The open number line strategy can be tricky for many students. There is a lot of drawing and mental math skills involved. But over the years of teaching how to add an open number to my 2nd grade students, I have found how to best scaffold this method so that students can find success.

 

So today I’m sharing exactly how I teach the open number line strategy along with my best tips.

 

But before we get started, it’s important to know that students do much better on these 3-digit addition strategies when they are fluent with their basic addition and subtraction math facts. I have a free workbook to help you get your students to math fact fluency: The 7 Steps to Ensure Math Fact Fluency. Download your free copy here.

 

Open Number Line Strategy

 

If you are not familiar with the open number line strategy, it is where you solve addition equations on a blank number line. For 3-digit addition, you make jumps of hundreds, tens, and ones until you get to your answer.

 

 

When I first taught the open number line strategy, I didn’t realize the mental math involved. Students need to be able to add 100 and 10 to any 3-digit number.

 

Luckily, students catch on to this pretty quickly if you help them discover the patterns involved in adding 100 and 10 to a number.

 

Now I say “help them discover these patterns” because when students notice them for themselves instead of you just pointing them out, students will remember these much better.

 

To do this, I display a bunch of equations of 3-digit numbers adding 100. As a class, we use place-value blocks to add 100 to each number. Soon students see the pattern that when we add a hundred to a number, the number in the hundreds place goes up by one.

 

 

You can see how it’s important for students to understand concepts of place value for this skill. Learn more about how I teach each place value standard in this blog post here: Place Value Standards: How to Best Teach Them to 2nd Grade Students

 

After students learn the pattern of adding 100 to a number, I help them see the pattern of adding 10 to a number. I display a page with a bunch of equations that have 3-digit numbers adding 10 to them. Again, we use place-value blocks to get to the answer. Students quickly discover that when you add 10 to a number, the digit in the tens place increases by 1.

 

But there is one more pattern students need to be aware of. I call it our “special 9s pattern.” I display a bunch of equations of 3-digit numbers adding 10, but the digit in the tens place is a 9.

 

So one equation may be 396 + 10. If we follow our regular tens pattern then the number would show as 3106. I show students this mistake and they all laugh. Then we use place-value blocks to show that if we add another ten to 396, it gives us 10 tens. We count by tens to discover that 10 tens equals 100, so the number comes to be 406. We continue this with a few more examples until students can see the pattern of when we add 10 to a 3-digit number where there is a 9 in the tens place, the hundreds digit increases by 1, the tens digit changes to 0, and the digit in the ones place stays the same.

 

Find the display pages I use to teach these important patterns here. 

 

After teaching these patterns to my students I like to give them lots of practice with them. I have students complete worksheets, do a scoot activity, and then a sorting activity. I find this skill so important for the open number line strategy that I teach this lesson the day before my open number line lesson.

 

 

Find all the lesson materials you need to teach these here.

 

Now that I know my students have a solid understanding of adding 100 and 10 to a number, I know they are ready to solve 3-digit addition equations on an open number line.

 

Let’s get into how I teach this strategy to my 2nd grade students.

 

Open Number Line Worksheets

 

Before my students are ready to practice the open number line strategy with worksheets, I introduce this strategy by displaying a page with a blank number line. There is an equation and I model making jumps of 100s, jumps of 10s, and jumps of 1s.

 

Then I point out to students that we can use the patterns we learned the day before to fill in the numbers below the number line and get to the answer.

 

I show a couple more problems on these display pages so that students can see the steps involved to solve 3-digit numbers on an open number line.

 

Also, I make sure to point out as I am modeling these that it’s important to not make jumps that are too close together. I also show how I write small underneath the number line. To make sure students understand the importance of this point, I show me solving a problem where I make too small of jumps and write too big underneath. My numbers get all jumbled up and my answer is not accurate. This helps students when they are ready to practice this strategy on their own worksheets.

 

After that, students are ready for practice. To give students this practice, I give them open number line worksheets. I like to start students off with a worksheet that has all the jumps made for them. Students just use the patterns to fill in the numbers underneath until they get to the answer.

 

 

Then students are ready for regular open number line worksheets. With all my worksheets, I like to do the first couple of problems together and then have students complete the rest by themselves. I love these worksheets because the number lines are long enough for students to make all their needed jumps. Find these worksheets here.

 

As students are completing the worksheets, I sit at our classroom table. Students know that if they need help, they come sit at the table. When students have completed their worksheets, they line up by the table. I quickly check their work and give any help as needed. Students fix any mistakes I point out. Once their work is good, I give them a big check mark on their page and students put away their paper in their Take Home Folder. Students love the check mark on their page because I use a different smelly marker each day. Find the smelly markers I use here.

 

I love setting up my math block this way because I can help students as needed and give immediate feedback. Plus, I save time because I am not correcting papers after school. I highly recommend it!

 

Find the open number line worksheets I have students use here.

 

After students have completed their open number line worksheets, I assign them a partner and they complete a number line scoot activity.

 

 

Around my room, I have taped up open number line task cards. Students have a recording sheet and they go around the room, look at the number line on the card, and record the equation it represents on their sheet. I like having students work with a partner to do this because they can give each other support and it gets them talking about the math. As I walk around, I love hearing what reasoning students are using to get to the answer.

 

Find the scoot activity I have students complete here.

 

Once students complete the scoot activity, I give them an open number line game to play with their partner.

 

Open Number Line Game

 

This open number line game is a puzzle. Students lay out cards with number lines on them. These cards have the jumps of the number line, but not the numbers underneath. Students have to take small number cards and place them where they should go on the number lines.

 

 

It’s a lot of fun for students! They love finding a place on the floor of our classroom to complete these puzzles. Once students are done, they raise their hands and I do a quick look over their work. When things look good, they mix up and stack the pieces. Then this puzzle is ready for the next students.

 

Find this open number line game to use in your classroom here.

 

To help assess where students are at with the open number line strategy, I then have them complete an exit ticket. This just has students solve a couple problems by themselves. Later I look over these and make note of which students may need a little more practice with this strategy.

 

Find the exit tickets I use for my open number line lesson here.

 

After students have completed their exit tickets, they can do a fast finisher activity until our math block time is over. Read about the fun fast finisher games my students love here in this blog post: 12 Fast Finisher Activities That Are So Fun

 

I hope this blog post has given you many great ideas on how to teach the open number line strategy. It comes down to making sure students know the pattern needed, modeling how to solve on an open number line, and then getting students plenty of practice with it.

 

Find all of my open number line 2nd grade resources I’ve shared today here.

 

Need to know how to teach this strategy with 2-digit addition? Check out this blog post here: How to Teach Number Line in Addition in a Way That Absolutely Works

 

Find my 2-digit open number line resource here.

 

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