Two open ended problems I came across that worked well with grade 7 students were:
1. T or F Neither 0 nor 1 are prime or composite numbers. Give a rationale for your answer. Use complete sentences, and give a thorough explanation.
2. A rectangle is shaded in on a centimeter grid. It is 3 x 4, but no numerical dimensions are given. Directons: Construct a triangle withthe same area. Follow up- there is more than one answer. How many can you find? What is the "tallest"? The most similar to a rectangle? How are the perimeters different? Are perimeter and area related in any way?