Three students have used base-10 blocks to provide an explanation of .01 x .5. Evaluate each of their explanations – and explain what you believe is each student’s mathematical thinking in his/her particular explanation and how they use the blocks to arrive at their solution. If their answer is incorrect, explain how you would address their misconception(s).

**Sheila**

If one long is .1 then 5 longs is .5 and one cube is .01. Since there are 50 cubes in 5 longs the answer is 50.

**Nacole**

I agree with Sheila that we should use longs to figure this out but I don’t agree with her answer. If I let a long equal .01 then five-tenths of a long is 5 cubes. Therefore a cube is .001 so the answer is .005.

**Mark**

I let the flat be .1 so one long is .01 and five flats is .5. There are five longs so the answer is .05.

**Jerome**

I like how Mark used the flats but I disagree with his answer. If one long is .01 then one cube is .001 so five of them is .005.

**Adapted from:** Fostering Children’s Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction by Arthur J. Baroody and Ronald T. Coslick, Lawrence Erlbaum Associates, 1998.