In 2nd grade we work on addition and subtraction of numbers within 1,200. The strategies your child uses may look different from the way you were taught in school with borrowing and carrying. Although many children learn the pattern of borrowing and carrying, they do not understand the why behind what they're doing which can lead to mistakes and confusion. They may end up borrowing or carrying unnecessarily. We believe this misunderstanding is what can cause students to become frustrated with math later on in their education.

When we teach addition and subtraction we show students a variety of strategies that they can use, but when students are working independently, they are free to choose the strategy that works best for them. If I notice that a student is struggling, I almost always steer them back to drawing the base 10 blocks. They seem to be most consistent when using this strategy. They are comfortable with base 10 blocks because we've used them all year long, and I think it helps them to be able to have the visual when working through the problem.

Here are a few strategies we use in the classroom:

Adding- Base 10 Blocks

Draw both numbers in flats (hundreds), longs (tens), and cubes (ones). Count up the total number of blocks. If you have more than 9 ones, you will make a new ten. If you have more than 9 tens, you will make a new hundred.

Adding- Number Line

This strategy does not require students to think about whether or not they regroup (make a new ten or hundred), but it does require them to be able to skip count. They use an open (or empty) number line and start with either of the numbers. Then, they make jumps on the number line for each hundred, ten, and one.

Adding- Tens to Tens, Ones to Ones

Draw a V connecting your tens and one connecting your ones. Add the tens and add the ones. If your ones create a new ten, don't forget to add it to the tens place as you add across. For students that use place value to add mentally, I usually encourage them to show this strategy on their paper.

Adding- Expanded Form

Break both numbers up into hundreds, tens, and ones. Add the ones place. If you have more than 9 ones, you will make a ten that moves to the tens place. Add the tens. If you have more than 9 tens, you will make a new hundred that moves to the hundreds place. Then add the hundreds.

Subtracting- Base 10 Blocks

For this strategy, they only draw the larger number in base 10 blocks. Then, they cross out or erase the hundreds, tens, and ones in the smaller number. If they do not have enough ones to subtract, they can take a trade a ten for ten ones and then subtract. (This is what I did in green) If they do not have enough tens to subtract, they can trade a hundred for ten tens and then subtract.

Subtracting-Expanded Form

Many students really liked adding by using the expanded forms of the numbers. This strategy is a new one I've introduced for subtraction and some have been working hard and trying it out. This strategy is a step towards the regular algorithm with borrowing, so when we are using this strategy, we talk a lot about why we're changing the 4 to 14 or the 70 to 60 (as in my problem below).

Subtracting- Number Line

This strategy does not require students to think about whether or not they need to borrow or trade a hundred or ten in order to subtract. They use an open (or empty) number line and start with either of the numbers. Then, they make jumps on the number line for each hundred, ten, and one.