What is this skill?
Placing fractions on a number line means seeing a fraction as a number with a position, not only as part of a shape. Third graders split the distance from 0 to 1 into equal parts. If it is split into 4 equal parts, each part is 1/4, and the marks are at 1/4, 2/4 and 3/4, with 4/4 landing on 1.
To find the fraction at a point, children count the equal jumps from zero. If the line is split into 6 parts and the dot is at the fourth mark, it is at 4/6. The denominator tells how many equal parts the whole is split into, and the numerator tells how many of those parts you have jumped.
Why it matters
The number line is one of the most powerful models for fractions. It shows that fractions are numbers that live between whole numbers, which makes it easier to compare them, to see why 2/4 and 1/2 are at the same spot, and later to understand mixed numbers like 1 1/2 and fractions greater than 1.
It also connects fractions to measurement. A ruler is a number line divided into fractions of an inch, and reading a measurement like 2 3/4 inches uses exactly this skill. In fourth and fifth grade, adding fractions and understanding decimals both rely on the number line picture.
Common mistakes
- Counting the tick marks instead of the spaces, so a line split into 4 parts (with 5 marks including 0 and 1) is read as fifths. Ask your child to count the jumps, not the lines.
- Starting the count at 1 instead of 0, which shifts every answer by one part. Remind your child that 0 is the starting point.
- Thinking fractions can only be parts of shapes, and not seeing them as points on a line. Using both pictures side by side helps.
- Not noticing that the parts must be equal in length, especially on hand-drawn lines.
How to help at home
- Use a ruler marked in halves and quarters of an inch to measure small objects, and talk about what each mark means.
- Draw a line from 0 to 1 on paper, fold it in half and then in half again, and label the fourths together.
- Lay a jump rope or string on the floor as a number line from 0 to 1 and have your child stand at 1/2, 1/4 and 3/4.
- Ask where a fraction would go before placing it: "Is 3/4 closer to 0 or to 1? Is it before or after 1/2?"
Worked examples
These are real questions from the Tutorsaurus fractions on a number line practice, with the answers worked out.
Example 1
Which fraction is at the dot?
Choices: 2/4, 3/4, 1/4, 1/5
Answer: 1/4. The line from 0 to 1 is split into 4 equal parts. The dot is at the 1th mark, so it is 1/4.
Example 2
Which fraction is at the dot?
Choices: 6/8, 7/9, 7/8, 1/8
Answer: 7/8. The line from 0 to 1 is split into 8 equal parts. The dot is at the 7th mark, so it is 7/8.
Example 3
Which fraction is at the dot?
Choices: 3/6, 4/6, 3/7, 2/6
Answer: 3/6. The line from 0 to 1 is split into 6 equal parts. The dot is at the 3th mark, so it is 3/6.