Carnival Logistics Teacher Guide Teacher Guide
Carnival Calculations
90 MINS
Objectives
Identify independent and dependent variables.
Analyze patterns in tables to write equations.
Represent relationships using graphs and equations.
Materials
Midway Math Slides
Ticket Booth Tasks (2 pgs)
Escape Room (3 pgs)
Answer Keys
Lesson Pacing
Intro & Direct Instruction 15 min
Ticket Booth Tasks 20 min
Midway Jeopardy Review 30 min
Escape Room Challenge 20 min
Wrap-up & Cleanup 5 min
Instructional Tips
The "Depends" Test
Have students test the logic: "Does the [Cost] depend on the [Tickets]?" or "Does the [Tickets] depend on the [Cost]?" This helps clarify the dependent variable (y).
Pattern Hunter
In tables, guide students to find the single operation (add, subtract, multiply, or divide) that works for EVERY row. This operation becomes the heart of the equation.
Graphing the Midway
Remind students that the independent variable (x) always goes on the horizontal axis (the ground) and the dependent variable (y) goes on the vertical axis.
Midway Math Slides Midway Math
Mastering Variables & Patterns
Tables
Graphs
Equations
Variable Vitals
Independent (x)
The "Cause" or the input. This is the variable that you change on purpose or that happens on its own (like time).
Dependent (y)
The "Effect" or the output. This variable depends on the independent variable.
Example: The more tickets you buy (x), the more money you spend (y).
The Midway Challenge
Tickets (x) Cost (y) 1 $3 2 $6 3 $9 x ?
Can you find the magic rule?
Look at what happens to the Cost (y) as the Tickets (x) increase. What is the pattern?
The Magic Rule
The Relationship:
Multiply the Tickets by 3!
The Equation:
\(y = 3x\)
Midway Graphs
Tickets (x)
Cost (y)
Analyze the Graph:
This graph represents our \(y = 3x\) equation.
If x = 4, what will y be?
Graph Results
y = 12
Just like our table, the graph shows that as we move right (more tickets), we move up three times as fast (more cost).
JEOPARDY!
Midway Edition
Variables Tables Graphs Equations
Variables for 100
"At the carnival, you buy bags of popcorn. Each bag costs $5."
Identify the Independent (x) and Dependent (y) variables.
Answer: Variables for 100
X (Independent):
Y (Dependent):
Tables for 200
Find the magic rule for this table:
Answer: Tables for 200
Rule: Multiply by 5
Equation:
\(y = 5x\)
Graphs for 300
If a graph shows the point (4, 12) and the relationship is \(y = kx\)...
What is the value of k?
(Hint: What do you multiply 4 by to get 12?)
Answer: Graphs for 300
\(k = 3\)
The equation is \(y = 3x\)
Equations for 400
"A ride ticket costs $4, but you also have to pay a $5 entry fee for the fairground."
Write the equation for Total Cost (y) based on Rides (x).
Answer: Equations for 400
\(y = 4x + 5\)
The 4 is the cost per ride (coefficient)
Ticket Booth Tasks Worksheet Ticket Booth Tasks
Part 1: Identifying Variables
Name:
Date:
Read each scenario. Identify the Independent (x) and Dependent (y) variables.
1. The more hours you spend at the carnival, the more money you spend on arcade games.
Independent (x):
Dependent (y):
2. A bucket of popcorn contains 120 calories for every serving inside.
Independent (x):
Dependent (y):
3. For every game round you play at the "Ring Toss", you win 4 prize tickets.
Independent (x):
Dependent (y):
Ticket Booth Tasks
Part 2: Patterns to Equations
Analyze the tables. Write the rule (the pattern) and the equation.
Ferris Wheel Heights
Turns (x) Height (y) 2 8 5 20 10 40
The Rule:
The Equation:
Cotton Candy Pricing
Base $ (x) Total $ (y) $4 $7 $10 $13 $15 $18
The Rule:
The Equation:
Grand Prize Escape Challenge Grand Prize Escape
Challenge Part 1: Booths 1 & 2
DIGITS
Team:
1
Ring Toss Booth
"Welcome! Pay a $1 entry fee plus $2 for every ring you toss (x)."
Equation (y=...):
Cost for 10 rings:
Digit 1 = First digit of answer.
2
Duck Pond
"Pick a duck! Your total points (y) equals 5 times the ducks (x) you pick."
Equation (y=...):
Points for 4 ducks:
Digit 2 = Second digit of answer.
Grand Prize Escape
Challenge Part 2: Booths 3 & 4
DIGITS
3
Speedy Coaster
"Wait time (y) is 5 mins more than ride time (x)."
Equation (y=...):
Wait time for 12 mins:
Digit 3 = First digit of answer.
4
Prize Counter
"Bonus tickets (y) equals 3 times the prizes (x) minus 1."
Equation (y=...):
Tickets for 3 prizes:
Digit 4 = The answer digit.
Master Lock
Enter Final Code
Midway Grand Finale
Ticket Booth Tasks Answer Key Answer Key
Ticket Booth Tasks
Teacher Only
Part 1: Variables
1. Hours/Money: x = Hours, y = Money spent
2. Popcorn/Calories: x = Servings, y = Total Calories
3. Rounds/Tickets: x = Game Rounds, y = Tickets Won
Part 2: Equations
Ferris Wheel
Rule: Multiply x by 4
\(y = 4x\)
Cotton Candy
Rule: Add 3 to x
\(y = x + 3\)
Grand Prize Escape Answer Key Answer Key
Grand Prize Escape
Full Solution
Booth 1: Ring Toss
Eq: \(y = 2x + 1\)
\(2(10) + 1 = 21\)
Digit 1: 2
Booth 2: Duck Pond
Eq: \(y = 5x\)
\(5(4) = 20\)
Digit 2: 0
Booth 3: Speedy Coaster
Eq: \(y = x + 5\)
\(12 + 5 = 17\)
Digit 3: 1
Booth 4: Prize Bonus
Eq: \(y = 3x - 1\)
\(3(3) - 1 = 8\)
Digit 4: 8
MASTER CODE
2 0 1 8
