How important are number lines? Montessorians know too well the story of Ancient Egyptians who tied knots at equidistance on a rope to measure crops. This is a form of a number line!
Every day we use number lines when measuring ingredients, length, or driving along a road. Not only are number lines everywhere, but they are also a great way to accelerate arithmetic processing.
Learners visualize how numbers are affected by the process in use. Working on a number line promotes mental calculation. Learners must imagine the path that a number takes using the graduated line. For example, 3 + 4 requires learners to start at three and jump over four segments. Number lines are used when working on fractions and decimal numbers as well. Learners know to use segmentation to break down a unit into fractional parts. For example, learners can select any whole number on the line and further segment it to work with 3 3/4 or 3.75.
The number line concept will also be used in the upper elementary years when exploring negative and positive numbers. Learners can observe the pattern of absolute values and transfer this knowledge to coordinate points where numbers are represented on two intercepting axes.
We believe a Montessori classroom should have a number line with movable parts. We created the Positive Number Line, which contains an informed cloth number line, one corresponding cloth mute chart, 21 wooden numbered tiles from 0-20, and 15 wooden strips with addition and subtraction equations.
Materials
Step 1 – Building the Number Line
Invite your young elementary learners to build the Positive Number Line. Lay out the mute Number Line and the numbered tiles in mixed order below the number line. Beginning to construct it starting at zero and continue placing tiles until a learner is ready to continue. Explain that the Number Line could continue to an infinity number but that you will work within 20 whole numbers, also known as integers (1, 2, 3, 4, 5, 6, etc.) Lay out the informed Number Line above the mute Number Line to compare the work. Inform your learners that they will practice addition and subtraction using the Number Line. Once they have built the Number Line, they may work with either the mute or informed lines.
Step 2 -Equations with Three Addends
We provide five wooden strips containing 3-addend addition equations (7 + 6 + 3 = __). You can help your learners with the first equation. Read it around and model how to start counting on the Number Line. If your learner is already comfortable with cardinality, add the second and third addend by counting from segment to segment with your finger. Read the number on which your finger landed. Restate the equation with the sum at the end. Let your learners practice with the strips left.
Step 3 – Equations with Mixed Processes
On the same day, you can use the five strips that contain a mix of addition and subtraction. Proceed like above, except your finger will go backward on the line when you have a subtrahend. This process will serve as a foundation when working with negative numbers.
Step 4 – Addition with Missing Addend
In this final step, your learners will practice counting the difference of segment between the first addend and the sum by counting up from the first addend all the way to the sum provided in the equation. Again, you can show the process using the first strips. Your learners can practice with the four remaining strips.
You may encourage learners to create their own equations and work with a partner. Later, they will be introduced to the Negative Number Line, which will look familiar. The contrast between the positive and negative numbers should be evident. Our Number Lines use a common color coding, with positive numbers on the blue line and negative numbers on the red line. The transition will be clear and easy!
We hope to enrich Montessori classrooms with modern study-based support materials! For more Montessori materials, please visit our website at www.alisonsmontessori.com.
