A focused Grade 7 learning session for Writing Equations for Proportional Relationships using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving writing equations for proportional relationships.
Writing Equations for Proportional Relationships is part of Grade 7 Ratios and Proportional Relationships. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of writing equations for proportional relationships using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Writing Equations for Proportional Relationships, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving writing equations for proportional relationships.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A car travels at a constant speed of \(55\) miles per hour. Which equation relates distance \(d\) (miles) to time \(t\) (hours)?
Answer D: \(d=55t\)
For a proportional relationship, \(d=kt\) where \(k\) is the constant of proportionality. Here \(k=55\).
A recipe calls for \(2\) cups of flour for every \(3\) cups of sugar. If \(f\) is flour and \(s\) is sugar, which equation shows this proportional relationship?
Answer D: \(f=\frac{2}{3}s\)
The ratio flour:sugar is \(2:3\), so \(f=\frac{2}{3}s\) where the constant of proportionality is \(\frac{2}{3}\).
A store charges $4 per pound for apples. Which equation gives the total cost \(c\) (dollars) for \(p\) pounds?
Answer D: \(c=4p\)
Cost is price times quantity. The constant \(k=4\) dollars per pound, so \(c=4p\).
Maya runs at \(8\) miles per hour. After running for \(t\) hours, she has covered \(d\) miles. Which equation is correct?
Answer D: \(d=8t\)
Distance equals speed times time. With speed \(k=8\) mph, the equation is \(d=8t\).
A phone plan charges $0.10 per minute. If \(m\) is the number of minutes and \(c\) is the cost in dollars, which equation models this?
Answer D: \(c=0.10m\)
The constant of proportionality is $0.10 per minute, so \(c=0.10m\).
A machine prints \(120\) pages every \(2\) minutes. What is the constant of proportionality \(k\) if \(p\) is pages and \(t\) is time in minutes?
Answer D: \(k=60\)
The rate is \(\frac{120 \text{ pages}}{2 \text{ minutes}}=60\) pages per minute, so \(k=60\).
A photo costs $0.50 each. If you buy \(n\) photos for a total cost of \(T\) dollars, which equation is correct?
Answer D: \(T=0.50n\)
Cost equals price per item times number of items. Here \(T=0.50n\).
The table shows a proportional relationship between hours worked and earnings. What is the constant of proportionality?
Answer D: \(k=9\)
Divide earnings by hours: \(\frac{18}{2}=9\), \(\frac{36}{4}=9\), \(\frac{54}{6}=9\). The constant is \(k=9\) dollars per hour.
The table shows the relationship between gallons of gas and cost. Which equation represents this relationship?
Answer D: \(C=4g\)
The ratio is \(\frac{12}{3}=4\), \(\frac{20}{5}=4\), \(\frac{32}{8}=4\). The equation is \(C=4g\).
A bike shop charges $25 to rent a bike per day. Write the equation for total cost \(T\) as a function of days \(d\).
Answer D: \(T=25d\)
Cost equals the daily rate times the number of days. The equation is \(T=25d\).
Which table represents a proportional relationship?
Answer B: Table B only
Table B has constant ratio: \(\frac{6}{2}=3\), \(\frac{12}{4}=3\), \(\frac{18}{6}=3\). Table A is not proportional (\(\frac{3}{1}=3\) but \(\frac{7}{3}\neq 3\)).
