Eighth Grade · Math · week 18

Checkpoint: functions and systems

Review and demonstrate mastery of functions, linear vs. nonlinear, systems, and break-even applications from weeks 10-17.

This checkpoint mixes function identification, linear-versus-nonlinear testing, and solving/classifying systems -- the whole toolkit from the last eight weeks.

A system problem actually combines two skills at once: the equation-solving from the first unit, plus the system setup from this one. If substitution feels shaky, check whether the gap is really in the equation-solving or in the setup.

📋 For the teacher

Teach it (10–15 min):

Diagnose which of the four skills (function-or-not, linear-vs-nonlinear, solving systems, classifying systems) feels least automatic, and spend extra time there.
If a system problem goes wrong, check separately whether the equation-solving step or the substitution setup is the real gap.
Re-anchor break-even thinking with a quick real example (two phone plans, two allowances) if the word-problem side feels weaker than the pure algebra.
Praise correctly identifying "no solution" or "infinitely many" exactly as much as finding a numeric answer -- both are equally correct outcomes.

Talk about it:

Which felt more natural this unit: solving a system by graphing or by substitution?
What is the fastest way to tell a system will have no solution, before fully solving it?
Which of this unit's four skills do you want to practice more this week?

Mastery looks like: They correctly work a mixed set covering function identification, linear-vs-nonlinear, system-solving, and system classification with minimal hints.

Common stumbles: Mixing up the function rule with the linear rule (one-output versus constant-rate are different questions); rushing a system problem and skipping the back-substitution step.

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

Records attendance + 15 min of Math for this learner.

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