Proportional Relationships Practice Worksheet
7
Proportional Relationships Fluency
RTI Tier 2 Skill Builder • N-Gen Math 7 Unit 3 Lesson 5
Name:
Date: Group:
Proportional Relationship: The quotient \( \frac{y}{x} \) is always constant.
•
Constant of Proportionality (\(k\)): \( k = \frac{y}{x} \) (also called the Unit Rate).
Part A
Fluency Drill: Find the Constant Ratio \( k = \frac{y}{x} \)
6 Practice Problems
- \(x = 3 \text{ hrs}, \ y = 45 \text{ mi}\)
\(k =\) mi/hr
- \(x = 5 \text{ tickets}, \ y = \$35\)
\(k = \$\) /tkt
- \(x = 4 \text{ cups}, \ y = 28 \text{ oz}\)
\(k =\) oz/cup
- \(x = 6 \text{ packs}, \ y = 48 \text{ cans}\)
\(k =\) cans/pk
- \(x = 8 \text{ boxes}, \ y = 56 \text{ bars}\)
\(k =\) bars/bx
- \(x = 4 \text{ notebooks}, \ y = \$10\)
\(k = \$\) each
Part B
Fluency Drill: Is the Table Proportional? Test \( \frac{y}{x} \)
Circle Yes or No
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">2</td><td class="px-1 border-b border-r border-slate-200">4</td><td class="px-1 border-b border-slate-200">6</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">8</td><td class="px-1 border-r border-slate-200">16</td><td class="px-1">24</td></tr></tbody></table>
Proportional?
YES NO
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">3</td><td class="px-1 border-b border-r border-slate-200">5</td><td class="px-1 border-b border-slate-200">7</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">9</td><td class="px-1 border-r border-slate-200">15</td><td class="px-1">20</td></tr></tbody></table>
Proportional?
YES NO
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">4</td><td class="px-1 border-b border-r border-slate-200">8</td><td class="px-1 border-b border-slate-200">12</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">10</td><td class="px-1 border-r border-slate-200">20</td><td class="px-1">30</td></tr></tbody></table>
Proportional?
YES NO
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">2</td><td class="px-1 border-b border-r border-slate-200">5</td><td class="px-1 border-b border-slate-200">8</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">6</td><td class="px-1 border-r border-slate-200">15</td><td class="px-1">24</td></tr></tbody></table>
Proportional?
YES NO
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">3</td><td class="px-1 border-b border-r border-slate-200">6</td><td class="px-1 border-b border-slate-200">9</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">7</td><td class="px-1 border-r border-slate-200">14</td><td class="px-1">20</td></tr></tbody></table>
Proportional?
YES NO
<table class="text-[10px] text-center border-collapse"><tbody><tr><td class="px-1.5 border-b border-r border-slate-200 font-medium">\(x\)</td><td class="px-1 border-b border-r border-slate-200">5</td><td class="px-1 border-b border-r border-slate-200">10</td><td class="px-1 border-b border-slate-200">15</td></tr><tr><td class="px-1.5 border-r border-slate-200 font-medium">\(y\)</td><td class="px-1 border-r border-slate-200">35</td><td class="px-1 border-r border-slate-200">70</td><td class="px-1">105</td></tr></tbody></table>
Proportional?
YES NO
Rule: Proportional means all quotients \( \frac{y}{x} \) are equal. If one is different, it is not proportional!
12/12 Complete
Page 2
Equation Setups \( y = kx \) & Targeted Exercise Mirrors
Student Name:
Part C
Rapid Equation Drill: Write the proportional equation \( y = kx \)
Independent Setup
13. Unit rate is \(k = 6\) miles per hour.
Relate distance \(d\) and hours \(h\):
14. Unit price is \(k = \$2.50\) per snack.
Relate total cost \(c\) and snacks \(s\):
15. Constant is \(k = 4\) cards per chip.
Relate cards \(c\) and chips \(p\):
16. Constant is \(k = 5.5\) grams per coin.
Relate weight \(w\) and coins \(n\):
Problem 17 Mirrors Exercise #1: Steady Snail Pace (Table & Unit Rate)
Constant Ratio
A toy bug crawls at a steady pace. Time \(t\) in seconds and distance \(d\) in inches are shown:
<table class="text-[10px] text-center border-collapse bg-white rounded border border-slate-200"><tbody><tr><td class="px-2 py-0.5 border-b border-r border-slate-200 font-semibold text-slate-700">Time, \(t\) (sec)</td><td class="px-2 border-b border-r border-slate-200">2</td><td class="px-2 border-b border-r border-slate-200">4</td><td class="px-2 border-b border-r border-slate-200">6</td><td class="px-2 border-b border-slate-200">8</td></tr><tr><td class="px-2 py-0.5 border-r border-slate-200 font-semibold text-slate-700">Distance, \(d\) (in)</td><td class="px-2 border-r border-slate-200">6</td><td class="px-2 border-r border-slate-200">12</td><td class="px-2 border-r border-slate-200">18</td><td class="px-2">24</td></tr></tbody></table>
Unit rate: in/sec
(a) Form the ratio \( \frac{d}{t} \) for first 2 columns:
(b) What is the constant of proportionality (\(k\))?
Problem 18 Mirrors Exercise #2: Constant of Proportionality Meaning
Real-World Meaning
Marcus earns money washing cars. The relationship between cars washed \(c\) and money earned \(m\) is proportional with constant \(k = 15\).
(a) What does this constant 15 represent?
(b) Write the equation for earnings \(m\):
Problem 19 Mirrors Exercise #3: Bakery Cupcakes (Testing Proportional Cost)
Division Check
Janelle bought muffins three different times: 3 for $6.75, 5 for $11.25, and 8 for $18.00.
(a) \( \frac{\text{Cost}}{\text{Muffins}} \) ratios:
(b) Is it proportional?
(c) Constant (\(k\)):
\(k = \$\)
Problem 20 Mirrors Exercise #4: Coin Weight Scale (Predicting with Equation)
Scale & Prediction
Quarters on a scale have weights: 4 quarters weigh 22 grams and 10 quarters weigh 55 grams.
(a) Find \( k = \frac{\text{grams}}{\text{quarters}} \):
\(k =\) g/coin
(b) Write the equation:
Weight \(w =\)
(c) Weight of 30 coins:
Total = g
Small-Group Self-Assessment: Rate your proportional reasoning fluency today
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