We’ve been talking about spatial ways to think of numbers, i.e. as points on a line. We saw that addition (& subtraction) and multiplication (& division) can be thought of as manipulations of a line segment.
Now, consider two numbers. Say we represent them on two lines, as shown above. Then we say that whatever the first number is, the second has to be twice that. So if the first is 1, the second is 2.
Think of arrows pointing where the numbers are. Imagine grabbing the first number’s arrow and sliding it up to a higher value. The second number’s arrow will have to slide, too. If you slide the first number to 3, the second will go to 6. Because it has to be twice as much.
Where ever you slide the arrow for the first number, the arrow for the second will shoot out even further, always being twice as much. This is math!
