MathematicsMathsElementaryPrimary
How to teach fractions on a number line
A fraction is a number with its own point on the number line, and students find it by splitting 0 to 1 into equal parts. This page shows how to teach fractions and decimals on a number line, with a free activity where Sparky checks every line a student draws.
Jemel Fanfan | Founding Member at Flint
"What makes it more powerful is that students are able to handwrite their mathematical process directly on the app. Using this, Flint AI is able to give immediate feedback on their mathematical reasoning skills based on what they have written. … Rather than discovering mistakes tomorrow, we address them right now when the learning moment is most powerful."
Lakshmi Saravanan, Math Teacher at American International School ChennaiWhy 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.
Fractions on a number line
A fraction is a number, and it has its own point on the number line. To place 3/10, students split the line from 0 to 1 into 10 equal parts and count 3 parts from 0 (Common Core 3.NF.A.2). Fractions with a denominator of 10 or 100 can also be written as decimals, so 3/10 sits on the same point as 0.3, and 75/100 on the same point as 0.75. To compare two decimals, students look at which point is farther from 0, so 0.8 is bigger than 0.75 even though 0.75 has more digits (Common Core 4.NF.C.6 and 4.NF.C.7). 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).
In the Flint activity, students draw each number line on a Flint whiteboard, write a number under every tick mark, and send it in their chat. Sparky, Flint's AI tutor, reads the numbers and finds the dot before it replies. When a dot is on the wrong tick, Sparky asks which tick the number belongs on instead of moving it, and a student who says 0.75 is bigger than 0.8 gets sent back to their own number line to see which dot is farther from 0.
How the number line activity works
The activity gives each student six tasks, one at a time:
- Put a dot on 3/10 on a number line split into tenths.
- Put dots on 0.3 and 0.7, and say which is bigger.
- Put a dot on 3/4 on a number line split into fourths.
- 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.
- Say which is bigger, 0.8 or 0.75.
- Say which is bigger, 0.5 or 0.45, on a number line from 0.4 to 0.5.
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. Her chat starts with the first task.
Maya
Maya
Sparky
Maya
Sparky
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.
Maya
Maya
Sparky
Maya
0.80 is farther, so 0.8 is bigger. 0.8 is the same as 0.80.Sparky
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.
Example activity page
After a class finishes the number line activity
The school and students are made up for this page. In this example, most of the class places tenths correctly, and the area to practice is comparing decimals like 0.8 and 0.75.
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 Use 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's Preview tab, 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 math. For more math activities, see Flint for math.
Other use cases
See all use cases →English Language ArtsEnglishHigh schoolKey Stages 4 and 5
How to teach Frankenstein
A Frankenstein lesson plan where students back every reading of the novel with a line from the text. In a free Flint activity, each student builds a five-track playlist from their own music, and a song that fits the mood but not the moment goes back to the chapter.
English Language ArtsEnglishMiddle schoolKey Stage 3
How to teach Greek and Latin roots
Greek and Latin roots with examples, and a free Flint activity: students build words from root tiles and invent one for their own hobby. Sparky draws the invented word exactly as its parts say, and sends a wrong guess back to a word the student already built.
English Language ArtsEnglishHigh schoolKey Stages 4 and 5
How to teach hexagonal thinking
How to run hexagonal thinking before a Macbeth seminar: fill a deck with the play's key ideas, have students link the cards and write a reason on each link, and turn the strongest links into seminar questions. Sparky reads each board and sends a reason like "both dark" back to the play.
