Number Patterns

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Answer Key & Explanations

Number Patterns · Grade 4 · Worksheet 2

1. A rectangular swimming pool is drawn on a grid where each square unit represents 1 square meter. The pool has a length of 15 meters and a width of 8 meters. A concrete walkway that is 2 meters wide surrounds the entire pool. What is the total area of the pool and walkway combined in square meters? Answer: 228 Solution: The pool has length 15 m and width 8 m. The walkway is 2 m wide and goes around the entire pool, so it adds 2 m to both the left and right sides, and 2 m to both the top and bottom.
   Full step-by-step solution

   Step 1: The pool has length 15 m and width 8 m. Step 2: The walkway is 2 m wide and goes around the entire pool, so it adds 2 m to both the left and right sides, and 2 m to both the top and bottom. Step 3: The total length including walkway is: 15 + 2 + 2 = 19 m Step 4: The total width including walkway is: 8 + 2 + 2 = 12 m Step 5: The total area is length × width: 19 × 12 Step 6: Calculate: 19 × 12 = (19 × 10) + (19 × 2) = 190 + 38 = 228 Step 7: The total area is 228 square meters.

2. Emma is practicing her skip counting by 7s. She starts at 7 and writes the numbers: 7, 14, 21, 28, 35, 42, 49. She notices a pattern: each number is 7 more than the one before it. If she continues this pattern, what will be the 12th number in her sequence? Answer: 84 Solution: The pattern starts at 7 and adds 7 each time. The first term is 7. To find the 12th term, we need to add 7 a total of 11 times (because we already have the first term).
   Full step-by-step solution

   Step 1: The pattern starts at 7 and adds 7 each time. The first term is 7. Step 2: To find the 12th term, we need to add 7 a total of 11 times (because we already have the first term). Step 3: 11 times 7 equals 77. Step 4: Add 77 to the starting number 7: 7 + 77 = 84. The answer is 84.

3. Liam is organizing his baseball card collection. He has 125 cards and wants to arrange them in an album with 5 cards on each page. How many pages will Liam need for all his baseball cards? Answer: 25 Solution: Liam has 125 baseball cards. He wants to put 5 cards on each page. To find how many pages he needs, we divide the total number of cards by the number of cards per page.
   Full step-by-step solution

   Liam has 125 baseball cards. He wants to put 5 cards on each page. To find how many pages he needs, we divide the total number of cards by the number of cards per page. Step 1: Write the division problem. 125 ÷ 5 Step 2: Solve the division. Think: how many times does 5 go into 125? 5 × 25 = 125, so 125 ÷ 5 = 25. Step 3: Interpret the result. Since 125 ÷ 5 = 25, Liam will need 25 pages to fit all his cards. Answer: 25

4. Pattern: 240, 200, 160, 120, __ Rule? Answer: 80 Solution: Look at the pattern: 240, 200, 160, 120 Find the relationship between consecutive terms: 200 - 240 = -40, 160 - 200 = -40, 120 - 160 = -40 The rule is 'subtract 40' Apply the rule to the last term: 120 - 40 = 80 The next term in the pattern is 80
   Full step-by-step solution

   Step 1: Look at the pattern: 240, 200, 160, 120 Step 2: Find the relationship between consecutive terms: 200 - 240 = -40, 160 - 200 = -40, 120 - 160 = -40 Step 3: The rule is 'subtract 40' Step 4: Apply the rule to the last term: 120 - 40 = 80 Step 5: The next term in the pattern is 80

5. Pattern: 512, 448, 384, 320, __ Rule? Answer: 256 Solution: Look at the pattern: 512, 448, 384, 320 Find the relationship between consecutive terms: 512 - 448 = 64, 448 - 384 = 64, 384 - 320 = 64 The rule is 'subtract 64' Apply the rule to the last term: 320 - 64 = 256 The next term in the pattern is 256
   Full step-by-step solution

   Step 1: Look at the pattern: 512, 448, 384, 320 Step 2: Find the relationship between consecutive terms: 512 - 448 = 64, 448 - 384 = 64, 384 - 320 = 64 Step 3: The rule is 'subtract 64' Step 4: Apply the rule to the last term: 320 - 64 = 256 Step 5: The next term in the pattern is 256

6. Hana is training for a charity run. She runs 150 meters on her first day. Each day, she increases her running distance by 25 meters. If this pattern continues, how many meters will Hana run on the eighth day? Answer: 325 Solution: Identify the pattern. The distances increase by 25 meters each day.
   Full step-by-step solution

   Step 1: Identify the pattern. The distances increase by 25 meters each day. Day 1: 150 meters Day 2: 150 + 25 = 175 meters Day 3: 175 + 25 = 200 meters Day 4: 200 + 25 = 225 meters Day 5: 225 + 25 = 250 meters Day 6: 250 + 25 = 275 meters Day 7: 275 + 25 = 300 meters Day 8: 300 + 25 = 325 meters The answer is 325.

7. Hana is drawing a number pattern on a grid. She starts at 104 and follows the rule: subtract 12 each time. What is the 6th number in her pattern? Answer: 44 Solution: The first number is 104. Subtract 12 each time, so the second number is 104 - 12 = 92. The third number is 92 - 12 = 80.
   Full step-by-step solution

   Step 1: The first number is 104. Step 2: Subtract 12 each time, so the second number is 104 - 12 = 92. Step 3: The third number is 92 - 12 = 80. Step 4: The fourth number is 80 - 12 = 68. Step 5: The fifth number is 68 - 12 = 56. Step 6: The sixth number is 56 - 12 = 44. The answer is 44.

8. Hana is saving stickers in an album. On the first page, she places 7 stickers. On the second page, she places 14 stickers. On the third page, she places 28 stickers, and on the fourth page, she places 56 stickers. If this pattern continues, how many stickers will Hana place on the sixth page? Answer: 224 Solution: Write down the pattern: Page 1: 7 stickers, Page 2: 14 stickers, Page 3: 28 stickers, Page 4: 56 stickers. Find the rule by checking the relationship between terms. From Page 1 to Page 2: 7 × 2 = 14.
   Full step-by-step solution

   Step 1: Write down the pattern: Page 1: 7 stickers, Page 2: 14 stickers, Page 3: 28 stickers, Page 4: 56 stickers. Step 2: Find the rule by checking the relationship between terms. From Page 1 to Page 2: 7 × 2 = 14. From Page 2 to Page 3: 14 × 2 = 28. From Page 3 to Page 4: 28 × 2 = 56. Step 3: The rule is multiply by 2 each time. Step 4: Continue the pattern: Page 5: 56 × 2 = 112 stickers. Page 6: 112 × 2 = 224 stickers. The answer is 224.