English Explanation of Mishnah Eduyot 3:9

Four things Rabban Gamaliel pronounces susceptible to impurity, and the Sages pronounce them not susceptible to impurity.
The covering of a metal basket, if it belongs to householders;
And the hanger of a strigil;
And metals vessels which are still unshaped;
And a plate that is divided into two [equal] parts. And the Sages agree with Rabban Gamaliel in the case of a plate that was divided into two parts, one large and one small, that the large one is susceptible to impurity and the small one is not susceptible to impurity.
The next three mishnayoth contain halakhic traditions revolving around Rabban Gamaliel. Mishnah nine continues the pattern of the previous mishnah, of a dispute over which things are susceptible to impurity.
In mishnah eight we learned of three things that Rabbi Zadok declared susceptible to impurity and the Sages not susceptible. In mishnah nine we will learn of the same type of dispute, this time between Rabban Gamaliel and the Sages. Again, they seem to be disputing about how to define when something is a “vessel” such that it is susceptible to impurity. They dispute over four items:
1) The covering of a metal basket which belongs to a householder. In another tractate we learn that there is a difference between this type of covering if it is owned by a doctor. The doctors used these coverings for various uses, and therefore everyone agrees that they are susceptible to impurity. Rabban Gamaliel holds that a covering of this type of basket is used by non-professionals as well, and is therefore susceptible to impurity even if it belongs to a non-professional (a householder). The Sages disagree.
2) The hanger of a strigil. A strigil was a type of comb used during baths to scrape off dead skin. All agree that the strigil itself is susceptible to impurity. They disagree about the small chain attached to the strigil to hang it on a hook. According to Rabban Gamaliel it too is considered a vessel and therefore receives impurity. According to the Sages it does not.
3) Generally speaking, unformed vessels cannot receive impurity. However, when it comes to metal vessels that have not been fully finished, in other words they have not been polished, Rabban Gamaliel holds that they are susceptible to impurity, since they can be used. The Sages insist that as long as they are not fully finished they cannot receive impurity.
According to Rabban Gamaliel, a plate broken in two can still receive impurity. The Sages hold that broken vessels cannot generally speaking receive impurity. However, they agree with Rabban Gamaliel that if one of the pieces was large, that it still can receive impurity, since it is still useful. The small piece cannot receive impurity.