Math in Japan is pretty much like Math anywhere else except that their textbooks are rather skimpy. As you may have read from my earlier article, textbooks are paperback and they are slim in size in Japan. With that said, their textbooks tend to teach and outline the subject succinctly and then have several pages of problems for practice and review afterward.
For 1st graders, for example, their math textbook is about 109 pages long for the whole year with 17 units of material and 4 review sections for the whole 40 weeks of school. One unit takes about an hour and half to explain the two pages that explain the topic in the textbook and then take several more days to review that same subject. The subject is taught physically using objects or an abacus and abstractly, using straight-up numbers, to solve the problem.
By the end of 1st grade, all students within the grade should have learned cardinal and ordinal numbers to 100, can add and subtract up to 100 without borrowing or carrying, tell time, do simple measurements and comparisons of length, and name several geometric shapes. Unfortunately, it has been a long time since I attended 1st grade but with a quick search on the net, most 1st grade students in the United States would be able to add and subtract, round numbers, compare numbers (same, greater, or equal), tell time, some geometric shapes, and count money. So what is taught in both countries is basically comparable in the beginning but it may accelerate in different paths once you go to the higher grades.
Students in Japan also get a workbook which they may use to practice and do on their own time. They may do all of it or none of it and there is no time limit or any requirements. What is neat about these workbooks for elementary school students though is that they have stickers included and if a student does well, they can give themselves stickers for doing an excellent job.