Worksheet Grade 7 Math
Verdin Brook Dissolved Oxygen: A Signed-Number Worksheet
A grade 7 signed-number worksheet on the fictional Verdin Brook, where students add and average positive and negative changes in dissolved oxygen downstream.
Objectives
- Students will add positive and negative decimal changes to track a measured value along a stream.
- Students will divide a total signed change by a count to find an average change.
Vocabulary
- Dissolved oxygen
- Dissolved oxygen is the oxygen gas mixed into water that fish and other underwater animals breathe. Cold, moving water holds more oxygen than warm, still water.
Also: downstream, average change
Teacher overview
Dissolved oxygen is the oxygen gas that fish and other stream life breathe from the water, and it rises and falls as water warms, mixes over rapids, or passes a pollution source. This worksheet follows a fictional stream, Verdin Brook, from an upstream station to a downstream one, giving students a chain of positive and negative changes to add. Most fish need dissolved oxygen above 5 mg/L, so several items ask students to compare a computed reading against that benchmark. A teaching note: students who are still shaky with signed numbers often treat every change as a subtraction, so remind them that a positive change means the level went up and to add it as written.
Student Worksheet
Verdin Brook is a fictional stream. Its dissolved oxygen, or DO, is measured in mg/L at five stations. Station 1 is farthest upstream. Most fish need DO above 5 mg/L. At Station 1 the DO is 8.4 mg/L. Moving downstream, the DO changes by these amounts:
- Station 1 to Station 2: −1.5
- Station 2 to Station 3: −2.1
- Station 3 to Station 4: +0.8
- Station 4 to Station 5: −1.2
- Find the DO at Station 2. Start from 8.4 and add the first change.
- Find the DO at Station 3.
- Find the DO at Station 4.
- Find the DO at Station 5.
- Add the four changes together to find the total change from Station 1 to Station 5.
- Now subtract the Station 1 DO from the Station 5 DO. Do you get the same total change?
- Which stations have DO below the 5 mg/L level that fish need?
- Divide the total change from item 5 by the 4 segments to find the average change per segment.
- The largest single drop is between Station 2 and Station 3. How many mg/L is that drop?
- Between Station 3 and Station 4 the DO rose. Explain why water tumbling over rapids can raise the dissolved oxygen.
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: 6.9 mg/L.
8.4 + (−1.5) = 6.9 mg/L. - Answer: 4.8 mg/L.
6.9 + (−2.1) = 4.8 mg/L. - Answer: 5.6 mg/L.
4.8 + 0.8 = 5.6 mg/L. - Answer: 4.4 mg/L.
5.6 + (−1.2) = 4.4 mg/L. - Answer: −4.0 mg/L.
(−1.5) + (−2.1) + 0.8 + (−1.2) = −4.0 mg/L. - Answer: Yes.
4.4 − 8.4 = −4.0 mg/L, the same total change found by adding the four steps. - Answer: Station 3 and Station 5.
Station 3 is 4.8 mg/L and Station 5 is 4.4 mg/L, both below the 5 mg/L level fish need. - Answer: −1.0 mg/L. −4.0 ÷ 4 segments = −1.0 mg/L on average per segment.
- Answer: 2.1 mg/L.
The change from Station 2 to Station 3 is −2.1, a drop of 2.1 mg/L. - Answer: Tumbling water mixes in air.
Fast water over rapids folds air into the stream, so more oxygen dissolves and the DO reading goes up.
Differentiation
Support
Give students a vertical number line marked from 0 to 10 and have them plot each station's reading as they compute it. Seeing 4.8 and 4.4 fall below the marked 5 line makes item 7 a reading task rather than a second calculation, and it reinforces that a negative change moves down the line.
Extension
Ask students to design a sixth change that would bring Station 6 back above the fish limit, state the change as a signed number, and show the addition that proves the new reading clears 5 mg/L. Then have them explain what real feature of a stream might cause that rise.
ELL supports
Pre-teach "rise," "drop," "upstream," and "downstream" with arrows on a simple stream sketch. Provide the sentence frame "The DO changed by ___, so the new reading is ___" so students can narrate their signed-number steps for items 1 through 4.
Extensions
If your class can visit a local stream or pond with a school dissolved-oxygen probe, take readings at two spots and record the change between them as a signed number. Keep the visit under adult supervision, have students sample from the bank or shallow, slow water only, and have everyone wash their hands afterward. Comparing a real measured change with the Verdin Brook data connects the arithmetic to a tool that water-quality technicians actually carry into the field.