Measuring Mass Worksheet with exercises for determining and marking masses on triple beam balances.

Problem Analysis:

The task involves solving problems related to triple-beam balances, which are used to measure mass accurately. The worksheet is divided into two parts:

1. Part 1: Determine the mass of the objects shown on the triple-beam balances.
2. Part 2: Make marks on the triple-beam balances to show the given masses.

#### Key Concepts:
- A triple-beam balance has three sliding weights (beams) that can be moved along calibrated scales. The mass is determined by adding the values of the positions of these weights.
- The beams typically have scales for different orders of magnitude (e.g., hundreds, tens, and ones).

Solution:

#### Part 1: Determine the mass of the objects

Each problem in Part 1 shows a triple-beam balance with the sliding weights positioned at specific points. We need to read the positions of the weights and sum them up to find the total mass.

##### Problem 1:
- Hundreds beam: Positioned at 200 g.
- Tens beam: Positioned at 30 g.
- Ones beam: Positioned at 4.5 g.
- Total mass: \( 200 + 30 + 4.5 = 234.5 \) g.

##### Problem 2:
- Hundreds beam: Positioned at 100 g.
- Tens beam: Positioned at 60 g.
- Ones beam: Positioned at 7.5 g.
- Total mass: \( 100 + 60 + 7.5 = 167.5 \) g.

##### Problem 3:
- Hundreds beam: Positioned at 100 g.
- Tens beam: Positioned at 30 g.
- Ones beam: Positioned at 4.5 g.
- Total mass: \( 100 + 30 + 4.5 = 134.5 \) g.

##### Problem 4:
- Hundreds beam: Positioned at 100 g.
- Tens beam: Positioned at 30 g.
- Ones beam: Positioned at 8.5 g.
- Total mass: \( 100 + 30 + 8.5 = 138.5 \) g.

#### Part 2: Make marks on the triple-beam balances to show the given masses

For each problem in Part 2, we need to position the sliding weights to match the given mass.

##### Problem 5:
- Given mass: 476.5 g.
- Hundreds beam: Position at 400 g.
- Tens beam: Position at 70 g.
- Ones beam: Position at 6.5 g.
- Mark these positions on the balance.

##### Problem 6:
- Given mass: 238.2 g.
- Hundreds beam: Position at 200 g.
- Tens beam: Position at 30 g.
- Ones beam: Position at 8.2 g.
- Mark these positions on the balance.

Final Answers:

#### Part 1:
1. \( \boxed{234.5} \) g
2. \( \boxed{167.5} \) g
3. \( \boxed{134.5} \) g
4. \( \boxed{138.5} \) g

#### Part 2:
- For Problem 5: Mark the hundreds beam at 400 g, the tens beam at 70 g, and the ones beam at 6.5 g.
- For Problem 6: Mark the hundreds beam at 200 g, the tens beam at 30 g, and the ones beam at 8.2 g.

Explanation:

- In Part 1, we read the positions of the sliding weights directly from the images and summed them to get the total mass.
- In Part 2, we decomposed the given mass into its hundreds, tens, and ones components and marked the corresponding positions on the balance.

This approach ensures accuracy and clarity in solving problems involving triple-beam balances.

Final Answer:
\[
\boxed{234.5, 167.5, 134.5, 138.5}
\]