Number Patterns

lessonbunny.com

Answer Key & Explanations

Number Patterns · Grade 4 · Worksheet 3

1. 324 ÷ 12 = ? Answer: 27 Solution: We are solving 324 ÷ 12. Think about how many times 12 fits into 324. First, 12 × 20 = 240.
   Full step-by-step solution

   Step 1: We are solving 324 ÷ 12. Step 2: Think about how many times 12 fits into 324. We can break 324 into parts that are easier to divide. Step 3: First, 12 × 20 = 240. Subtract 240 from 324: 324 - 240 = 84. Step 4: Now, see how many times 12 fits into 84. 12 × 7 = 84. Step 5: Add the partial results: 20 + 7 = 27. Step 6: Therefore, 324 ÷ 12 = 27.

2. 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.

3. Emma is creating a pattern with colored tiles for her art project. She starts with 2 blue tiles, then adds 4 red tiles, then 6 blue tiles, then 8 red tiles. If this pattern continues, how many tiles will be in the 6th group of the pattern? Answer: 12 Solution: Identify the pattern sequence: Group 1: 2 tiles, Group 2: 4 tiles, Group 3: 6 tiles, Group 4: 8 tiles Notice the pattern increases by 2 tiles each time: 2, 4, 6, 8...
   Full step-by-step solution

   Step 1: Identify the pattern sequence: Group 1: 2 tiles, Group 2: 4 tiles, Group 3: 6 tiles, Group 4: 8 tiles Step 2: Notice the pattern increases by 2 tiles each time: 2, 4, 6, 8... Step 3: Continue the pattern: Group 5 would be 8 + 2 = 10 tiles Step 4: Group 6 would be 10 + 2 = 12 tiles Step 5: The 6th group in the pattern has 12 tiles.

4. Emma is planting flowers in her garden in a special pattern. She plants 2 red flowers, then 4 yellow flowers, then 6 red flowers, then 8 yellow flowers. If this pattern continues, how many flowers will be in the 6th group she plants? Answer: 12 Solution: Look at the pattern of group sizes: Group 1: 2 flowers, Group 2: 4 flowers, Group 3: 6 flowers, Group 4: 8 flowers Identify the pattern: Each group has 2 more flowers than the previous group Continue the pattern: Group 5: 8 + 2 = 10 flowers Group 6: 10 + 2 = 12 flowers The 6th group will have 12…
   Full step-by-step solution

   Step 1: Look at the pattern of group sizes: Group 1: 2 flowers, Group 2: 4 flowers, Group 3: 6 flowers, Group 4: 8 flowers Step 2: Identify the pattern: Each group has 2 more flowers than the previous group Step 3: Continue the pattern: Group 5: 8 + 2 = 10 flowers Step 4: Group 6: 10 + 2 = 12 flowers Step 5: The 6th group will have 12 flowers The answer is 12.

5. Liam is organizing his book collection on shelves. He puts 12 books on the first shelf, 18 books on the second shelf, 24 books on the third shelf, and 30 books on the fourth shelf. If this pattern continues, how many books will Liam put on the sixth shelf? Answer: 42 Solution: Identify the pattern in the number of books per shelf First shelf: 12 books Second shelf: 18 books Third shelf: 24 books Fourth shelf: 30 books 18 - 12 = 6 24 - 18 = 6 30 - 24 = 6 The pattern increases by 6 books each shelf Fifth shelf: 30 + 6 = 36 books Sixth shelf: 36 + 6 = 42 books The answer…
   Full step-by-step solution

   Step 1: Identify the pattern in the number of books per shelf First shelf: 12 books Second shelf: 18 books Third shelf: 24 books Fourth shelf: 30 books Step 2: Find the difference between consecutive shelves 18 - 12 = 6 24 - 18 = 6 30 - 24 = 6 The pattern increases by 6 books each shelf Step 3: Continue the pattern to find the sixth shelf Fifth shelf: 30 + 6 = 36 books Sixth shelf: 36 + 6 = 42 books The answer is 42.

6. A rectangular garden is drawn with a length of 12 meters and a width of 8 meters. A path is built around the outside of the garden that is 2 meters wide. What is the total area of the garden and the path combined? Answer: 192 Solution: - Length = 12 m - Width = 8 m A path 2 m wide is built around the outside of the garden. We need the total area of garden + path. The path goes around all four sides, so it adds 2 m to the top, bottom, left, and right.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** We have a rectangular garden: - Length = 12 m - Width = 8 m A path 2 m wide is built around the outside of the garden. We need the total area of garden + path. --- **Step 2: Visualize the path** The path goes around all four sides, so it adds 2 m to the top, bottom, left, and right. That means: - New length = original length + 2 m (left) + 2 m (right) = 12 + 2 + 2 = 16 m - New width = original width + 2 m (top) + 2 m (bottom) = 8 + 2 + 2 = 12 m --- **Step 3: Calculate the total area (garden + path)** Total area = new length × new width = 16 × 12 --- **Step 4: Perform the multiplication** 16 × 12 = 16 × (10 + 2) = 160 + 32 = 192 --- **Step 5: Final answer** The total area of the garden and the path combined is 192 square meters. --- **Answer:** 192

7. 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