Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Number Sense and Operations → Addition and Subtraction ↓


Addition with Regrouping


When we add numbers, sometimes they are too large for just one place. Then we use addition with regrouping. Regrouping is also called carrying. It helps us add numbers larger than 9 by moving the additional value to the next place value. If you have heard of carry over before, it is another term for regrouping.

Understanding place value

To understand addition with regrouping, it's important to first understand place value. Numbers are made up of digits, and each digit has a place. For example, in the number 345, the digit 5 is in the ones place, 4 is in the tens place, and 3 is in the hundreds place.

        hundreds tens unit
          3 4 5

When you're adding, you typically start in the ones place and move to the left toward the tens, hundreds, etc. When the sum of a column of numbers is 10 or more, regrouping becomes necessary.

Basic addition without regrouping

Let's start by looking at a simple example of addition without the need for regrouping:

        32
       +15
    ,

We start by adding the numbers in the ones column:

            32
       + 15
       ,
       (2 + 5)

The sum of 2 and 5 is 7, so we write 7 in the ones column:

            32
       + 15
       ,
           7

Next, we add the numbers in the tens column:

            32
       + 15
       ,
       (3 + 1)

The sum of 3 and 1 is 4, so we write 4 in the tens column:

            32
       + 15
       ,
          47

Sum with regrouping

Now, let's explore addition with regrouping. Consider this example:

        58
      + 37
    ,

We start with the units place:

            58
       + 37
       ,
       (8 + 7)

The sum of 8 and 7 is 15. Since 15 is more than 9, we must regroup. We write the 5 in the ones column and move the 1 to the tens column.

            1 <- carried forward
            58
       + 37
       ,
             5

Now, let's add the tens digit, including the carried forward 1:

            1
            58
       + 37
       ,
       (1 + 5 + 3)

1 + 5 + 3 = 9. Therefore, we write 9 in the tens column:

            58
       + 37
       ,
          95

We have successfully added 58 and 37 to get 95 using regrouping.

Another example with visual representation

Let's take another example that requires regrouping, 76 + 47:

        76
      + 47
    ,

We start by adding the unit column:

            76
       + 47
       ,
       (6 + 7)

The sum of 6 and 7 is 13. We write the 3 in the ones column and carry the 1 to the tens column.

            1
            76
       + 47
       ,
             3

Now add the ones, including the 1 in the tens column:

            1
            76
       + 47
       ,
       (1 + 7 + 4)

1 plus 7 plus 4 equals 12. We write the 2 in the tens column and carry the 1 to the hundreds column:

           1
         12
       ,
            ,
            ,
            1 (carried forward)

Since there is no hundreds column in the current addition problem, you write the 1 like this:

            76
       + 47
       ,
         123

Step-by-step description

Let's break this down into more steps, as it may be easier for younger learners to give a more detailed explanation:

  1. Align the numbers: Make sure the numbers you're adding are aligned correctly according to place value — ones under ones, tens under tens.
  2. Add a units place: Start at the units place on the right.
  3. Check the sum: Look at the sum in the ones place. If it is 10 or more, put the second digit down and move the first digit to the tens place.
  4. Add the tens place: Go to the tens place and include the number you carried over, if any.
  5. Regroup if necessary: If the sum in the tens place is 10 or greater, move it to the hundreds place, if applicable.
  6. Write down the results: After you add each place value, the number you wrote down becomes your answer.

Tips for practicing regrouping

Here are some tips to make learning addition with regrouping easier:

  • Regular practice: Regular practice at short intervals, such as using number lines or counting blocks, can help understanding.
  • Use stories or real-life scenarios: Sometimes creating stories with practical examples, such as adding apples, oranges or toys, can help visualize the process.
  • Double-check your work: After you solve an addition problem, it can help to double-check your work by re-working the problem or checking it with a calculator.

Practice problems

Try the following practice problems using addition with regrouping:

  1.  47
    + 35
    ,
  2.  63
    + 29
    ,
  3.  88
    + 77
    ,
  4.  99
    + 18
    ,
  5.  56
    + 48
    ,

Working through these examples will help you master addition with regrouping. Happy adding!


Grade 2 → 1.3.3


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Basic subtraction up to 20
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Subtraction with Borrowing

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Addition with Regrouping

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