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
Fresh day Master, let's solve. Here are the solutions for Exercise 12.2: Step 1: Draw the next building in the sequence (Question 1). The sequence shows buildings with 1, 2, and 3 levels. The next building will have 4 levels. It will be structured as: • 1 block at the top (Level 4) • 2 blocks below that (Level 3) • 3 blocks below that (Level 2) • 4 blocks at the bottom (Level 1) Based on the color pattern (Blue for topmost, Red for second from top, Green for third from top, then cycling), the colors for Building 4 would be: • Topmost (1 block): Blue • Second from top (2 blocks): Red • Third from top (3 blocks): Green • Bottommost (4 blocks): Blue Step 2: Count the blocks in level 1 and fill in the table (Questions 2 and 5). For a building with 'n' levels, the number of blocks in its bottommost row (labeled "level 1" in the diagram) is 'n'. | Building number | 1 | 2 | 3 | 4 | 6 | 10 | 12 | 20 | |---|---|---|---|---|---|---|---|---| | Blocks in level 1 | 1 | 2 | 3 | 4 | 6 | 10 | 12 | 20 | Step 3: Write down the rule for the pattern of numbers (Question 3). The rule is: The number of blocks in level 1 is equal to the building number (which is also the number of levels). Expressed as a formula: Blocks in Level 1 = Building number Step 4: Test your rule for buildings 3 and 4 using number sentences (Question 4). • For Building 3: Building number is 3. According to the rule, Blocks in Level 1 = 3. From the image, Building 3 has 3 blocks in its bottommost row (Level 1). So, 3 = 3. The rule is correct. • For Building 4: Building number is 4. According to the rule, Blocks in Level 1 = 4. From the pattern, Building 4 would have 4 blocks in its bottommost row (Level 1). So, 4 = 4. The rule is correct. Step 5: Calculate the number of levels for a building with 37 blocks in level 1 (Question 6). Using the rule from Step 3: Blocks in Level 1 = Building number If a building has 37 blocks in Level 1, then: 37 = Building number Therefore, the building will have 37 levels. What's next? Send 'em! 📸