Subtraction - The Equal Change Algorithm- It's Fun!

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SWBAT explain and use the equal change algorithm to solve 2 and 3 digit subtraction problems.

Big Idea

An alternative approach can increase understanding of regrouping!


2 minutes

I let students know that the algorithm I'm going to teach them today, the Equal Change Algorithm, is an alternative to the standard algorithm that some of them will like and some of them might not.  It's important to try out different methods because that's the way that each of them will begin to discern their own particular preferences.  Even if this isn't an algorithm that all of them end up using, their is value in teaching it because it forces them to examine their understanding of subtraction from a different perspective.  Additionally, as the goal is to move the subtrahend to an even ten or hundred, it helps them with the skill of rounding as well, though it's important to note that in this algorithm the subtrahend doesn't need to be moved to the closest ten or hundred, simply one of the two.  (It would work even if you rounded to the nearest 200, but I don't suggest letting students play with that concept).  

Guided Lesson

25 minutes

I begin teaching the equal change algorithm for subtraction by showing them examples with 2 digit subtraction.  This is a brief video, intended for you (too fast for students) that explains this method.

I have observed that some students seem to instantly fall in love with this method - to them it feels like finding the correct interlocking puzzle pieces.  Other students see that it produces the correct answer, but don't understand why the add or subtract the same number to "both sides".  For that reason, I also demonstrate with place value blocks.  I have demonstrated how I would do that in this brief teacher video:


Finally, here is a teacher example of how to use the equal change algorithm with a 3-digit subtraction problem.

These are some examples for equal change guided practice that I find useful.

Active Engagement

33 minutes

I write up 3 sets of equal change - independent practice problems on the board: 2 digit, 3 digit with some regrouping and 3 digit with regrouping in both the tens and hundreds place.  All students need to do at least 2 of the 2 digit problems, but after that if they feel like they are ready, they may move on to column B or column C.

I provide a fourth choice -- students who wish to stay at the carpet and work through some additional problems as group practice are welcomed to do so.  In my classroom, this is a common choice, and there is no stigma associated with it, as often some of the more successful students choose to stay on for a little bit because they are self-aware enough to know they need a little additional guidance.  Other students have observed this and in most cases students make a wise choice.  Occasionally there are students who are over-confident or lack sufficient meta-cognitive skills to make this decision for themselves, and I'll ask them to stay on as well.  


5 minutes

I ask students to write the key way in which the equal change algorithm of subtraction differs from the equal and opposite change algorithm for addition.  I reteach the word differ if necessary, distinguishing between this the verb form and the noun, difference, having the quality of differing.