Creating a number line will help you see how fractions have the same value. It’s a big idea that will help you order fractions, add fractions, and subtract fractions.
First tape together five pieces of paper and draw a line across all five pieces of paper.
Use a ruler to mark “1” at 1 foot, “2” at 2 feet, “3” at 3 feet, and “4” at 4 feet.
Now, you can mark your halves. One half is exactly in between 0 and 1. It is 6 inches from 0. Every 6 inches add another 1/2. You will have:
You probably know that:
When you have an even number of halves, you will have a whole number. Why is that?
Now, we will add fourths. “Fourths” are often called quarters because a whole divided into four equal sections has four equal quarters. There are four fourths in one whole. So one fourth is smaller than one half. In numbers, this inequality is:
In fact, you will quickly find that
In fact, this equation shows the phrase “four fourths in one whole”:
Add, fourths until you have at least 17 fourths on your number line. Look at how many fourths and halves are at the same spot.
Now, you will add eighths. It reinforces the ideas from adding the fourths. But, this time you will have over 35 eights. This time you will use these two equations to make sure you put the eighths in the right places.
Double check your growing number line by making sure these numbers are at the same place:
This video shows an expertly made number line (and challenges you to make your own with thirds and sixths!).