Model the following addition problem using the base ten blocks. Draw out all base ten blocks, clearly show all trades and include an answer to the problem. (5 points) 394 + 148 How many trades?
The Correct Answer and Explanation is:
Step 1: Representing Each Number with Base Ten Blocks
- 394 consists of 3 hundreds blocks, 9 tens blocks, and 4 ones blocks.
- 148 consists of 1 hundred block, 4 tens blocks, and 8 ones blocks.
Step 2: Adding the Blocks
- Combine the hundreds: 3 + 1 = 4 hundreds blocks.
- Combine the tens: 9 + 4 = 13 tens blocks.
- Combine the ones: 4 + 8 = 12 ones blocks.
Step 3: Trading Excess Blocks
- Trade ones: Since there are 12 ones, we trade 10 ones for 1 ten block, leaving 2 ones.
- Trade tens: Now we have 14 tens blocks (13 from before plus 1 from the ones trade). We trade 10 tens for 1 hundred block, leaving 4 tens.
- Final count: 5 hundreds blocks, 4 tens blocks, and 2 ones blocks.
Answer: 394 + 148 = 542
Number of Trades: 2 trades (one for ones, one for tens)
Explanation
Base ten blocks help visualize addition by grouping values. The process ensures correct place value representation and simplifies carrying operations. First, numbers are modeled using blocks representing hundreds, tens, and ones. When added, excess values in smaller units are traded for higher units. In this case, 12 ones required trading 10 for one ten, and 14 tens required trading 10 for one hundred. The final sum, 542, is obtained after these adjustments. This method reinforces foundational arithmetic and enhances numerical comprehension.
