D. Data · Data Literacy and Probability

Broken-Line Graphs

D1.3 D1.6About 50 minutes

Learning goals

I can explain when a broken-line graph is a good choice.
I can make a broken-line graph with a title, labels, a scale and a source.
I can read a broken-line graph, describe how the data changes, and estimate values between points.

Words to know

broken-line graph
A graph of points joined by straight line segments. It shows how something changes, usually over time.

trend
The general direction of the data: going up, going down, or staying about the same.

interpolate
To estimate a value between two data points.

data point
One dot on the graph, showing one pair of values (like Day 6 and 6 cm).

Where we're going

Histograms show how data is spread out. Today's graph shows how something changes. It is new in Grade 6, but you already know how to read a scale and plot a point.

Watching something change

Ava planted a bean seed. Every 2 days she measured the plant's height. Height is continuous data: between two measurements, the plant grew a little bit every hour.

To show how the height changed over time, Ava made a broken-line graph:

The horizontal axis shows the time (days), in order, equally spaced.
The vertical axis shows the height, with a scale.
She plotted one point for each measurement.
She joined the points in order with straight line segments. The line is "broken" into pieces, which gives the graph its name.

A young bean seedling with two leaves growing in a clay pot on a sunny classroom windowsill. — A bean seedling like Ava's. Its height changes a little every hour, which is why a broken-line graph is a good way to show its growth over time. AI-generated image

Heights: Day 2, 1 cm; Day 4, 3 cm; Day 6, 6 cm; Day 8, 10 cm; Day 10, 13 cm; Day 12, 15 cm; Day 14, 16 cm. The scale counts by 4s.

Reading the line

Steep line going up: the height is changing fast. From Day 6 to Day 8 the plant grew 4 cm, the most for any 2 days.
Gentle line: changing slowly. From Day 12 to Day 14 it grew only 1 cm.
Line going down: the value is decreasing.
Flat line: no change.

The overall trend of Ava's plant is up, growing fast in the middle and slowing down at the end.

Because height is continuous, the line between two points gives a sensible estimate for times in between. This is called interpolating. On Day 9, halfway between 10 cm and 13 cm, the plant was probably about 11.5 cm. It's only an estimate: Ava didn't measure on Day 9.

When to use a broken-line graph

Use one to show how continuous data changes over time: temperature through a day, a plant's height, the depth of snow, the level of a river.

Don't use one for categories (favourite sport) or to show how data is spread out. Joining the points only makes sense when the values are in order and something is really happening between them.

Worked example

Example 1: Make a broken-line graph

Sam poured a cup of hot cocoa and measured its temperature every 5 minutes.

0 min: 80°C
5 min: 66°C
10 min: 55°C
15 min: 47°C
20 min: 41°C
25 min: 37°C

Make a broken-line graph.

Title: "Temperature of a Cooling Cup of Cocoa".
Horizontal axis: "Time (minutes)", with 0, 5, 10, 15, 20, 25 equally spaced.
Vertical axis: "Temperature (°C)". The values go up to 80, so use 0 to 80 counting by 20s.
Plot each point. For 5 minutes, go across to 5 and up to 66, a little above the 60 line (about a third of the way from 60 to 80).
Join the points in order with a ruler.

See the graph below. The line goes down, steeply at first and then more gently: the cocoa cooled quickly at first, then more slowly.

Temperatures: 80, 66, 55, 47, 41 and 37 °C at 0, 5, 10, 15, 20 and 25 minutes. The scale counts by 20s.

Worked example

Example 2: Describe a change

Use the cocoa graph. In which 5 minutes did the temperature drop the most? Predict the temperature at 30 minutes.

Find each drop: 80 − 66 = 14, 66 − 55 = 11, 55 − 47 = 8, 47 − 41 = 6, 41 − 37 = 4.
The biggest drop, 14°C, was in the first 5 minutes. That's where the line is steepest.
The drops are getting smaller: 14, 11, 8, 6, 4. The next drop will probably be about 2 or 3.
37 − 3 = 34.

The biggest drop was from 0 to 5 minutes. At 30 minutes the cocoa will probably be about 34°C (an estimate; anything from about 33 to 35°C is reasonable).

Just for fun

A broken-line graph isn't actually broken, so please don't send it to the repair shop. It's just a line taking a break at every point to look around.

Hands-on activity

Shadow tracker

You need: a sunny day, a stick or a pencil stuck upright in a lump of modelling clay (or a garden stake), a ruler or measuring tape, and paper.

Safety: never look directly at the sun. If you stay outside in the sun, wear a hat and sunscreen and drink water.

Put the stick in a sunny spot outside (or on a sunny windowsill) where it won't be moved.
Measure the length of its shadow every hour, from morning to late afternoon. Write the time and length in a table.
Make a broken-line graph: time on the horizontal axis, shadow length on the vertical axis. Add a title, labels, a scale and a source.
Describe the trend. When was the shadow shortest? Estimate the length at a half hour you didn't measure.

What to look for: the shadow should get shorter until around the middle of the day and then longer again, so the line goes down, then up.

Use this graph for the Your turn questions. Depths: 5, 12, 20, 18, 30, 35, 28 and 15 cm in weeks 1 to 8. The scale counts by 10s.

Your turn

In which week was the snow deepest? How deep?

How much did the snow depth change from Week 1 to Week 3?

Between which two weeks did the depth increase the most?

Between which two weeks did the depth decrease the most? What might have happened?

Name all the times the snow depth went down from one week to the next.

Estimate the snow depth halfway between Week 5 and Week 6.

Is a broken-line graph a good choice for this data? Explain.

More practice: warm-up

What does a broken-line graph usually show?

Bean graph: how tall was the plant on Day 10?

Cocoa graph: what was the temperature at 15 minutes?

A line segment goes down from left to right. What is happening to the data?

Bean graph: what is the trend?

More practice: on your own

Bean graph: how much did the plant grow from Day 2 to Day 14?

Bean graph: estimate the height on Day 5.

Cocoa graph: how much did the temperature drop over the whole 25 minutes?

Would you use a broken-line graph to show the favourite fruit of 30 students? Explain.

Kai measured his height on his birthday each year: 9 years, 132 cm; 10 years, 138 cm; 11 years, 143 cm. Describe what a broken-line graph would show.

Challenge

Snow graph: what was the mean weekly snow depth over the 8 weeks?

Water in a rain barrel: Monday 20 L, Tuesday 20 L, Wednesday 45 L, Thursday 40 L. Describe the shape of the broken-line graph and tell a possible story.

Two plants were measured on the same days. Plant A's line is steep at first, then nearly flat. Plant B's line rises at the same steepness the whole time. Both end at 20 cm. Describe how each plant grew.

Check your understanding

Quiz

When is a broken-line graph the best choice?

On a broken-line graph, a steep line segment going up means:

Snow graph: what was the depth in Week 4?

Bean graph: the plant was 6 cm on Day 6 and 10 cm on Day 8. A good estimate for Day 7 is:

What does a flat line segment show?

Why are the points joined in a broken-line graph?

For parents and teachers

What this lesson teaches: making and reading broken-line graphs (new in Grade 6), describing trends, and estimating values between points (D1.3, D1.6).

How to help at home:

Look for broken-line graphs in weather apps (temperature through the day) and talk about what a steep or flat part means.
When estimating between points, ask your child to find the two nearby points first and go "about halfway".
Remind them that an in-between value is only an estimate.

Common difficulties:

Using a broken-line graph for categories, where joining the points makes no sense.
Unequal spacing of times on the horizontal axis.
Reading the value of a point instead of the change between two points when the question asks "how much did it increase?"
Thinking a steep line means a big value, rather than a big change.