Public Practice Guide
Use this guide to see the type of reasoning MathRoutine expects for grade 9 exponential & logarithmic models word problems. The goal is not worksheet volume; it is helping students read the situation, choose a model, and explain why the answer fits.
What Students Practice
Reasoning Patterns
Sample Problems
These grade-specific examples show the kind of student-visible reasoning MathRoutine is designed to support: identifying the important quantities, choosing the right structure, and checking the final answer against the story.
A lab culture starts with 120 cells and grows by 35% each hour. How many cells are expected after 6 hours?
Reasoning Strategy
Use initial value times a growth factor raised to the number of hours.
AI Support Preview
Translate 35% growth into a factor of 1.35, not 0.35.
A medication amount starts at 500 milligrams and 18% leaves the bloodstream each hour. How much remains after 5 hours?
Reasoning Strategy
Use a decay factor of 0.82 for each hour.
AI Support Preview
Explain why losing 18% means keeping 82%.
A server starts with 600 requests and triples each year. The limit is 16,800 requests. What is the greatest whole number of years the server can grow without reaching the limit?
Reasoning Strategy
Set up 600(3^t) < 16800 and test or solve the threshold.
AI Support Preview
Focus on the phrase 'without reaching' as a strict limit.
Practice Ladder
Modeled after Algebra 1/Algebra 2 workbook expectations: interpret a function or equation in context, solve or compare it, then justify the meaning of the answer.
Connect the equation form to the real situation before calculating.
Evaluate, reverse, or compare the model while tracking restrictions and units.
Use the result to answer the actual question, not just the algebraic expression.
Assessment Signals
A guide is useful only if it clarifies what teachers and parents should look for in student work. MathRoutine tracks these signals during practice instead of treating every miss as the same mistake.
Common Mistakes
Learning Loop
A strong word problem platform should not only say right or wrong. It should notice the pattern: missed unit rate, ignored leftover, reversed comparison, wrong base percent, or equation setup error.
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Attempt
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Diagnosis
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Next practice
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