Number Line Addition
Illustrating Addition of Real Numbers on a Number Line and with Signed Blocks
This activity begins by allowing the user to show the natural numbers, whole numbers, or integers as a set of ordered collinear dots, i.e. as locations on a number line. There is also a checkbox to make the number line thicker, representing the set of all real numbers.
Next, the user can enter in two real numbers via the slider/input box combinations. In the earliest years one can limit the inputs to natural numbers or whole numbers. Clicking the Illustration of Solution action button provides a physical illustration of the solution. Blue and Green (blocks, areas, vectors, numerals) represent positive quantities, but Red and Orange (blocks, areas, vectors, numerals) represent negative quantities.
This illustration actually combines 3 standard illustrations of basic addition of integers. The number a is first illustrated by a number of blocks (unit squares) of either a positive charge (blue) or a negative charge (red). These are lined up starting at the origin (0 on the number line). They go to the right if a is positive and they go to the left if a is negative. The vector <0, a> is illustrated on the top of this row of blocks, indicating a movement of |a| units to the right (+) or left (-) from 0 to a. The end of the vector is at a on the number line. The area of the corresponding rectangle is |a|.
The number b is also similarly illustrated by a number of blocks with green for positive and orange for negative. The blocks for b start at a on the number line and go |b| units to the right (+) or left (-), ending at the point a+b on the number line. The vector <0,b> indicates a movement of |b| from a to a + b on the number line.
We can think of addition as starting at the origin, then going to the a units to a and then from there going b units to a+b. Teachers can show counting up and counting on strategies with the illustration. We can also think of the illustration showing adding two natural numbers as simply combining the total number of blocks and counting them up. When the two numbers have different signs, we can think of a positive and a negative pair of blocks annihilating each other, leaving only one color (sign) of blocks remaining.
The sliders produce integer inputs only, but non-integer real numbers can also be entered into the blanks. Notice that in this case the illustration is basically a mixed number illustration with a whole number of whole blocks (unit squares) with one additional partial block.