Worksheet

School Roof Solar: Balancing the Changes

Interpret opposite quantities that combine to zero using energy records, roof loads, and plans for a school solar project.

Grade 7MathInteractive · Printable

Aligned to7.NS.A.1.a

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1 Common Core standard
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14 questions
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Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students identify opposite quantities with equal magnitudes and opposite signs.
Students interpret zero net change in rooftop solar project situations.
Students determine quantities needed to balance energy, mass, and project adjustments.

How to use

Have students identify the quantity and units before deciding whether changes cancel. Discuss why opposite directions alone are not enough to make zero.

Curriculum

Common Core standard covered

7.NS.A.1.a

Describe situations where opposite quantities combine to make 0, like gaining and then losing the same amount.

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School Roof Solar: Balancing the Changes

Interpret opposite quantities in a rooftop solar project.

Read the Energy Balance

The school is installing rooftop solar panels. In these energy records, energy entering the school's battery is positive and energy leaving it is negative. Energy is measured in kilowatt-hours (kWh). Ignore energy losses.

During one test interval, the panels send 7 kWh into the battery while school equipment draws 7 kWh from it. Which statement describes the battery's net energy change?

A. The net change is +14 kWh because both amounts count.
B. The net change is +7 kWh because panels produce energy.
C. The net change is −7 kWh because equipment uses energy.
D. The net change is 0 kWh because equal opposite amounts balance.

Select every statement that must be true when two nonzero signed energy changes are opposites.

Their magnitudes are equal.Both changes are positive.Their signs are different.Their combined change is zero.The positive change has a greater magnitude.

The battery monitor records a net change of zero during a test. One energy transfer is shown in the table.

Battery Test
Transfer	Signed energy (kWh)
Energy entering	?
Energy leaving	−2.75

What positive signed value belongs in the missing cell? kWh

Which description fits the equation +4.5 + (−4.5) = 0 in the battery's energy record?

A. The battery receives 4.5 kWh and supplies 4.5 kWh.
B. The battery supplies 4.5 kWh and supplies 4.5 kWh more.
C. The battery receives 4.5 kWh and receives 4.5 kWh more.
D. The battery receives 4.5 kWh and supplies no energy.

During a demonstration, the panels send 3/4 kWh into the battery. A lamp and a fan draw energy from it. Which plan makes the battery's net energy change zero?

A. The lamp draws 1/2 kWh and the fan draws 1/2 kWh.
B. The lamp draws 1/4 kWh and the fan draws 1/2 kWh.
C. The lamp draws 3/4 kWh and the fan draws 1/4 kWh.
D. The lamp draws 1/4 kWh and the fan draws 1/4 kWh.

Balance the Project Plans

Identify what is changing and check the units. Quantities cancel only when they describe equal amounts of the same quantity in opposite directions.

Adding equipment increases the mass on the roof; removing equipment decreases it. Which installation plan leaves the total mass on the roof unchanged?

Installation Plans
Plan	Mass added (kg)	Mass removed (kg)
Cedar	48	42
Birch	54	54
Elm	42	48
Maple	54	45

A. The Birch plan leaves the mass unchanged.
B. The Maple plan leaves the mass unchanged.
C. The Elm plan leaves the mass unchanged.
D. The Cedar plan leaves the mass unchanged.

Each of four new panels adds 12 kg to the roof. The installer will remove old equipment so that the total mass on the roof does not change.

What signed mass change must the removal produce? kg

In a roof layout, eastward movement is positive and westward movement is negative. A mounting rail is shifted 5/8 meter west. Which movement would cancel that shift?

A. Shift the rail 3/8 meter east.
B. Shift the rail 5/8 meter east.
C. Shift the rail 8/5 meter east.
D. Shift the rail 5/8 meter west.

Select every project record in which the two changes can combine to make zero. Consider both the amounts and what they measure.

A roof load increases by 16 kg and decreases by 16 kg.A delivery adds 8 panels and a cleanup removes 8 kg of packing.A project fund receives $65 and pays out $65.A battery receives 2 kWh and supplies 3 kWh.A rail moves 0.4 meter north and then 0.4 meter south.

10.

A design revision adds 2 1/2 m² of panel-covered area to the roof plan. The designers also remove an equal area of planned panels elsewhere. Increases in panel-covered area are positive.

What is the combined signed change in panel-covered area? m²

Check the Claims

Use opposite quantities to evaluate the project team's conclusions.

11.

The energy record contains +5 kWh and −4 kWh. Jordan says the changes cancel because one is positive and one is negative. Which correction is valid?

A. They cancel because both changes use kilowatt-hours.
B. They do not cancel because neither entry is zero.
C. They do not cancel because the magnitudes differ.
D. They cancel because the two signs are different.

12.

During a battery test, the panels supply two equal energy inputs. School equipment draws 9 kWh in total. These are the only transfers, and the net energy change is zero.

How much energy does each input supply? kWh

13.

The battery's net energy change is zero during a test. Which additional record would prove that energy moved both into and out of the battery?

A. The roof held twelve panels throughout the test.
B. The battery monitor stayed on throughout the test.
C. The battery received 1.25 kWh during the test.
D. The test began at the scheduled starting time.

14.

Two groups of rooftop panels each send 1.5 kWh into the battery. School equipment draws 3 kWh. These are the only transfers. Priya says, “The net change cannot be zero because no single positive entry is the opposite of −3.” Explain why the net change is zero even without a single +3 entry. Include an equation.