Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, closed-world), so the bar is lower. The description still adds real behavior: results are ordered by textbook sequence and each entry carries a unit ID, Japanese name, and the number of creatable problem types — meaningful return-shape information given no output schema exists.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

One sentence with no filler, front-loading the scope (grade) before the returned fields. Nothing redundant is included, though it is terse enough that a little more routing guidance could have been added at near-zero cost.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple single-parameter read tool with no output schema, the description adequately explains what comes back and in what order. Minor gaps remain: nothing about list size, whether the grade parameter must be supplied (it is required in schema), or how this list relates to the problem-type discovery tool.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100% with a single required parameter whose bounds (1–6) are already declared in the schema, and the description restates '学年（1〜6）' without adding new semantics. Baseline 3 is correct when the schema fully documents the parameter.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('returns the math units for a grade'), plus the scope (grades 1–6, textbook order) and the payload (unit ID, Japanese name, count of problem types creatable). It is clearly distinct from siblings like find_math_problem_types or create_math_worksheet, though it never names a sibling to sharpen that distinction.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is only implied: an agent can infer you call this to see what units exist before picking one for a worksheet. There is no explicit when-to-use, no prerequisite (e.g. 'call before create_math_worksheet'), and no pointer to find_math_problem_types as the drill-down alternative.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.