1. Describe fractional parts. What are the two distinct requirements of fractional parts? Explain how childrens' concepts of partitioning need to be refined to produce a concept of fractional parts.
2. Give a fourth grade explanation of the meaning of the top number and the bottom number in a fraction.
3. Explain why it is obvious that 3/4 x 8/5 = 6/5 without using the algorithm and without first getting 24/20.
4. Explain why the place-value system extends infinitely in two directions. How can this idea be developed with students in the fifth or sixth grade?