Everyone Try It! (Equal & Opposite Change)

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Objective

SWBAT use and explain the equal and opposite change algorithm with 2 & 3 digit addition. They will express an opinion about this method.

Big Idea

Don't be afraid to teach struggling students an alternative method; sometimes it can provide a breakthrough!

Opener

7 minutes

I remind students that this is an alternative algorithm.  I review the word algorithm. Then I let them know that after they have demonstrated that they can do this, it will become optional.  To a certain point I want to see that the students can apply the equal and opposite change algorithm, because it shows me how well they understand certain concepts and skills.  (Basic addition and subtraction, rounding to the closest the ten or hundred.)

I also tell them that today I want them to think about which method they prefer, the standard algorithm, expanded form, or equal and opposite change.  At the end of math, I will ask them to explain their choice in writing.  For now, I want them to turn to a neighbor and tell their neighbor something they found helpful about using the place block cubes.

Guided Practice

23 minutes

In this set of differentiated equations I lead students through sets of examples that work on particular sub-skills (problems in which no or minimal regrouping is necessary, one-step problems, problems in which there is regrouping).  I find I need to post problems at two levels in order to keep everyone engaged because some students take to this like a duck to water, while others need more initial support.  The degree to which they acclimate to this new algorithm is also dependent on their basic fact fluency.  If they haven't mastered basic addition facts this will not seem any simpler to them than the standard or expanded form algorithms, but it's still important to present it because one never knows what will appeal to certain students.

Differentiated Independent Practice/ Small Groups

35 minutes

In the equal and opposite change independent practice, the disparity in students' understanding and methodology is very apparent because while some take the most most efficient route to solving the equation, others still walk unseeing into situations that require regrouping when it wasn't unavoidable. Sometimes students add in extra steps and I let them work through this as well.  It is far more effective for me to let them discover on their own that some of their steps are unhelpful, redundant, or otherwise necessary.

Finally, there are also students who, when looking at a given equation, are thinking of it differently than I am and often (correctly) combine steps in an unanticipated way.  This is also correct, and  a great way to demonstrate to students how many different approaches can still end up at the same, correct result.

Here are a few more examples of student work, one with 2-digits (47 + 38), one with 3- -digits (178 + 257) and one paper in which two students completed partner work.