1. Algebra, Geometry, and Geoboards

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

3. Review What is the slope of the line that passes through:
(2, -3) and (-4, 3)?
(0,0) x y

4. Review
Graph the following line on your Geoboard:
(0,0) x y

5. 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)

6. 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)

7. Questions? Suggestions?
Geoboards and Algebra
Questions?
Suggestions?

8. Geoboards and Geometry/Measurement
Parallel Lines and transversals

9. Parallel Lines Graph y=1 and y=3
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).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)

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

14. 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. A B

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

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

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

19. Perimeter

20. Perimeter

21. Perimeter
Create another figure, that is NOT a rectangle, with the same perimeter.

22. Perimeter
Create another figure, that IS a rectangle, with the same perimeter.

23. Area
Establish that each “square” is 1 unit

24. Area
Establish that each “square” is 1 unit

25. Area and Perimeter
Create a rectangle whose perimeter and area are the same

26. Area of triangles
Determine the area of this triangle as many ways as you can--- discuss

27. 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?

29. Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?

30. Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?

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

32. Area of quadrilaterals
Create a trapezoid with an area of 8 square units

33. 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)

34. Geoboards and Tangrams
What is the area of each piece?

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