This phrase is a biggy in Grade Three. In fact, it's a "phrase that pays". We use "I know this because" in both Math and Language Arts.
What this phrase does it is sets students up on the right path for explaining and defending their ideas. In Math, students might have to explain how they know their answer is correct. In writing, we might ask students to describe a character who shows bravery or good judgement.
This really is the very first step in expository essay writing and we use it A LOT.
One of the biggest hurdles in writing for children is simply not knowing how to phrase things. Kids know what they want to say, they just don't always know how to say it. By providing a set of phrases that really pay off, we set them up for future success because a) they're more productive in the class and b) they start thinking about their own phrases that pay.
We all have certain ways we like to say things, ways that make our writing sound polished and sophisticated and "I know this because" is a great first step in toward that goal of becoming an effective writer.