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Geometry Manual Volume 2
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.”
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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:
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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:
to measure
peri:
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.
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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:
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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:
scalene triangle
Two sides the same length:
isosceles triangle
Three sides the same length:
equilateral triangle
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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:
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Drawing:
Type of Triangle:
Scalene
Isosceles
Calculations:
Long side
cm.
Sum of two shorter sides
=
cm.
Conclusion:
Impossible Case
=
Limited Case
Possible Case
Drawing:
Type of Triangle:
Scalene
Isosceles
Calculations:
Long side
cm.
Sum of two shorter sides
=
cm.
Conclusion:
Impossible Case
=
Limited Case
Possible Case
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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.
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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.
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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.
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