When should kids know their combinations?

I have had many parents ask me when their child should know their addition or multiplication facts. I would first like to say that Investigations prefers to call them combinations. Calling them facts implies that you can't learn them through reasoning. However, if I know 8 x 3 = 24, then I should be able to reason that 8 x 6 is double 8 x 3 or 48.

What does it mean to know your combinations? Fluency means that you can immediately recall an answer or quickly perform a calculation to get the answer. If it takes longer than two seconds to figure a combination, a student is not fluent. This includes single digit addition and multiplication pairs and their counterparts for subtraction and division. We encourage students to work on combinations that they don't immediately know. This can be done during downtime in class or at home. I also encourage 3rd, 4th, and 5th graders to use arrays when working on their combinations.

The following are guidelines for learning combinations through the grades:

Addition - fluent by the end of Grade 2, with review and practice in Grade 3.

Subtraction - fluent by the end of Grade 3, with review and practice in Grade 4.

Multiplication - fluent with multiplication combinations with products to 50 by the end of Grade 3; up to 12 x 12 by the middle of Grade 4, with continued review and practice.

Division - fluent by the end of Grade 5.