Unit 1 Learning Task: Helicopters and Submarines Name: ______

Standards - MCC7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a Describe situations in which opposite quantities combine to make 0.

b Understand as the number located a distance from, in the positive or negative direction depending on whether is positive or negative. Show that a number and its opposite have a sum of 0 (additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c Understand subtraction of rational numbers as adding the additive inverse, . Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d Apply properties of operations as strategies to add and subtract rational numbers.

You are in charge of testing new equipment that can detect underwater submarines form the air. This is the data that you will have to consider while testing the equipment.

Part 1 – The First Three Hours

During this part of the test, you are in a helicopter maintaining an exact distance of 250feet above the surface of the ocean. What integer would be used to represent the location of the helicopter? ______The helicopter moves horizontally (not vertically) across the surface to remain directly above the submarine. The submarine begins the test positioned at 275 feet below sea level. What real number would be used to represent the starting positions of the submarine? ______

  1. During the first hour, the submarine descended another -50.8 feet. To figure the depth of the submarine at the end of the first hour, addthe depth the submarine began the experiment plusthe distance the submarine descended the first hour. This will equal the depth of the submarine at the end of first hour. ______+ ______= ______
  1. During the second hour, the submarine dove another -23 feet. To figure the depth of the submarine at the end of the second hour, addthe depth of the submarine at the end of the first hourplusthe distance the submarine descended the second hour. This will equal the depth of the submarine at the end of second hour. ______+ ______= ______
  1. During the third hour, the submarine dove again. It descended an amount equal to the average of the first two dives. To find the average of the first two dives, add the first descent to the second decent and divide by 2 (______+ ______) / 2 = ______the distance the submarine dove the third hour.To figure the depth of the submarine at the end of the third hour, addthe depth of the submarine at the end of the second hourplusthe distance the submarine descended the third hour. This will equal the depth of the submarine at the end of third hour. ______+ ______= ______

Enter your data in the table below. Remember, although we are using the absolute value to compute the distances, the submarines numbers will always be negative numbers.

Time / Helicopter Position in feet / Submarine Position in feet / Mathematical Sentence
Use absolute value for distances. / Distance between
Helicopter and Submarine
Start / ‌
hour
1
hour
2
hour
3

Part 2 – The Next Three Hours

The equipment in the helicopter is able to detect the submarine within a total distance of 750 feet. For each scenario, determine the maximum or minimum location for the other vehicle in order for the helicopter to detect the submarine; and write a mathematical sentence to show your thinking. Enter your data in the table below.

  1. During the fourth hour, the helicopter remains 250 feet above the surface of the ocean.

What is the minimum depth of the submarine?______

What is the maximum depth the submarine can go and still be detected?______

  1. During the fifth hour, the submarine returns to the same depth that it was at the end of the third hour, which is ______.

If the submarine stays at this depth and the helicopter moves, what is the minimum height the helicopter? ______

What is the maximum height the helicopter can go and still detect the submarine?______

  1. At the end of the sixth hour, the helicopter is free to move as needed and the submarine descends to three times the depth of its second hour position. The depth of the submarine at the end of the second hour ______times 3 = ______the depth at the end of the sixth hour.

At this depth, is the helicopter able to detect the submarine? ______Why or Why Not?

Time / Position of
The Helicopter / Position of
The Submarine / Mathematical Sentence
Use the absolute value when computing the distances. / Distance between the
Helicopter and the
Submarine
hour
4 / Minimum (do not graph)
Maximum (graph)
hour
5 / Minimum (do not graph)
Maximum (graph)
hour
6 / 0 ft

1