Teaching 2-digit by 2-digit Subtraction Using the CRA Method

One of the trickiest concepts in subtraction is to have multi-digit numbers with regrouping. This is why we always encourage teachers to use the CRA method. As a reminder, CRA stands for Concrete, Representational and Abstract. 

When you use the CRA method to teach subtraction, you start with concrete where the students “do” the problem using manipulatives to show and explain how to solve multi-digit subtraction with regrouping. Next, you move to Representational where the student can “see” how to solve the problem using drawings. Last, the students solidify what they’ve learned in abstract by solving the problem only using numerical values.

When I taught second grade, I explained the standard algorithm only in the abstract stage. Most of my students were able to make progress with this way of teaching, but there were a few that did not understand the steps. Why? Because I skipped the first two stages of the CRA method and some of my students did not grasp the number sense behind it. I would argue that even some of the students that were accurate with regrouping probably did not fully understand why they were crossing out numbers and putting a “1” in front of another…they were simply following a pattern.

Here is an explicit and direct way of teaching 2-digit by 2-digit subtraction with regrouping using the CRA method (note:  if the student is struggling with any step, verify the student has the skill of identifying place value. Do not skip steps unless there is data to show that the student has mastered this).

Concrete Stage

This stage is skipped so often in upper grades! It’s so important for the student to be able to understand the meaning behind the strategies and numbers…especially with students with disabilities. Concrete builds (literally) number sense behind whatever skill that is being taught. This is the reason why 2-digit by 2-digit subtraction with regrouping is one of the hardest skills for students with disabilities to understand. If the process that you are teaching does not make sense, then the students will continue to struggle with it and allowing the student to engage in the “do” part of the process will help solidify the meaning behind it. 

With this particular skill in the Concrete stage, the student’s end goal would be that they could independently use manipulatives to show and EXPLAIN how to regroup with tens and ones. If the student cannot explain what they are doing, then they do not fully understand what’s happening with the manipulatives. Let’s talk about the importance of explaining:  if the student can explain each step, then the teacher knows that this was not just rote memorization of a strategy. Memorization does NOT create connections from one skill to the next. When working with students with disabilities (and really any student), being able to make connections from one concept to the next is so powerful! Imagine someone introducing himself to you and you don’t know anything about them and have little interest in what they are saying, but as soon as they tell you that they are your dad’s cousin BOOM! There’s a connection and you are completely engaged in the conversation. That is the same type of reaction when connecting concepts. As soon as the teacher shows how this concept relates to the next one, not only is the student more likely to be engaged in the lesson, but number sense will follow suit.

The most common manipulatives to use with 2-digit by 2-digit subtraction is base ten blocks and unifix cubes. I prefer to use unifix cubes because then the student can physically break apart the stack. Whatever you choose to use, just make sure that you label what they are and that the student can label everything too. I always referred to the stack of 10 as a “rod” and the ones as a “unit”. 

Here’s an example:  I told my students that I had 4 tens and 1 one and I need to take away 2 tens and 4 ones. I use “Think Aloud” to explain and label how I set up the numbers with the manipulatives. Here are some tips when working with students with disabilities in the Concrete Stage:

• Model only a couple of times. If they are sitting without doing anything for too long, then they lose any enthusiasm and mentally check out
• Make a list of steps they need to follow. This visual prompt will help them become more independent and give them the confidence to try it on their own
• Spend the majority of your instruction time solving problems together to solidify the process

Representational Stage

Now that the student has mastered this skill in the Concrete stage, then they are ready to slide into the Representational stage. I say “slide” because this is not a quick check and onto the next stage. It’s important to make the vital connection from one stage to the next so that the student can engage and not feel like they are being taught something completely new. Representational is where the student can “see” how to solve the problem. This stage is important because it’s semi-concrete meaning that the student still relies on something other than numbers to make sense of the problem.

When we move between stages it is important that we help build a connection. Remember – connections build engagement and number sense. In this case we want to build a connection between Concrete and Representational. An effective way to do this is to solve the 2-digit by 2-digit subtraction problem with regrouping simultaneously using Concrete and Representational.

Let’s take that same example of 4 tens and 1 one and subtract 2 tens and 4 ones and build that with the rods and units. Show them that this could also be drawn on paper using lines and dots where a line represents a rod and a dot represents a unit. Take away the number 2 tens and 4 ones and build the number using rods and units. Show them again how you can draw that same number using lines and dots. After modeling this stage, have the students practice with you several times.

Don’t feel like you have to stay within both stages for a long period of time. When the student can independently work through a 2-digit by 2-digit problem with both steps successfully, then it’s time to drop the concrete step (manipulatives). Another indication is if you ask the student. Many times they’ll let you know when they’re ready to move on. It all depends on what student you’re working with. Typically, I noticed that my students needed to see both stages for a few different problems and then they can move on in isolation in Representational. Again, use “Think Aloud” by labeling and discussing the steps within solving the problem. The end goal here is just like in Concrete: student will be able to solve and explain the problem independently. Here are the tips when working with students with disabilities in the Representational Stage:

• Model only a couple of times. If they are sitting without doing anything for too long, then they lose any enthusiasm and mentally check out
• Make a list of steps they need to follow. This visual prompt will help them become more independent and give them the confidence to try it on their own
• Spend the majority of your instruction time solving problems together to solidify the process
• If the student is struggling with Representational in isolation, do not hesitate to connect with Concrete again

Abstract Stage

Final stage! You’ve probably noticed the pattern and know that you’ll be sliding into Abstract by connecting this stage with Representational. Again, model for the student how to solve the problem in Representational and Abstract simultaneously. This is the stage where the student will be solving the problem numerically without manipulatives or drawings. They will be relying solely on the strategy with numbers.

Here are the tips when working with students with disabilities in the Abstract Stage:

• Determine what strategy you’ll be teaching the student how to solve the 2-digit by 2-digit subtraction with regrouping. Will you be using standard algorithm? Expanded form? There are many options, but make sure you consider what strategy would be best for the student’s learning style and/or history of success with experience teaching other students
• Model only a couple of times. If they are sitting without doing anything for too long, then they lose any enthusiasm and mentally check out
• Make a list of steps they need to follow. This visual prompt will help them become more independent and give them the confidence to try it on their own
• Spend the majority of your instruction time solving problems together to solidify the process
• If the student is struggling with Abstract in isolation, do not hesitate to connect with Representational again. In fact, I have even used all three stages with students before

Using this CRA method for this skill is worth the time put into the planning. Not only is it research-based, but it hits all learning styles. This works for all students, but especially students with learning disabilities. Teaching them concepts before rules and shortcuts creates connections from background knowledge and allows for generalization to other skills that come up in their instruction in the future.