Minds On
Different patterns
In this learning activity, we will be learning all about tables of values and graphing.
Explore the following four different patterns. One of them is different from the other three. Can you indicate which one does not belong? Explain your thinking using the method of your choice.
| Pattern 1 | Pattern 2 |
|---|---|
|
4, 8, 12, … |
21, 25, 29, … |
| Pattern 3 | Pattern 4 |
|
14, 17, 20, … |
12, 16, 20, … |
Table of values
Patterns can also be represented in a table of values. Use the patterns that do belong, from the table in the previous section to complete the following fillable and printable document Table of Values. You can also complete this activity in your notebook or using the method of your choice.
| Term | Term Values |
|---|---|
|
Pattern rule: |
|
Press the ‘Activity’ button to access Table of Values.
Answer the following questions and record your thoughts using a method of your choice.
- What is similar about each pattern?
- What is different?
Action
Graphing patterns
Graphing a pattern is another way to represent a pattern.
When you use the information from a table of values to create a graph, you are translating that pattern into another form.
A table of values is one way that we can represent a pattern. In a table of values, there is the term number and the term value. We can use these points, (term number, term value) to create a graph.
Examine the following anchor chart to explore how a table of values helps us create a graph.
When we graph a pattern, we need to know what the x (term number) and y (term value) values are. Use the x-axis for the term number and the y-axis for the term value. We graph by making a dot where the x-axis and y-axis meet for the term number and term value. We can extend the pattern using the graph.
Explore the following video:
Task one
Extend values using a graph
Using the pattern on the anchor chart, consider the following questions. Record your thoughts using a method of your choice.
- What is the pattern rule?
- What would be the value of the 7th term?
- What is the value of the 10th term? How do you know?
- Graph the pattern.
Press ‘Answer’ to reveal the answers and check your work.
- The pattern rule is multiply the term number by five.
- The 7th term: 35
- The 10th term: 50. I know because I multiplied seven by five, and ten × five to get the term value. I also used the graph to see what the number on the y-axis would be when my x-axis was seven and 10.
Task two
Comparing patterns
Think about the four patterns from the beginning of the learning activity. Select one of the patterns that belonged from the Minds On and graph the pattern using a method of your choice.
|
4,8,12, … |
21,25,29, … |
|
14, 17, 20, … |
12, 16, 20, … |
Reflect on the following questions and record your thoughts using a method of your choice.
- What do you notice about the graph(s)?
- How is the pattern rule connected/related to the lines?
Press ‘Answer’ to reveal the answers and check your work.
- I notice the graph goes up to the right in a straight line.
- The pattern rule is connected because I go over and up the same amount from one plotted point to the next each time. The term value goes up by the same number every time too.
Task three
Creating graphs from table of values
Table one
Using the following table of values, graph the pattern using a method of your choice and extend the pattern. Be sure to include titles for each axis and one for the graph itself.
A student has decided to save money and every month they put $100 into a savings account.
| Month | Total amount saved |
|---|---|
|
1 |
100 |
|
2 |
200 |
|
3 |
300 |
Reflect on the following questions and record your thoughts using a method of your choice.
- How much will they have saved after six months?
- What is the pattern rule?
Press ‘Answer’ to reveal the answers and check your work.
- After six weeks they will have saved $600.
- The pattern rule is Month × 100. The total amount saved is going up by $100 each time.
Table two
Using the following table of values, graph the pattern using a method of your choice, and extend the pattern.
A design expert is saving money to purchase a used computer for their job. Their account has $500 in it. Every month they deposit $50 into their account to pay for the computer.
| Month | Account balance |
|---|---|
|
1 |
500 |
|
2 |
550 |
|
3 |
600 |
Reflect on the following questions and record your thoughts using a method of your choice.
- If the computer costs $1,100, how many months will it take to save the money for it?
- What is the pattern rule?
Press ‘Answer’ to reveal the answers and check your work.
- If the computer costs $1,100, it will take 13 weeks to save.
- The pattern rule is that the term value increase by 50 each time.
Consolidation
Creating and extending patterns
Record your work for the following activity using a method of your choice.
A classroom fundraiser is collecting food items to donate to a local foodbank.
Here is how much was collected in the first five days.
| Day | Number of food items collected |
|---|---|
|
1 |
10 |
|
2 |
15 |
|
3 |
20 |
|
4 |
25 |
|
5 |
30 |
- What is the pattern rule?
- Translate this pattern onto a graph.
- The class has a goal of 200 items of food. If the pattern remains the same, on what day will they reach this goal? Show and explain your thinking.
Complete Blank Grid in your notebook or using the following printable document to create a graph for this pattern.
Press the ‘Activity’ button to access a Blank Grid.
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.