Flexible Thinking while Adding and Subtracting

Common Core Math has ushered in new ways of doing addition and subtraction.  No longer do we have to align numbers vertically as done in the ‘old’ standard algorithm. Gone are the terms ‘carry’ when adding and ‘borrow’ when subtracting. The term most often used now is ‘regroup’.

Let’s think about solving 43 + 19 using the old method. We would align the two numbers up vertically and say 3 + 9 is 12, so ‘carry’ the 1 and put it over the 4. Well, it really isn’t 1 that we’re carrying, instead it is 1 ten. In essence, we have regrouped the 1’s into a group of 10 and thus we put a 1 in the 10’s column.                                                          

1

  43

+19

  62

Let’s try subtracting 43 – 19. First align the two numbers vertically. Since we can’t take 3 – 9 we would say let’s borrow 1 and make it 13. Like addition, we are actually taking a group of 1 ten. When using the term ‘borrow’, the expectation is that we pay it back, which doesn’t happen when solving subtraction problems.

                                                                                                           3 13                                                               

  43

-19

 24

Second graders have been taught five different ways to solve addition and subtraction problems. Here’s the list of strategies that have been presented:

Addition Strategies

• Building to the Next Ten
• Building to the Next Hundred
• Decomposing Numbers
• Counting Up on a Number line
• Standard Algorithm

Subtraction Strategies

• Counting Up and Back Using a Number Line
• Subtraction Make 10's
• Subtraction Make 100's
• Subtraction by Decomposing Numbers
• Standard Algorithm

     Some of the comments students have made:

“When I learned the other ways of doing addition, I felt excited because it taught me more ways to find the answer.”

 “I love decomposing, it’s so much fun.”

Common Core encourages students to be flexible in their thinking while solving problems mentally with or without paper and pencil.

Here are a few snapshots of students during our guided math groups.