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Number Patterns

Grade 4 · Mathematics · Worksheet 2

  1. Pattern: 128, 64, 32, 16, __ Rule? Answer: ______________
  2. 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: ______________
  3. Mason is organizing his toy cars into rows for a display. He puts 7 cars in the first row, 12 cars in the second row, 17 cars in the third row, and 22 cars in the fourth row. If this pattern continues, how many cars will Mason put in the seventh row? Answer: ______________
  4. 245 × 6 = ? Answer: ______________
  5. Emma is practicing her skip counting by following a pattern. She starts at 7 and adds 9 each time. The first five numbers in her pattern are 7, 16, 25, 34, 43. If she continues this pattern, what will be the 9th number in her sequence? Answer: ______________
  6. Charlotte is training for a charity run. She runs 4 miles on her first day. Each day after that, she increases her distance by 3 miles. If she continues this pattern, how many miles will she run on the 9th day? Answer: ______________
  7. Mason is drawing a visual number pattern on a grid. He starts with a row of 7 squares. Each new row has 5 more squares than the row before it. If the pattern continues, how many squares will be in the 7th row? Answer: ______________
  8. Liam is saving money to buy a new video game that costs $45. He already has $18 saved from his allowance. His grandmother gives him $12 for his good grades. How much more money does Liam need to buy the video game? Answer: ______________
  9. Pattern: 8, 16, 32, 64, __ Rule? Answer: ______________
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Answer Key & Explanations

Number Patterns · Grade 4 · Worksheet 2

  1. Pattern: 128, 64, 32, 16, __ Rule? Answer: 8 Solution: Look at the pattern: 128, 64, 32, 16 Find the relationship between consecutive terms: 128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16 The rule is 'divide by 2' or 'multiply by 1/2' Apply the rule to the last term: 16 ÷ 2 = 8 The next term in the pattern is 8
    Full step-by-step solution

    Step 1: Look at the pattern: 128, 64, 32, 16 Step 2: Find the relationship between consecutive terms: 128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16 Step 3: The rule is 'divide by 2' or 'multiply by 1/2' Step 4: Apply the rule to the last term: 16 ÷ 2 = 8 Step 5: The next term in the pattern is 8

  2. 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

  3. Mason is organizing his toy cars into rows for a display. He puts 7 cars in the first row, 12 cars in the second row, 17 cars in the third row, and 22 cars in the fourth row. If this pattern continues, how many cars will Mason put in the seventh row? Answer: 37 Solution: Find the pattern rule. Look at the difference between consecutive rows: 12 - 7 = 5, 17 - 12 = 5, 22 - 17 = 5. The rule is add 5 cars to each row.
    Full step-by-step solution

    Step 1: Find the pattern rule. Look at the difference between consecutive rows: 12 - 7 = 5, 17 - 12 = 5, 22 - 17 = 5. The rule is add 5 cars to each row. Step 2: Continue the pattern from the fourth row to the seventh row. Fifth row: 22 + 5 = 27 cars Sixth row: 27 + 5 = 32 cars Seventh row: 32 + 5 = 37 cars The answer is 37.

  4. 245 × 6 = ? Answer: 1470 Solution: Write the multiplication vertically for clarity. 245 × 6 Multiply the ones place. 6 × 5 = 30 Write down 0 in the ones place, and carry over 3 to the tens place.
    Full step-by-step solution

    Let's multiply 245 by 6 step by step. Step 1: Write the multiplication vertically for clarity. 245 × 6 Step 2: Multiply the ones place. 6 × 5 = 30 Write down 0 in the ones place, and carry over 3 to the tens place. 245 × 6 ----- 0 (carry 3) Step 3: Multiply the tens place. 6 × 4 = 24 Add the carried-over 3: 24 + 3 = 27 Write down 7 in the tens place, and carry over 2 to the hundreds place. 245 × 6 ----- 70 (carry 2) Step 4: Multiply the hundreds place. 6 × 2 = 12 Add the carried-over 2: 12 + 2 = 14 Write down 4 in the hundreds place and 1 in the thousands place. 245 × 6 ----- 1470 Step 5: Combine the result. The final answer is 1470. Therefore, 245 × 6 = 1470.

  5. Emma is practicing her skip counting by following a pattern. She starts at 7 and adds 9 each time. The first five numbers in her pattern are 7, 16, 25, 34, 43. If she continues this pattern, what will be the 9th number in her sequence? Answer: 79 Solution: Identify the rule. The pattern starts at 7 and adds 9 each time.
    Full step-by-step solution

    Step 1: Identify the rule. The pattern starts at 7 and adds 9 each time. Step 2: List the terms: 1st: 7 2nd: 7 + 9 = 16 3rd: 16 + 9 = 25 4th: 25 + 9 = 34 5th: 34 + 9 = 43 6th: 43 + 9 = 52 7th: 52 + 9 = 61 8th: 61 + 9 = 70 9th: 70 + 9 = 79 Step 3: The 9th number in the pattern is 79. The answer is 79.

  6. Charlotte is training for a charity run. She runs 4 miles on her first day. Each day after that, she increases her distance by 3 miles. If she continues this pattern, how many miles will she run on the 9th day? Answer: 28 Solution: Identify the pattern. Day 1: 4 miles. Day 2: 4 + 3 = 7 miles.
    Full step-by-step solution

    Step 1: Identify the pattern. Day 1: 4 miles. Day 2: 4 + 3 = 7 miles. Day 3: 7 + 3 = 10 miles. Day 4: 10 + 3 = 13 miles. The rule is add 3 miles each day. Step 2: Continue the pattern from Day 4 to Day 9. Day 5: 13 + 3 = 16 miles Day 6: 16 + 3 = 19 miles Day 7: 19 + 3 = 22 miles Day 8: 22 + 3 = 25 miles Day 9: 25 + 3 = 28 miles The answer is 28.

  7. Mason is drawing a visual number pattern on a grid. He starts with a row of 7 squares. Each new row has 5 more squares than the row before it. If the pattern continues, how many squares will be in the 7th row? Answer: 37 Solution: Row 1 has 7 squares. Step 2: Each new row adds 5 squares. So Row 2 = 7 + 5 = 12 squares.
    Full step-by-step solution

    Step 1: Row 1 has 7 squares. Step 2: Each new row adds 5 squares. So Row 2 = 7 + 5 = 12 squares. Step 3: Row 3 = 12 + 5 = 17 squares. Step 4: Row 4 = 17 + 5 = 22 squares. Step 5: Row 5 = 22 + 5 = 27 squares. Step 6: Row 6 = 27 + 5 = 32 squares. Step 7: Row 7 = 32 + 5 = 37 squares. The 7th row has 37 squares.

  8. Liam is saving money to buy a new video game that costs $45. He already has $18 saved from his allowance. His grandmother gives him $12 for his good grades. How much more money does Liam need to buy the video game? Answer: 15 Solution: 1. Liam wants a video game that costs $45. This is the total amount needed.
    Full step-by-step solution

    Let's go step-by-step. 1. Liam wants a video game that costs $45. This is the total amount needed. 2. He already has $18 saved from allowance. So, starting from $45, we can subtract what he already has: 45 - 18 = 27 This means after using his savings, he still needs $27. 3. His grandmother gives him $12 for good grades. Now, from the $27 still needed, subtract the $12 from his grandmother: 27 - 12 = 15 4. So, Liam still needs $15 more to buy the video game. Final answer: 15

  9. Pattern: 8, 16, 32, 64, __ Rule? Answer: 128 Solution: Look at the pattern: 8, 16, 32, 64 Check the relationship between consecutive numbers: 8 × 2 = 16, 16 × 2 = 32, 32 × 2 = 64 The rule is 'multiply by 2' Apply the rule to find the next term: 64 × 2 = 128 The answer is 128.
    Full step-by-step solution

    Step 1: Look at the pattern: 8, 16, 32, 64 Step 2: Check the relationship between consecutive numbers: 8 × 2 = 16, 16 × 2 = 32, 32 × 2 = 64 Step 3: The rule is 'multiply by 2' Step 4: Apply the rule to find the next term: 64 × 2 = 128 The answer is 128.