  We calculate $\mathrm K_*(k[x]/x^e;\mathbf Z_p)$ by evaluating the syntomic
cohomology $\mathbf Z_p(i)(k[x]/x^e)$ introduced by Bhatt-Morrow-Scholze and
Bhatt-Scholze. This recovers calculations of Hesselholt-Madsen and Speirs, and
generalizes an example of Mathew treating the case $e=2$ and $p>2$. Our main
innovation is systematic use of the floor and ceiling functions, which
clarifies matters substantially even for $e=2$. We furthermore observe a
persistent phenomenon of slopes. As an application, we answer some questions of
Hesselholt.
