6th Grade Math End of Course Exam Review Answers

Engage NY Eureka Math sixth Class Module 3 Finish of Module Assessment Answer Primal

Eureka Math Grade half-dozen Module 3 End of Module Assessment Answer Central

Question ane.
Mr. Kindle invested some money in the stock market place. 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 twenty-four hours. This morning, his email read as follows:
Adept forenoon, Mr. Kindle,
Yesterday's investment activeness included a loss of $800, a proceeds 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:

Clarification	Integer Representation
Loss of $800	– 800
Gain of $960	960
Proceeds 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 characterization both points that represent "a loss of $800" and "a gain of $800" on the number line beneath. Describe the human relationship of these ii numbers when zip represents no change (gain or loss).

Answer:

– 800 and 800 are opposites.

c. Mr. Kindle wanted to correct the error, then 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 reverse 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, information technology was – 20°F.
a. Write a statement comparing – ten°F and – 20°F.

Answer:
– x°F is warmer than – 20°F.

b. Write an inequality argument that shows the relationship between the 3 recorded temperatures. Which temperature is the warmest?
Answer:
– twenty < – x < 10
10°F is the warmest temperature.

c. Explain how to apply 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.thou. was – 12°F. At noon, the temperature was the exact opposite of Buffalo's temperature at vi:00 a.m. At midnight, a meteorologist recorded the temperature every bit – 6°F in Peekskill. He ended that "For temperatures below zero, every bit 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.
Reply:

|- 12| = 12
|- x| = x
|- 6| = 6
The absolute values are decreasing.

Yes, his determination is valid. Absolute value is a number's distance from cypher. As the temperature increases from – 12 to – 10 to – six 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 bespeak P. Locate and label each of the following points and their values on the number line.

Reply:

a. Label indicate A: the reverse of point P.
Reply:
three

b. Characterization bespeak B: a number less than bespeak P.
Answer:
– 5

c. Label point C: a number greater than point P.
Answer:
0

d. Label point D: a number halfway betwixt point P and the integer to the right of point P.
Answer:
– 2.5

Question 4.
Julia is learning well-nigh height in math course. She decided to enquiry some facts about New York State to better sympathize the concept. Here are some facts that she found.

• Mount Marcy is the highest point in New York Land. It is 5,343 feet above bounding main level.
• Lake Erie is 210 feet below body of water level.
• The tiptop of Niagara Falls, NY, is 614 feet above sea level.
• The lobby of the Empire Land Building is l anxiety in a higher place bounding main level.
• New York State borders the Atlantic Coast, which is at body of water level.
• The lowest indicate of Cayuga Lake is 435 feet below body of water level.

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

Mount Marcy
Lake Erie
Niagara Falls, NY
Empire State Building
Atlantic Declension
Cayuga Lake

Respond:

Mountain Marcy	5,343
Lake Erie	– 210
Niagara Falls, NY	614
Empire State Building	fifty
Atlantic Coast	0
Cayuga Lake	– 435

b. Explain what negative and positive numbers tell Julia virtually tiptop.
Respond:
A  negative number means the elevation is below sea level. A positive number ways the summit is higher up sea level.

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

Reply:

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 accented values.
Answer:
The elevations below bounding main level take absolute values that are their opposites, so the order is opposite. – 435 < – 210  but 435 > 210. The elevations above body of water level are the same as their accented 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 (- nine\(\frac{ane}{2}\), 0), B(- 3, – 4.75), C(9, 2), and D(8, – 2.v).
Answer:

b. Over fourth dimension, about of the sightings occurred in Quadrant Ill. Write the coordinates of a betoken that lies in Quadrant III.
Answer:
(- 6, – 3)

c. What is the distance between point A and the point (ix\(\frac{i}{2}\), 0)? Prove your piece of work to back up your respond.
Answer:

d. What are the coordinates of signal Due east on the coordinate aeroplane?
Answer:
(5, ii)

eastward. Point F is related to point E. Its x-coordinate is the aforementioned as point E's, just its y-coordinate is the reverse of bespeak E's. Locate and label signal F. What are the coordinates? How far apart are points Due east and F? Explain how you arrived at your reply.
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 (betwixt their y- Coordinates), and that is 4.

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