Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b
A number line from 0 to 1 can be split into equal parts, the way a bed splits into equal strips. Split it into 5 equal parts, and each part is 1/5 long. To find 3/5, start at 0 and count 3 jumps of 1/5.
To find 3/4, start at 0 and count three jumps of 1/4: 1/4, then 2/4, then 3/4. You land on 3/4.
Each number in a fraction has its own job. The bottom number tells you how many equal parts to split the line into. The top number tells you how many jumps to count from 0. The two jobs cannot be swapped: splitting the line into the top number and then jumping the bottom number lands you somewhere else entirely.
To place a fraction on a number line, split 0 to 1 into as many equal parts as the bottom number says. Then count off as many parts as the top number says, starting at 0.
You have named parts of the herb bed before: 3 planted strips out of 4 equal strips is 3/4 of the bed. Today 3/4 is a place to stand. The fence rail runs from the gate to the shed, and posts split it into 4 equal gaps. Each post in the picture is numbered by how many gaps it sits from the gate.
The whole walk from the gate to the shed is 1. How long is one gap?
This opens up
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.