Describing Patterns — Solutions

1. Fill in the Tables

   1. Marbles table: Total = w + 8 ▶ View Solution
   2. 12 white marbles: 12 + 8 = 20 marbles ▶ View Solution
   3. Score table: Total score = p + 15 ▶ View Solution
   4. p = 25 (initial score) ▶ View Solution
   5. Skyscraper table: Skyscraper height = 3t ▶ View Solution
   6. Tree = 25 m: 3 × 25 = 75 m tall ▶ View Solution
   7. Car speed table: Truck speed = s − 20 ▶ View Solution
   8. s = 100 km/h ▶ View Solution

2. Equivalent Algebraic Expressions

   1. Two alternatives: v − 2 × 15  or  v − 30 ▶ View Solution
   2. $50 card: 50 − 30 = $20 remaining ▶ View Solution

3. Number Puzzles

   1. Expression: 3x − 4 ▶ View Solution
   2. x = 10 ▶ View Solution

4. Create a Word Story

   1. m + m + 5: Many possible answers — e.g. two bags each with m items plus 5 extra ▶ View Solution
   2. 3b − 2: Many possible answers — e.g. 3 boxes of b cookies, eat 2 ▶ View Solution
   3. 100 − 4k: Many possible answers — e.g. 100 km tank, use 4 km every hour ▶ View Solution

5. Compact Notation

   2m + 5  |  3b − 2  |  100 − 4k ▶ View Solution

6. Are the Expressions Equal? 5 × m + 2 vs 2 + 5 × m

   Yes — both give the same result for any value of m (commutative addition) ▶ View Solution

7. Is 2a + 3a = 5a?

   Yes — like terms can be combined: 2a + 3a = 5a ▶ View Solution

8. Square Dining Tables

   1. 4 tables: 10 people ▶ View Solution
   2. Complete the table: t=1: 4, t=2: 6, t=3: 8, t=4: 10 ▶ View Solution
   3. p = 2t + 2 ▶ View Solution

9. The Taxi Fare

   1. Expression: Cost = 2k + 5 ▶ View Solution
   2. 12 km trip: 2 × 12 + 5 = $29 ▶ View Solution
   3. $25 maximum km: 10 km (2 × 10 + 5 = $25) ▶ View Solution

10. Find the Rule

    1. Pattern description: Output increases by 5 each time ▶ View Solution
    2. Output when x = 10: 52 ▶ View Solution
    3. y = 5x + 2 ▶ View Solution