## IM Commentary

The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal." Students can make observations which reinforce the topic at hand as well as lay groundwork for later developments.

This task allows students to engage in standard for mathematical practice 8, Look for and express regularity in repeated reasoning. Students are not asked explicitly to compare what they find in the second and third parts with 29, since by this grade they should make note of that on their own.

While the first part asks for application of long division (by hand), the multiplications could be done by calculator, at the teacher's discretion. The trade-offs in this choice are between further development of number fluency and opportunity for reflection if these calculations are done by hand versus greater likelihood of accuracy and answers provided more quickly (which can help observing the trend) if done by calculator.