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Patterns to Algebra

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Patterns to Algebra

Patterns to Algebra

Algebraic patterns illustration

🔢 Part 1: Identifying Pattern Rules

1. Look at this number pattern: 4, 7, 10, 13, 16...

a) What is the constant difference? ________

b) What would the next two terms be? ________ and ________

2. For the pattern 5, 10, 15, 20, 25...

The rule is +3

The rule is +5

The rule is +10

The rule is ×2

3. Circle the patterns that are linear (have a constant difference):

2, 4, 6, 8, 10...

1, 4, 9, 16, 25...

3, 8, 13, 18, 23...

2, 4, 8, 16, 32...

📝 Part 2: Writing Algebraic Expressions

4. For the pattern 6, 9, 12, 15, 18... where n represents the term number:

a) The constant difference is: ________

b) The algebraic expression is: ________________

c) Check: When n = 3, the term should be ________ (show your working)

5. Match each pattern with its correct algebraic expression:
1. Pattern: 2, 4, 6, 8...
2. Pattern: 1, 5, 9, 13...
3. Pattern: 10, 20, 30, 40...
4. Pattern: 3, 7, 11, 15...
A. 4n - 3
B. 2n
C. 10n
D. 4n - 1
6. Create your own pattern and write its algebraic expression:

My pattern: _______, _______, _______, _______, _______

Constant difference: ________

Algebraic expression: ________________

🧮 Part 3: Using Expressions to Find Terms

7. For the expression 5n + 2, find:

a) The 4th term: ________________

b) The 10th term: ________________

c) The 15th term: ________________

8. If the 6th term of a pattern is 23 and the expression is 3n + 5:

a) Check if this is correct by substituting n = 6:

b) Is the answer correct?

Yes, 3(6) + 5 = 23

No, the answer should be different

9. A cinema charges $8 per ticket plus a $3 booking fee. If n represents the number of tickets:

a) Write an expression for the total cost: ________________

b) How much would 5 tickets cost? ________________

c) How much would 12 tickets cost? ________________

🎯 Part 4: Problem Solving Challenge

10. Sarah is saving money. She starts with $15 and saves $7 each week.

a) Complete the table:

Week (n) Total Money ($)
1 ________
2 ________
3 ________

b) Write an algebraic expression: ________________

c) How much money will Sarah have after 10 weeks? ________________

11. Explain in your own words what a variable represents in an algebraic expression:
12. Draw a visual representation of the pattern 2, 5, 8, 11... using dots or shapes:

Algebraic expression for this pattern: ________________

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