Below, you will find different strategies for 2-digit addition and subtraction. In 2nd grade, students will begin adding 2-digit and 3-digit problems with regrouping. Here are ways to break down these problems so that students have different ways to solve the problems. Since students learn in different ways, it’s important to show them different methods to learning. You’ll find concrete strategies, mental math strategies, and even algorithm methods for pencil and paper solving. As you teach your students each method, give them the freedom to pick and choose the method that works best for them.
Common Core Standards for 2-Digit Addition and Subtraction
Let’s take a look at the standards that focus specifically on these next few strategies. You can certainly use these strategies in first grade (without regrouping) and third grade, too. However, the specific standard in focus here is 2.NBT.5, which focuses all on fluently adding and subtracting using place value strategies.
- 2nd Grade 2.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.
- Focused standards-based resource: 2.NBT.5 and 2.NBT.5 Regrouping Bonus
Base-Ten Blocks: Strategy 1
The first two digit addition and subtraction strategy that I’m going to discuss is actually a kid’s favorite. Using base ten blocks to add and subtract two digit numbers is a very concrete model for students to use. It’s very easy for them to visually see the process of putting together the tens and ones plus the act of regrouping is a lot easier to visually see here as well.
One way that I like to have the students using base ten blocks is to do two things. The first would be to actually use base ten blocks as they’re adding and subtracting for every single problem. The next option would be to draw sticks and circles to represent tens and ones if your classroom is limited on base ten block materials. If you give students a whiteboard it is very easy for them to draw out every single problem that they without using base ten blocks. But ideally they will have their hands on those manipulatives to visually see their problems being solved.
Break-Apart: Strategy 2
Strategy number 2 is all about the break-apart method which also could be known as the expanded form method. The reason I called it the break apart math just because the students are actually taking apart the two digit and splitting it into tens and ones. Then they’re going to add the tens from each number and the ones from each number and make their math a little bit easier. It does get a bit difficult when students have to do some regrouping on their addition or subtraction problem so that is definitely a big step that you have to teach when using this strategy.
Here are two ways that I use the break apart strategy for two different levels. In the picture at the bottom you see my remediation group activity which give the students a more scaffolded view of breaking apart there two digit where’s to add together. In the picture at the top, you see what I would give my on level or my enrichment group. They have to draw a problem and solve it on their own without the scaffolded boxes for them to guide them and breaking apart their numbers.
Give and Take: Strategy 3
Our third 2-digit addition and strategy would be the give-and-take method. The process of this method is different between the addition and subtraction problems. So it is important that you give the students a lot of practice here. When you have an addition problem if you take two from one number you have to add two to the other number. However, on a subtraction problem if you take two from one number you have to take two from the second number as well.
This strategy does practice because the students really have to focus on which strategy fits with addition or subtraction. Giving them lots of hands-on ways to practice is one suggestion. It’s also very important to teach the strategy of finding the number that’s closest to a 10 to make their problem as easy as they can.
Open Number Line: Strategy 4
Open number lines are the fourth strategy for 2-digit addition and subtraction problems. An open number line is where students have make jumps in order to represent adding or subtracting tens and ones. On a subtraction problem the students will begin on the biggest number. Then, they will jump back the number that they are supposed to subtract. When a student makes these jumps, they will represent the tens with a bigger jump and the ones with smaller jumps. It is important that the students label each of these jumps at the bottom of the number line. This will help them see the act of taking 10/1 or adding 10/1.
Standard Algorithm: Strategy 5
My final 2-digit addition subtraction strategy is the standard algorithm. The standard algorithm is lining up the addition or subtraction problem vertically where the tens and ones are stacked on top of each other. This can be done with or without regrouping. I do suggest breaking up your lessons into teaching the standard algorithm without regrouping first. And then once your kids master that then you can start teaching standard algorithm with regrouping.
It’s very important to give your students lots of ways to practice each strategy. Some ways are hands-on partner activities. Other ways maybe independent worksheets where students have to show what they’ve learned so far on their own. I also think it’s very important to tie in writing with every single strategy. If you’re having the students explain their place value strategies in writing, I think that’s a very strong way of practicing and understanding that strategy in their mind.
Looking for 2-digit addition and subtraction resources?
These standards-based resources break down the standard and teach the students how to add and subtract 2-digit numbers with and without regrouping. It focuses on each strategy for a mini-lesson. All of the images you see above in this blog post come from the 2.NBT.5 unit. The regrouping bonus unit is for remediation if you need to take a step back and teach your students how to regroup when adding and subtracting.
Need it DIGITALLY?
I have created a few activities in ready-made Google Slides. These 2-Digit Addition and Subtraction activities are for second grade.
Thanks for reading all about addition and subtraction strategies. Hopefully, this blog post helped you find ways to introduce this big math skill into easier steps for your students.
Want more math blog posts on other topics?
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