Proportion Power Worksheet
Proportion Power
Solving Proportions • Step-by-Step Practice
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Strategy Anchor Toolkit
1. Scaling Factor: Find a common multiplier across numerator and denominator (\(\times k\)).
2. Cross-Products: If \(\frac{a}{b} = \frac{c}{d}\), then cross-multiply \(a \cdot d = b \cdot c\) and divide.
3. Unit Rate: Find the value per 1 item (\(\frac{y}{x}\)), then multiply by the target quantity.
A
Scaling Factor Strategy
Identify multiplier/divisor to solve for the missing term
1. Solve for \(x\):
\(\frac{4}{7} = \frac{x}{35}\)
Multiplier rule:
Solution:
x =
2. Solve for \(m\):
\(\frac{18}{24} = \frac{3}{m}\)
Multiplier / Divisor:
Solution:
m =
B
Cross-Product Equations
Set cross-products equal and show step-by-step division
\(\frac{5}{8} = \frac{15}{w}\)
Show cross-products:
Answer:
w =
\(\frac{9}{12} = \frac{k}{28}\)
Show cross-products:
Answer:
k =
\(\frac{6}{y} = \frac{14}{35}\)
Show cross-products:
Answer:
y =
C
Real-World Situations
Set up a proportion ratio with units labeled
6. Fruit Punch Recipe Kitchen Scale
A recipe requires 3 cups of cranberry juice for every 5 cups of sparkling water. If Maya uses 25 cups of sparkling water, how many cups of cranberry juice does she need?
Setup ratio with units: Solve:
Answer:
____ cups
7. Road Trip Distance Map Travel
On a state map, 2 inches represents 70 miles. The measured highway distance between two cities on the map is 5.5 inches. What is the actual driving distance?
Setup ratio with units: Solve:
Answer:
____ miles
8. Strategy Check: Explain Your Choice Self-Evaluation
Look back at Problem 1 and Problem 4. Which method did you prefer for each (scaling multiplier vs. cross products), and why?
Proportion Power • Proportional Reasoning Practice Page 1 of 1
Proportion Power Answer Key
Proportion Power
Answer Key
Complete Worked Solutions • Scoring Reference
Total Points: 20 pts (2 pts each #1-5, 3 pts each #6-7, 4 pts #8)
Standard: CCSS.MATH.CONTENT.7.RP.A.2
Teacher Look-Fors:
• Check that units are consistently aligned in numerators and denominators • Encourage simplifying fractions before cross-multiplying
A
Scaling Factor Strategy • Solutions
2 Points Each
1. \(\frac{4}{7} = \frac{x}{35}\) Multiplier \(\times 5\)
\(7 \times 5 = 35 \implies 4 \times 5 = x\)
Work: \(x = 4 \times 5\)
x = 20
2. \(\frac{18}{24} = \frac{3}{m}\) Divisor \(\div 6\)
\(18 \div 6 = 3 \implies 24 \div 6 = m\)
Work: \(m = 24 \div 6\)
m = 4
B
Cross-Product Equations • Solutions
2 Points Each
- \(\frac{5}{8} = \frac{15}{w}\)
\(5 \cdot w = 8 \cdot 15\)
\(5w = 120\)
\(w = \frac{120}{5}\)
Exact: w = 24
- \(\frac{9}{12} = \frac{k}{28}\)
\(12 \cdot k = 9 \cdot 28\)
\(12k = 252\)
\(k = \frac{252}{12}\) (or \(\frac{3}{4} = \frac{k}{28}\))
Exact: k = 21
- \(\frac{6}{y} = \frac{14}{35}\)
\(14 \cdot y = 6 \cdot 35\)
\(14y = 210\)
\(y = \frac{210}{14}\) (or \(\frac{6}{y} = \frac{2}{5}\))
Exact: y = 15
C
Real-World Situations • Solutions
3 Points Each
6. Fruit Punch Recipe Setup + Solution
\(\frac{\text{cranberry}}{\text{sparkling}} = \frac{3\text{ cups}}{5\text{ cups}} = \frac{c}{25\text{ cups}}\)
Method 1: Scale factor \(\times 5 \implies c = 3 \times 5 = 15\)
Method 2: \(5c = 3 \times 25 \implies 5c = 75 \implies c = 15\)
Point breakdown: 1 pt setup, 2 pts calc
15 cups
7. Road Trip Distance Setup + Solution
\(\frac{\text{map inches}}{\text{actual miles}} = \frac{2\text{ in}}{70\text{ mi}} = \frac{5.5\text{ in}}{d\text{ mi}}\)
Method 1: Unit rate = \(70 \div 2 = 35\text{ mi/in} \times 5.5 = 192.5\)
Method 2: \(2d = 70 \cdot 5.5 = 385 \implies d = 192.5\)
Point breakdown: 1 pt setup, 2 pts calc
192.5 miles
8. Strategy Reflection • Exemplar & Scoring (4 Points) Rubric Guide
Exemplar Response: "For Problem 1, scaling is faster because 7 multiplies evenly into 35 (\(\times 5\)), so I can just multiply \(4 \times 5 = 20\) mentally. For Problem 4, 12 does not divide evenly into 28, so using cross-multiplication or reducing \(\frac{9}{12}\) to \(\frac{3}{4}\) first avoids mistakes."
