Worksheet Grade 7 Math
Havenmere Reservoir Water Budget: A Grade 7 Signed-Number Worksheet
A grade 7 worksheet where students add positive inflows and negative losses to track a fictional reservoir's level change over a week using rational numbers.
Objectives
- Students will add positive and negative rational numbers to find a reservoir's net level change.
- Students will use a starting level and signed daily changes to find a later reservoir reading.
Vocabulary
- Reservoir
- A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
- Water budget
- A water budget is a way of tracking all the water coming into an area, like rain and snowmelt, against all the water leaving it, like evaporation and streamflow. Scientists use water budgets to see whether a watershed or aquifer is gaining or losing water over time.
Also: inflow, net change
Teacher overview
A water budget adds up everything that raises a reservoir and subtracts everything that lowers it. The fictional Havenmere Reservoir gains water from rain and inflow and loses water to evaporation, releases, and withdrawals. This worksheet has students write each daily change as a signed number and add them to track the level. Watch for the common error of dropping the negative sign when adding, which turns a loss into a gain and throws off the whole week.
Student Worksheet
A gauge measures the water level at Havenmere Reservoir. This table lists the level change for each day of one week. A plus sign means the level rose; a minus sign means it fell.
| Day | Level change (feet) |
|---|---|
| Monday | +1.5 |
| Tuesday | −0.8 |
| Wednesday | −1.2 |
| Thursday | +2.3 |
| Friday | −0.5 |
| Saturday | −0.9 |
| Sunday | +0.4 |
- Monday the level rose 1.5 feet and Tuesday it fell 0.8 foot. Add the two signed numbers to find the total change over those two days.
- Find the net change in level from Monday through Wednesday.
- Find the net change in level from Monday through Thursday.
- Add all seven daily changes to find the net change for the whole week.
- The gauge read 24.0 feet early Monday. What does it read Sunday night?
- Which single day had the greatest drop, and how many feet did the level fall that day?
- Add just the three days when the level fell by more than half a foot: Tuesday, Wednesday, and Saturday. What is that total fall?
- Suppose next week has no inflow and evaporation lowers the level 0.3 foot each day for 7 days. Write this as a product of signed numbers and find the total change.
- The dam must release water when the level rises above 26.0 feet. Starting from your Sunday-night reading, how many more feet of rise would reach that release line?
- Explain why you get the same weekly net change no matter what order you add the seven daily numbers.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
- Answer: +0.7 foot. (+1.5) + (−0.8) = 0.7, so the level was 0.7 foot higher after Tuesday.
- Answer: −0.5 foot. 1.5 + (−0.8) + (−1.2) = 1.5 − 2.0 = −0.5, a net drop of half a foot.
- Answer: +1.8 feet. Add Thursday's +2.3 to the −0.5 from item 2: −0.5 + 2.3 = 1.8 feet.
- Answer: +0.8 foot. 1.5 − 0.8 − 1.2 + 2.3 − 0.5 − 0.9 + 0.4 = 0.8, so the reservoir ended the week 0.8 foot higher.
- Answer: 24.8 feet. Start of 24.0 feet plus the week's net change of +0.8 foot: 24.0 + 0.8 = 24.8 feet.
- Answer: Wednesday, 1.2 feet. Wednesday's −1.2 is the largest drop, more than Saturday's −0.9, Tuesday's −0.8, and Friday's −0.5.
- Answer: −2.9 feet. (−0.8) + (−1.2) + (−0.9) = −2.9, a total fall of 2.9 feet across the three days.
- Answer: −2.1 feet. (−0.3) × 7 = −2.1, so the level would drop 2.1 feet over the week.
- Answer: 1.2 feet. From the Sunday reading of 24.8 feet, the release line of 26.0 feet is 26.0 − 24.8 = 1.2 feet higher.
- Answer: Adding rational numbers is commutative and associative, so the seven values can be grouped and reordered in any way. Every order gives the same sum, which is why the weekly net change does not depend on the order.
Differentiation
Support
Give students a number line marked in tenths so they can model each addition as a move right for a rise and left for a fall. Provide a running-total column beside the table so they add one day at a time instead of all at once.
Extension
Ask students to design a different seven-day set of changes that ends with a net change of exactly zero, then explain what balance between gains and losses makes the net change zero.
ELL supports
Pre-teach "inflow," "net change," and "water budget" with up and down arrows beside the words. Provide the sentence frame "The level changed by ___ feet, so the total is ___" and allow students to answer items 6 and 10 with a labeled number line.