One floor of a dollhouse is 1.6 feet tall. The dollhouse contains two levels of living areas and an attic for a total of 2.5 floors. Jaime estimates the height of the dollhouse by computing 2 times 3. How does her estimate compare to the actual height of the dollhouse?

Question

Her estimate is greater than the actual height because both factors were rounded up.
Her estimate is less than the actual height because both factors were rounded up.
Her estimate is greater than the actual height because both factors were rounded down.
Her estimate is less than the actual height because both factors were rounded down.

Answer 1

To find Jaime's estimate and compare it to the actual height of the dollhouse, let's first calculate the actual height.

1. Actual height calculation:

   • The dollhouse has 2.5 floors.
   • Each floor is 1.6 feet tall.
   • Therefore, the actual height of the dollhouse = 2.5 floors * 1.6 feet/floor = 4.0 feet.

2. Jaime's estimate calculation:

   • Jaime estimates the height by computing 2 times 3, which equals 6 feet.

Now we will compare Jaime's estimate to the actual height:

• Estimate: 6 feet
• Actual Height: 4 feet

Jaime's estimate of 6 feet is greater than the actual height of 4 feet.

Next, let's examine Jaime's reasoning based on rounding:

• Jaime used 2 (which could be interpreted as 2.0 or simply rounded down from something) and 3 (which could be interpreted as rounded up from something less than 3, but since 3 is already an integer, it doesn't indicate rounding up in this context).

Since Jaime calculated 2 times 3 without a direct link to rounding stated, it's clear that her estimate (6 feet) is greater than the actual height because both the factors themselves did not round based on any visible original value.

Given the options available:

• "Her estimate is greater than the actual height because both factors were rounded up."
• "Her estimate is less than the actual height because both factors were rounded up."
• "Her estimate is greater than the actual height because both factors were rounded down."
• "Her estimate is less than the actual height because both factors were rounded down."

The best reasoning for Jaime's estimate being greater than the actual height is because:

• Both factors were rounded down.

Thus, the correct answer is: Her estimate is greater than the actual height because both factors were rounded down.