Addition on the Train

There are many advantages to introducing addition and subtraction on the trains. Students can find the answer to addition and subtraction problems without having to be able to read or write numbers. The teacher does not have to explain or teach regrouping, because the regrouping happens implicitly when making good trains. Also, depending on the students’ level of understanding, they can take advantage of groups of ten, or they can add and subtract blocks one at a time.

	Let’s start with the problem 18 + 27. The first step is to make a good train of 18 and 27. Here is a train of 18.
	And here is a train of 27.
	The goal is to combine the two trains to form one good train. Then we can count the blocks on the train to find the sum, 45.
	But wait! How do the students combine the two trains to form a good train?
	Students often start by placing one train behind the other like this. At this point they will realize, on their own or with help, that this is not a good train.
	How can the train be turned into a good train? A beginning strategy is to move the blocks forward one by one to make a good train.
	But a more efficient strategy is to rearrange the train cars by combining the full cars at the front of the train . . .
	and then rearrange the blocks in the partially filled cars at the back of the train . . .
	to form a good train.

Transition to the algorithm: The challenge of combining the blocks from two trains into one good train leads the students to discover for themselves the advantage of combining the full cars separately and the ones separately! This is the key idea of the formal algorithm.