Minds On
Analyze the pattern
Analyze the following pattern and attempt to figure out what its pattern rule is. You may do so with a partner, if possible.
Student Tips
Student tips
Remember, for growing patterns, the pattern rule tells us where the starting point is and how the pattern changes from term to term.
Now that you have examined the pattern, record answers to the following questions in a format of your choice.
- What do you notice about this pattern?
- How is the pattern changing?
- What is the pattern rule?
Action
Table of values
A table of values is one way that we can represent a pattern. In a table of values, we have the term number and the term value.
- The term number is the position or iteration in a pattern.
- The term value is the number of elements in an iteration.
We will examine an example of a table of values. But first, let’s examine the pattern. The information from the pattern will help us understand the table of values!
Now, let’s examine the table of values for the pattern we just analyzed. Complete the following fillable and printable document Table of Values. You can also complete this activity in your notebook or using a method of your choice.
Use the given vocabulary to fill in the missing titles. Also, fill in any blanks in the table.
Table of Values Vocabulary:
- term number
- term value
| 1 | 2 |
| 2 | 8 |
| ? | 14 |
| 4 | ? |
Press the ‘Activity’ button to access Table of Values.
Creating tables of values from pattern rules
Choose three of the following pattern rules and represent them using a table of values. You will extend each pattern to the fifth term. You can also represent the pattern by using objects or drawings, not just numbers. Use the following fillable and printable document Creating a Table of Values to create your table of values. You can also complete this activity in your notebook or using the method of your choice.
Pattern rules (choose three):
- Start at 4, add 2 each time
- Start at 80, add 10 each time
- Start at 5, add 5 each time
- Start at 13, add 3 each time
- Start at 2, add 2 then 3 alternately
- Start at 15, add 15 each time
| Term number | Term value |
|---|---|
Press the ‘Activity’ button to access Creating a Table of Values.
Predicting patterns using a table of values
Patterns in tables can be used to help us predict what comes next.
Examine the following table.
| Number of children (term number) |
Number of candies (term value) |
|---|---|
|
1 |
6 |
|
2 |
12 |
|
3 |
18 |
|
4 |
24 |
|
5 |
30 |
|
6 |
36 |
How can it be used to predict the total number of candies needed for any number of children at a party?
Press the 'Hint' button to access a suggested answer.
This table of values indicates that for one child, we need six candies, and two children will require 12 candies.
Notice the rule for the patterns is to multiply the term number by six to get the term value.
To find out how many candies are needed for 11 children, you can extend the pattern/table or you can use the rule of “multiply the number or children by six candies.”
11 × 6 = 66
Therefore, 66 candies are needed for 11 children.Try it
Complete the table for each problem. Use the following fillable and printable document Making Predictions to access the tables. You can also complete this activity in your notebook or using the method of your choice.
Press the task to access each problem.
A gardener receives four dollars a day in tips.
Predict how much money will she have earned after eight days? Also include the pattern rule.
| Days | Chore money |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | |
| 4 | |
| 5 |
A gardener cuts three lawns a week.
Predict how many lawns he will have cut after 10 weeks? Write the pattern rule.
| Weeks | Number of lawns |
|---|---|
| 1 | 3 |
| 2 | |
| 3 | |
| 4 | |
| 5 |
Press the ‘Activity’ button to access Making Predictions.
When you are ready and have completed the activity, press ‘Answer’ to access a possible response to check your answer.
Task 1
| Days | Chore money |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
The pattern rule is add four dollars each day to chore money. The gardner will have earned 32 dollars after eight days.
Task 2
| Weeks | Number of lawns |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |
The pattern rule is add three lawns each week to number of lawns. The gardener would have cut 30 lawns by 10 weeks.
Consolidation
The popsicle problem
Explore the following word problem about two friends selling popsicles. Record your answers to the following questions using a method of your choice.
Two friends are selling popsicles to raise money for their local foodbank.
The first day they open a box and sell all 15 popsicles.
The next day, they open another box, and after selling all day they have a total of 30 popsicles sold.
On the third day, they open a third box, and they work hard all day. By the end of the day, they have a total of 45 popsicles sold.
- How many days would they need to sell 105 popsicles?
- What is the pattern?
- How does the popsicle total change after each day?
- What is the pattern rule?
Self-reflection
Reflect on the following questions:
- How comfortable do you feel with identifying pattern rules for growing patterns?
- How comfortable do you feel with translating patterns and extending patterns?
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.
Learning goals
We are learning to…
- create and translate growing patterns into tables of values
- determine pattern rules and use them to extend patterns
Success criteria
I am able to…
- translate growing patterns using tables of values
- explain how given patterns are growing
- identify pattern rules
- explain the difference between the term number and term value
- extend patterns using a table of values