Backstage Numbers: Sets, Seats, and Signs

Use signed numbers to describe positions, changes, and differences from a target.

Set Positions

The stage floor is the reference height, 0. Heights above the floor are positive; heights below it are negative.

The top of a platform is 65 centimeters above the stage floor.

Write its signed height: cm

The bottom of a recessed storage space is 38 centimeters below the stage floor.

Write its signed height: cm

The set crew records these heights. Which statement describes the cable opening?

Set Measurements
Set feature	Signed height (cm)
Window ledge	+95
Cable opening	−18
Doorway base	0

A. It is 18 cm above the stage floor.B. It is 18 cm below the stage floor.C. It is 95 cm below the stage floor.D. It is level with the stage floor.

A new ramp ends at a signed height of 0 cm. What does that tell the crew?

A. The ramp has no length.B. The ramp is below the floor.C. The ramp is above the floor.D. The ramp ends at floor level.

A hanging panel has one edge 1.5 meters above the stage floor. The crew marks a second point the same distance below the floor.

Write the signed height of the second point: m

Seat-Sale Changes

The ticket desk records changes in the number of seats sold. New sales are positive; canceled sales are negative. A change of 0 means the number sold stays the same.

During lunch, customers buy 23 seats. There are no cancellations during lunch.

Write the signed change in seats sold: seats

A group cancels its purchase of 9 seats. No other sales change at that time. Which entry represents this change?

A. The entry is −9 seats.B. The entry is +9 seats.C. The entry is 0 seats.D. The entry is −1 seat.

Match each ticket-desk event to its signed change in seats sold.

The ticket desk reports a change of 0 seats during an hour. Which conclusion must be true?

A. No seats have been sold for the show.B. Every seat for the show has been sold.C. The number of seats sold did not change.D. No customers contacted the ticket desk.

10.

For a new seating report, the club records changes in seats still available, rather than seats sold. An increase in seats available is positive. A customer cancels 6 sold seats, making those seats available again.

Write the signed change in seats available: seats

Compare Spending with the Plan

For each set supply, the club records actual spending compared with planned spending. Positive means over the plan; negative means under the plan; 0 means exactly on the plan.

11.

The crew spends $17 less than planned on fabric for the set.

Write the signed difference from the plan: dollars

12.

Which supply cost more than planned?

Spending Differences
Supply	Difference (dollars)
Paint	−12
Fasteners	0
Wood	+28
Tape	−5

A. Paint cost more than planned.B. Fasteners cost more than planned.C. Tape cost more than planned.D. Wood cost more than planned.

13.

The club planned to spend $72 on a backdrop and spent exactly $72.

Write the signed difference from the plan: dollars

14.

Amira says, “A spending difference of −8 dollars means the club has no money. A difference of 0 dollars means the supplies were free.” Explain both mistakes using the club's spending convention.