Public Practice Guide
Use this guide to see the type of reasoning MathRoutine expects for grade 7 proportional relationship tables with answers. 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 table pairs hours x with distance y: (2, 9), (5, 22.5), and (8, 36). Is the relationship proportional, and what is its constant of proportionality?
Answer
Yes; k = 4.5 miles per hour
Reasoning Strategy
Calculate y/x for every pair and verify that each ratio equals 4.5.
AI Support Preview
Write the unit next to each ratio and use y = 4.5x to check one row.
A recipe uses 2 1/4 cups of flour for 3 batches. The baker already has 5 cups. After making 8 batches, how many more cups of flour does the baker need?
Reasoning Strategy
Find the cups per batch, scale to 8 batches, then subtract the amount already available.
AI Support Preview
Show the unit rate and shortage as two separate reasoning moves.
A map scale says 3 centimeters represents 14 kilometers. Two towns are 10.5 centimeters apart on the map. How far apart are the towns?
Reasoning Strategy
Use a proportional relationship with fractional scale factor.
AI Support Preview
Keep map distance and real distance in labeled columns.
A runner completes 5 laps in 6 minutes 40 seconds. At the same pace, how long will 18 laps take?
Reasoning Strategy
Convert time to seconds, find the time per lap, then scale.
AI Support Preview
Avoid mixing minutes and seconds inside the proportion.
A drink mix uses 3 cups of juice for every 5 cups of water. If a pitcher has 24 cups of juice, how many cups of water are needed?
Reasoning Strategy
Scale the ratio from 3 to 24, then scale water by the same factor.
AI Support Preview
Mark the scale factor instead of adding 2 repeatedly.
A cyclist rides 18 miles in 1.5 hours. At the same rate, how far will the cyclist ride in 4 hours?
Reasoning Strategy
Find the unit rate, then multiply by 4.
AI Support Preview
Explain miles per hour as a rate.
Three identical notebooks cost $8.25. How much would 10 notebooks cost at the same price?
Reasoning Strategy
Find the cost per notebook and scale to 10.
AI Support Preview
Keep money rounding tied to cents.
A recipe uses 4 cups of oats for 10 snack bags. At the same rate, how many cups are needed for 35 bags?
Answer
14 cups
Reasoning Strategy
Find or scale the ratio from 10 bags to 35 bags.
AI Support Preview
Keep cups and bags paired in the ratio table.
Keep Practicing
Practice 1000+ more problems with grade-fit AI support.
Practice Ladder
Modeled after middle-school workbook expectations: combine fluency with ratio, percent, equation, and geometry reasoning rather than only isolated computation.
Begin with unit rate or percent-part-whole identification.
Add a missing value, comparison, discount, markup, or scale factor.
Finish with a context where the base quantity is hidden or changes during the problem.
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.
1
Attempt
2
Diagnosis
3
Next practice
Diagnosis Examples
Each word problem should create evidence about setup, calculation, vocabulary, hidden quantities, or final-question confusion. These examples show what MathRoutine is designed to separate after an attempt.
If the attempt shows
The student divides in the wrong direction and gets the reciprocal rate.
Likely diagnosis
The unit rate's numerator and denominator are being swapped.
Next practice
Use rate labels on every quotient before scaling.
If the attempt shows
The student finds a unit rate but answers the per-one value instead of the target amount.
Likely diagnosis
The bridge quantity is being mistaken for the final answer.
Next practice
Practice unit-rate bridge problems with a clearly different target quantity.
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