Uncover the rules behind patterns! Analyze number sequences, build tables, and create expressions that explain how patterns grow. 🔢➡️
Discover rules, extend sequences, and create expressions for growing patterns!
Identify the rule that generates each pattern!
Find the next terms and describe the growth!
Match patterns to expression rules!
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Solve a real-world growing pattern!
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Analyze number patterns, describe rules, and build early algebra expressions
Growing patterns help us understand how quantities change. They’re the bridge between arithmetic and algebra!
Repeating vs. Growing
Repeating patterns cycle (red, blue, red, blue). Growing patterns increase by a rule (2, 4, 6, 8). We focus on growing patterns!
Number Sequences
Sequence is the list of numbers a pattern produces: 2, 5, 8, 11. Understanding order matters!
Rules
Rules describe how to get from one term to the next. They can be words or expressions!
Real-Life Patterns
Allowance per week, plant growth, stacking blocks—patterns appear everywhere change repeats!
Write the sequence vertically. It’s easier to see how each term changes!
Assuming the rule stays the same long-term. Always verify the pattern continues!
Science data trends, business projections, radial designs
Find a real-world pattern (weather, steps). Write the first 5 terms.
Patterns can be described in words, making them easy to communicate. Translate language into operations to uncover hidden algebra!
Addition Rule
Add 4 each time → 3, 7, 11, 15
Multiplication Rule
Multiply by 2 each time → 1, 2, 4, 8
Mixed Rules
Add 2, then multiply by 3 → 1, 3, 9, 27, ...
Context Rule
'Each day the tree grows 5 cm' describes a rule without numbers!
Say the pattern out loud. Listening to yourself describe it reveals the rule!
Summarizing only the first few terms. Ensure the rule works for the entire pattern!
Instruction manuals, recipe steps, daily routines
Write patterns for daily chores. 'Each week we add 2 days of reading.'
Tables organize pattern data. They show how input numbers transform into outputs. From tables, creating algebraic rules becomes easier!
Input → Output
Tables show how inputs (term numbers) connect to outputs (pattern values). Example: n → 3n + 1
Identify Constant Difference
Subtract consecutive outputs to find consistent change (first differences).
Build Rule
Use table to create algebraic expression: If n → 2n + 5, output = 2 × term number + 5
Explain Growth
Table shows how each term grows. Left column: term (#). Right column: value. Find relationship!
Add third column for differences to detect growth trend quickly!
Confusing term position with value. Remember: term n uses rule to compute value!
Budget spreadsheets, scientific data logs, business profit projections
Make a table for family savings plan. Fill rule and apply expressions!
Expressions generalize patterns. They let you calculate ANY term without listing all previous values!
Linear Expressions
Patterns adding the same amount use expressions like an + b. Example: 5, 8, 11 → 3n + 2
Multiples
Patterns multiplying use expressions like kn. Example: 3, 6, 9 → 3n
Squares
Square numbers (1, 4, 9, 16) use n². Recognize rapid growth!
Combined Rules
Patterns growing by multiple steps use combined expressions like 2n + 3
Try plugging in term numbers (n = 1, 2, 3) to test if your expression matches the sequence!
Assuming expressions only add. Multiplication and powers also appear!
Computer programming loops, engineering formulas, music rhythms
Write expression for your steps per day if you add 200 each day. Use table to check!
Patterns help predict and plan. From architecture to finance to coding, understanding how things grow saves time and drives decisions!
Staircase Design
Steps increase by same number of bricks. Use rule to estimate bricks needed for nth step!
Savings Plan
Deposit $10 each week. Savings pattern: 10n. Know total after any week!
Coding
Loops run repeated rules. Example: i = i + 1. Patterns run programs!
Sports Stats
Team scores increase by 7 each touchdown. Score pattern = 7n!
Whenever you notice repeated change, ask: 'What's the rule?' Write it down!
Missing hidden patterns in data. Charting helps reveal growth!
Investment growth, manufacturing schedules, class attendance tracking
Graph a pattern of your choice. Write expression and test future predictions!