You know how to measure with a ruler in whole inches, and you can place fractions on a number line. A ruler is a number line, so the marks between the inches are halves and quarters.
Why it works
Each inch on the ruler is cut into 4 equal parts, so each small part is $\frac{1}{4}$ inch, just like fourths on a number line. The middle mark of each inch is $\frac{2}{4}$, which is the same as $\frac{1}{2}$. When the object starts at 0, the mark at its other end tells its length.
Key idea
Line one end up with 0. Count the whole inches, then count the quarter marks past the last whole inch. 1 quarter is $\frac{1}{4}$, 2 quarters is $\frac{1}{2}$, 3 quarters is $\frac{3}{4}$.
Worked example: Quarters
A pencil starts at 0 and ends 3 small marks past the 2. How long is it?
- 2 whole inches.
- 3 quarters more: $\frac{3}{4}$.
Answer: $2\frac{3}{4}$ inches
Worked example: Not starting at 0
A ribbon starts at the 1 and ends at the halfway mark between 3 and 4. How long is it?
- From 1 to 3 is 2 inches.
- From 3 to the halfway mark is $\frac{1}{2}$ inch more.
Answer: $2\frac{1}{2}$ inches
Common mistake
Starting at the 1 mark, or not checking where the object starts: then the end mark is not the length. Subtract the start, or count the inches from where the object begins.
Counting marks instead of lengths. The length is how far the end is from the start, not how many tick marks you see.
Counting marks instead of lengths. The length is how far the end is from the start, not how many tick marks you see.