A focused Grade 7 learning session for Finding the Constant of Proportionality using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving finding the constant of proportionality.
Finding the Constant of Proportionality 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 finding the constant of proportionality 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 Finding the Constant of Proportionality, 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 finding the constant of proportionality.
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.
The cost \(c\) of buying \(n\) identical books is proportional to \(n\). If \(4\) books cost \($18\), what is the constant of proportionality (unit price per book)?
Answer D: \($4.50\)
The constant of proportionality is \(k=c/n=18/4=$4.50\) per book.
A bike rental costs \($2.50\) per hour. If \(h\) is the number of hours and \(c\) is the total cost, what is the constant of proportionality in the equation \(c = kh\)?
Answer D: \(2.5\)
In the equation \(c = 2.5h\), the coefficient \(k = 2.5\) is the constant of proportionality (unit rate per hour).
The table shows a proportional relationship between pounds of sugar (\(s\)) and the number of cookies baked (\(c\)). In the equation \(c = ks\), what is the constant of proportionality (\(k\))?
Answer D: \(12\)
Using any pair in \(c = ks\): \(k = c/s = 24/2 = 12\) cookies per pound of sugar.
Which equation represents a proportional relationship with a constant of proportionality of \(3\)?
Answer D: \(y = 3x\)
A proportional relationship has the form \(y = kx\) with no constant term. Here \(k = 3\).
A car travels \(120\) miles in \(2\) hours at a constant speed. What is the constant of proportionality (miles per hour)?
Answer D: \(60\) mph
Speed is distance divided by time: \(k = 120/2 = 60\) miles per hour.
The table shows the relationship between gallons of paint (\(g\)) and square feet painted (\(p\)). What is the value of \(k\) in the equation \(p = kg\)?
Answer D: \(400\)
\(k = p/g = 400/1 = 400\) square feet per gallon.
A recipe calls for \(3\) cups of flour to make \(12\) cookies. At this rate, what is the constant of proportionality (cups per cookie)?
Answer D: \(0.25\)
\(k = \frac{\text{flour}}{\text{cookies}} = \frac{3}{12} = 0.25\) cups per cookie.
The graph shows a proportional relationship. One point on the graph is \((4,5)\). What is the constant of proportionality?
Answer D: \(1.25\)
The point \((4,5)\) is on the line; \(k = y/x = 5/4 = 1.25\).
A streaming service charges a proportional rate. If \(8\) months of service costs \($96\), what is the constant of proportionality (cost per month)?
Answer D: \($12\)
\(k = 96/8 = $12\) per month.
In the proportional relationship \(y = \frac{2}{3}x\), what is the constant of proportionality?
Answer D: \(\frac{2}{3}\)
The coefficient of \(x\) is the constant of proportionality: \(k = \frac{2}{3}\).
A water pump fills a tank at a constant rate. The table shows the gallons of water (\(w\)) pumped over time (\(t\)) in minutes. What is the constant of proportionality?
Answer D: \(8\) gallons/min
\(k = 16/2 = 8\) gallons per minute.
