Number Patterns

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Answer Key & Explanations

Number Patterns · Grade 4 · Worksheet 1

1. Liam is organizing his baseball card collection. He has 156 cards and wants to arrange them in an album with 12 cards on each page. How many pages will Liam need for all his baseball cards? Answer: 13 Solution: Liam has 156 baseball cards. He wants to put 12 cards on each page. To find how many pages he needs, divide the total number of cards by the number of cards per page.
   Full step-by-step solution

   Liam has 156 baseball cards. He wants to put 12 cards on each page. To find how many pages he needs, divide the total number of cards by the number of cards per page. Step 1: Write the division problem. 156 ÷ 12 Step 2: Perform the division. 12 × 10 = 120 156 − 120 = 36 12 × 3 = 36 36 − 36 = 0 Step 3: Add the partial results. 10 + 3 = 13 So, 156 ÷ 12 = 13. This means Liam will fill 13 pages completely with his 156 cards. Answer: 13 pages.

2. Matiu is training for a cross-country race. He runs 150 meters on his first lap, 300 meters on his second lap, 450 meters on his third lap, and 600 meters on his fourth lap. If this pattern continues, how many meters will Matiu run on his sixth lap? Answer: 900 Solution: Identify the pattern. Lap 1: 150 meters, Lap 2: 300 meters, Lap 3: 450 meters, Lap 4: 600 meters. The difference between each lap is 150 meters (300 - 150 = 150, 450 - 300 = 150, 600 - 450 = 150).
   Full step-by-step solution

   Step 1: Identify the pattern. Lap 1: 150 meters, Lap 2: 300 meters, Lap 3: 450 meters, Lap 4: 600 meters. The difference between each lap is 150 meters (300 - 150 = 150, 450 - 300 = 150, 600 - 450 = 150). So the rule is: add 150 meters each lap. Step 2: Continue the pattern. Lap 5: 600 + 150 = 750 meters. Lap 6: 750 + 150 = 900 meters. The answer is 900 meters.

3. Pattern: 320, 280, 240, 200, __ Rule? Answer: 160 Solution: Look at the pattern: 320, 280, 240, 200 Find the relationship between consecutive terms: 280 - 320 = -40, 240 - 280 = -40, 200 - 240 = -40 The rule is 'subtract 40' Apply the rule to the last term: 200 - 40 = 160 The next term in the pattern is 160
   Full step-by-step solution

   Step 1: Look at the pattern: 320, 280, 240, 200 Step 2: Find the relationship between consecutive terms: 280 - 320 = -40, 240 - 280 = -40, 200 - 240 = -40 Step 3: The rule is 'subtract 40' Step 4: Apply the rule to the last term: 200 - 40 = 160 Step 5: The next term in the pattern is 160

4. Kaia is arranging tiles in a pattern on a grid. The first row has 1 tile, the second row has 3 tiles, the third row has 5 tiles, and the fourth row has 7 tiles. If the pattern continues in the same way, how many tiles will be in the ninth row? Answer: 17 Solution: List the number of tiles in each row: Row 1: 1, Row 2: 3, Row 3: 5, Row 4: 7. Find the rule. Subtract consecutive terms: 3 - 1 = 2, 5 - 3 = 2, 7 - 5 = 2.
   Full step-by-step solution

   Step 1: List the number of tiles in each row: Row 1: 1, Row 2: 3, Row 3: 5, Row 4: 7. Step 2: Find the rule. Subtract consecutive terms: 3 - 1 = 2, 5 - 3 = 2, 7 - 5 = 2. The rule is add 2 each time. Step 3: Continue the pattern from row 4 to row 9: Row 5: 7 + 2 = 9 Row 6: 9 + 2 = 11 Row 7: 11 + 2 = 13 Row 8: 13 + 2 = 15 Row 9: 15 + 2 = 17 The ninth row has 17 tiles.

5. Noah is building a fence around his rectangular vegetable garden. The garden measures 15 feet long and 9 feet wide. How many feet of fencing does Noah need to go around the entire garden? Answer: 48 Solution: A rectangle has two lengths and two widths. The two lengths are each 15 feet, so 15 + 15 = 30 feet. The two widths are each 9 feet, so 9 + 9 = 18 feet.
   Full step-by-step solution

   Step 1: A rectangle has two lengths and two widths. Step 2: The two lengths are each 15 feet, so 15 + 15 = 30 feet. Step 3: The two widths are each 9 feet, so 9 + 9 = 18 feet. Step 4: Add the total length and width distances: 30 + 18 = 48 feet. Step 5: Noah needs 48 feet of fencing to go around his entire garden.

6. Pattern: 375, 450, 540, 648, __ Rule? Answer: 777.6 Solution: Look at the pattern: 375, 450, 540, 648 Find the relationship between consecutive terms: 450 ÷ 375 = 1.2, 540 ÷ 450 = 1.2, 648 ÷ 540 = 1.2 The rule is 'multiply by 1.2' Apply the rule to the last term: 648 × 1.2 = 777.6 The next term in the pattern is 777.6
   Full step-by-step solution

   Step 1: Look at the pattern: 375, 450, 540, 648 Step 2: Find the relationship between consecutive terms: 450 ÷ 375 = 1.2, 540 ÷ 450 = 1.2, 648 ÷ 540 = 1.2 Step 3: The rule is 'multiply by 1.2' Step 4: Apply the rule to the last term: 648 × 1.2 = 777.6 Step 5: The next term in the pattern is 777.6

7. Liam is organizing his rock collection into display cases. He notices a pattern in how he arranges them: the first case has 5 rocks, the second has 8 rocks, the third has 11 rocks, and the fourth has 14 rocks. If this pattern continues, how many rocks will be in the seventh display case? Answer: 23 Solution: Identify the pattern by finding the difference between consecutive cases. Case 1: 5 rocks Case 2: 8 rocks (5 + 3) Case 3: 11 rocks (8 + 3) Case 4: 14 rocks (11 + 3) The pattern increases by 3 rocks each time.
   Full step-by-step solution

   Step 1: Identify the pattern by finding the difference between consecutive cases. Case 1: 5 rocks Case 2: 8 rocks (5 + 3) Case 3: 11 rocks (8 + 3) Case 4: 14 rocks (11 + 3) The pattern increases by 3 rocks each time. Step 2: Continue the pattern to find the number of rocks in the seventh case. Case 5: 14 + 3 = 17 rocks Case 6: 17 + 3 = 20 rocks Case 7: 20 + 3 = 23 rocks The answer is 23.