Balance a carbon reservoir

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Final carbon stock equals starting stock plus inflow minus outflow. Formula: a+b-c. Variable key: a = initial carbon stock (model units), b = annual inflow (same units), c = annual outflow (same units)
• Distinct worked inputs and result: A distinct stock starts at 90 units, receives 14 and loses 11: 90+14-11=93 units.
• Assessment case 1: Supplied case 1: initial carbon stock (model units)=100; annual inflow (same units)=15; annual outflow (same units)=10, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?
• Assessment case 2: Supplied case 2: initial carbon stock (model units)=150; annual inflow (same units)=20; annual outflow (same units)=25, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?
• Assessment case 3: Supplied case 3: initial carbon stock (model units)=200; annual inflow (same units)=30; annual outflow (same units)=18, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?
• Assessment case 4: Supplied case 4: initial carbon stock (model units)=80; annual inflow (same units)=12; annual outflow (same units)=16, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?
• Assessment case 5: Supplied case 5: initial carbon stock (model units)=120; annual inflow (same units)=25; annual outflow (same units)=20, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?
• Assessment case 6: Supplied case 6: initial carbon stock (model units)=180; annual inflow (same units)=24; annual outflow (same units)=30, using the explicitly named quantities. Final carbon stock equals starting stock plus inflow minus outflow. What result follows?

Learn the idea

A stock is an amount at a time; a flow is an amount per interval. This fictional closed accounting model supplies every inflow and outflow for one year.

Final carbon stock equals starting stock plus inflow minus outflow. The formula in the supplied model is a+b-c. Variable key: a = initial carbon stock (model units), b = annual inflow (same units), c = annual outflow (same units). Use the same interval for flows. Do not confuse stock with yearly flow.

A distinct stock starts at 90 units, receives 14 and loses 11: 90+14-11=93 units. Real accounting may include unmeasured pathways. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with initial carbon stock (model units)=101; annual inflow (same units)=15; annual outflow (same units)=10. Expected result: 106 model carbon units. Explain what changes and keep this assumption: Real accounting may include unmeasured pathways.

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