Teaching how to subtract 3 digit numbers on an open number line can get messy. If students aren’t shown best practices, their jumps on the number line and numbers get all jumbled up. This leads to their frustration. Their answers are not accurate and many students can feel like giving up. Maybe you’ve had an open number line 3 digit subtraction lesson in the past where so many students needed one-on-one help where you felt frustrated and like giving up.

 

I’ve been there too. But I wanted to help my students and improve my instruction. So I did some research and a deep dive into 3 digit subtraction on a number line and I discovered ways to help my students learn this strategy so they can be successful every single time.

 

 

But first, it’s important to note that students do well with 3 digit strategies when they have learned 3 digit place value concepts first. So read my blog post about how to teach each place value standard for 2nd grade here.

 

Now, let’s get into the best way to teach how to subtract 3 digit numbers on an open number line. I actually break down this strategy into 3 different lessons for students to find the most success.

 

How to Subtract 3 Digit Numbers

 

Lesson 1: Subtracting 100 and 10

 

What’s the main part of 3-digit subtraction on a number line? It’s subtracting hundreds, tens, and ones. Specifically subtracting 100 from a number, subtracting 10 from a number, and subtracting 1 from a number.

 

Students need to know the patterns of subtracting 100, 10, and 1 from a 3-digit number in order to be successful with the open number line 3 digit subtraction strategy.

 

That’s why I have a full lesson on these patterns the day before I teach the actual strategy.

 

For the lesson opener, I first display a page up on my whiteboard that has a 3 digit number built out with base ten blocks. Then I have students subtract 10 by crossing off a tens rod. Students give me the answer. I do the same thing with the number but now cross off a hundreds block to subtract 100.

 

This helps things be visual and concrete for students. It helps them find better understanding.

 

Then I list up a bunch of equations of 3-digit numbers minusing 100 and 3-digit numbers misusing 10. Students help me solve these. Then I ask, “What patterns do you see?”

 

 

I want students to see that when you subtract 100, the number in the hundreds place decreases by 1. Students also need to see the pattern that when you subtract 10, the number in the tens place decreases by 1.

 

But here is a special pattern that students also need to know. It’s when they subtract 10 from the 3-digit number that has a 0 in the tens place. I post up a bunch of these equations and have students solve them. Again, I ask them what patterns they see.

 

They should see that the tens number changes to a 9, and the number in the hundreds decreases by 1.

 

Once students learn all these patterns, they are ready for some practice so that these patterns become automatic.

 

I first get students started with a worksheet. We do a few together and they do the rest by themselves. I wait at our classroom table. As students finish, they line up by me, I check their work and then I assign them a partner.

 

With this partner, they complete a scoot activity. I tape up task cards around my classroom with different equations subtracting 100 or 10 from a number. Students go around the room and solve the equations. They write their answer on a recording sheet and then check their work with an answer key I’ve set out.

Then I have students complete a sorting activity with that same partner. They have to sort the cards on whether or not the equation is subtracting 10 or 100. The equations are missing what they are subtracting so students have to rely on patterns to know. They love the challenge!

 

 

When students are finished with the sorting activity, I have them complete an exit ticket individually. They rate themselves on how they think they understood the lesson and solve a few equations. I look at these later and see who could use some more practice during centers.

 

This lesson of subtracting 100 and 10 from a number is essential. It prepares students the next day from when I teach them the open number line 3 digit subtraction strategy.

 

Open Number Line 3 Digit Subtraction

 

Lesson 2: Counting Back to Subtract

 

There are two ways to do 3 digit subtraction on an open number line. You can make jumps back and count back to your answer, or you can add up to subtract. I first do a lesson on counting back to subtract on a number line.

 

First, I model the strategy to my students. I display pages on our whiteboard. These have number lines and equations. I model making jumps and subtracting 100s, making jumps and subtracting 10s, and making jumps subtracting 1s. I show students how we can use the patterns that they learned the day before to write the numbers underneath the number line.

 

I also make sure to show an example with an equation that includes the special pattern of subtracting 10 to a number with a 0 in the tens place. This will help students find better success when they come across an equation like this.

 

I also model what happens when they make their jumps too small or write their numbers too large underneath. They see all my numbers get jumbled up and get a ridiculous answer. They laugh at this, but it helps them to remember that when solving on an open number line, they need to make big jumps and write numbers small underneath.

 

To make our lesson on how to subtract 3 digit numbers on an open number line more engaging, I make it interactive. To do this, I tell students to “switch” their brains to hundreds, tens, or ones when it’s time to write the numbers down below. We put our hands up to our heads and pretend like we are making a “clicking” noise. This helps students follow the patterns that they learned the day before. It works really well and students think it’s a lot of fun!

Then it’s time to get students their own practice. I give them a worksheet that I also display on the board. We do a few problems together where I ask students what we should do each step of the way. They practice making the jumps with me, labeling them, following patterns, and writing the numbers down below to solve.

 

 

Then I have students do the rest of the problems by themselves, but this time I am walking around and giving support to students when needed. I take note of common mistakes and misconceptions I see students have.

 

Then I call back everyone’s attention and address those. I may model solving a couple more problems from the worksheets to help clarify things for them.

 

Then I give them one more worksheet. Students complete it on their own and I wait over by our classroom table. As students finish, they line up by me and I check their work and help them fix any mistakes. I love how this gets students immediate feedback. When their work looks good, I draw a big check mark with a smelly marker. It’s like a fun little reward for students as they  finish their work.

After that, I pair students up and they complete a scoot activity. I have task cards taped up around the classroom and students have to work with their partner, solve the problems, and write the answers on their recording sheets. These cards have jumps already made, students just have to follow the jumps to get the final answer. I set out an answer key so that students can check their work when they are finished.

 

 

I want to give my students more hands-on practice so I have them do a fun puzzle activity. This puzzle has number line sheets that have made the jumps for them, but students have to put the little cards with the numbers underneath to solve. This helps them focus on the patterns to solve.

 

To save you prep time, you can have students cut out the number cards, or place the number line pages in sheet protectors and have students use dry-erase markers to write the numbers below.

 

 

Find these puzzle activities here.

 

Then I want to see how well students did with how to subtract 3 digit numbers on a number line,  so I have them complete an exit ticket. They rate themselves and then solve a couple problems. I review these later and take note of students who could use more practice. I incorporate more practice activities in our math centers.

 

Find all of my open number line 3 digit subtraction lesson materials I’ve mentioned so far here.

 

The next day I teach a lesson on using addition to subtract 3 digit numbers on a number line.

 

3 Digit Subtraction on a Number Line

 

Lesson 3: Add up to Subtract

 

For this lesson, I like to do a quick review of fact families. I remind students how addition and subtraction are related to each other and how we can use addition to subtract. Learn more about teaching fact families here in this blog post here.

 

Then I move into our lesson where I model how to subtract 3 digit numbers through addition. I show how we take the greater number from our equation and put that on the right side of the number line. Then I show them that we take the lesser number and put it on the left side of the number line.

 

To help my students remember this, I tell them that the lesser number goes on the left side because they both start with L.

 

 

Then I model making jumps of hundreds, tens, and ones from the lesser number until we get to our greater number. I label the jumps and record the numbers below the number line.

 

To get the final answer, we add up the jumps.

 

This is a helpful strategy if students just struggle with subtraction. Our brains like addition more, so why not use addition to subtract!

 

Then I follow the same process as the previous lesson. I get students practice with a worksheet. We do a couple problems together. Then I let them do a few problems on their own while I walk around giving support.

 

I get the class’s attention back and I address any common mistakes and model more problems if needed.

Then students complete their own worksheet while I wait at my table. Students line up and I quickly check their work and help them fix mistakes.

 

 

Then they get with a partner and complete a scoot activity around the classroom. The cards have numbers lines where they used addition to subtract, but students have to add up the jumps to get the final answer and write the number line’s equation.

After that, students complete a puzzle activity where they match the solved number line with its equation and answer.

 

 

Finally, I check student’s understanding by having them complete an exit ticket.

 

I love setting up my open number line 3 digit subtraction lessons in this way because it gives students a lot of support. As the lesson goes on, support is taken away in little increments until students can subtract 3 digit numbers on a number line by themselves.

 

The curriculum your school uses probably has 3 digit subtraction on a number line lessons, but maybe you have seen your students need more practice. That’s where you can use the worksheets, scoot activities, and puzzle activities.

 

Find all the resources I’ve shared in this blog post here.

 

You can find these resources in a money-saving bundle with all my 3 digit subtraction strategies here.

 

I hope you have found this blog post helpful on how to teach 3 digit numbers on an open number line. These lessons work best when you help students discover and use the patterns involved in the strategy and when you give them plenty of support practice.

Learn more about teaching each 3 digit subtraction strategy in this blog post here.