Geoboards

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

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 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(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?

Geoboards and Geometry

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