Geoboards
Review of Algebra
Review
What is the slope of the line that passes through: (2, -3) and (-4, 3)?
(0,0) x
y
Review
Graph the following line on your Geoboard:
(0,0) x
y
33
2 xy
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?
(0,0) x
y
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?
(0,0) x
y
Geoboards
Geometry, Measurement and Geoboards
Back of Geoboard
Think of as many possible uses for the circle part of the Geoboard in Geometry
Geoboards and Geometry/Measurement
Parallel Lines and transversals
Parallel Lines
Graph y=1 and y=3 Graph transversal
line through (-2,3) and (1,0)
Measure the angles(0,0) x
y
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?
(0,0) x
y
Transformations
Draw triangle WVY and translate it (3,-1).
W(-1,0) V(-3,-3) Y(2,-3) (0,0) x
y
Transformations
Draw triangle RST and reflect it over the y-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
Transformations
Draw triangle RST and reflect it over the x-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
Transformations
Draw triangle RST and rotate it 90° clockwise. R(-5,0) S(-2,-5) T(-1,-1)
Can use graph paper too
(0,0) x
y
Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is a right triangle.
A
Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an isosceles triangle.
A
Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an acute triangle.
A
Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an obtuse angle.
A
Perimeter
Perimeter
Perimeter
Create another figure, that is NOT a rectangle, with the same perimeter.
Perimeter
Create another figure, that IS a rectangle, with the same perimeter.
Area Establish that each “square” is 1 unit
Area Establish that each “square” is 1 unit
Area and Perimeter
Create a rectangle whose perimeter and area are the same
Area of triangles
Determine the area of this triangle as many ways as you can--- discuss
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?
Area of triangles
Determine the area of this triangle.
Does your method work for this triangle too?
Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?
Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?
Area of quadrilaterals
Create these trapezoids on your Geoboard.
Prove the formula for determining the area of a trapezoid
2
)( 21 hbb
Area of quadrilaterals
Create a trapezoid with an area of 8 square units
Geoboards and Tangrams
Use your Geoboard and bands to form a special geometric shape following the steps below.
1. Band together: (0,0) (0,8) (8,8) and (8,0)2. Band together: (0,8) and (8,0)3. Band together: (0,4) and (4,0)4. Band together: (2,2) and (8,8)5. Band together: (2,2) and (2,6)6. Band together: (6,2) and (4,0)
Geoboards and Tangrams
What is the area of each piece?
Math Playground
National Virtual Manipulatives
Geoboards and Geometry
What other areas of Geometry could we use the Geoboard for in our classrooms?