How to Teach Q1, Median, and Q3 (A Simple Hands-On Lesson Before Box Plots)

count on kupe

6 days ago

After teaching mean, median, mode, and range, I wanted my students to actually understand how to find Q1 and Q3 as well as the mean mean before jumping into box plots.

Because let’s be honest… students can follow steps for quartiles, but they don’t always get what they’re doing.

So instead, we built the idea first.

This activity helped students see where quartiles come from—and made our box plot lesson so much easier after.

What You Need

A printable with 4 number strips (different lengths like 22, 23, 24, 25) – you can download it FREE HERE
Scissors
Highlighters or markers
Tape or glue

Students cut out all 4 strips and write how many boxes each strip has. Each box represents one piece of data. So, a strip with 22 boxes = 22 data values

Step 1: Find the Median First

Start with one strip (I used 22 boxes).

Have students fold it in half.

Then notice where the fold lands:

If it lands on a line → highlight the line
If it lands inside a box → shade the whole box

Repeat with 23, 24, and 25.

Then pause and make this explicit: This is the median

Even number of data → median is between two values
Odd number of data → median is one value

This is the part students usually memorize… but here they actually see it.

Step 2: Split the Data to Find Q1 and Q3

Now go back to the first strip. This time, fold each side into the center (the median).

Where those folds land is important:

If it lands on a line → highlight it
If it lands in a box → shade the box

These points represent:

Q1 (lower quartile)
Q3 (upper quartile)

Important Teaching Moment

When the median is a full box (odd data): Do NOT include it when folding

Students fold to the edge of that box. This is one of the biggest sticking points with quartiles, and this makes it very clear.

Step 3: Make Sense of Quartiles

Now ask:

“How many sections did we split the data into?”

Students will see: 4 sections = quartiles

Then define:

Q1 → middle of the lower half
Median (Q2) → middle of all data
Q3 → middle of the upper half

Also point out: Whether folds land on lines or boxes depends on how many data points are in each half (even or odd)

Step 4: Connect to Position (This Part Matters)

Now glue or tape the strips down and label:

Median
Q1
Q3

Then connect it to position in a list.

Example (22 data points):

Median → between 11th and 12th values
Q1 → 6th value
Q3 → 17th value

This is where everything clicks: Quartiles are based on position in ordered data!

Why This Works

Students don’t just follow a procedure like:

“Find the median, then split the data…”

They actually:

fold the data
see where the middle falls
understand why quartiles divide data into four equal parts

So when you move into box plots, students already understand:

why the median matters
where Q1 and Q3 come from
what the sections represent

If You Try This Tomorrow

Works well for grades 6–7
Do it whole group or small groups
Fold together first, then release students

This is a simple way to make quartiles and box plots actually make sense.