Do you use the CPA approach when teaching mathematical concepts? And no, I’m not talking about accounting or taxes! The CPA approach is a research-based system for teaching math that helps students grasp the concepts by introducing them in a way that allows them to shift the learning from concrete to pictorial to abstract learning. This is an effective way to help students understand the concepts being taught.
It’s no secret that addition with regrouping is one of the toughest math concepts to teach in 2nd grade. Therefore, by incorporating fun addition with regrouping activities and games that follow the CPA approach into your math stations, your students will begin to understand this concept and succeed with it independently. Read on for 6 engaging addition with regrouping examples that you can add to your regrouping math stations.
What is the CPA Approach for Teaching Math?
The CPA approach for teaching math stands for Concrete, Pictorial, and Abstract. This approach represents the natural shift we want our students to make when they are learning a new concept.
This approach can be used with any mathematical concept, but in this blog post, we’re going to look at how we can apply the CPA approach to your math stations, specifically when teaching addition with regrouping.
To learn more about the CPA approach and to see these addition with regrouping examples in action, check out my YouTube video below!
The concrete stage focuses on using manipulatives and concrete objects to guide students to solve a problem. This is where students are working with the concept in a hands-on way. When teaching addition with regrouping, students my use base ten blocks of place value disks.
The pictorial stage focuses on using visual pictorial representations of concrete objects. This stage is key because students may not always have access to concrete objects, but they’ll likely always be able to draw a picture. In the example of teaching addition with regrouping, students may draw sticks to represent tens blocks and dots to represent ones blocks.
The abstract stage focuses on solving problems using abstract symbols and algorithms, AKA, mental math. This is where students would simply solve an addition with regrouping problem, such as 45+38 using the standard algorithm and “carry” a ten over to the tens place when they need to regroup.
The CPA approach for teaching math is highly effective because it allows students to shift their thinking from concrete to pictorial and finally, abstract. This is the natural progression they should follow in order to grasp mathematical concepts and apply them to their learning and everyday life.
Addition with Regrouping Games and Activities That Follow the CPA Approach
While you can apply the CPA approach with any addition with regrouping games and activities you have on hand, I wanted to break how the CPA approach works with your math stations using a few addition with regrouping examples that I’ve created and have available in my website store and TpT store.
Concrete Addition with Regrouping Examples
Concrete addition with regrouping activities are those that allow students to physically move objects and manipulatives around to solve the math problem.
Place Value Addition Mats
This place value addition mat is one of my favorite fun addition with regrouping activities to include in my math stations. There are a ton of ways you can use this place value mat, such as with dice, number cards, or task cards to represent the number. Students can also use a variety of manipulatives to solve, such as base ten blocks, place value disks, or pipe cleaners and pom pom balls.
To use this addition with regrouping activity, students can draw an addition with regrouping task card or use dice or number cards to create the two addends. In this example, 47+36, students will begin by building out each addend vertically using base ten blocks and writing out the equation.
When it’s time to solve, I like to ask my students where they should start first when solving. We create mathematical discussions around always starting in the ones place when adding.
Since 7+6=13, students should know from prior knowledge that since 13 is greater than 10, they must regroup. In this concrete addition with regrouping example, they can PHYSICALLY move the manipulatives to exchange 10 ones for a 1 tens block with 3 ones left over. This process allows them to SEE regrouping in action.
Then, they are ready to count by tens and ones to solve for the sum.
Open Number Line
Another fun addition with regrouping activity that you can incorporate into your math stations is a simple open number line activity. This activity represents the concrete stage of learning in the CPA approach, but this time, uses the open number line addition with regrouping strategy.
While the open number line strategy is more complex, by pairing a concrete process using manipulatives with a more complex strategy like the open number line, students will have a visual representation, which will help them grasp this strategy.
In this example, students are solving 36+38 using the open number line strategy and base ten blocks ON the open number line.
Students will write the problem and circle the larger addend. This is the number that goes first on the open number line. Then, they will build the second addend on the open number line horizontally using base ten blocks.
This is a powerful activity and helps them visually see the tens “hops” and ones “skips” on the number line. Then can also draw their hops and skips along with their base ten blocks. This will help them solve for the sum easier and make the connection between base ten blocks and the open number line.
Pictorial Addition with Regrouping Examples
Once students have mastered the concrete process of addition with regrouping, they’re ready for fun addition with regrouping activities that use the pictorial process of drawing out the problem to solve. The concrete and pictorial stages go hand-in-hand and build on one another.
Hunt, Find, Add Addition with Regrouping Game
To represent the base ten strategy, Hunt, Find, Add is an effective and engaging game to incorporate into your math stations.
Students will be given a picture card, and inside the picture, they’ll hunt for addition with regrouping problems. You can make this more fun with magnifying glasses to help them “hunt” and find the problems.
They will write the addition problems in the box on their recording sheet. To solve, they will draw the addends vertically using lines to represent the tens and dots to represent the ones.
In the example of 29+45, they will add 9+5 first in the ones place and find the sum of 14. They should know to regroup since this is greater than 10. Next, they will mark out 10 ones and replace it with 1 tens block before counting to solve.
By drawing the addends and marking out the ones and replacing it with a tens block, they are using pictorial representations.
Crack the Code Addition with Regrouping Activity
To represent the expanded form strategy, Crack the Code is another one of my favorite addition with regrouping games to include in your math stations.
Students will use the key to crack the code and create their addition problem. They can use scratch paper or the back of the page to solve using expanded form.
In the example 55+76, students would write the expanded form of 50+5 and 70+6 vertically to represent the addends and create a new addition problem. I like to have students circle the + sign to remind them that they are adding. The expanded form strategy allows students to use the pictorial process by drawing out the expanded form and new problem.
Adding on a Number Line Addition with Regrouping Activity
To practice the open number line strategy in a pictorial way, students can use this adding on a number line activity to solve.
While the open number line strategy can be challenging, after modeling and teaching it, many students actually prefer it.
When first starting out with this addition with regrouping strategy, have students think through and write out the process for how to solve this.
First, they should put the bigger addend first on the number line. Then, they should think about how many tens “hops” and how many ones “skips” they need to count. Then, they can draw the hops and skips to count and solve for the sum.
To take their picture representation a step further, they can write out +10 and +1 above their skips and hops.
Abstract Addition with Regrouping Examples
After mastering the concrete and pictorial stages of the CPA approach, students are ready for the abstract stage of learning and solving problems using mental math, which is the ultimate goal. The abstract stage does not involve any manipulatives or pictorial representations.
Flip and Add Mat
To solve addition with regrouping problems using the standard algorithm, students can use a flip and add mat to practice solving various 2-digit addition with regrouping problems. They can record their answers on a piece of scratch paper or a whiteboard.
To use this addition with regrouping game, students will flip the number cards to create an addition problem.
Students will then use the standard algorithm to solve for the sum. If there are ten or more in the ones place, they should carry a ten next door to regroup.
When following the guided math framework in your math instruction, a big goal of math stations is for students to work independently on their own level.
As you can see, there are several addition with regrouping examples that use the CPA approach to encourage students to work independently during math stations and succeed at their level, whether they are working in the concrete, pictorial, or abstract stage of learning.
Almost all of the addition with regrouping activities shown in this post use a different approach and strategy. This is exactly what you want in your math stations, as it helps you reach all or your learners and differentiate.
With many of these activities, such as the Hunt and Find addition with regrouping game, you can differentiate with the CPA approach by having students work in the concrete stage with base ten blocks or the pictorial stage with an open number line. They could also work in the abstract stage by using the standard algorithm and using mental math to solve.
If you want to get your hands on more fun addition with regrouping activities and games including the ones shown today, be sure to check them out in my store below.
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