Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

You hear a lot about open number lines these days, but what exactly is an open number line? Well, it’s a number line with no numbers or tick marks. Open number lines are great models for working with place value or, in the case below, addition. In previous posts, I’ve talked about mental strategies for addition. The number line is a fantastic way to record the different strategies used by students. The three number lines below all show strategies for adding 37 + 48. Look at each one and see if you can explain how the addition was done in each case.

Number Line 1: This student added the tens (30 + 40) and then the ones (7 + 8). The number line starts at 30 (the tens from the first number) and adds on the 4 tens from the second number, landing on 70. The student then added 7 + 8 to get 15 and added that to the 70 to get 85.

Number Line 2: This student left 37 whole and added on the 4 tens from the second number. He then broke the 8 ones into 3 + 5 and used the 3 ones to make 80. Finally, he added on the remaining 5 ones.

Number Line 3: This student took 3 of the 8 ones from the second number to get make a ten out of the 37 (37 + 3 = 40). Then, she jumped on the 4 tens to get to 80. Last, she added the remaining 5 ones.

Notice the number sense required for this type of math. Students have to be able to think flexibly about numbers, understand place value, and decompose numbers. This might be out of your comfort zone! If so, try some problems on your own. When you do this with your class, it is a good idea to anticipate the strategies students might use, so you’ll be ready to draw them.

I really appreciate this open number line. I am a first year teacher, teaching second grade. For all of the strategies I have taught for double digit addition, I have taught my kiddos to start with the ones, then the tens. My reasoning was so they become accustomed to ones always going first, like with regrouping. I’m finding that most worksheets begin with tens on an open number line. Do you think it makes a difference to start with tens?

Why doesn’t the first solution not adding up to 37 + 48. I mean the top numbers when added should equal to 48 right? Shouldn’t the number line start at 37? Thanks!

Thank you for your question! This particular student’s strategy was to add the tens first (30 + 40) and then to add the ones (7 + 8). The number line shows starting at 30 and jumping 40 (30 + 40), which lands on 70. Then the student mentally added the ones (7 + 8 = 15) and jumped 15 from 70 to 85. The landing point, 85, is the sum of 37 + 48.

I also find open number lines are a great formative/ diagnostic assessment tool. I ask my students to place a given number on the open number line, and observe how they represent intervals and the position of the number in relation to numbers greater then or less than the given number.

I’m not really sure what the question is asking. I don’t know that there’s just one number that’s always included. I’d say that three numbers are represented–the two parts (addends) and the total (sum).

Thank you for this, Donna! I appreciate that you spell out the reasoning behind it. I hope you’ll share more about your math practices.

You’re so welcome, Lori! Stay tuned for more!

Yep this is soooo cool!!!

Thank you for the freebie!

My pleasure, Chasity!

This is wonderful! Thank you 😀

You’re welcome, Chanel! 🙂

Thank you so much. How can I modify and explain this method to first graders.

You could use a regular, marked number line for 1st grade and you could use the same process for showing addition and subtraction.

Great explaination! Thanks

I really appreciate this open number line. I am a first year teacher, teaching second grade. For all of the strategies I have taught for double digit addition, I have taught my kiddos to start with the ones, then the tens. My reasoning was so they become accustomed to ones always going first, like with regrouping. I’m finding that most worksheets begin with tens on an open number line. Do you think it makes a difference to start with tens?

We are trying this with three digits in second grade and it has been very challenging. Any suggestions on the instructional approach?

Why doesn’t the first solution not adding up to 37 + 48. I mean the top numbers when added should equal to 48 right? Shouldn’t the number line start at 37? Thanks!

Thank you for your question! This particular student’s strategy was to add the tens first (30 + 40) and then to add the ones (7 + 8). The number line shows starting at 30 and jumping 40 (30 + 40), which lands on 70. Then the student mentally added the ones (7 + 8 = 15) and jumped 15 from 70 to 85. The landing point, 85, is the sum of 37 + 48.

I just finished a workshop called Number Talks and the presenter used this number line frequently to give students a visual. I love your page!!

I also find open number lines are a great formative/ diagnostic assessment tool. I ask my students to place a given number on the open number line, and observe how they represent intervals and the position of the number in relation to numbers greater then or less than the given number.

Hi Donna

I am a math coach as well. Wondering if you feel number lines have a place in Kindergarten and if so in what capacity? BTW huge fan of yours.

I definitely use number lines in Kinder, but they are marked number lines, not open number lines.

Hi Donna, I have a question on a sheet of paper, it says, “What number is always included on an open number line when you add.

It is in a 1st grade math book, I am not sure what the book is called I only have a paper copy of it.

Not to be rude but I need an answer soon?

I’m not really sure what the question is asking. I don’t know that there’s just one number that’s always included. I’d say that three numbers are represented–the two parts (addends) and the total (sum).