# How to Teach Subtraction Across Zeros

In upper elementary, it’s pretty common for teachers to struggle with teaching fractions and decimals. They are tough concepts and kids need lots of time and quality instruction and interaction with the content to build those concepts deeply. Ask any third, fourth, or fifth grade teacher what math subject they most dread, and ‘fractions’ is a fairly common answer. I get it, really. However, I would also like to argue that subtracting across zeros deserves one of those top spots for most challening concept to teach in upper elementary math.

At first glance, it seems like, well, I’m just teaching subtraction, easy, right? Most kids are slightly confused by borrowing at first, but once they get the idea, it starts to make sense to them. But, once you start getting zeros involved, oh boy. Who would have thought a number that means ‘nothing’ would cause so much struggle?!!

## First, let’s look at why subtracting across zeros is a challenging concept.

Pro tip: If your students are struggling with computation in general, it might be best to build up some of those skills first, and then tackle subtracting across zeros. Check out this blog post on how to make computation practice more engaging and effective.

If you want to save time and find something done for you that already encompasses these techniques, check out this interactive lesson plan on Subtraction Across Zeros.

## Okay, so what’s a teacher to do? How to teach subtraction across zeros without reaching insane frustration aggression levels?

There are a few things you can do, for sure. If your kids are struggling with either basic math facts or place value, focus on building up those concepts first. Sometimes taking a step ‘backwards’ actually helps you move forward more quickly.

### Go back to basics and use the base ten blocks.

Sometimes kids struggling with more complicated computation is a sign that there are cracks in the foundation of their understanding. They understood enough and were able to get through the easier things, but now that the going is a little more rough, they just don’t have the foundation they need to rely on. Build up those place value concepts by using the base ten block manipulatives. Have them do the actual trades and subtraction and practice writing down what they traded and subtracted. Connecting the numbers on the paper in the algorithm with the actual blocks is one of the best ways to help kids understand what they are doing.

### Practice with money.

What’s the change if something is 95 cents and you pay with a dollar?

These kinds of problems might be a little outdated practically, but they’re still great for teaching kids to make sense of subtraction. The ‘count up’ strategy works great here. We start at 95 and count up – 96, 97, 98, 99, 100. If we add 5 to 95, we get up to 100, so 100-95 is 5.

When you have nice round numbers, or when you get to decimals later on, this strategy can help make things more concrete for kids. It’s a great way to have them check if their answer makes sense, as well. If you pay for something that’s 12.95 with \$20, you’re not going to et 10.95 back!

### Teach & try lots of different strategies, then let kids choose the one that works best for them (and that might be different, depending on the problem!).

Anyone who’s been a teacher for more than 3 seconds knows that every kid’s brain works just a little differently. You can say the exact same thing and one kid will have an ‘aha’ moment and another will become more confused than ever. It’s just good teaching in general to teach a lot of different strategies and let kids decide for themselves which one to use and when and how.

Give them lots of opportunities to practice and show that they understand and let them talk about which strategies they prefer and why. Let them explain things to each other and maybe even settle their own disagreements about which way is better for which kind of problem. Not only will their subtraction computation get better, but so will their problem solving, reasoning, and explanations.

### Try this ‘trick’: Think of 3 hundreds and 0 tens as 30 tens.

Here’s an example: 5307 – 429.

So, using the standard algorithm, we would need to borrow from the 0 to have enough to subtract 7-9. You can’t borrow from a 0, so we’d need to go over to the 3 and borrow, then make the 0 a 10 and borrrow 1 from that.

But we can cut out a step if we think of the 3 and the 0 instead as 30. Then, we can borrow 1 from the 30 and make it 29. We get to the same place, with a 2 for the 3 and a 9 for the 0, but we just get there one step quicker.

For some kids, this little shift really helps them with understanding the concepts because it’s 30 tens instead of 3 hundreds and 0 tens. I’ve found that this little ‘trick’ greatly reduces the number of errors kids make when trying to subtract across 0 with the standard algorithm.