You will want to make sure that your child is familiar with comparing logarithms for Common Core math. In addition to comparing numbers with ratio and unit rate, you can actually compare numbers a third way — with logarithms.
A logarithm is basically an exponent. In the equation 10x = 100, writing log10(100) is how you solve for x; log is short for logarithm (in this case, x = 2). Comparing numbers with logarithms is a high school and college-level topic, but people use logarithms instinctively. As an example that logarithms are instinctive — the distance between 1 and 1,000 doesn’t feel all that different from the distance between 1,000 and 1,000,000 for most people.
Try this: Draw a number line with 1 at one end and 1,000,000 at the other end. Now put 1,000 on that number line.
Most people end up putting 1,000 a bit to left of center on the number line. If this is true for you, it’s because your brain reacts to the logarithms of large numbers, not to their actual values. According to the values of these numbers, 1,000 should be half of the way along the line — so small a fraction of the distance that it’s difficult to see the space between 1 and 1,000.
