A water tank starts with 35 gallons and fills at 4.5 gallons per minute. Write a function for the amount of water after m minutes and find the amount after 12 minutes.
Reasoning strategy
Use initial value plus rate times time.
Difficulty Practice Guide
Hard Grade 8 Linear Functions Word Problems
This page shows what hard practice should demand for grade 8 linear functions word problems. The goal is not a larger worksheet. The goal is to make the student's reasoning visible enough to choose the next better problem.
What Changes At This Difficulty
Stress-test transfer: multi-step structure, constraints, distractors, or reverse reasoning.
Expected structure: 3-4 step problem solving.
Vocabulary load: high with intentional distractors.
Reasoning depth: at least 3 relationship layers.
Student Work Signals
A good hard problem should expose the bottleneck
MathRoutine watches for whether the student understood the situation, wrote a useful setup, handled the calculation, and answered the exact question asked.
1
model hidden constraints or changed quantities
2
avoid tempting but incomplete first answers
3
explain why the final answer fits the original context
Sample Problems
Two tutoring plans charge $30 plus $18 per session and $54 plus $12 per session. For how many sessions do the plans cost the same?
Reasoning strategy
Set the two linear cost functions equal and solve.
Why This Matters
The paid value is diagnosis, not answer lookup
Basic gives repeated targeted practice. Pro becomes useful when the student needs help understanding wording, recovering the setup, or seeing the same misconception return across attempts.
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