Geoboards

1
Geoboards

• Review of Algebra

2
Review

• What is the slope of the line that passes
  through
• (2, -3) and (-4, 3)?

3
Review

• Graph the following line on your Geoboard

4
Review Plus

• Connect (-3,-2) and (3,2)
• What is the slope of the line that connects these
  points?
• Connect (-2,2) and (2,-4)
• What is the slope of the line that connects these
  points?

y
x
(0,0)
5
Review Plus

• Connect (-3,-2) and (3,2)
• What is the slope of the line that connects these
  points?
• Connect (-4,-1) and (2,3)
• What is the slope of the line that connects these
  points?

y
x
(0,0)
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Geoboards

• Geometry, Measurement and Geoboards

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Back of Geoboard
Think of as many possible uses for the circle
part of the Geoboard in Geometry
8
Geoboards and Geometry/Measurement

• Parallel Lines and transversals

9
Parallel Lines

• Graph y1 and y3
• Graph transversal line through (-2,3) and (1,0)
• Measure the angles

y
x
(0,0)
10
Parallel Lines

• Connect (-3,-2) and (3,2)
• Connect (-4,-1) and (2,3)
• Create a transversal (-4,2) and (3,-3)
• What angles are congruent?

y
x
(0,0)
11
Transformations

• Draw triangle WVY and translate it (3,-1).
• W(-1,0) V(-3,-3) Y(2,-3)

y
x
(0,0)
12
Transformations

• Draw triangle RST and reflect it over the y-axis.
  R(-5,0) S(-2,-5) T(-1,-1)

y
x
(0,0)
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Transformations

• Draw triangle RST and reflect it over the x-axis.
  R(-5,0) S(-2,-5) T(-1,-1)

y
x
(0,0)
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Transformations

• Draw triangle RST and rotate it 90 clockwise.
  R(-5,0) S(-2,-5) T(-1,-1)
• Can use graph paper too

y
x
(0,0)
15
Triangles

• Find three locations for a point P, above segment
  AB, so that triangle APB is a right triangle.

B
A
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Triangles

• Find three locations for a point P, above segment
  AB, so that triangle APB is an isosceles triangle.

B
A
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Triangles

• Find three locations for a point P, above segment
  AB, so that triangle APB is an acute triangle.

B
A
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Triangles

• Find three locations for a point P, above segment
  AB, so that triangle APB is an obtuse angle.

B
A
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Perimeter
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Perimeter
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Perimeter
Create another figure, that is NOT a rectangle,
with the same perimeter.
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Perimeter
Create another figure, that IS a rectangle, with
the same perimeter.
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Area

• Establish that each square is 1 unit

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Area

• Establish that each square is 1 unit

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Area and Perimeter

• Create a rectangle whose perimeter and area are
  the same

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Area of triangles

• Determine the area of this triangle as many ways
  as you can--- discuss

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Area of triangles

• Determine the area of this triangle as many ways
  as you can--- discuss

How efficient was your approach? Would you
approach it differently now?
28
Area of triangles

• Determine the area of this triangle.
• Does your method work for this triangle too?

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Area of quadrilaterals

• Determine the area of this polygon.
• Does your method from the triangle work for this
  polygon?

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Area of quadrilaterals

• Determine the area of this polygon.
• Does your method from the triangle work for this
  polygon?

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Area of quadrilaterals

• Create these trapezoids on your Geoboard.
• Prove the formula for determining the area of a
  trapezoid

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Area of quadrilaterals

• Create a trapezoid with an area of 8 square units

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Geoboards and Tangrams

• Use your Geoboard and bands to form a special
  geometric shape following the steps below.
• Band together (0,0) (0,8) (8,8) and (8,0)
• Band together (0,8) and (8,0)
• Band together (0,4) and (4,0)
• Band together (2,2) and (8,8)
• Band together (2,2) and (2,6)
• Band together (6,2) and (4,0)

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Geoboards and Tangrams

• What is the area of each piece?

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Math Playground
36
National Virtual Manipulatives
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Geoboards and Geometry

• What other areas of Geometry could we use the
  Geoboard for in our classrooms?