How to teach fractions and decimals with number lines

Why this matters

In one 4th grade class, a student writes 3/10 = 0.3 and puts her dot on the tick marked 0.5. A week later she says 0.75 is bigger than 0.8 because it has more digits. Her worksheet shows the right decimal both times, and the teacher has to wait for quiz day to find out.

Strategies for teaching fractions and decimals on a number line

A number line shows that a fraction is a number with its own place between 0 and 1. The Institute of Education Sciences' fractions practice guide recommends number lines as "a central representational tool" for teaching fractions from the early grades on (Siegler et al., IES, 2010).

1. Write a number under every tick mark
2. Put the dot on a tick, then check it against the numbers
3. Compare decimals by their distance from 0

A teacher with 30 students can't look at every number line the moment it's drawn. Sparky, Flint's AI tutor, looks at each one in the student's chat.

How the number line activity works

The activity gives each student six tasks, one at a time:

1. Put a dot on 3/10 on a number line split into tenths.
2. Put dots on 0.3 and 0.7, and say which is bigger.
3. Put a dot on 3/4 on a number line split into fourths.
4. Write 3/4 as a decimal, then put a dot on 0.75 on a number line from 0.7 to 0.8, numbered 0.70, 0.71 and so on.
5. Say which is bigger, 0.8 or 0.75.
6. Say which is bigger, 0.5 or 0.45, on a number line from 0.4 to 0.5.

Students draw every number line on a Flint whiteboard and send it in their chat. Before Sparky replies, it reads the numbers under the tick marks and finds the dot. Sparky can't measure whether the parts are the same size, so on each new kind of number line it asks the student how they made the parts equal. Tasks 4 to 6 zoom in on one tenth, so 0.75 and 0.45 each get a tick mark of their own.

One student's number lines, from 3/10 to 0.8

Maya is an example student we wrote for this page, based on a test run of the library activity. Her chat starts with the first task.

Sparky reads Maya's drawingSparky asks a question instead of fixing the mistake

M

Maya

Task: 1 of 6: 3/10 on a tenths line

Maya

3/10 is 0.3

Sparky

Your tick marks are numbered in order, from 0 all the way to 1. But your dot is on the tick marked 0.5. Which tick should 3/10, or 0.3, go on? And how did you make sure all your parts are the same size?

Maya

I moved my dot to 0.3. I made every space the same, about 2 fingers wide.

Sparky

Your dot is on 0.3. That's exactly right, and equal finger widths are a smart way to keep the parts the same size. Now task 2: on your number line, put a dot on 0.7. Which is bigger, 0.3 or 0.7?

Moved her dot to 0.3 and explained how she made equal parts

Tasks 2 to 4 go the same way. Maya puts 0.3 and 0.7 on one line, cuts a line in half twice to make fourths, and puts 0.75 on a line from 0.7 to 0.8. Then she reaches task 5.

M

Maya

Task: 5 of 6: which is bigger, 0.8 or 0.75?

Maya

0.75 is bigger because it has more numbers

Sparky

Both dots are on the right ticks. But check your answer. Look at your number line: which dot is farther from 0, the one on 0.75 or the one on 0.80?

Maya

0.80 is farther, so 0.8 is bigger. 0.8 is the same as 0.80.

Sparky

Exactly right, and you figured it out from your number line. Now the last task: which is bigger, 0.5 or 0.45?

Used her own number line to see that 0.8 is bigger

Sparky never fixed Maya's drawing or told her an answer. When she said 0.75 is bigger because it has more digits, Sparky sent her back to her own number line, and she found the answer there. The activity's guidelines tell Sparky to do both.

See which students can place and compare decimals

Sparky grades each chat against the activity's rubric. The activity page shows who needs help right now, what the class can do, and what to practice next. Open any session to see that student's number lines.

Set up the activity for free

The number line activity is in Flint's public library, with Sparky's role, guidelines, greeting and a rubric already written. Open it, select Try this activity to copy it into a free Flint account, and move it to a class. Students open the whiteboard with the whiteboard button under the message box. In the activity settings, select Try session myself to test the activity as a student before you assign it.

For practice that gets harder one problem at a time, see how to support productive struggle in middle school math. For more math activities, see Flint for math.