Use a "linkage strip" to to build quadrilaterals with different sets of lengths. Once you build a quadrilateral, see if you can deform it into a different quadrilateral with the same side lengths.
Use a "linkage strip" to build triangles with different side lengths. When you build a triangle, see if you can deform it into a different triangle while keeping the side lengths the same.
Count the number of raisins in seventeen half-ounce boxes of raisins. Then come up with a solution to determine how many raisins are in Brand X's or Brand Y's box of raisins.
Look at patterns of solids made with Cuisenaire rods. Make a table of the surface area and volume for each term of this sequence and view graphs of your data. Find the rule for the nth term.
Is there a relationship between the volume of a sphere and the volume of a cylinder of equal diameter and height? What about the volume of the sphere and the cone?