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🔬 Science · Scientific Reasoning · Lesson 6 of 6 · 5 min

Predicting relationships: direct, inverse and food-web effects

🔮 Science is useful because it predicts. TEAS items ask what happens next when one part of a system changes.

💡 Key idea

Direct = same direction, inverse = opposite directions; follow each link in a chain to predict the effect.

🧠 The idea

In a DIRECT relationship, two variables change in the same direction: as one increases, the other increases (more exercise, higher heart rate). In an INVERSE relationship, they change in opposite directions: as one increases, the other decreases (as altitude rises, air pressure falls). To predict, find the rule in the data, then apply it to the new value, staying close to the tested range. In a FOOD CHAIN, energy passes from producers (plants) to primary consumers (herbivores) to secondary consumers and beyond; only about 10% of the energy passes to each next level. A change at one level ripples through the others. In PREDATOR-PREY cycles, more prey lets predators increase; then predators eat more prey, so prey fall; then predators fall from lack of food, and the cycle repeats, with predator peaks lagging behind prey peaks. If-then reasoning works the same way: state the change, follow the links, predict the effect.

✏️ Worked example

Food chain: grass → rabbits → foxes. A disease kills most of the foxes. Predict the effects. Step 1: fewer foxes means fewer rabbits are eaten, so rabbits increase. Step 2: more rabbits eat more grass, so grass decreases. Step 3: over time, with less grass, the rabbit population may drop again. A second example: a table shows that doubling the pressure on a gas at constant temperature halves its volume (10 L at 1 atm, 5 L at 2 atm). This is an inverse relationship, so at 4 atm you would predict 2.5 L.

📌 Takeaways

  • Direct: both go up or both go down. Inverse: one up, one down.
  • Food chains: follow each link; about 10% of energy moves up each level.
  • Predator peaks follow prey peaks in a repeating cycle.

✅ Check yourself

Question 1 of 3

As the number of people sharing a pizza increases, the number of slices each person gets decreases. What kind of relationship is this?

  1. Constant
  2. Random
  3. Direct
  4. Inverse
Show the answer and rationale

Answer: D

The variables move in opposite directions (more people, fewer slices each), which is an inverse relationship. A direct relationship would have both increasing together.

Question 2 of 3

In the chain algae → small fish → large fish, what is the most likely immediate effect if the small fish are overfished?

  1. Algae and large fish both increase
  2. Algae decrease and large fish increase
  3. Algae increase and large fish decrease
  4. Algae and large fish both decrease
Show the answer and rationale

Answer: C

With fewer small fish eating them, algae increase; with less food, large fish decrease. Large fish cannot increase when their food source shrinks, and algae lose their main grazer rather than gaining one.

Question 3 of 3

A spring stretches 2 cm with a 100 g mass and 4 cm with a 200 g mass. If the pattern holds, how far will it stretch with 300 g?

  1. 5 cm
  2. 8 cm
  3. 6 cm
  4. 3 cm
Show the answer and rationale

Answer: C

This is a direct relationship: the stretch is 2 cm per 100 g, so 300 g gives 3 × 2 = 6 cm. The answer 8 cm assumes the stretch doubles again, and 3 cm forgets to multiply by 2 cm per 100 g.

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