Question

The table below shows the temperature changes one winter morning in Denver, Colorado over a 4-hour period after a cold front came through. ​3:00 am-4:00 am ​-6oF 4:00 am-5:00 am ​-4oF​ ​5:00 am-6:00 am ​-3oF ​6:00 am-7:00 am ​5oF Part A If the beginning temperature was -1°F at 3:00 a.m., what was the temperature at 7:00 a.m.? oF Part B A different cold front hit New York City, NY that day. The temperature dropped by 5℉ each hour from 3:00 a.m. to 6:00 a.m. What was the beginning temperature at 3:00 a.m. if the temperature at 6:00 a.m. was −10℉? oF ​Part C ​In answering part (b), Mark and Keisha used different methods. Keisha said her method involved multiplication, while Mark said he did not use multiplication. Both students arrived at the correct answer. How is this possible? Explain. ​

Answer 1

Part A: The temperature in Denver at 7:00 am was -9°F, decreasing from -1°F.

Part B: In NYC, starting at 3:00 am was 5°F, decreasing 5°F/hour.

Part C: Keisha multiplied, Mark added; both reached the correct answer, showcasing diverse valid approaches.

**Part A:**

The temperature changes are given as follows:

- From 3:00 am to 4:00 am: -6°F

- From 4:00 am to 5:00 am: -4°F

- From 5:00 am to 6:00 am: -3°F

- From 6:00 am to 7:00 am: +5°F

Starting at -1°F at 3:00 am, we can calculate the temperature at 7:00 am by adding the changes successively:

-1°F - 6°F - 4°F - 3°F + 5°F = -9°F

Therefore, the temperature at 7:00 am was -9°F.

**Part B:**

Given that the temperature dropped by 5°F each hour from 3:00 am to 6:00 am, and the temperature at 6:00 am was -10°F, we can calculate the beginning temperature at 3:00 am:

-10°F + 5°F + 5°F + 5°F = 5°F

Therefore, the beginning temperature at 3:00 am was 5°F.

**Part C:**

Keisha's method involves multiplication, and Mark's method does not, yet both arrived at the correct answer. This is possible if Keisha multiplied the rate of change (-5°F per hour) by the number of hours, while Mark might have added the changes individually. For example:

Keisha:
`\( -5°F/hour * 3 \text{ hours} = -15°F \)`

Mark:
`\( -5°F + (-5°F) + (-5°F) = -15°F \)`

Both methods yield the same result, showing that there are multiple valid approaches to solving the problem, and the choice of method may vary based on personal preference or mathematical understanding.