# Geometry and visual spatial activities

## Volume

• Exploration and building experiences are important for developing visual spatial abilities. One activity young kids like is to build. Do a cooperative activity and build a town or city.

Use lock blocks to construct buildings for a town. Compare the buildings by counting the number of cubes in each. While young children are developing number sense ideas they will also construct spatial reasoning abilities and begin to construct a concept of volume. Students can build neighborhoods and cities and challenge each other to find how many blocks/cubes are in each. The analogy of floors and rooms might help. If each block = a room, and each level = a floor, then how many rooms in each level? How many floors in the building? How many rooms in the building? How does the number of rooms increase with each floor?

• Measure the inside of an object with the shape of a cube and/or rectangular prism and calculate the volume in cubic cm. Fit cubes that are one cubic entimenter inside and count the number of cubes. Then measure the volume of water it holds in ml. Display the results of all three and determine a pattern. Then write a relationship between them. Create a procedure to calculate the volume by using the linear dimensions of the object. Containers with 90 degree corners are hard to find. You can buy liter container sets that have 1/8, 1/2 and 1-liter containers in different shapes. I also have found Display containers that are rectangular prisms.

The same can be done with cylinders by measuring the volume of cylindrical plastic bottles and invent a procedure or formula to calculate the volume. A prerequisite for this is that students know how to find area of a circle and why the procedure or formula works (circle with four squares inscribed that have sides = the radius of the circle can be used ot show the relationship of area = pi * radius squared).

• Visualization puzzles for surface area and volume. E.g. Make a big cube with 27 small white cubes and paint the outside of the big cube red, how are the sides of each of the 27 small cubes painted (number and location of white and red on the twenty-seven cubes).
• How does the surface area and volume of cubes compare? Chart the surface area and volume of cubes 1x1x1 ...10x10x10. Calculate their area & volume and see if there is a pattern.
• Make a cube pattern.
• Find the area of leaves. Trace a leaf on square graph paper, identify different shapes that would equal the shape of the leaf. Find the sum of the areas of the different shapes.
(A = 1/2 h2; A = l x w) Count the squares the leaf covers. Compare the two totals.
• Collect three leaves of different sizes from the same tree. Calculate the area of all three leaves. Plot the length and area of the leaves and see what the relationship is between the leaves. Linear? quadratic?