In Georgia, we have a “new” set of standards for math. However, they are still verrry similar to the previous Common Core. These “Georgia Standards of Excellence” still have much of the same (if not identical) verbiage.
This includes using strategies outside the traditional algorithm to add and subtract. The “new” Georgia standard is:
“MGSE2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”
By encouraging students to use other strategies to add and subtract, we can strengthening their mental math skills, understanding of the base ten system, as well as have a deeper understanding of WHY the, “More on top? Need to stop!” poem WORKS.
I focused on several different strategies in my classroom. I am NOT an expert, I am just a teacher, like you. This is how I chose to introduce the strategies in my classroom.
I do believe in beginning with using the most concrete methods to the most abstract methods. If you want to learn more about concrete to abstract relationships in math, this webpage is a nice, simple overview.
We WERE somewhat mandated in that we had to teach multiple strategies, but I felt we were given leeway in WHICH strategies we could teach. This was my personal sequencing for teaching. I have also included photos of the addition and subtraction math centers that I created to practice each strategy. Just click on the pictures to see the centers.
Base Ten Blocks
I am a HUGE fan of base ten blocks. I always began EVERY addition and subtraction unit with base ten blocks. Most students were able to be successful.
Some years before I ever pulled out the base ten blocks, I used unifix cubes in rods of 10. This made it an easy, PHYSICAL way to pop apart the ten to regroup.
The base ten block strategy also transferred easily to a semi-concrete level where kids could draw the blocks to add. Some of my most struggling learners mastered this skill in second, but never full got to the full abstract stage. They had a way to solve the problem- it just took them awhile.
We went from base ten blocks to base ten blocks while recording the work on white boards to only using whiteboards to scaffold support.
I actually did a video at the beginning of the school year, showing several different math strategies that could be taught with the hundreds chart, including arrow math. This is essentially addition and subtraction.
Expanded Form/ Partial Products
The next strategy I taught depended on whether we were studying addition or subtraction. If we were working on addition, I would introduced adding with expanded form. You can also lead into the partial sum strategy if kids get the expanded form strategy- they pair very nicely and kids “get” it. This was a personal favorite of mine because it lends itself easily to mental math. It also happens to be how I add in my head! LOL!
I DO NOT prefer this was for subtraction. It is fine for problems without regrouping, but for problems with regrouping? There is a bunch of crossing out happening. This would make sense though, if it lead to teaching the traditional algorithm. We didn’t even TEACH the traditional algorithm in second grade.
Open Number Line
Open Number Lines can be really hard for some kids. I often used closed number lines. In fact, I used these all the time. The different between an open and closed number line is simply that the closed number line is labeled for kids, while an open is blank so kids can determine a starting point and increments.
This can be a hard strategy to find materials. I created this pack to scaffold from beginning to end!
Mandy Gregory is a 2007 and 2012 Teacher of the Year. She has taught 4th, 3rd, and 2nd grade in both the general education and inclusion setting. She is the owner and creator of the Teaching Tips website (www.mandygregory.com) and has over 10 years of experience. She is married with two beautiful children.