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Patterns to Equations

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Patterns to Equations worksheet preview
Patterns to Equations

Patterns to Equations

Mathematical patterns and equations illustration

🔢 Part 1: Identifying Pattern Rules

1. Look at this number pattern: 4, 8, 12, 16, 20, ...

a) What is the constant difference? ________

b) Describe the rule in words: _________________________________

2. Complete the table for the pattern: 5, 10, 15, 20, ...
3. Which of these patterns has a constant difference of 3?

2, 4, 6, 8, ...

3, 6, 9, 12, ...

1, 4, 7, 10, ...

5, 8, 11, 14, ...

📝 Part 2: Writing Algebraic Expressions

4. For the pattern 2, 4, 6, 8, 10, ...

a) The algebraic expression for the nth term is: ________

b) Check your answer: When n = 3, the term should be ________

5. Match each pattern with its algebraic expression:
1. 7, 14, 21, 28, ...
2. 1, 3, 5, 7, ...
3. 4, 8, 12, 16, ...
4. 6, 12, 18, 24, ...
A. 4n
B. 2n - 1
C. 7n
D. 6n
6. Write the algebraic expression for this pattern: 3, 6, 9, 12, 15, ...

Expression: ________________

⚖️ Part 3: Creating Equations

7. For the pattern 5, 8, 11, 14, 17, ...

a) The constant difference is: ________

b) The first term is: ________

c) The algebraic expression is: ________________

d) Write this as an equation where T represents the term value: T = ________

8. Complete the table and write the equation:

Pattern: 10, 8, 6, 4, 2, ...

Equation: T = ________________

9. Check all the equations that could represent decreasing patterns:

T = 20 - 3n

T = 5n + 2

T = 15 - 2n

T = 4n

🎯 Part 4: Problem Solving

10. Sarah is saving money. She starts with $8 and saves $3 each week.

a) How much money will she have after 1 week? $________

b) How much money will she have after 2 weeks? $________

c) Write an equation for the amount of money (M) after n weeks: M = ________

d) How much money will she have after 10 weeks? $________

11. A candle is 15 centimetres tall and burns 2 centimetres every hour.

a) Write an equation for the height (H) of the candle after n hours: H = ________

b) What will be the height after 4 hours? ________ cm

12. Create your own pattern and equation:

a) Write a number pattern with 5 terms: ________, ________, ________, ________, ________

b) What is the constant difference? ________

c) Write the algebraic expression: ________________

d) Write the equation: T = ________________

🤔 Part 5: Reflection

13. Explain in your own words how algebraic expressions help us describe patterns:
14. What is the difference between an expression and an equation?

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