Question

2. Some fourth-grade students are practicing reading and comparing decimal numbers. They created two different numbers using decimal squares. Stephanie reads the decimal squares below as “zero and forty-five hundredths” and “zero and one tenth.” She says: “Zero and forty-five hundredths is thirty five hundredths greater than one tenth.” Her partner, Ingrid says: “That’s not right. The square on the left is thirty-five squares bigger than the one on the right.”

a) What does Stephanie seem to understand? What does Ingrid seem to understand?

b) What could you talk about with these students to help improve their understanding?

Answer 1

(a) Stephanie's understanding is right. She understands that when comparing decimal numbers, it is necessary to mention what each square represents. Whether a square represents a tenth or a hundreth is important. She counts the squares and understands that each square is a hundredth to correctly infer than 0.45 is 35 hundreths greater than 0.1.

On the other hand, Ingrid's understanding is slightly incorrect. She understands that 0.45 is 35 squares bigger than 0.1 but fails to understand what each square represents. She is unable to understand that each square on the left represents a hundredth and thus what Stephanie is saying is correct.

(b) Stephanie's understanding is correct. So it is unnecessary to tell her anything.

I should talk with Ingrid. I should explain to her what each square represents. Saying that a number is 35 squares greater than another number is notnot sufficient. It is crucial to say whether each square is a tenth or a hundredth or a thousandth. In this case, since each square represents a hundredth and the number on the left is 35 squares bigger, thus the number is 35 hundreths bigger.