Rate Runner Maze Worksheet
7th Grade Math • 7.RP.A Proportional Reasoning
RATE RUNNER Maze Quest
Name:
Date: Period:
Mission: Start at Chamber A. Solve each problem, follow the arrow with the correct proportional answer, collect rune letters, and reach the Vault!
8 Path Chambers
CHAMBER A • START Rune: R
A bakery uses 12 cups of flour to bake 4 loaves of bread. Find the constant of proportionality (\(k\)) in cups per loaf.
→ East \(k = 3\)
↓ South \(k = \frac{1}{3}\)
CHAMBER B Rune: A
Which table shows a proportional relationship with constant ratio \(\frac{y}{x}\)?
T-1: (2, 7), (4, 14), (6, 21)
T-2: (2, 5), (4, 9), (6, 13)
↓ South Table 1
→ East Table 2
CHAMBER C DEAD END
Phone plan: \(\$15\) monthly base fee plus \(\$5\) per GB. Is the total cost proportional to GBs?
TRAP! Total cost does not pass through \((0,0)\). Turn back!
← Return to Chamber B
CHAMBER D Rune: I
A distance-time graph passes through \((0,0)\) and \((1, 45)\). What does point \((1, 45)\) represent?
↓ South Car travels 45 mi in 1 hr
→ East Car takes 45 hrs for 1 mi
CHAMBER E Rune: T
A train travels 186 miles in 3 hours at steady speed. Write an equation for distance (\(d\)) in \(h\) hours.
← West \(d = 62h\)
↓ South \(d = h + 183\)
CHAMBER F DEAD END
Is the area of a square proportional to its side length \(s\)? (\(A = s^2\)).
TRAP! \(A/s = s\) is not constant! The corridor is blocked!
← Return to Chamber E
CHAMBER G Rune: O
A lemonade recipe uses 5 lemons for every 2 cups of sugar. How many lemons are needed for 8 cups of sugar?
→ East 20 lemons
↓ South 11 lemons
CHAMBER H Rune: P
Which equation represents a proportional relationship with a unit rate of \(0.75\)?
→ East \(y = \frac{3}{4}x\)
↓ South \(y = x - 0.75\)
CHAMBER I Rune: A
Store A: 6 notebooks for \(\$9.00\). Store B: 8 notebooks for \(\$10.40\). Which has the lower unit price?
↓ South Store B (\(\$1.30\) / book)
← West Store A (\(\$1.50\) / book)
PITFALL J ADDITION TRAP
You chose 11 lemons! You added \(6\) instead of multiplying by the constant scale factor \(4\).
Proportions are MULTIPLICATIVE! Retrace your steps back North.
↑ Return to Chamber G
PITFALL K SUBTRACTION TRAP
\(y = x - 0.75\) has a non-zero intercept \((0, -0.75)\). Proportions must fit \(y = kx\)!
The corridor is collapsed! Return North to Chamber H.
↑ Return to Chamber H
CHAMBER L • VAULT! Rune: TH
Master Lock: In this golden chamber, \(y = 3.5x\). Calculate the value of \(y\) when \(x = 12\) to crack the vault!
Vault Number: ____
Correct Path Chambers Log (Record your 8 visited chambers in order):
A → ___ → ___ → ___ → ___ → ___ → ___ → L
Secret Rune Phrase:
_ _ _ _ _ _ _ _ _
Next Page →
Proof Lab
Rate Runner • Step-by-Step Evidence
THE PROPORTION PROOF LAB
Show your mathematical calculations
Handwriting-Ready Workpad
True mathematicians prove their path! Complete the calculation stations below for the chambers you traversed, demonstrating your unit rate calculations and equation setups.
STATION 1 • Chamber A (Unit Rate) \(k = \frac{y}{x}\)
Calculate constant \(k\) for 12 cups of flour across 4 loaves. Include units in your final answer.
Unit Rate \(k\) = ____________________
STATION 2 • Chamber B (Ratio Test) Table Proof
Prove Table 1 is proportional by computing \(\frac{y}{x}\) for all 3 ordered pairs: \((2,7)\), \((4,14)\), \((6,21)\).
\(\frac{7}{2} =\) _______ • \(\frac{14}{4} =\) _______ • \(\frac{21}{6} =\) _______
Is \(k\) constant? [ ] Yes [ ] No
STATION 3 • Chamber E (Equation \(y = kx\)) Speed Equation
Find the unit speed for 186 miles in 3 hours, then write the proportional equation connecting distance \(d\) and hours \(h\).
Speed \(k = \frac{186\text{ mi}}{3\text{ hr}} =\) __________________ mph
Equation: \(d =\) ______________________
STATION 4 • Chamber G (Recipe Proportion) Equivalent Ratios
Set up and solve a proportion or unit rate to find how many lemons are needed for 8 cups of sugar (recipe: 5 lemons to 2 cups sugar).
Total Lemons = ____________________
STATION 5 • Chamber H (Fraction & Decimal) Decimal \(k\)
Convert the fraction \(\frac{3}{4}\) to a decimal to verify it matches the required unit rate of \(0.75\). Explain why \(y = kx\) applies.
\(\frac{3}{4} =\) _________ • Does it pass through \((0,0)\)? [ ] Yes
STATION 6 • Chamber I (Unit Price Comparison) Best Buy
Calculate the unit price per notebook for both stores. Show division steps.
Store A: \(\$9.00 \div 6 =\) \(\$__________\) per notebook
Store B: \(\$10.40 \div 8 =\) \(\$__________\) per notebook
Better deal: Store ________ (saves \(\$______\)/notebook)
TRAPDOOR AUTOPSY: Mathematical Error Analysis
Critical Thinking
Select one incorrect distractor path that you avoided in the maze (e.g., Pitfall J adding 6 instead of scaling, Pitfall K having a subtraction intercept, Chamber C's flat fee, or Chamber A's inverted fraction). Explain mathematically why it is NOT a proportional relationship:
Trap Chamber Chosen: [ ] C • [ ] F • [ ] J • [ ] K • Other: ___________
Reason it fails: ________________________________________________________________________________
