## Engage NY Eureka Math 6th Grade Module 3 End of Module Assessment Answer Key

### Eureka Math Grade 6 Module 3 End of Module Assessment Answer Key

Question 1.

Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a computer program. Mr. Kindle receives a daily email that updates him on all his transactions from the previous day. This morning, his email read as follows:

Good morning, Mr. Kindle,

Yesterday’s investment activity included a loss of $800, a gain of $960, and another gain of $230. Log in now to see your current balance.

a. Write an integer to represent each gain and loss.

Description | Integer Representation |

Loss of $800 | |

Gain of $960 | |

Gain of $230 |

Answer:

Description | Integer Representation |

Loss of $800 | – 800 |

Gain of $960 | 960 |

Gain of $230 | 230 |

b. Mr. Kindle noticed that an error had been made on his account. The “loss of $800” should have been a “gain of $800.” Locate and label both points that represent “a loss of $800” and “a gain of $800” on the number line below. Describe the relationship of these two numbers when zero represents no change (gain or loss).

Answer:

– 800 and 800 are opposites.

c. Mr. Kindle wanted to correct the error, so he entered – (- $800) into the program. He made a note that read, “The opposite of the opposite of $800 is $800.” Is his reasoning correct? Explain.

Answer:

Yes, he is correct. The opposite of 800 is – 800, and the opposite of that is 800.

Question 2.

At 6:00 a.m., Buffalo, NY, had a temperature of 10°F. At noon, the temperature was – 10°F, and at midnight, it was – 20°F.

a. Write a statement comparing – 10°F and – 20°F.

Answer:

– 10°F is warmer than – 20°F.

b. Write an inequality statement that shows the relationship between the three recorded temperatures. Which temperature is the warmest?

Answer:

– 20 < – 10 < 10

10°F is the warmest temperature.

c. Explain how to use absolute value to find the number of degrees below zero the temperature was at noon.

Answer:

|- 10| = 10

The temperature at noon was 10° below zero.

d. In Peekskill, NY, the temperature at 6:00 a.m. was – 12°F. At noon, the temperature was the exact opposite of Buffalo’s temperature at 6:00 a.m. At midnight, a meteorologist recorded the temperature as – 6°F in Peekskill. He concluded that “For temperatures below zero, as the temperature increases, the absolute value of the temperature decreases.” Is his conclusion valid? Explain and use a vertical number line to support your answer.

Answer:

|- 12| = 12

|- 10| = 10

|- 6| = 6

The absolute values are decreasing.

Yes, his conclusion is valid. Absolute value is a number’s distance from zero. As the temperature increases from – 12 to – 10 to – 6 they get closer to zero, So their distance from zero is decreasing.

Question 3.

Choose an integer between 0 and – 5 on a number line, and label the point P. Locate and label each of the following points and their values on the number line.

Answer:

a. Label point A: the opposite of point P.

Answer:

3

b. Label point B: a number less than point P.

Answer:

– 5

c. Label point C: a number greater than point P.

Answer:

0

d. Label point D: a number halfway between point P and the integer to the right of point P.

Answer:

– 2.5

Question 4.

Julia is learning about elevation in math class. She decided to research some facts about New York State to better understand the concept. Here are some facts that she found.

- Mount Marcy is the highest point in New York State. It is 5,343 feet above sea level.
- Lake Erie is 210 feet below sea level.
- The elevation of Niagara Falls, NY, is 614 feet above sea level.
- The lobby of the Empire State Building is 50 feet above sea level.
- New York State borders the Atlantic Coast, which is at sea level.
- The lowest point of Cayuga Lake is 435 feet below sea level.

a. Write an integer that represents each location in relationship to sea level.

Mount Marcy | |

Lake Erie | |

Niagara Falls, NY | |

Empire State Building | |

Atlantic Coast | |

Cayuga Lake |

Answer:

Mount Marcy | 5,343 |

Lake Erie | – 210 |

Niagara Falls, NY | 614 |

Empire State Building | 50 |

Atlantic Coast | 0 |

Cayuga Lake | – 435 |

b. Explain what negative and positive numbers tell Julia about elevation.

Answer:

A negative number means the elevation is below sea level. A positive number means the elevation is above sea level.

c. Order the elevations from least to greatest, and then state their absolute values. Use the chart below to record your work.

Answer:

d. Circle the row in the table that represents sea level. Describe how the order of the elevations below sea level compares to the order of their absolute values. Describe how the order of the elevations above sea level compares to the order of their absolute values.

Answer:

The elevations below sea level have absolute values that are their opposites, so the order is opposite. – 435 < – 210 but 435 > 210. The elevations above sea level are the same as their absolute values, so the order is the same.

50 < 614 < 5,343

Question 5.

For centuries, a mysterious sea serpent has been rumored to live at the bottom of Mysterious Lake. A team of historians used a computer program to plot the last five positions of the sightings.

a. Locate and label the locations of the last four sightings: A (- 9\(\frac{1}{2}\), 0), B(- 3, – 4.75), C(9, 2), and D(8, – 2.5).

Answer:

b. Over time, most of the sightings occurred in Quadrant Ill. Write the coordinates of a point that lies in Quadrant III.

Answer:

(- 6, – 3)

c. What is the distance between point A and the point (9\(\frac{1}{2}\), 0)? Show your work to support your answer.

Answer:

d. What are the coordinates of point E on the coordinate plane?

Answer:

(5, 2)

e. Point F is related to point E. Its x-coordinate is the same as point E’s, but its y-coordinate is the opposite of point E’s. Locate and label point F. What are the coordinates? How far apart are points E and F? Explain how you arrived at your answer.

Answer:

The coordinates of F are (5, -2). Points E and F are 4 units apart. Since their x-coordinates are the same, I just counted the number of units from 2 to – 2 (between their y- Coordinates), and that is 4.