# Minds On

## Creating stories from graphs

Graphs can tell us a story. The following describes what is happening in this graph. What story do you think it could be telling?

The following graph is a line graph with no title, labels, or scale. The graph has a line that starts in the bottom left corner of the graph. It begins to climb to the middle of the graph, flattens out and continues to climb higher at a steady rate.

Press ‘Hint’ to reveal an example.

#### Story: This graph represents an actor.

A group of actors began their career by moving to Los Angeles. They started to get auditions for small commercials. Only after the second or third commercial did they book any jobs. They would audition once or twice and then book a job once a month. Then one day they auditioned for a film and got the job! From there they became very busy and have been ever since.

Student Success

### Think-Pair-Share

Examine the following graph. Tell a story about what the graph could be showing.

The graph is a line that starts in the bottom left corner of the graph. It begins to climb to the middle of the graph, straightens out and then dips halfway down. It then begins to climb again and flattens out as it continually travels to the right.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

# Action

## Features of broken-line graphs

What is a broken-line graph?

A broken-line graph:

• displays data that is connected
• has values on the graph which are points connected by lines
• shows a change over time
• allows us to examine trends and patterns

Broken-line graphs should have:

• a title
• a labelled x and y-axis
• data points on the graph that have been connected by straight lines

The following is an example of a topic that would be shown on a broken-line graph:

The amount of precipitation over twelve weeks in a city.

Come up with some other examples of when you would use a broken-line graph and be ready to share your ideas.

### Pros and cons of broken-line graphs

Pros Cons
• Able to tell the range of the data set, the highest and lowest points, and any gaps in the clusters quickly.
• Makes it easy to observe changes over time, even for small changes.
• Can use exact values from the data.
• Shows comparisons between data sets well.
• Can be confusing to interpret when there are too many points plotted.
• Are best suited for data with a small range.

## Analyzing a broken-line graph

Let’s examine the following broken-line graph.

What can you tell from this graph? Answer the following questions about the graph in a method of your choice:

1. What does this graph represent?
2. What does the direction of the line tell us about the data?
3. What can we infer from this graph about when donut sales are highest during the week? Explain your thoughts.

## Scales

A scale shows the way numbers or pictures are used in data. It shows the possible values of the numbers in a set on an axis. The scale is often found on the Y-axis of the graph.

The scale on a graph can have any unit, it just depends on what the data is! The distance between two numbers indicates a unit and this unit must stay the same throughout a scale. This means if I start at 0 and my next mark is 1, my unit is 1 and I need to continue going up by 1s.

Example:

In the graph we examined about donut sales, the scale was increasing by 100s. This made sense because we were examining the number of sales made and the earnings were in dollars.

The scale on this graph is equal to 100 units.

If the scale was increasing by twos instead, would this make sense for this particular graph? Why or why not?

Examine the following topics and the scale that has been chosen for the data set. Decide if the scale is appropriate. If the scale is not appropriate, how would it need to be changed?

Topic: Number of sales of stuffed animals at a store in a year.

Chosen scale: 1 interval that is equal to 5 (The y-axis value is increasing by 5 each time).

Scale is not appropriate; y-axis should be increasing by 20-50 each time or the graph would be really large because the store sells a lot of stuffed animals.

Topic: The weather trends in a country over 1 month.

Chosen scale: 1 interval that is equal to 2 (The y-axis value is increasing by 2 degrees Celsius each time).

The scale is appropriate.

Topic: Ice cream sales at the beach from spring to summer (in dollars)

Chosen scale: 1 interval that is equal to 1 (The y-axis value is increasing by \$1 each time).

Scale is not appropriate; y-axis should be increasing by a bigger dollar amount because as the weather gets hotter more people will come to the beach and eat ice cream.

Now, choose a topic for a possible broken line graph. What would you use as the scale? Why? Share your topic and scale choice with a partner, if possible, and compare what each person has done. If you do not have a partner, record your thoughts in a method of your choice.

# Consolidation

## Creating broken-line graphs

Create a broken line-graph with the following data set.

Temperature (°C) Month
January
-2° February
March
10° April
18° May
22° June
24° July
23° August
16° September
14° October
November
December

Complete? Broken-line Graph checklist
Examine your data and identify a title for the graph.
Determine what labels will be used for the x-axis and the y-axis.
Decide on an appropriate scale to use for your y-axis.
Create your graph: insert title, labels, and scale.
Plot each data point on the graph.
Using a ruler (if creating the graph on paper) connect all the data points with straight lines.
Check your work to make sure it is accurate and that you did not miss anything!

You can complete the activity using TVO Mathify or a method of your choice.

Press the ‘TVO Mathify’ button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window) Activity (Open PDF in a new window)

## Understanding broken-line graphs

• What parts of creating a broken-line graph can be the most challenging? Why?
• Why are broken-line graphs important to understand? Where can they be seen in the real-world?

## Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

### I feel…

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.

### Finding broken-line graphs

Using a variety of sources (e.g., internet, magazines, newspapers, etc.) find different broken-line graphs!

#### Option 1: With a partner

Choose one graph that you have found and show it to a partner, if possible. After examining both of the broken-line graphs you have found, discuss:

• What type of data is displayed on these graphs?
• What are the similarities between the two graphs?
• What are the differences between the two graphs?
• What have you learned from these graphs?

#### Option 2: Independent

Choose one graph that you have found. After examining the broken-line graph you have found, record:

• What type of data is displayed on the graph?
• What is a question you have about the graph?
• What is an interesting observation you can make about the graph?
• What have you learned from the graph?

### Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window)