The intuition behind partial practice is reasonable. The kid struggles with the 7s, so spend the practice time on the 7s. Don't waste minutes on facts the kid already knows. It feels obviously correct.
It isn't, and the reason is in the unstated assumption. "Stuck on the 7s" sounds like the kid doesn't know the row. That's almost never what's actually happening.
What "stuck on the 7s" actually looks like
A kid who's stuck on the 7s already knows 7 × 1 (the ones rule). They know 7 × 2 (twos / doubling). They know 7 × 5 (counting by fives). They know 7 × 10 (tens / add a zero). They know 7 × 11 (elevens, repeat the digit). They know 7 × 7 if they memorized the squares.
What they don't know, in most cases, is some combination of 7 × 3, 7 × 4, 7 × 6, 7 × 8, and 7 × 12. Maybe four facts. Maybe five. Out of twelve.
"Practice the 7s" sends the kid into a Kata of twelve problems, eight of which they already know. They answer the same easy problems over and over while the four hard ones — the actual problem — get diluted. They spend ten minutes proving they know things they already know, and the four facts at the heart of the issue get a tiny fraction of the attention.
What the whole Kata does instead
A full Kata has 144 problems. Math Katas's pacing — answer quickly if you know it, fall back on a rule if you don't, use the calculator if you must — automatically isolates the facts the kid doesn't know. Easy facts pass through quickly. Hard facts take longer. By the end of a session, the kid has spent most of their attention exactly where it needed to go: on the handful of facts that aren't yet automatic.
It also surfaces the right facts. A kid who insists they're stuck on the 7s might actually be stuck on 6 × 8 and 4 × 7 — not a row, but a small set of products in the middle of the table. Whole-Kata practice surfaces the real shape of the problem. Partial-row practice hides it.
The confidence argument
There's a second reason to run the whole Kata, and it's the more important one.
A whole Kata starts with 1 × 1 = 1. The first problem is something the kid can do in their sleep. They get it right. Then 1 × 2 = 2. They get that right too. 2 × 1 = 2. Right. 2 × 2 = 4. Right. By the time the kid reaches a hard problem, they're a dozen problems in, every one of them correct. They're on a roll.
Compare that with starting in the middle. 7 × 7 = 49. Already a hard one. The kid hesitates. They get it. 7 × 8. They don't know it. They guess wrong. 7 × 6. They guess wrong. By the time they get a few right, they've already spent the first minutes of the session feeling slow and confused.
The order matters. The protocol is engineered around getting a kid to discover, on their own, that the table is doable. The first move toward that discovery is a string of small wins. You cannot construct that string out of the 7s.
What about an older kid who really does know most of the table?
A sixth grader who already knows most of the table but struggles with three specific facts is a real case, and I'll grant that on paper it sounds like the partial-Kata case. In practice, the same arguments apply.
A kid who knows 141 of 144 facts cold can finish a full Kata in under three minutes, because all but the three trouble facts are answered on sight. The trouble facts get the same isolation they'd get in a partial Kata, and the kid still gets the confidence boost of a clean run. There's no scenario where whole-Kata practice costs an experienced kid meaningful time.
Run the Kata. The "wasted" easy problems aren't wasted; they're the part that makes the protocol work.