Week 20 · Fractions of sets and on number lines · 3 lessons
3
Fractions on a number line
Discover Mathematics P3: Term 2, Lessons 71–80
GoalPlace fractions between 0 and 1 on a number line cut into equal parts and read fractions from it.
New words
number line · a line with numbers placed in order at equal spacesequal spaces · gaps that are all the same lengthmark · a point or tick on the line
Explanation
We can show fractions on a number line from 0 to 1. The distance from 0 to 1 is the whole. Cut it into equal spaces. If there are 4 equal spaces, each space is 1/4. The first mark after 0 is 1/4, the second is 2/4, the third is 3/4 and the last mark is 4/4, which is the same point as 1. The bottom number of the fraction is the number of equal spaces, and the top number is how many spaces we have counted from 0. The marks farther to the right are greater fractions. We can show a path 1 km long, a rope 1 m long or a piece of wood 1 m long.
Worked examples
A path is 1 km long, with a bench at each fourth of the way. The benches are at 1/4 km, 2/4 km and 3/4 km from the start.
A rope 1 m long is marked in thirds. The marks are at 1/3 m and 2/3 m. The next mark after 2/3 is 3/3, which is 1 m.
A piece of wood 1 m long is marked in eighths. The mark just before 1 is 7/8. The mark in the middle is 4/8, which is half way.
Class activity
Number line walk. Use chalk or a long strip of paper. Mark 0 at one end and 1 at the other end, 1 metre apart. Fold the strip in half, then in half again, and mark the folds. Write the fractions 1/4, 2/4 and 3/4 on the marks. Stand on 3/4 and walk to 1/4. How many fourths did you walk?
Practice
1
The number line is cut into fourths. What fraction does the dot show?
The dot is at the third mark after 0, so it shows 3/4.
2
A number line from 0 to 1 has marks at 1/6, 2/6 and so on. Into how many equal spaces is it cut?
It is cut into 6 equal spaces, because the bottom number is 6.
3
The number line is cut into thirds. What fraction does the dot show?
The dot is at the second mark, so it shows 2/3.
4
On a number line cut into fourths, which is closer to 0, 1/4 or 3/4?
1/4 is closer to 0, because it is the first mark after 0.
5
A rope of 1 m is marked in eighths. How many marks are between 0 and 1, and what fraction is the last of them?
There are 7 marks between 0 and 1: 1/8, 2/8 up to 7/8. The last is 7/8.
