Mathematics/Physics

Introduction To The Number Line

 Sheila Alexander Manley School 2935 W. Polk St. CHICAGO IL 60612 (773) 534-6900

Objectives:

The students will learn how to add and subtract using the number line with positive and negative numbers.  The lesson is designed for third through ninth grades.

Materials:

Magnets that stick to the board.

Strategy:

First draw the positive side of the number line on the board.  Point out the following; 0 is neither positive nor negative, a positive number is greater than 0, and positive numbers are to the right of 0.  Begin by giving sample problems such as  (8 + 1 = 9) to solve using the number line.  Place the first magnet under the number eight, and then explain that the plus sign is telling you to move in the positive direction once, then place the second magnet where you ended, and that would be your answer (9).  Show several examples with simple problems such as the one above.  Make sure everybody understands this technique before moving on.

We can also show how to subtract using the positive number line (8 - 1), tell me what number should I place the magnet under?  “Eight “ Why? Because that is the first number in the problem, then explain that the subtraction sign means to take something away, therefore we need to move back one space to the number (7), and that would be our answer.  We can now give the following rule:  when adding two positive integers, the answer will be positive.

At this point draw the other half of the number line on the board, this side of the number line is for the negative numbers.  The important points regarding the negative numbers are; 0 is neither positive nor negative, a negative number is less than 0, and the negative numbers are to the left of zero.  I would proceed by giving examples of adding with negative numbers. For example:

-7 + -2 = -9

Place the first magnet under the number seven (negative), then explain that the plus sign is telling us to add two more negative integers, move two steps to the left of the number seven and that will give you the correct answer (-9).   Give more examples of problems using negative numbers.  The rule that applies here is: when adding two negative integers the answer will be negative.

There is one more piece to this puzzle and that is learning to subtract using unlike signs (positive and negative).  For example:

7 - -2  = 7 + 2 = 9.

The rule is: do the opposite of the sign number and change everything to positive.  The sign number is the second number in the problem (-2); therefore we would change the subtraction sign to an addition sign and change the negative two (-2) to a positive two (+2).   You could also answer this problem using the number line.

We would begin at the number seven (place the magnet under the number), the subtraction sign is telling us to move two steps towards the origin (which is zero) but our sign number is telling us to do the opposite of that, move two steps further away from the origin beginning at the number seven (+7), and that is how we arrived at the number (+9) for our answer.

Performance Assessment:

I will have the class solve several problems using the number line.  They will answer the problems on their papers and on the board.

Conclusion:

When you move in the negative direction on the number line, it does not mean that you are going backwards, but simply that you have changed direction.