Position, Speed, and Direction

Warmup

Activity #1

Use a Number Line to Fill a Table.

• Use the number line below to help you fill in the table that follows.

• After each move, record your location in the table.

Then write an expression to represent the ending position that uses the starting position, the speed, and the time. The first row is done for you. If you get stuck, use the number line above to help you.

Activity #2

Use a Number Line to Fill a Table.

A traffic safety engineer was studying travel patterns along a highway. She set up a camera and recorded the speed and direction of cars and trucks that passed by the camera. Positions to the east of the camera are positive, and to the west are negative.

Vehicles that are traveling towards the east have a positive velocity, and vehicles that are traveling towards the west have a negative velocity.

• Use the number line below if you get stuck on filling in the table that follows.

• Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period.

(1.) Then write an equation.

(2.) If a car is traveling east when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera?

(3.) If we multiply two positive numbers, is the result positive or negative?

(4.) If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera?

(5.) If we multiply a negative and a positive number, is the result positive or negative?

Activity #3

Plot Positions on a Number Line.

• Study the following Diagrams and answer the questions that follow.

A number line can represent positions that are north and south of a truck stop on a highway. Decide whether you want positive positions to be north or south of the truck stop.

• Then plot the following positions on a number line.

• The truck stop
• 5 miles north of the truck stop
• 3.5 miles south of the truck stop

(2.) How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words “east” and “west”?

Four people are cycling. They each start at the same point. (0 represents their starting point.)

• Plot their finish points after five seconds of cycling on the number line below.

Challenge #1

(1.) An airplane moves at a constant speed of 120 miles per hour for 3 hours.

(2.) A train moves at constant speed and travels 6 miles in 4 minutes.

(3.) A car moves at a constant speed of 50 miles per hour.

Challenge #2

In many contexts we can interpret negative rates as “rates in the opposite direction.” For example, a car that is traveling -35 miles per hour is traveling in the opposite direction of a car that is traveling 40 miles per hour.

(1.) What could it mean if we say that water is flowing at a rate of -5 gallons per minute?

(2.) Make up another situation with a negative rate, and explain what it could mean.

Challenge #3

In many contexts we can interpret negative rates as “rates in the opposite direction.” For example, a car that is traveling -35 miles per hour is traveling in the opposite direction of a car that is traveling 40 miles per hour.

(1.) What could it mean if we say that water is flowing at a rate of -5 gallons per minute?

(2.) Make up another situation with a negative rate, and explain what it could mean.

Quiz Time

https://www.ixl.com/math/grade-7/follow-directions-on-a-coordinate-plane