Equal & Opposite Change Model of Addition

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SWBAT manipulate place value in 2- and 3-digit addends using the equal and opposite change model.

Big Idea

Different approaches work for different students!


2 minutes

I let the students know that today I'll be teaching them what is considered an alternative algorithm.  An alternative is a choice.  I give them several real-world context sentences using alternative:

There was a lot of traffic on the highway, so my mom took an alternative route and drove on tiny roads.

An alternative to studying for 2 hours before a test is to study for 20 minutes every night for about a week!

Seltzer water is an alternative to soda that takes some adjustment, so try adding some fruit juice to make it sweeter.

Then I ask them to think of and share a sentence using the word "alternative" with a partner.

They will learn this algorithm and demonstrate that they can use it but then they get to choose the algorithm that works best for them.  We aren't all the same!

Whole Group Review

18 minutes

Using the model they used in 2nd grade (tree diagram), I review 2 digit addition.   I ask students to explain the steps as I go through the process of solving this problems.  "What do I do next?"


87 + 63 =


24 + 26  + 65 =


17 + 75 + 36=


487 + 63 =


123 + 188=


217 + 375=


Differentiated Guided Practice: Equal & Opposite Change or Place Value Block Practice

30 minutes

I split the students into two groups based on a review of their work from the previous lesson, but if a student expresses a strong desire (for academic reasons) to be in a group different from the one to which I assigned them, I allow the switch.

One group continues to work with place value blocks to develop their understanding of regrouping in addition problems.  I write these problems up on the board:

36 + 72 =

72 + 183 =

49 + 81 =

154+ 117=

135 + 109=

115 + 129 =

48 + 89 =

183 + 179 =

145 + 136 =

143 + 178 =

143 + 178 =

143 + 178 =

They copy the equations and work in their journals  They work it out with the cubes.   That is why my problems are never more than one hundred something... I don't have enough flats!  

The additional problems in which there is no regrouping are not a mistake. *(See reflection.)

I introduce the second group to the equal and opposite change algorithm.

We work through this set of equal and opposite change problems together.

Then I give them some to work on independently. Here are some examples of student work: