFIED NOMENCLATURE: STUDY OF TRIANGLES ACCORDING TO ANGLES Material: Geometry Stick Box and Board Paper labels Geometric Cabinet: Triangle Drawer with Seventh Triangle Presentation: The Right Triangle 1. Allow each child to select two sticks. 2. Have the children form a right triangle with the two sticks. 3. Verify the right angle by using the measuring angle. 4. Allow each child to select a third stick which will connect the other two sticks to form a right triangle. 5. Note that the right triangle has one right angle. 6. Allow the children to explain why a right triangle has only one right angle. 7. Allow the children to experiment in an attempt to construct a triangle with two right angles. Presentation: The Obtuse Triangle 1. Allow each child to select two sticks. 2. Have the children form an obtuse angle with the two sticks. 3. Verify the obtuse angle by using the measuring angle. 4. Allow each child to select a third stick which will connect the other two sticks to form an obtuse triangle. Montessori Research and Development 2004 28
5. Note that the obtuse triangle has one obtuse angle. 6. Allow the children to explain why an obtuse triangle has only one obtuse angle. 7. Allow the children to experiment in an attempt to construct a triangle with two obtuse angles. Presentation: The Acute Triangle 1. Allow each child to select two sticks. 2. Have the children form an acute angle with the two sticks. 3. Verify the acute angle by using the measuring angle. 4. Allow each child to select a third stick which will connect the other two sticks to form an acute triangle. 5. Note that the acute triangle has three acute angles. 6. Allow the children to explain why an acute triangle has three acute angles. 7. Allow the children to experiment in an attempt to construct an acute triangle without three acute angles. Montessori Research and Development 2004 29
CLASSIFIED NOMENCLATURE: STUDY OF TRIANGLES ACCORDING TO ANGLES AND SIDES Material: Geometry Stick Box and Board Paper labels Geometric Cabinet: Triangle Drawer with Seventh Triangle Presentation: 1. Examine each of the seven triangles and name each in terms of its sides. There are three (3) scalene, three (3) isosceles, and one (1) equilateral. 2. Examine each of the seven triangles and name each in terms of its angles. There are three (3) acute, two (2) obtuse, and two (2) right. 3. Triangles are named for both their sides and their angles. Examine the triangles in the Geometric Cabinet and name each by its angle(s) and its sides: 1. right-angled scalene 2. right-angled isosceles 3. obtuse-angled scalene 4. obtuse-angled isosceles 5. acute-angled scalene 6. acute-angled isosceles 7. acute-angled equilateral (conventionally the acute-angled is not stated) 4. There are seven (7) possible triangles. Montessori Research and Development 2004 30