A focused Grade 7 learning session for Recognizing Proportional Relationships using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving recognizing proportional relationships.
Recognizing 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 recognizing 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 Recognizing 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 recognizing 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.
Which table shows a proportional relationship between \(x\) and \(y\)?
Answer D: Option A only
Check constant \(y/x\): A gives \(4,4,4,4\) (constant — proportional). B gives \(2,2.5,2.33,2.5\) (not constant).
A smoothie recipe uses \(2\) cups of berries for every \(3\) cups of yogurt. If you use \(8\) cups of berries, how many cups of yogurt do you need?
Answer D: \(12\) cups
Set up proportion: \(\frac{2}{3} = \frac{8}{y}\). Cross multiply: \(2y = 24\), so \(y = 12\).
Which equation represents a proportional relationship?
Answer D: \(y = 7x\)
Proportional relationships have form \(y = kx\) (passing through origin with no constant term). Only \(y = 7x\) fits.
A car travels at a constant speed. After \(2\) hours, it has gone \(110\) miles. After \(5\) hours, it has gone \(275\) miles. Is the distance proportional to time?
Answer D: Yes
Check the constant-of-proportionality across rows: \(\frac{110}{2} = 55\) mph and \(\frac{275}{5} = 55\) mph. The ratio is constant, so distance is proportional to time.
Which table does NOT show a proportional relationship?
Answer D: All the above show proportional relationships
The table has ratio \(y/x: 5/1=5, 10/2=5, 15/3=5, 20/4=5\) (constant). Option B: \(y=6x\) is proportional. Option C: line through origin \((0,0)\) and \((3,12)\) has slope \(4\), so \(y=4x\) (proportional). All are proportional.
A recipe calls for \(\frac{1}{2}\) cup of flour for every \(\frac{1}{4}\) cup of sugar. Which ratio represents the proportional relationship?
Answer D: \(2:1\)
Divide: \(\frac{1/2}{1/4} = \frac{1}{2} \times \frac{4}{1} = 2\). For every 1 cup sugar, you need 2 cups flour.
The graph of which equation is a straight line passing through the origin?
Answer D: \(y = -5x\)
Proportional equations pass through origin: substitute \(x=0\), get \(y=0\). Only \(y=-5x\) gives \((0,0)\).
A phone plan costs $15 per month plus $0.10 per text message. Is the total cost proportional to the number of text messages?
Answer D: No
The equation is \(\text{Cost} = 15 + 0.10t\). The constant $15 (fixed fee) means not proportional.
Jamal buys notebooks at $3 each. The table below shows his total cost for different numbers of notebooks. Does the table show a proportional relationship?
Answer D: Yes, ratio is \(3:1\)
Each row: \(6/2=3\), \(12/4=3\), \(18/6=3\), \(24/8=3\). Constant ratio of 3 dollars per notebook.
Which pair of points lies on a line representing a proportional relationship?
Answer B: \((0,0)\) and \((3,9)\)
Must pass through origin \((0,0)\). Only option B qualifies. Slope is \(\frac{9}{3}=3\), so \(y=3x\).
A rental car costs $25 per day. Which table represents the cost for different numbers of days?
Answer A: Option A
At $25/day: 1 day costs $25, 2 days cost $50, 3 days cost $75. Option A is correct.
