Below Proficiency Practice Worksheet Level 1 • Below Proficiency (DOK 1)
Proportional Relationships: Equations from Words
Standard 7.RP.3 • Write \(y = mx\) equations given verbal descriptions
Name:
Date: Period:
Key Rule: Proportional equations use \(y = mx\), where \(m\) is the unit rate (constant of proportionality).
y = (rate) · x
1 Guided Model: Honeycrisp Apples Item Spec Anchor
Apples cost $5 per pound . Let \(p\) represent the number of pounds purchased, and let \(c\) represent the total cost in dollars.
a. Identify the unit rate (\(m\)):
$ ________ per pound
b. Write the equation for cost \(c\):
\(c =\) __________________
2 Direct Verbal Practice Write the Equation
Write an equation in the form \(y = mx\) for each real-world situation:
a. Tickets to the talent show cost $8 each . (Let \(t\) = tickets, \(y\) = total cost)
b. A drone climbs at a steady speed of 14 feet per second . (Let \(s\) = seconds, \(h\) = height)
c. A bakery packs 12 muffins in each box . (Let \(b\) = boxes, \(m\) = total muffins)
3 Assessment Multiple Choice ILEARN Format
A car wash charges a flat price of $15 per vehicle . Which equation represents the total earnings, \(E\), in dollars for washing \(v\) vehicles?
A \(E = v + 15\)
B \(E = 15v\)
C \(15E = v\)
D \(E = \frac{v}{15}\)
4 Application & Reasoning Apply the Equation
A print shop produces custom t-shirts for $9 per shirt .
a. Write an equation for total cost \(y\) for \(x\) t-shirts:
b. Use your equation to find the total cost of 8 shirts:
$ ________
Indiana Academic Standard 7.RP.3 • Level 1 Practice Target: Write equations in form \(y = mx\) from verbal descriptions (whole numbers)
Approaching Proficiency Practice Worksheet Level 2 • Approaching Proficiency (DOK 2)
Tables & Graphs with Given Unit Rates
Standard 7.RP.3 • Identify equations & graph when \((1, r)\) is given
Name:
Date: Period:
Spotting the Unit Rate: Look for the input value \(x = 1\). The paired output \((1, r)\) gives the constant of proportionality \(m = r\).
(1, m) \(\rightarrow\) y = mx
1 Table to Equation: Sweet Treats Bakery Assessment Item
Cupcakes (\(x\))
Cost (\(y\))
1
$2.25
6
$13.50
12
$27.00
A bakery sells specialty cupcakes according to the prices shown. Which equation represents the total cost \(y\), in dollars, for \(x\) cupcakes?
A \(y = 27x\)
B \(12y = x\)
C \(2.25y = x\)
D \(y = 2.25x\)
2 Graph to Equation: Cargo Weight Interpret Graph
Tons (x) Pounds (y) 1 2 3 4 5 0 2k 4k 6k 8k (1, 2000) (3, 6000)
The graph shows the conversion between tons, \(x\), and pounds, \(y\).
What is the constant of proportionality (\(m\)) from the point \((1, 2000)\)?
\(m =\) ________
Write an equation representing pounds \(y\) for \(x\) tons:
\(y =\) __________________
3 Draw the Graph: Art Workshop Tuition Graphing Task
Students in a community pottery class pay a proportional fee based on studio hours attended.
Hours (\(h\))
Cost (\(c\))
1
$20.00
2
$40.00
3
$60.00
4
$80.00
Graphing Instructions:
Plot the point for 0 hours (origin).
Plot the point for 1 hour \((1, 20)\).
Plot the remaining points from the table.
Draw a straight ray starting at \((0, 0)\).
Studio Hours (h) Cost ($) 0 1 2 3 4 5 0 20 40 60 80 100
Write the equation for this relationship: \(c =\) ______________
Indiana Academic Standard 7.RP.3 • Level 2 Practice Target: Identify/write equations & graph given tables/graphs containing \((1, r)\)
At Proficiency Practice Worksheet Level 3 • At Proficiency (DOK 2 / DOK 3)
Calculating Constants & Graphing Relationships
Standard 7.RP.3 • Calculate \(m = \frac{y}{x}\) from non-consecutive data & graph from context
Name:
Date: Period:
When \((1, r)\) is missing: Calculate unit rate \(m = \frac{y}{x}\) using any given pair, then write \(y = mx\).
m = \(\frac{y}{x}\)
1 Non-Consecutive Table: Bulk Gourmet Taffy ILEARN Alignment
A shop sells candy. The table shows cost \(y\) for \(x\) pounds. Notice it does not include 1 pound.
Pounds (\(x\))
Cost (\(y\))
4
$9.96
8
$19.92
10
$24.90
a. Calculate unit rate \(m = \frac{y}{x}\):
\(m = \) ________ / ________ = $ ________
b. Write equation representing cost \(y\) for \(x\) pounds:
\(y =\) __________________
2 Non-Consecutive Graph: Cider Mill Production Analyze Coordinates
Pounds of Apples (x) Cups of Cider (y) 0 2 4 6 8 0 2 4 6 8 10 (3, 4.5) (4, 6) (6, 9)
The graph plots cups of cider \(y\) made from pounds of apples \(x\).
Use point \((4, 6)\) to find constant \(m\):
\(m = \frac{6}{4} =\) ________
Write the equation for this relationship:
\(y =\) __________________
3 Calculate & Graph: Banana Bread Recipe Construct Graph (DOK 3)
Four loaves of banana bread require 2 cups of sugar to bake. Create a graph where \(y\) = loaves of bread and \(x\) = cups of sugar.
Step 1: Calculate Unit Rate
\(m = \frac{4\text{ loaves}}{2\text{ cups}} =\) ____
Step 2: Key Ordered Pairs
(0, 0), (1, ____), (2, 4), (3, ____)
Equation:
\(y =\) ________
Cups of Sugar (x) Loaves (y) 0 1 2 3 4 5 0 2 4 6 8 10
Plot coordinates and draw a ray through \((0,0)\).
Indiana Academic Standard 7.RP.3 • Level 3 Practice Target: Calculate constant \(m = \frac{y}{x}\) from non-consecutive tables/graphs & draw graphs
Above Proficiency Practice Worksheet Level 4 • Above Proficiency (DOK 3)
Interpreting Equations & Multi-Step Reasoning
Standard 7.RP.3 • Explain, evaluate multi-select claims, predict, & compare rates
Name:
Date: Period:
DOK 3 Focus: In \(y = mx\), each point \((x, y)\) represents \((x\text{ units of input}, y\text{ units of output})\). Proportional lines must pass through \((0, 0)\).
Interpret & Predict
1 Multi-Select Assessment Item: Carnival Admission Select ALL That Apply
The equation \(y = 5x\) represents the relationship between \(x\), the number of ride tickets purchased for a county fair, and \(y\), the total cost in dollars.
Select ALL true statements:
A. The total cost of 4 tickets is $9.
B. The total cost of 5 tickets is $25.
C. The point \((3, 15)\) on the graph represents 3 tickets costing $15.
D. The graph of this relationship is a horizontal line through \(y = 5\).
E. The graph is a line starting at \((0,0)\) that passes through \((5, 1)\).
F. The relationship between tickets bought and total cost is proportional.
2 Interpret Points & Make Predictions: EV Rapid Charging Interpret & Solve
An electric vehicle station delivers energy at a constant rate modeled by \(d = 22.5h\), where \(h\) is charging hours and \(d\) is added driving range in miles.
a. What specific real-world meaning does the ordered pair \((1, 22.5)\) represent in this context?
b. Prediction: Added miles after 6 hours
\(d = \) 22.5(____) = ________ miles
c. Backwards Prediction: Hours for 180 miles
\(h = 180 \div 22.5 =\) ________ hours
3 Comparing Two Relationships: Lawn Care Services Comparative Analysis
Two lawn maintenance companies charge proportional rates for mowing acreage.
GreenThumb Pros
Cost is modeled by the equation:
\(y = 35.50x\)
where \(x\) = acres and \(y\) = total cost in dollars.
LawnMaster Co.
Unit rate \(m =\) $ ________ per acre
a. Which company charges a lower price per acre? GreenThumb Pros / LawnMaster Co.
b. Graphical Comparison: If both relationships are graphed on the same coordinate plane, which company's line will be steeper? Explain why.
Indiana Academic Standard 7.RP.3 • Level 4 Practice Target: Explain and interpret equations, make predictions, and compare relationships
Proficiency Tiered Answer Key Teacher Reference & Solution Guide • Part 1
Standard 7.RP.3 Answer Key: Levels 1 & 2
Below Proficiency (DOK 1) & Approaching Proficiency (DOK 2)
Full Solutions
L1 Level 1: Below Proficiency Solutions Equations from Words (DOK 1)
Item 1: Honeycrisp Apples
a. Unit rate: $5 per pound
b. Equation: \(c = 5p\) (or \(y = 5x\))
Item 2: Direct Verbal Practice
a. Talent Show: \(y = 8t\)
b. Drone Climb: \(h = 14s\)
c. Muffin Boxes: \(m = 12b\)
Item 3: Assessment Multiple Choice
Correct Answer: B (\(E = 15v\))
Distractor Analysis: A confuses addition with multiplication; C reverses the independent and dependent variables; D erroneously divides.
Item 4: Application & Calculation
a. Equation: \(y = 9x\)
b. Cost for 8 shirts: \(y = 9(8) = \) $72
Diagnostic Tip: Watch for students writing \(y = x + 5\) instead of \(y = 5x\). Remind them unit rates describe repeated multiplication.
L2 Level 2: Approaching Proficiency Solutions Unit Rates in Tables & Graphs (DOK 2)
Item 1: Cupcake Bakery Table
Look at row 1 where cupcakes (\(x\)) = 1. The cost is $2.25. Therefore, \(m = 2.25\).
Answer: D (\(y = 2.25x\))
Item 2: Cargo Weight Graph
The coordinate point \((1, 2000)\) gives the constant directly: \(m = 2000\).
Equation: \(y = 2000x\) (or \(P = 2000T\)).
Equation: \(y = 2000x\)
Item 3: Pottery Class Graphing Task
Plotted Points: Must accurately plot \((0, 0)\), \((1, 20)\), \((2, 40)\), \((3, 60)\), and \((4, 80)\).
Graph Check: A continuous straight ray starting at \((0, 0)\) and passing through all 4 points.
Equation: \(c = 20h\) (or \(y = 20x\)).
Diagnostic Tip: Ensure students start their graph at the origin \((0,0)\). A proportional relationship must have zero cost for zero hours.
Indiana Academic Standard 7.RP.3 • Answer Key Page 1 of 2 Levels 1 & 2 Scoring Guide
Teacher Reference & Solution Guide • Part 2
Standard 7.RP.3 Answer Key: Levels 3 & 4
At Proficiency (DOK 2/3) & Above Proficiency (DOK 3)
Full Solutions
L3 Level 3: At Proficiency Solutions Calculating Constants & Graphing (DOK 2/3)
Item 1: Non-Consecutive Table (Bulk Taffy)
a. Unit Rate Calculation: \(m = \frac{9.96}{4} = 2.49\) (also verifiable as \(\frac{19.92}{8} = 2.49\) and \(\frac{24.90}{10} = 2.49\)). Rate = $2.49/lb.
b. Equation: \(y = 2.49x\)
Item 2: Non-Consecutive Graph (Cider Mill)
Constant Calculation: Using point \((4, 6)\): \(m = \frac{6}{4} = 1.5\) (or from \((3, 4.5)\): \(\frac{4.5}{3} = 1.5\); or from \((6, 9)\): \(\frac{9}{6} = 1.5\)).
Equation: \(y = 1.5x\) (or \(c = 1.5p\))
Item 3: Banana Bread Recipe (Calculate & Graph)
Step 1: \(m = \frac{4\text{ loaves}}{2\text{ cups}} = 2\) loaves per cup. Equation: \(y = 2x\).
Step 2 Coordinates: \((0, 0)\), \((1, 2)\), \((2, 4)\), \((3, 6)\), \((4, 8)\), \((5, 10)\).
Graph Check: Straight line connecting origin \((0, 0)\) with slope 2.
Diagnostic Tip: The most frequent error is inverting the division (\(\frac{x}{y}\) instead of \(\frac{y}{x}\)). Reinforce that \(m = \frac{\text{dependent}}{\text{independent}}\).
L4 Level 4: Above Proficiency Solutions Multi-Select & Comparative Analysis (DOK 3)
Item 1: Multi-Select Assessment (Carnival Tickets)
Correct Options: B, C, F
• B is True: \(y = 5(5) = 25\).
• C is True: Point \((3, 15)\) indicates 3 tickets cost $15 (\(5 \times 3 = 15\)).
• F is True: The equation is in form \(y = mx\), which defines a proportional relationship.
• Non-selected: A is False (\(5 \times 4 = 20 \neq 9\)); D is False (sloped line, not horizontal); E is False (passes through \((1, 5)\), not \((5, 1)\)).
Item 2: EV Rapid Charging Predictions
a. Meaning of \((1, 22.5)\): In 1 hour of charging, the vehicle gains exactly 22.5 miles of range (the unit rate).
b. Forward Prediction: \(d = 22.5(6) = \) 135 miles.
c. Backwards Prediction: \(h = 180 \div 22.5 = \) 8 hours.
Item 3: Lawn Care Services Comparison
Rates: GreenThumb = $35.50/acre. LawnMaster = \(\frac{75.00}{2} = \) $37.50/acre.
a. Lower Price: GreenThumb Pros ($35.50 < $37.50).
b. Graph Comparison: LawnMaster Co. will have a steeper line because its constant of proportionality (unit rate/slope) is greater (\(37.50 > 35.50\)).
Diagnostic Tip: Connect unit rate directly to graphical slope: higher unit rate = steeper line when axes have identical scales.
Indiana Academic Standard 7.RP.3 • Answer Key Page 2 of 2 Levels 3 & 4 Scoring Guide
