Math Buzz worksheet featuring fraction comparisons, multiplication problems, factor identification, and a data analysis task involving national park sizes.

Problem Breakdown and Solution:

The worksheet contains several sections, each with specific tasks. Let's solve them step by step.

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#### Section 1: Comparing Fractions
The task is to determine which comparison is true for the given fractions:
- $\frac{3}{4} < \frac{2}{3}$
- $\frac{3}{4} > \frac{2}{3}$
- $\frac{3}{4} = \frac{2}{3}$

Step 1: Compare $\frac{3}{4}$ and $\frac{2}{3}$.
To compare these fractions, we need a common denominator. The least common denominator (LCD) of 4 and 3 is 12.

Convert each fraction:
- $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
- $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

Now compare $\frac{9}{12}$ and $\frac{8}{12}$:
- Since $9 > 8$, it follows that $\frac{3}{4} > \frac{2}{3}$.

Answer: $\frac{3}{4} > \frac{2}{3}$

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#### Section 2: Finding Products
The task is to calculate the following products:
1. $55 \times 10$
2. $55 \times 100$
3. $55 \times 1,000$

Step 1: Calculate $55 \times 10$.
$$
55 \times 10 = 550
$$

Step 2: Calculate $55 \times 100$.
$$
55 \times 100 = 5,500
$$

Step 3: Calculate $55 \times 1,000$.
$$
55 \times 1,000 = 55,000
$$

Answers:
1. $55 \times 10 = 550$
2. $55 \times 100 = 5,500$
3. $55 \times 1,000 = 55,000$

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#### Section 3: Identifying Factors of 36
The task is to determine whether the given numbers are factors of 36:
- 9
- 18
- 13
- 16
- 12
- 8

A number is a factor of 36 if 36 can be divided by it without leaving a remainder.

Step 1: Check each number:
- $36 \div 9 = 4$ (no remainder, so 9 is a factor)
- $36 \div 18 = 2$ (no remainder, so 18 is a factor)
- $36 \div 13 = 2.769$ (remainder, so 13 is not a factor)
- $36 \div 16 = 2.25$ (remainder, so 16 is not a factor)
- $36 \div 12 = 3$ (no remainder, so 12 is a factor)
- $36 \div 8 = 4.5$ (remainder, so 8 is not a factor)

Answers:
- 9: Yes
- 18: Yes
- 13: No
- 16: No
- 12: Yes
- 8: No

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#### Section 4: Estimating Differences in National Park Sizes
The task involves comparing the sizes of national parks and estimating differences.

Given Data:
- Squaw Valley: 91,715 acres
- Great Basin: 77,180 acres
- Mesa Verde: 52,185 acres
- Bryce Canyon: 35,635 acres

##### Part 1: Estimate how much larger Squaw Valley is than Bryce Canyon.
Estimate by rounding each number to the nearest thousand:
- Squaw Valley: $91,715 \approx 92,000$
- Bryce Canyon: $35,635 \approx 36,000$

Calculate the difference:
$$
92,000 - 36,000 = 56,000
$$

Answer: Approximately 56,000 acres.

##### Part 2: Find the exact difference between Squaw Valley and Bryce Canyon.
Use the actual values:
$$
91,715 - 35,635 = 56,080
$$

Answer: Exactly 56,080 acres.

##### Part 3: Is your answer reasonable? Explain.
The estimated difference was 56,000 acres, and the exact difference is 56,080 acres. The estimate is very close to the exact value, so the answer is reasonable.

Explanation: Rounding to the nearest thousand introduces a small error, but it does not significantly affect the overall magnitude of the difference. Thus, the estimate is a good approximation.

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Final Answers:

1. Comparing Fractions: $\boxed{\frac{3}{4} > \frac{2}{3}}$
2. Finding Products:
- $55 \times 10 = \boxed{550}$
- $55 \times 100 = \boxed{5,500}$
- $55 \times 1,000 = \boxed{55,000}$
3. Factors of 36:
- 9: Yes
- 18: Yes
- 13: No
- 16: No
- 12: Yes
- 8: No
4. National Park Sizes:
- Estimated difference: $\boxed{56,000}$ acres
- Exact difference: $\boxed{56,080}$ acres
- Reasonable: Yes, because the estimate is very close to the exact value.