Ask AI: Use Dienes blocks to illustrate the following operations: a) 34 + 47 b) 296 + 205 c) 64 – 27 d) 516 – 209

Dienes blocks, also known as base-10 blocks, are useful for visualizing mathematical operations. They consist of unit blocks (1s), rods (10s), flats (100s), and cubes (1000s). Here's how you can use them to illustrate the given operations: ### a) 34 + 47 - **34**: - 3 rods (representing 30) - 4 unit blocks (representing 4) - **47**: - 4 rods (representing 40) - 7 unit blocks (representing 7) **Adding**: 1. Combine the rods: 3 rods (30) + 4 rods (40) = 7 rods (70) 2. Combine the unit blocks: 4 units + 7 units = 11 units Since 11 units can be converted into 1 rod and 1 unit: - 7 rods + 1 rod = 8 rods (80) - 1 unit **Result**: 80 + 1 = 81 ### b) 296 + 205 - **296**: - 2 flats (representing 200) - 9 rods (representing 90) - 6 unit blocks (representing 6) - **205**: - 2 flats (representing 200) - 0 rods (representing 0) - 5 unit blocks (representing 5) **Adding**: 1. Combine the flats: 2 flats (200) + 2 flats (200) = 4 flats (400) 2. Combine the rods: 9 rods (90) + 0 rods (0) = 9 rods (90) 3. Combine the unit blocks: 6 units + 5 units = 11 units Since 11 units can be converted into 1 rod and 1 unit: - 9 rods + 1 rod = 10 rods (100, which is 1 flat) - 1 unit Total conversion: - 4 flats + 1 flat = 5 flats (500) - 1 unit **Result**: 500 + 1 = 501 ### c) 64 – 27 - **64**: - 6 rods (representing 60) - 4 unit blocks (representing 4) - **27**: - 2 rods (representing 20) - 7 unit blocks (representing 7) **Subtracting**: 1. First, we need to make sure we have enough units to subtract: - Take 1 rod (10) from 6 rods, converting it into 10 units - Now, we have 5 rods (50) and 14 units blocks 2. Subtract units: 14 units - 7 units = 7 units 3. Subtract rods: 5 rods (50) - 2 rods (20) = 3 rods (30) **Result**: 30 + 7 = 37 ### d) 516 – 209 - **516**: - 5 flats (representing 500) - 1 rod (representing 10) - 6 unit blocks (representing 6) - **209**: - 2 flats (representing 200) - 0 rods (representing 0) - 9 unit blocks (representing 9) **Subtracting**: 1. First, we need to make sure we have enough units to subtract 9 units: - Take 1 rod (10) from the 1 rod and add to units - Now, we have transferred flats as well for completeness: - 4 flats (400), 11 rods (110), and 6 units 2. Then convert again as per needed: - Take 1 rod (10) from 1 rod and add to units - 4 flats (400), 1 rod (10), 16 units 3. Subtract units: 16 units - 9 units = 7 units 4. Subtract rods: 1 rod (10) – 0 rods (0) = 1 rod (10) 5. Subtract flats: 5 flats (500) - 2 flats (200) = 3 flats (300) **Result**: 300 + 10 + 7 = 317 Using Dienes blocks helps break down these operations into visual, easy-to-understand steps, which can be particularly helpful for younger learners or anyone who benefits from a visual representation of arithmetic.