Base Blocks: Part 2 - Add using base-10 blocks to find the correct sum.

Problem Explanation and Solution

The task involves using base-10 blocks to add two numbers. Base-10 blocks are visual tools that help represent numbers in a concrete way:
- Cubes represent units (1s).
- Longs represent tens (10s).
- Flats represent hundreds (100s).

We need to solve the addition problems step by step and match the result with the correct option.

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#### Problem 1: \( 341 + 25 \)

1. Break down the numbers using base-10 blocks:
- 341:
- 3 flats (3 × 100 = 300)
- 4 longs (4 × 10 = 40)
- 1 cube (1 × 1 = 1)
- 25:
- 2 longs (2 × 10 = 20)
- 5 cubes (5 × 1 = 5)

2. Add the blocks:
- Hundreds place: 3 flats (300)
- Tens place: 4 longs + 2 longs = 6 longs (60)
- Units place: 1 cube + 5 cubes = 6 cubes (6)

3. Combine the results:
- Total = 3 flats + 6 longs + 6 cubes
- This represents \( 300 + 60 + 6 = 366 \).

4. Match with the options:
- The correct answer is a. 366.

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#### Problem 2: \( 267 + 22 \)

1. Break down the numbers using base-10 blocks:
- 267:
- 2 flats (2 × 100 = 200)
- 6 longs (6 × 10 = 60)
- 7 cubes (7 × 1 = 7)
- 22:
- 2 longs (2 × 10 = 20)
- 2 cubes (2 × 1 = 2)

2. Add the blocks:
- Hundreds place: 2 flats (200)
- Tens place: 6 longs + 2 longs = 8 longs (80)
- Units place: 7 cubes + 2 cubes = 9 cubes (9)

3. Combine the results:
- Total = 2 flats + 8 longs + 9 cubes
- This represents \( 200 + 80 + 9 = 289 \).

4. Match with the options:
- The correct answer is d. 289.

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Final Answers:

1. \( 341 + 25 = \boxed{366} \)
2. \( 267 + 22 = \boxed{289} \)

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Summary of Steps:

1. Break down each number into its base-10 components (flats, longs, cubes).
2. Add the corresponding blocks (hundreds, tens, units) separately.
3. Combine the results to get the total sum.
4. Match the total with the given options.

This method ensures accuracy and helps visualize the addition process using base-10 blocks.