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Which option will balance the weighing scale?

To solve this balance puzzle, we need to compare the items on each side of the scales and determine which option from the provided set will balance the scales.

### First Balance (Top)
- **Left Side:** 1 half-circle (orange), 2 triangles (orange), 3 purple squares.
- **Right Side:** 3 purple squares, 3 orange triangles.

From this, we can infer that:
- 1 half-circle + 2 triangles + 3 squares is equivalent to 3 squares + 3 triangles.

### Second Balance (Bottom)
- **Left Side:** 1 half-circle.

We need to figure out what set of shapes from the given options will balance with 1 orange half-circle.

Based on the top scale:
- 1 half-circle + 2 triangles + 3 squares = 3 squares + 3 triangles.
- Therefore, 1 half-circle must equal 1 triangle + 1 square (since removing the common terms on both sides leaves the half-circle equivalent to 1 triangle and 1 square).

### Comparing Options:
We need an option that includes 1 triangle and 1 square to balance the half-circle.

- **Option 1:** 4 purple squares → Not balanced.
- **Option 2:** 1 triangle, 1 half-circle, 2 squares → Not balanced (extra half-circle).
- **Option 3:** 4 orange squares → Not balanced.
- **Option 4:** 2 triangles, 2 purple squares → Balanced! 1 triangle + 1 square is equivalent to the half-circle.
- **Option 5:** 3 triangles → Not balanced.

Thus, **Option 4** is the correct answer, as it will balance the scale.

Do you want further details on this explanation, or do you have any questions?

### Here are 5 related questions to think about:
1. How would you set up an equation to represent the balance from the first scale?
2. Can you use algebra to solve a similar puzzle with different shapes and weights?
3. How can you simplify puzzles by identifying common elements on both sides?
4. What strategies are helpful in analyzing balance problems without using numbers?
5. How can we check that Option 4 balances the scale mathematically?

### Tip:
In balance puzzles, look for elements that appear on both sides of the scale. Canceling them out simplifies the problem.

Solve this balance puzzle involving geometric shapes such as half-circles, triangles, and squares. Learn how to compare and balance different shapes using logical reasoning and pattern recognition. Suitable for students in Grades 4-6.

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