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Do your primary students have a number line posted on their desk? Is there one hanging above the chalkboard in your classroom? Although teachers today have many options for modeling mathematics, the number line is still an important and useful math tool. While cubes and other manipulatives support learning by representing numbers, the number line actually develops learning by giving students another look at number relationships. Your primary students may find using a number line more challenging for some concepts. However, it’s important to stick with it as number lines provide learning opportunities for later skills that can’t be replicated with cubes, such as negative numbers, decimals, rounding and graphing.

That’s why at Happy Numbers we include the number line early and often throughout our exercises. In this post, we’ll share some of these activities that you can use with your class at different stages of learning.

*[Be sure to use your own account at HappyNumbers.com to try the activities described in this post!]*

## Counting and Numeration

Our first number line exercises help reinforce the count sequence and number recognition. Students count to reach a given point on the number line:

or identify a number corresponding to a given point:

These activities can be replicated off-line, but an advantage of using them online at HappyNumbers.com is that students receive immediate support after any errors, such as being reminded of the count sequence for this exercise:

which allows them to understand the error and to correct it:

Eventually, students work to complete a number line using non-sequential numbers. Here, students begin with a number line only labeled with 0 and 10:

An error reveals the rest of the numbers:

## Basic Addition and Subtraction

Another great opportunity for exploring a number line is when learning the first steps of addition and subtraction. Assuming your students are familiar with number line basics mentioned above, you can start relating movements of objects along the line to their corresponding numbers on the number line:

and then to equations:

The same for subtraction:

The visual support that the number line provides helps young learners grow from concrete to abstract to algebraic thinking.

In later exercises, students complete the equation themselves based on the model given using the number line. For addition:

and for subtraction:

Once students are familiar with the movements of addition and subtraction on the number line, we can challenge their understanding by presenting this information in a new way. This type of multiple-choice exercise helps students develop deeper understanding of number relationships:

## Transitioning through 10 in Addition and Subtraction

A particularly challenging point in understanding basic operations is the transition through 10. In our recent post, Teacher’s Best Friend: Base-10 Blocks, we shared some ideas on how you can support this concept using base-10 blocks. Another great model for building deeper understanding and fluency with this concept is the number line.

For example, at the stage when your students are learning to add/subtract through ten by adding/subtracting 1s, you can have them model this strategy on the number line. Begin with problems that show the second addend (or subtrahend) of an equation in steps of 1:

and use the number line model to solve the equation:

This same exercise increases in difficulty when the numbers are removed from the number line:

This ability leads into adding/subtracting to 10 and then beyond by breaking an addend (or subtrahend) into two parts. Thus, students visualize the strategy of finding 8+6 by breaking it into 8+2+4:

In the exercises above, students were shown the jumps to make on the number line and had to relate them to numbers. To replicate this idea on paper, teachers would have to provide an equation and a number line with arrow ‘jumps’ indicated. Once students have mastered this step, they advance to determining the last ‘jump’ on their own, without being given the arrow. This requires them to think about how the second addend (or subtrahend) needs to be broken down. Rather than just using the model, they are now building the model. Here, a teacher using pencil-and-paper exercises would provide the equation, a number line, and the first two arrows only. Practicing this skill with a model leads toward using the strategy mentally down the road:

Again the advantage of using these exercises online is that we provide instant feedback, which illustrates the logic behind how this step should be done:

And then allows the student to correct his mistake:

And continue with this exercise on the right track:

We hope these ideas will give a little boost to your instruction by using number lines in new ways or just more frequently. Whether you use traditional paper number lines or your account at HappyNumbers.com, this tool will bring greater conceptual understanding and mathematical fluency to your students. If you have found this post helpful, please forward it to your grade-level colleagues or send us your feedback! We are always working to make math learning better for your students!

Yours,

Happy Numbers Team