Minds On
Patterns in graphs
Analyze the graph and consider the following questions:
- Do you notice any patterns?
- What could this be a graph of? Why could that be?
Record your answers using a voice recorder, speech-to-text, or writing tool.
Action
Graphing patterns
We can demonstrate how patterns grow, shrink, and change using a model, a pattern rule, or a table of values. We can also translate this information on a graph.
A graph must consist of certain elements:
- a title
- x-axis and y-axis that are labelled
- an appropriate scale
Explore the following anchor chart as an example.
Graphing. Patterns can be expressed using graphs and tables of values. A table has two columns, one labelled Term, and the second labelled Term Value. For term 1, the term value is 75. For term 2, the term value is 65.For term 3, the term value is 55. Examine the pattern in the table. The pattern rule starts at 75. Subtract 10. A graph must have known x and y-axis values. The x axis is labelled Term and the scale is from 0 to 10. The y-axis is labelled Term Value and the scale is from 0 to 80. There are 8 points on the graph at the following coordinates: (1,75), (2,65), (3,55), (4,45), (5,35), (6,25), (7,15), (8,5).
The x-axis is the term number.
The y-axis is the term value.
We graph by making a dot where the corresponding term number and term value meet.
A graph allows us to extend a pattern.
What would be the value of the 7th term?
Press ‘Reveal’ to check your answer.
The value of the 7th term would be: 15.
Your turn
Task 1
Use the Table of Values to complete a graph, making sure that you pick a scale interval that will fit the pattern. You can create a line graph or a bar graph.
| Term | Term value |
|---|---|
|
1 |
6 |
|
2 |
10 |
|
3 |
14 |
|
6 |
Complete the Values on a Graph chart in your notebook or using the following fillable and printable document to record your answers. You may also use a method of your choice to describe the pattern.
Press the ‘Activity’ button to access Values on a Graph.
- How can you predict what the 6th term value will be?
- Is there a rule?
Task 2
Examine the following graph. Use the data to make a table of values and a model.
Complete the Values Table to Graph chart in your notebook or using the following fillable and printable document to record your answers. You may also use a method of your choice to describe the pattern.
| Term | Term value |
|---|---|
- How did you determine the term and term values?
- What’s the pattern?
Press the ‘Activity’ button to access Values Table to Graph.
Activity(Open PDF in a new window)
Problem-solving scenarios
Crawly the centipede crawls 8 centimeters per day.
Make a table of values showing at least 5 days, and graph the values from the table using a graph of your choice, such as a line graph, bar graph, or dot plot graph. Extend your graph as far as you can and answer the following questions:
- How far does it get in 10 days?
- What is the pattern rule?
Complete the Centipede chart in your notebook or using the following fillable and printable document to record your answers. You may also use a method of your choice to describe the values and pattern.
| Term | Term value |
|---|---|
Press the ‘Activity’ button to access Centipede.
Consolidation
The jumping horse
The horse has jumped the fence and is running through the field.
When it jumped the fence, it was already 6 km from home. Every day it runs 12 km.
- Make a table of values showing 5 days.
- Graph the values from the table using the type of graph of your choice, such as a line graph, bar graph, or dot plot graph.
- How far away is the horse after 12 days?
- What is the pattern rule?
Reflect on which representation you find most useful in helping to determine a pattern rule.
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.