Algebra, Geometry, and Geoboards

Back of Geoboard Think of as many possible uses for the circle part of the Geoboard in Geometry

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

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) y x (0,0)

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) y x (0,0)

Questions? Suggestions? Geoboards and Algebra Questions? Suggestions?

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 y x (0,0)

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)

Transformations Draw triangle WVY and translate it (3,-1). x (0,0)

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

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

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)

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

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

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

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

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

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. 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)

Geoboards and Tangrams What is the area of each piece?

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