1. A common assessment that teachers use with young children is to write a two-digit number such as 25 on a piece of paper. The teacher first points to the 5 in the number and asks the student, "What does the 5 mean? Show me with counters." The student responds, "It tells how many ones there are" and indicates five counters. Next the teacher points to the 2 in the number and again asks, "What does the 2 mean? Show me with counters." This time the student indicates two counters and says "there are two ones." What mathematical ideas are being confused? Explain.
2. Describe how the different place values in base ten are related. Namely how are ones, tens, hundreds, thousands etc. related to each other? Be sure to also explain the relationship among smaller place values such as tenths, hundredths, thousandths and ten-thousandths.
3. How is zero used in our base ten system?
4. Can you place zero anywhere in a number and not change the value? Explain using examples.