geoboards algebra, geometry, and geoboards. back of geoboard think of as many possible uses for the...
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![Page 1: Geoboards Algebra, Geometry, and Geoboards. Back of Geoboard Think of as many possible uses for the circle part of the Geoboard in Geometry](https://reader035.vdocuments.site/reader035/viewer/2022062519/5697bff71a28abf838cbeef1/html5/thumbnails/1.jpg)
Geoboards
Algebra, Geometry, and Geoboards
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Back of Geoboard
Think of as many possible uses for the circle part of the Geoboard in Geometry
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Review
What is the slope of the line that passes through: (2, -3) and (-4, 3)?
(0,0) x
y
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Review
Graph the following line on your Geoboard:
(0,0) x
y
33
2 xy
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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
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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
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Geoboards and Algebra
Questions?
Suggestions?
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Geoboards and Geometry/Measurement
Parallel Lines and transversals
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Parallel Lines
Graph y=1 and y=3 Graph transversal
line through (-2,3) and (1,0)
Measure the angles(0,0) x
y
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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
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Transformations
Draw triangle WVY and translate it (3,-1).
W(-1,0) V(-3,-3) Y(2,-3) (0,0) x
y
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Transformations
Draw triangle RST and reflect it over the y-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
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Transformations
Draw triangle RST and reflect it over the x-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
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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
(0,0) x
y
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is a right triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an isosceles triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an acute triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an obtuse angle.
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?
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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
2
)( 21 hbb
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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.
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)
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Geoboards and Tangrams
What is the area of each piece?
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Geoboards and Geometry
What other areas of Geometry could we use the Geoboard for in our classrooms?