Worksheet Grade 7 Math
Willow Marsh Wetland: A Grade 7 Signed-Number Nitrogen Worksheet
A grade 7 worksheet where students add and subtract signed nitrogen-concentration changes through a fictional constructed wetland's four treatment cells.
Objectives
- Students will add and subtract positive and negative rational numbers to track a changing water-quality measurement.
- Students will interpret a signed running total against a stated discharge limit.
Vocabulary
Key words: constructed wetland, nitrogen concentration, biological uptake, net change
Teacher overview
Willow Marsh is a fictional constructed wetland that treats wastewater by routing it through four planted cells in sequence, where plants and microbes take up nitrogen and lower its concentration in the water. Along the way, two small stormwater inflow points add a little extra nitrogen back into the flow before it reaches the next cell, so the concentration does not simply fall step by step; it rises at some points and falls at others. This worksheet has students track that changing concentration using positive numbers for increases and negative numbers for decreases, then combine every step into one running total. A common misconception in this math is dropping the negative sign when adding a decrease to a running total, which makes the water appear more polluted at the end than the arithmetic actually shows.
Student Worksheet
Water enters Cell 1 of Willow Marsh with a nitrogen level of 12.5 mg/L. Willow Marsh is a fictional built wetland used for this worksheet. As the water flows through the wetland, each step below changes that level by the signed amount shown. Use these six changes, in order, for every problem below.
- Cell 1 (biological uptake): −3.2 mg/L
- Stormwater inflow A: +1.4 mg/L
- Cell 2 (biological uptake): −4.6 mg/L
- Cell 3 (biological uptake): −2.8 mg/L
- Stormwater inflow B: +0.9 mg/L
- Cell 4 (biological uptake): −1.5 mg/L
- Write an addition expression for the level after Cell 1. Then find its value.
- Find the level after stormwater inflow A is added.
- Find the level after Cell 2's uptake.
- Find the level after Cell 3's uptake.
- Find the level after stormwater inflow B is added.
- Find the final level leaving Cell 4, after its uptake.
- Add all six signed changes together as one sum. Then check: subtract the start level (12.5) from your answer to problem 6. Do the two totals match?
- Willow Marsh has a discharge limit (fictional, for this worksheet) of 3.0 mg/L for water leaving Cell 4. Does the water above meet that limit? By how much? Use a signed number to show above or below the limit.
- Suppose inflow B turns out larger than planned. It adds 2.5 mg/L instead of 0.9 mg/L. Every other change stays the same. Find the new final level leaving Cell 4.
- Using your answer to problem 9, does the water still meet the 3.0 mg/L limit? Explain with a signed number.
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: 9.3 mg/L.
12.5 + (−3.2) = 9.3 mg/L. - Answer: 10.7 mg/L.
9.3 + 1.4 = 10.7 mg/L. - Answer: 6.1 mg/L.
10.7 + (−4.6) = 6.1 mg/L. - Answer: 3.3 mg/L.
6.1 + (−2.8) = 3.3 mg/L. - Answer: 4.2 mg/L.
3.3 + 0.9 = 4.2 mg/L. - Answer: 2.7 mg/L.
4.2 + (−1.5) = 2.7 mg/L. - Answer: −9.8 mg/L, and yes it matches.
Adding all six changes: −3.2 + 1.4 − 4.6 − 2.8 + 0.9 − 1.5 = −9.8 mg/L. Subtracting the start from the end gives the same result: 2.7 − 12.5 = −9.8 mg/L. - Answer: yes, it is 0.3 mg/L below the limit (−0.3 mg/L).
2.7 − 3.0 = −0.3 mg/L; the negative sign shows the exiting water is under the 3.0 mg/L limit. - Answer: 4.3 mg/L.
Replacing +0.9 with +2.5 changes the sum of changes by +1.6 mg/L, so the new total change is −9.8 + 1.6 = −8.2 mg/L, and the new final concentration is 12.5 + (−8.2) = 4.3 mg/L. - Answer: no, exceeds by 1.3 mg/L (+1.3 mg/L).
The new exiting concentration (4.3 mg/L) is above the 3.0 mg/L limit; 4.3 − 3.0 = +1.3 mg/L over the limit, so the water would not meet the permit in this scenario.
Differentiation
Support (below grade level)
Provide a printed running-total table with the starting value (12.5) already filled in and blank cells for each of the six steps, so students only need to add one signed number at a time. Allow students to use a calculator for the addition once they have written the correct signed expression.
Extension (above grade level)
Ask students to find, using only addition and subtraction of the same six changes in a different order, whether the final concentration would be different if Cell 4's uptake happened before stormwater inflow B instead of after. Have them explain why the order of the same set of changes does or does not change the final total.
ELL supports
Provide a simple flow diagram of Willow Marsh's four cells and two inflow points, with up and down arrows next to each step to show whether nitrogen increases or decreases there. Allow students to show their signed-number reasoning using the arrows plus the running-total numbers rather than full written sentences.
Extensions
Have students design their own six-step sequence of positive and negative changes for Willow Marsh (the fictional constructed wetland used in this worksheet), keeping the same starting concentration of 12.5 mg/L, that still ends at or below the 3.0 mg/L discharge limit, and show the addition that proves it works.