Pattern Hunter Worksheet
Pattern Hunter
Algebraic Growth & Linear Expressions
Hunter Name:
Hunt Date:
Mission Briefing
Analyze how each visual pattern grows. The blue tiles represent the constant (the part that stays the same). The grey tiles represent the growth (the part that increases each step). Write an algebraic expression for the total tiles in the \(n\)-th figure.
1 Pattern Alpha
Fig 1
Fig 2
Fig 3
Expression (\(n\)-th Figure)
Total in Figure 10?
2 Pattern Bravo
Fig 1
Fig 2
Fig 3
Expression (\(n\)-th Figure)
Total in Figure 10?
3 Pattern Charlie
Fig 1
Fig 2
Fig 3
Expression (\(n\)-th Figure)
Total in Figure 10?
4 Pattern Delta
Fig 1
Fig 2
Fig 3
Expression (\(n\)-th Figure)
Total in Figure 10?
5 Pattern Echo
Fig 1
Fig 2
Fig 3
Expression (\(n\)-th Figure)
Total in Figure 10?
Growth Expert Reflection
In your own words, explain how the constant and the rate of change help you predict what Figure 100 would look like.
Pattern Hunter Key
Answer Key
Pattern Hunter Unit
Subject Algebra I / Pre-Algebra
| Pattern | Growth (\(m\)) | Constant (\(b\)) | Expression (\(f(n)\)) | Figure 10 |
|---|
| 1. Alpha | +3 | 2 | \(3n + 2\) | 32 tiles |
| 2. Bravo | +2 | 3 | \(2n + 3\) | 23 tiles |
| 3. Charlie | +1 | 4 | \(n + 4\) | 14 tiles |
| 4. Delta | +4 | 1 | \(4n + 1\) | 41 tiles |
| 5. Echo | +5 | 0 | \(5n\) | 50 tiles |
Key Concepts
- Rate of Change (\(m\)): The number of grey tiles added per figure. This becomes the coefficient of \(n\).
- Constant (\(b\)): The number of blue tiles that remain the same across every figure. This is the \(y\)-intercept.
- Verification: Students should plug \(n=1\) into their expression to ensure it matches the total tiles in Figure 1.
Discussion Prompts
- "Why didn't Pattern Echo have any blue tiles?" (Answer: The constant was zero.)
- "Which pattern would reach 1,000 tiles first?" (Answer: Pattern Echo, because it has the highest rate of change at +5 per figure.)
Bonus Solution
"If a pattern grows by 10 tiles each step and starts with 15 tiles in Figure 1, what is its expression?"
\(10n + 5\)
Note: If Fig 1 has 15 tiles and growth is 10, then the constant \(b\) is 5 (\(15 - 10 = 5\)).
