Table Rates Worksheet 7.RP.1 Practice Indiana Academic Standards
Table Rates & Proportionality
Name:
Date:
Class/Period:
Core Rule: For proportional tables, \( \frac{y}{x} = k \) must be constant for all pairs. \( k \) is the constant of proportionality.
Level 1: Foundation Whole Number Unit Rates
1. Which table shows a proportional relationship?
Table A:
Table B:
Proportional Table:
2. Hours worked (\(x\)) and money earned (\(y\)):
Hours (\(x\)) Earnings (\(y\)) 3 $48 5 $80 7 $112
Find constant of proportionality \( k \) in dollars per hour.
Constant \(k\):
Level 2: On-Level Rational Rates & Non-Consecutive Inputs
3. Weight in pounds (\(x\)) and cost in dollars (\(y\)):
Pounds (\(x\)) Cost (\(y\)) 4 $18.00 6 $27.00 10 $45.00
What is the unit rate in dollars per pound?
Unit Rate:
4. Minutes (\(t\)) and distance in miles (\(d\)) traveled:
Minutes (\(t\)) Miles (\(d\)) 8 2 20 5 36 9
Find speed in miles per min (simplified fraction):
Rate \(k = \frac{d}{t}\):
Level 3: Challenge Multi-Relationship Comparison & Predictions
5. Which water pump is faster (gallons per minute)?
Pump 1
MinGal
4130
6195
Pump 2
MinGal
5170
8272
Faster Pump & Rate:
6. Proportional relationship: grams flour (\(g\)) to cups water (\(w\)).
Flour grams (\(g\)) Water cups (\(w\)) 150 1.2 375 ?
Find \( k = \frac{w}{g} \), then calculate missing water for 375 g.
Missing Water:
Rule of Thumb: Compute \( \frac{y}{x} \) for each pair. If all ratios are equal, that ratio is the constant \( k \).
7.RP.1 Practice • Set 1/4
Graph Rates Worksheet 7.RP.1 Practice Indiana Academic Standards
Graph Rates & Proportionality
Name:
Date:
Class/Period:
Core Rule: A proportional graph is a straight line through origin \( (0,0) \). The point \( (1, r) \) directly gives the unit rate \( r \). For any point \( (x, y) \), \( k = \frac{y}{x} \).
Level 1: Foundation Locating \( (1, r) \) & Proportional Graph Recognition
1. Distance traveled over time by a road trip driver:
0 1 2 3 4 Time (hours) 45 90 135 180 (1, 45)
What is the unit rate in miles per hour?
Unit Rate:
2. Which graph shows a proportional relationship?
Graph A Starts at (0, 15)
Graph B Starts at (0, 0)
Identify the proportional graph and state why.
Graph & Reason:
Level 2: On-Level Calculating \( k = \frac{y}{x} \) from Arbitrary Points
3. An athlete runs at a steady pace. Time (\(t\)) is in minutes, distance (\(d\)) is in miles.
0 2 4 Distance (miles) 16 32 48 Time (min) (4, 34)
Point \( (4, 34) \) is on the line. What is the runner's pace in minutes per mile?
Minutes per Mile:
4. Blueberry picking cost: Weight in lbs (\(x\)) vs Cost (\(y\)).
0 2 4 6 Pounds (\(x\)) $7 $14 $21 (6, 21)
What ordered pair \( (1, r) \) represents the unit price?
Unit Point \( (1, r) \):
Level 3: Challenge Comparing Constants of Proportionality from Multiple Lines
0 2 4 6 Hours (\(x\)) 60 120 180 Miles (\(y\)) Train: (4, 140) Bus: (4, 100)
5. The graph compares distance traveled over time for a Train and a Bus.
a) Train constant rate \( k_1 \) (mph):
b) Bus constant rate \( k_2 \) (mph):
c) How much faster is the train each hour?
Key Takeaway: Steeper line = greater constant of proportionality. The y-value when \( x = 1 \) is always the unit rate.
7.RP.1 Practice • Set 2/4
Equation Rates Worksheet 7.RP.1 Practice Indiana Academic Standards
Equation Rates & Proportionality
Name:
Date:
Class/Period:
Core Rule: All proportional equations have the exact structure \( y = kx \). The multiplier \( k \) is the constant of proportionality (unit rate). There is no added or subtracted constant!
Level 1: Foundation Identifying \( y = kx \) & Whole Number Constants
1. Which equation represents a proportional relationship between \( x \) and \( y \)?
A. \( y = 6x + 2 \)
B. \( y = 6x \)
C. \( y = x - 6 \)
D. \( y = \frac{6}{x} \)
Proportional Equation:
2. Total cost \( c \) for buying \( t \) concert tickets is given by the equation:
\( c = 24t \)
What is the constant of proportionality, and what does it represent in this context?
Constant \( k \) (ticket price):
Level 2: On-Level Rational Numbers & Multi-Step Interpretations
3. The weight of water in ounces (\(y\)) relative to tablespoons (\(x\)) is modeled by:
\( y = \frac{4}{5}x \)
Identify the constant of proportionality as both a fraction and a decimal.
Fraction: ____ Decimal:
4. Granola costs $3.50 for 5 ounces. Let \( c \) be total cost and \( w \) be weight in ounces.
Which equation represents this relationship?
A. \( c = 1.4w \)
B. \( c = 0.70w \)
C. \( c = 3.5w \)
D. \( c = 0.35w \)
Correct Equation:
Level 3: Challenge Contextual Prediction & Comparing Rate Equations
5. Trail mix costs $4.20 for 12 ounces.
Part A: Find constant rate \( k = \frac{\text{cost}}{\text{ounces}} \) and write the equation \( c = kw \).
Equation:
Part B: Use your equation to find the cost of 28 ounces.
Cost for 28 oz:
* Remember: multiply \( k \) by the input value.
6. Two car rental companies charge based on miles (\(m\)):
DriveRite: \( C = 0.35m \)
QuickWheels: \( C = 0.28m \)
Which company charges less per mile, and how much will you save after driving 150 miles?
Lower rate company:
Savings on 150 mi:
Equation Fact: If there is an added constant \( b \neq 0 \) (e.g. \( y = kx + b \)), the relationship is not proportional.
7.RP.1 Practice • Set 3/4
Verbal Rates Worksheet 7.RP.1 Practice Indiana Academic Standards
Verbal Rates & Proportionality
Name:
Date:
Class/Period:
Core Rule: A verbal scenario is proportional if zero input gives zero output with no flat startup fees or base charges. A unit rate compares a quantity specifically to 1 unit of another.
Level 1: Foundation Proportional Scenarios & Unit Rate Recognition
1. Which description represents a proportional relationship?
A. A cleaning crew charges $45 per hour plus a $20 travel fee.
B. A gym membership costs a flat $35 every month.
C. A taxi ride costs $3.00 to start plus $1.75 per mile.
D. A movie club costs $12 registration plus $4 per ticket.
Proportional Option:
2. Which statement represents a unit rate?
A. $6.00 for 4 juice bottles
B. 150 miles on 5 gallons of gas
C. $2.75 for 1 gallon of milk
D. 18 pages read in 12 minutes
Unit Rate Option:
Level 2: On-Level Calculating Rational Unit Rates (Fractions & Decimals)
3. Maya types 147 words in 6 minutes at a constant keyboarding speed.
What is Maya's typing rate in words per minute? Give your answer as a simplified mixed number or decimal.
Rate (words/min):
4. A city bus travels \( \frac{3}{4} \) of a mile in 9 minutes at steady traffic speed.
What is the unit rate of the bus in miles per minute? Write your answer as a fully simplified fraction.
Rate (miles/min):
Level 3: Challenge Rate Comparisons & Contextual Applications
5. Comparing Two Paint Stores:
Store A: 5 gallons for $142.50
Store B: 8 gallons for $216.00
Which store offers the better buy per gallon, and by how much?
Better Buy Store:
Price difference/gal:
6. Organic Honey Packaging:
A beekeeper bottles 18 ounces of wildflower honey for $13.50.
Part A: Find constant of proportionality \( k \) in dollars per ounce.
Cost per oz (\(k\)):
Part B: At this same rate, what would a 32-ounce jar cost?
Cost of 32 oz jar:
* Set up \( c = kw \) to compute Part B.
Key Strategy: To calculate unit rate, divide the dependent variable by the independent variable: \( \text{rate} = \frac{\text{amount}}{\text{time}} \) or \( \frac{\text{total cost}}{\text{units}} \).
7.RP.1 Practice • Set 4/4
Rate Radar Answer Key Teacher Resource Standards-Aligned Solution Guide
Rate Radar Answer Key: Tables & Graphs
Grade 7 • 7.RP.1
Page 1 of 2
Scoring Guidance: Accept exact fraction, decimal, or mixed number equivalents (e.g. \( 24.5 \) or \( 24\frac{1}{2} \)). Per ILEARN specs, unit labels are recommended during instruction but numerical values are graded.
1 Worksheet 1 Solutions: Table Rates & Proportionality
6 Total Items
Item 1 (Foundation):
Answer: Table A
In Table A, \( \frac{10}{2} = \frac{20}{4} = \frac{30}{6} = 5 \). In Table B, \( \frac{8}{2}=4 \) but \( \frac{12}{4}=3 \).
Item 2 (Foundation):
Answer: \( k = 16 \)
Compute \( \frac{48}{3} = \frac{80}{5} = \frac{112}{7} = 16 \). Unit rate is $16 per hour.
Item 3 (On-Level):
Answer: $4.50
Compute \( \frac{18.00}{4} = 4.50 \). Verify with \( \frac{27}{6} = 4.50 \) and \( \frac{45}{10} = 4.50 \).
Item 4 (On-Level):
Answer: \( \frac{1}{4} \) (or 0.25)
Speed \( k = \frac{d}{t} = \frac{2}{8} = \frac{1}{4} \) miles per minute. Also \( \frac{5}{20} = \frac{1}{4} \).
Item 5 (Challenge):
Answer: Pump 2 (34 gpm)
Pump 1: \( \frac{130}{4} = 32.5 \) gpm.
Item 6 (Challenge):
Answer: 3.0 cups
Constant \( k = \frac{1.2}{150} = 0.008 \).
2 Worksheet 2 Solutions: Graph Rates & Proportionality
5 Total Items
Item 1 (Foundation):
Answer: 45 mph
Directly read coordinate \( (1, 45) \). The y-coordinate when \( x = 1 \) is the unit rate.
Item 2 (Foundation):
Answer: Graph B
Graph B is a straight line through origin \( (0,0) \). Graph A has a y-intercept of 15, not proportional.
Item 3 (On-Level):
Answer: 8.5 min/mi
Given point \( (4, 34) \). Rate \( k = \frac{y}{x} = \frac{34}{4} = 8.5 \) (or \( 8\frac{1}{2} \)) minutes per mile.
Item 4 (On-Level):
Answer: (1, 3.50)
Point \( (6, 21) \to k = \frac{21}{6} = 3.5 \). The ordered pair for unit rate is \( (1, 3.5) \).
Item 5a & 5b (Challenge):
Train: 35 mph | Bus: 25 mph
Train: \( \frac{140}{4} = 35 \).
Item 5c (Challenge):
Difference: 10 mph
Train is \( 35 - 25 = 10 \) mph faster. The steeper line has the higher unit rate.
