Addition Strategies- Open Number Line

addition math skills Oct 18, 2022


Number lines help children build mathematical meaning. Seeing the numbers arranged in order and then hoping up and down the number line helps children develop a better understanding of number relationships. It gives them a way of seeing number relationships and the position of numbers. It also supports children in making sense of operations. Using the number line model children can communicate their mathematical thinking and make visible their mental math strategies.

Using the Number Line With Young Learners

In this post we will focus on how to use the number line for addition through the grades. A useful way to help kindergarteners think about adding is to think about it as jumping along a number line.  Draw a chalk numberline along the ground and kids can jump from one number to another, thinking about how far they have gone.  

            Start at 7, jump 3.  Where do you land?

            Start at 12, jump 5.  Where do you land?

The key is helping children count the jumps, not the numbers.  A common error for young children is to think of 5+2 and then count – 5,6 – and think the answer is six because they have counted two more numbers.  Emphasizing that we are counting the jumps helps children understand that seven is the correct answer. 

Children also enjoy using counters to jump along a paper number line. You can easily create a number line on a long piece of paper and roll a die to indicate how far to move along the line. You can also add in a spinner with a plus and a minus. Plus means you move up the number line. Minus means you move down the number line.

Working With Larger Numbers

By the time children are in second grade, they are able to use number lines to add larger numbers.  They can use an open number line (one that does not yet have numbers on it that allows students to partition in a way that makes sense to them) as a tool.  The number line affords children the opportunity to model their thinking.  Let’s look at how this tool is used.

This student jumps to a landmark number (50) first. Then they methodically jump along the number line using jumps of 10. After five jumps they land on 100 and then add the last small jump of 3 for a total value of 55 jumps. They land on 103.
This student jumps to a landmark number (50) first and then jumps to another landmark number (100). Then they add on the last little bit to get to 103.
This student jumps 50 first and lands on 98. Then they add on the 5 by first doing a jump of 2 and then a jump of 3.

Using the number line gives students the ability to make their thinking visible.  In the examples above, each student thought about the problem differently. We can see their strategies by the way they have modeled the problem. Using the number line also reduces the amount of information children need to keep in their head.  

Applications for Older Students

Students who are proficient at using the number line for addition (and subtraction) with whole numbers can later use this same model to add and subtract fractions and decimals.  What seems like a very abstract problem such as – 3.72+1.2= _____ - becomes concrete when we start to model it on a number line.  I have found that many children struggle when adding and subtracting fractions and decimals because it seems very abstract. Using the number line to model these operations makes it more concrete and leads to better understanding of the concept.

Here the student first jumps 1 and then jumps 0.2 for a total of 1.2 jumps. They land on 4.92.

Practice Using The Open Number Line

If you would like to practice some problems on your own, you can just use a piece of paper and a pencil or the Math Learning Center Number Line App is also a great tool.  To learn more about the open number line, take my course for parents of 2nd-5th graders.