# Equal & Opposite Change Model of Addition

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## Objective

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!

## Opener

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: