Recycling Drive: Signed Moves

Use number-line moves to track collection totals above and below a goal.

Model Collection Changes

The drive collects cans, bottles, and paper. Each station tracks kilograms above or below its own goal: 0 means exactly at the goal. Positive changes add material; negative changes remove material from the accepted total.

The can station is 4 kg below its goal. Volunteers add 7 kg of cans. Which move models −4 + 7?

A. Start at −4 and move 7 units left.B. Start at 4 and move 7 units left.C. Start at 7 and move 4 units right.D. Start at −4 and move 7 units right.

The bottle station is 5 kg above its goal. A sorting check removes 8 kg of unaccepted material. Start at 5 and model 5 + (−8).

What is the signed endpoint? kg relative to the goal

The paper station models −6 + (−3). What do the second addend's sign and absolute value tell you?

A. Move 3 units left from −6.B. Move 9 units right from −6.C. Move 3 units right from −6.D. Move 6 units left from −3.

On this number line, a can-station update starts at −8 and ends at −2.

What signed addend completes the update? −8 + = −2

The bottle station is 2 kg below its goal. Its next update is −2 + 0. Which description models this sum?

A. Start at −2 and move 2 units right.B. Start at −2 and move 0 units.C. Start at −2 and move 2 units left.D. Start at 0 and move 2 units right.

Return to the Goal

Use opposite numbers to identify changes that end at 0. Remember that 0 represents the goal, not an empty collection bin.

The paper station is 6.5 kg below its goal. One delivery brings it exactly to the goal.

How many kilograms does the delivery add? kg

A can-station update begins 9 kg above the goal and ends exactly at the goal.

What signed change completes the update? 9 + = 0

A bottle-station record shows −7 + 7 = 0. Which statement correctly interprets the result?

A. The station has no bottles left after the delivery.B. The station reaches its goal after the delivery.C. The station remains 7 kg below its goal.D. The station finishes 14 kg above its goal.

Which pair of paper-station changes has a total change of 0 kg?

A. Add 4 1/2 kg, then remove 4 kg.B. Remove 4 1/2 kg, then remove 4 1/2 kg.C. Add 4 1/2 kg, then remove 4 1/2 kg.D. Add 4 1/2 kg, then remove 1/2 kg.

Interpret the Updates

Apply signed addition to each new drive record. Keep the direction of a change separate from the position where it ends.

10.

The paper station is 1 3/4 kg below its goal. A student adds 1/2 kg of paper.

What is the new signed position? kg relative to the goal

11.

The bottle station starts 3.5 kg above its goal. A sorting check removes 5 kg from its accepted total. Which statement describes 3.5 + (−5)?

A. The result is −1.5 kg, or 1.5 kg below the goal.B. The result is 1.5 kg, or 1.5 kg above the goal.C. The result is −8.5 kg, or 8.5 kg below the goal.D. The result is 8.5 kg, or 8.5 kg above the goal.

12.

The can station begins 10 kg below its goal. A delivery adds 6 kg, and a second delivery adds 7 kg. Model the two updates in order.

What is the signed position after both deliveries? kg relative to the goal

13.

The paper station's goal is 40 kg. It has collected 34 kg, so its signed position is −6 kg. Another class adds 9 kg.

What is the station's new signed position relative to its goal? kg

14.

The bottle station is 8 kg below its goal and receives 5 kg of bottles. Amira says, “The endpoint is negative, so the move for −8 + 5 must go left.” Explain the mistake. State the start, direction, distance, endpoint, and what the endpoint means.