Here are some questions for the 5th grade that has students representing figures while also developing concepts about measurement, specifically area. In order to determine if students have understasnding, have them hold up their geo-boards each time they've completed the question.
15 Questions for the Geo-board
1. Show a triangle that has an area of one square unit.
2. Show a triangle with an area of 3 square units.
3. Show a triangle with an area of 5 square units.
4. Show an equilateral triangle.
5. Show an isosceles triangle.
6. Show a scalene triangle.
7. Show a right triangle with an area of more than 2 square units.
8. Show 2 triangles that have the same shape but that are different sizes. What is the area of each?
9. Show a rectangle with a perimeter of 10 units.
10. Show the smallest square on your geo-board.
11. What is the largest square you can make on your geo-board?
12. Show a square with 5 square units.
13. Show a square with 10 square units.
14. Make a rectangle with an area of 6 and state what the perimeter is.
15. Make a hexagon and determine the perimeter.
These questions can be modified to meet learners at various grades. When introducing the geo-board, begin with an exploring type of activity. As the comfort level increases when working with geo-boards, it is useful to have students begin transferring their figures/shapes to dot paper. To extend some of the questions above, you can also include concepts like which figures are congruents, which figures have 1 or more lines of symmetry. Questions like this should be followed up with, 'How do you know?' which requires students to explain their thinking.
The geo-board is just one of many math manipulatives that can be used in math to support understanding of concept. Math manipulatives help teach concepts in a concrete method which is preferred before attempting the symbolic format.