Singapore Math is well-known for teaching kids mental math strategies. While they do have supplementary books that focus on mental math, I’ve found the mental math drills listed in the back of the Home Instructor’s Guide to be sufficient. Teaching my kids these strategies has really helped my math skills too. The mental math drills in the back of the teacher’s manual are scheduled in the Singapore Home Instructor’s Guide. I’ve done it that way, but right now I’m doing the mental math drills at a slower pace. By the time my middle child completes Singapore he will have completed all the mental math drills from 1B through 4B. We are sticking with Singapore through 5B, but I didn’t get the Home Instructor’s Guides for that level.
Here is a little close-up from the drill he is doing.
This is an example from 3B Home Instructor’s Guide.
Singapore teaches mental math strategies in their regular textbook, but I’ve found that doing the mental math drills in the back of the teacher’s book to be crucial for my kids to develop their mental math skills. I’ve only used the Standards edition, but I’m guessing the US edition also has mental math drills.