Sixth Grade · Math · week 25

Independent and dependent variables

Identify the independent and dependent variables in a real-world relationship and write an equation connecting them.

In a relationship between two changing quantities, the independent variable is the one you choose or control, and the dependent variable is the one that responds - its value DEPENDS on the independent variable.

A good test: ask "does this quantity change BECAUSE of the other one?" The one that changes because of the other is dependent; the one driving the change is independent.

Once you know the relationship, often a rate, you can write an equation: dependent variable equals a rule using the independent variable. If earnings depend on hours worked at $8 per hour, e = 8h, where e depends on h.

📋 For the teacher
Teach it (10–15 min):
  • Practice the "because of" test out loud on several real examples before writing any equation.
  • Point out that the dependent variable usually sits alone on one side of the equation, like c = ..., and gets its value FROM the rule.
  • Connect to earlier unit-rate work - the rate from the ratio unit becomes the coefficient in the equation.
  • Try flipping a familiar scenario, like asking whether temperature depends on time or time on temperature, to sharpen the distinction.
Talk about it:
  • How do you decide which variable is independent and which is dependent?
  • Why does the dependent variable usually sit alone on one side of the equation?
  • Can you think of a real situation with an independent and dependent variable?

Mastery looks like: They correctly identify the independent and dependent variable in a real scenario and write a matching equation.

Common stumbles: Reversing which variable is independent versus dependent; writing the equation with the variables in the wrong roles.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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