This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for Activity 3: 3.1 Draw Pattern 3, Pattern 4 and Pattern 5 in the spaces provided and then complete the table. Step 1: Analyze the given patterns and identify the rules. Let n be the pattern number. Number of matches along one side: This value is equal to n. Number of small squares: This value is n^2. Number of matches used for the whole shape: This value follows the formula 2n(n+1). For Pattern 1 (n=1): 2(1)(1+1) = 2(1)(2) = 4. For Pattern 2 (n=2): 2(2)(2+1) = 2(2)(3) = 12. Step 2: Describe the drawings for Pattern 3, 4, and 5. Pattern 3: This pattern should be a square grid made of matchsticks, with 3 matches along each side, forming 3 × 3 = 9 small squares. Pattern 4: This pattern should be a square grid made of matchsticks, with 4 matches along each side, forming 4 × 4 = 16 small squares. Pattern 5: This pattern should be a square grid made of matchsticks, with 5 matches along each side, forming 5 × 5 = 25 small squares. Step 3: Complete the table using the identified rules. For Pattern 3 (n=3): Number of matches along one side: 3 Number of small squares: 3^2 = 9 Number of matches used for the whole shape: 2(3)(3+1) = 2(3)(4) = 24 For Pattern 4 (n=4): Number of matches along one side: 4 Number of small squares: 4^2 = 16 Number of matches used for the whole shape: 2(4)(4+1) = 2(4)(5) = 40 For Pattern 5 (n=5): Number of matches along one side: 5 Number of small squares: 5^2 = 25 Number of matches used for the whole shape: 2(5)(5+1) = 2(5)(6) = 60 Here is the completed table: | | | Number of matches along one side | Number of small squares | Number of matches used for the whole shape | | :---------- | 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