Minds On
Which one doesn’t belong?
Examine the following graphs, patterns, and tables of values. They are organized as Round 1, Round 2, and Round 3.
For each round, determine the item that does not belong. Come up with as many reasons as you can to describe why this item does not belong to the set.
Record your ideas digitally, orally, in print, or in an organizer of your choice.
Round 1
Which graph doesn’t belong?
Round 2
Which pattern doesn’t belong?
| Pattern 1: 1, 4, 7, 10 | Pattern 2: 21, 24, 27, 30 |
| Pattern 3: 2, 7, 12, 17 | Pattern 4: 5, 8, 11, 14 |
Round 3
Which table of values doesn’t belong?
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Action
Review
Review the following definitions.
A value that remains the same in the pattern. Also known as the 0 term.
What the pattern is changing by.
An unspecified value often represented using a letter or a symbol. For example, the number of students can be represented by the letter “n.”
Making an algebraic expression
In coding, a variable is a temporary storage location for a piece of data; for example, a numerical value or a series of characters.
Recall Pattern 2 from “Round 2” of the Minds On activity:
Pattern 2: 21, 24, 27, 30
Using Pattern 2 as our example, let’s examine how to create an algebraic expression once the constant and multiplier are determined.
As you follow along, you can record your ideas digitally, orally, or in print.
First, create a table of values with the headings “Term Number” and “Term Value.”
Next, fill in the table of values.
| Term number | Term value |
|---|---|
| 1 | 21 |
| 2 | 24 |
| 3 | 27 |
| 4 | 30 |
The multiplier is what the term value is changing by. In this example, the multiplier is 3.
The variable represents the term number which can change. In this example, we can call the variable “t.”
The constant is the 0 term. Work backwards to determine the constant.
(21 − 3) : 18
The algebraic expression is: (multiplier)(variable) +/- constant. For Pattern 2, the algebraic expression is:
3t + 18
Task 1
Create algebraic expressions for the other three patterns: 1, 3, and 4.
Pattern 1: 1, 4, 7, 10
Pattern 3: 2, 7, 12, 17
Pattern 4: 5, 8, 11, 14
Complete the Algebraic Expressions in your notebook or using the following fillable and printable document.
Press the ‘Activity’ button to access Algebraic Expressions.
When you are finished, press ‘Answers’ to reveal the answers for this activity.
| Pattern 1: 1, 4, 7, 10 | |
|---|---|
| Multiplier | 3 |
| Variable | t |
| Constant | -2 |
| Algebraic expression | 3t − 2 |
| Pattern 3: 2, 7, 12, 17 | |
|---|---|
| Multiplier | 5 |
| Variable | t |
| Constant | -3 |
| Algebraic expression | 5t − 3 |
| Pattern 4: 5, 8, 11, 14 | |
|---|---|
| Multiplier | 3 |
| Variable | t |
| Constant | 2 |
| Algebraic expression | 3t + 2 |
Task 2
Create each of the following. You can use the following fillable and printable Task 2 document or record your responses using another method.
A table of values with a growing pattern
A table of values with a shrinking pattern
A growing pattern in words
A shrinking pattern in words
A growing pattern and a positive constant
A growing pattern and a negative constant
A number pattern that is growing
A number pattern that is shrinking
Press the ‘Activity’ button to access Task 2.
Consolidation
Practice questions
Task 1: Toothpick pattern
Examine the following toothpick pattern:
Build the next two terms in the pattern using toothpicks.
You can draw the terms, describe them, or use another method of your choice.
Once you’ve built the next two terms, create a table of values using the number of toothpicks and write an expression for the nth term.
Task 2: Your turn to teach!
Imagine you have a new student arriving to your class. You need to teach this student how to create an algebraic expression using a pattern.
What is most important to remember when creating an algebraic expression using a pattern?
What are some tips you might be able to share that you have learned as you worked through this learning activity?
Record your understanding digitally, orally, or in print. Explain using a variety of representations.
Task 3: Skyscraper algebra
Solve the following word problem.
Imagine a rectangular skyscraper.
Each story of the building has 4 windows, one on each wall.
There is also a skylight (1 big window) on the roof of the building.
If the building is 48 stories how many windows does the building have?
Record your thinking using a method of your choice.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.