Pattern Analysis

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Answer Key & Explanations

Pattern Analysis · Grade 5 · Worksheet 3

1. At the school carnival, Mason is running the beanbag toss. The rule for scoring is: the number of tickets you win equals 4 times the number of the ring you hit. Mason records the results as points (ring number, tickets won). If Mason hits ring 1, how many tickets does Mason win? Answer: 4 Solution: The pattern rule is tickets = 4 × ring number. Step 2: Mason hit ring number 1. Step 3: Multiply: 4 × 1 = 4.
   Full step-by-step solution

   Step 1: The pattern rule is tickets = 4 × ring number. Step 2: Mason hit ring number 1. Step 3: Multiply: 4 × 1 = 4. Mason wins 4 tickets.

2. (2.5 × 4.8) + (3.6 ÷ 1.2) = ? Answer: 15 Solution: Calculate the multiplication: 2.5 × 4.8 = 12 Calculate the division: 3.6 ÷ 1.2 = 3 Add the results: 12 + 3 = 15 The answer is 15.
   Full step-by-step solution

   Step 1: Calculate the multiplication: 2.5 × 4.8 = 12 Step 2: Calculate the division: 3.6 ÷ 1.2 = 3 Step 3: Add the results: 12 + 3 = 15 The answer is 15.

3. (2.5 × 4) + (3.75 × 2) = ? Answer: 17.5 Solution: Calculate the first multiplication: 2.5 × 4 = 10 Calculate the second multiplication: 3.75 × 2 = 7.5 Add the two results: 10 + 7.5 = 17.5 The answer is 17.5.
   Full step-by-step solution

   Step 1: Calculate the first multiplication: 2.5 × 4 = 10 Step 2: Calculate the second multiplication: 3.75 × 2 = 7.5 Step 3: Add the two results: 10 + 7.5 = 17.5 The answer is 17.5.

4. Tom is plotting points for a treasure map. The points follow a rule where the y-coordinate is 5 times the x-coordinate. If Tom plots a point at x = 4, what will be the y-coordinate? Answer: 20 Solution: The rule is that the y-coordinate equals 5 times the x-coordinate. For x = 4, the y-coordinate is 5 × 4 = 20.
   Full step-by-step solution

   Step 1: The rule is that the y-coordinate equals 5 times the x-coordinate. Step 2: For x = 4, the y-coordinate is 5 × 4 = 20. The answer is 20.

5. Emma is plotting points on a coordinate grid. The points follow a pattern where the y-coordinate is always 5 times the x-coordinate. She has plotted the points for x = 1, x = 2, x = 3, and x = 4. What are the coordinates of the point she should plot next when x = 5? Answer: (5, 25) Solution: The pattern is y = 5 × x. For x = 1, y = 5 × 1 = 5 → point (1, 5). For x = 2, y = 5 × 2 = 10 → point (2, 10).
   Full step-by-step solution

   Step 1: The pattern is y = 5 × x. Step 2: For x = 1, y = 5 × 1 = 5 → point (1, 5). Step 3: For x = 2, y = 5 × 2 = 10 → point (2, 10). Step 4: For x = 3, y = 5 × 3 = 15 → point (3, 15). Step 5: For x = 4, y = 5 × 4 = 20 → point (4, 20). Step 6: For x = 5, y = 5 × 5 = 25 → point (5, 25). The next point is (5, 25).

6. Pattern: (1, 7), (3, 21), (5, 35). Find the next point in the pattern. Answer: (7, 49) Solution: Look at the pattern: (1, 7), (3, 21), (5, 35). Notice that the x-coordinates are odd numbers: 1, 3, 5. The next odd number is 7.
   Full step-by-step solution

   Step 1: Look at the pattern: (1, 7), (3, 21), (5, 35). Step 2: Notice that the x-coordinates are odd numbers: 1, 3, 5. The next odd number is 7. Step 3: Find the relationship between x and y. For (1, 7): 1 × 7 = 7. For (3, 21): 3 × 7 = 21. For (5, 35): 5 × 7 = 35. Step 4: The rule is y = x × 7. Step 5: For x = 7, y = 7 × 7 = 49. The answer is (7, 49).

7. Noah is tracking the growth of his sunflower plant each week. He plots the height of the plant on a coordinate plane where the x-coordinate is the week number and the y-coordinate is the height in centimeters. The pattern of points he plots is: (1, 6), (2, 11), (3, 16), (4, 21). If the pattern continues, what will be the y-coordinate (height in centimeters) of the point when the x-coordinate (week number) is 6? Answer: 31 Solution: Identify the pattern. Looking at the points: (1, 6), (2, 11), (3, 16), (4, 21). Each week, the y-coordinate (height) increases by 5.
   Full step-by-step solution

   Step 1: Identify the pattern. Looking at the points: (1, 6), (2, 11), (3, 16), (4, 21). Each week, the y-coordinate (height) increases by 5. From week 1 to week 2: 11 - 6 = 5. From week 2 to week 3: 16 - 11 = 5. From week 3 to week 4: 21 - 16 = 5. Step 2: Write the rule. The height starts at 6 cm on week 1 and increases by 5 cm each week. So the rule is: y = 5x + 1. Check: For x = 1, 5(1) + 1 = 6. For x = 2, 5(2) + 1 = 11. For x = 3, 5(3) + 1 = 16. For x = 4, 5(4) + 1 = 21. The rule works. Step 3: Apply the rule for week 6. Substitute x = 6 into the rule: y = 5(6) + 1 = 30 + 1 = 31. Step 4: The y-coordinate for week 6 is 31. The answer is 31.

8. Liam is designing a treasure map on a coordinate plane. He marks the treasure chest at point (3, 7) and a palm tree at point (8, 7). If Liam walks from the treasure chest to the palm tree in a straight line, how many units does he walk? Answer: 5 Solution: Identify the coordinates of the two points. Treasure chest: (3, 7) Palm tree: (8, 7) Notice that both points have the same y-coordinate (7). This means they are on a horizontal line.
   Full step-by-step solution

   Step 1: Identify the coordinates of the two points. Treasure chest: (3, 7) Palm tree: (8, 7) Step 2: Notice that both points have the same y-coordinate (7). This means they are on a horizontal line. Step 3: To find the distance between two points on a horizontal line, subtract their x-coordinates. Distance = |8 - 3| = |5| = 5 Step 4: Conclusion. Liam walks 5 units from the treasure chest to the palm tree. Final answer: 5