b. Compute using the order of operations, including parentheses.
As I look back on my own school experiences in Japan, I really don't remember explicitly learning about the order of operations. As I examine the current Japanese elementary school mathematics textbooks, there is really no unit titled "Order of Operations." Of course, that does not mean that Japanese children do not learn the order of operations. What is important to notice is that how they study order of operations is more from the perspective of writing mathematical expressions.
For example, in Grade 4, students are given the following problem:
860 - 460 = 400
1000 - 600 = 400
A little later in the unit, students are given the following problem:
a) You have a 100-yen coin. You buy 3 sheets of paper, and each sheet costs 25 yen. How much change will you get?
b) You buy a 500-yen pencil case and a half dozen pencils. A dozen of pencils cost 480 yen. How much will you pay?
Finally, after a few practice problems, the textbook summarizes the rules about the order of operations:
- Generally goes from left to right.
- If there are any parentheses, we calculate inside the parentheses first.
- Multiplication and division are performed before addition and subtraction.