Formula Fraction Racing Game Formula Fraction GP 4th Grade Math Dash • Addition
Race to 3: The Hazard Speedway
Driver / Team
Date
Driver's Gearbox: How The Die Moves Your Car
WIN CONDITION: Land EXACTLY on 3 !
Roll
ODD
THIRDS GEAR (\(\frac{1}{3}\)s) Rolls 1, 3, 5
Roll 1 : +\(\frac{1}{3}\) Roll 3 : +\(\frac{2}{3}\) Roll 5 : +\(\frac{3}{3}\) (1)
Roll
EVEN
SIXTHS GEAR (\(\frac{1}{6}\)s) Rolls 2, 4, 6
Roll 2 : +\(\frac{1}{6}\) Roll 4 : +\(\frac{2}{6}\) Roll 6 : +\(\frac{3}{6}\)
Spinout Rule: If your roll jumps past 3, your car spins out! Stay at your current spot and forfeit the turn. Example: At \(2\frac{2}{3}\), jumping \(\frac{2}{3}\) reaches \(3\frac{1}{3}\) (Overshoot! Stay at \(2\frac{2}{3}\)).
1 Lap 1: Starting Grid to Pit Stop 1 (0 to 1) Hazard: Oil Slick at \(\frac{2}{3}\) (\(\frac{4}{6}\))
Start: 0 \(\frac{1}{3}\) \(\frac{2}{3}\) Mile 1 (\(\frac{3}{3}\))
START
⚠️
PIT 1
0 \(\frac{1}{6}\) \(\frac{2}{6}\) (=\(\frac{1}{3}\)) \(\frac{3}{6}\) (=\(\frac{1}{2}\)) \(\frac{4}{6}\) (=\(\frac{2}{3}\)) \(\frac{5}{6}\) \(\frac{6}{6} = 1\)
2 Lap 2: Mid-Race Speedway (1 to 2) Hazard: Blown Tire at \(1\frac{1}{2}\) (\(1\frac{3}{6}\))
Mile 1 \(1\frac{1}{3}\) \(1\frac{2}{3}\) Mile 2
🛞
PIT 2
1 \(1\frac{1}{6}\) \(1\frac{2}{6}\) (=\(1\frac{1}{3}\)) \(1\frac{3}{6}\) (=\(1\frac{1}{2}\)) \(1\frac{4}{6}\) (=\(1\frac{2}{3}\)) \(1\frac{5}{6}\) 2
3 Lap 3: Final Dash to the Checkered Flag (2 to 3) Finish Target: Exactly 3.0
Mile 2 \(2\frac{1}{3}\) \(2\frac{2}{3}\) WINNER: 3!
⛽
🚧
2 \(2\frac{1}{6}\) \(2\frac{2}{6}\) (=\(2\frac{1}{3}\)) \(2\frac{3}{6}\) (=\(2\frac{1}{2}\)) \(2\frac{4}{6}\) (=\(2\frac{2}{3}\)) \(2\frac{5}{6}\) \(2\frac{6}{6} = 3\)
Official Pit Stop Hazards: Land on an icon to trigger its effect! Play with coins, classroom counters, or erasers
⚠️ Oil Slick Spot: \(\frac{2}{3}\)
Your tires lose grip! Slide back -\(\frac{1}{6}\) (move backwards to \(\frac{3}{6}\) = \(\frac{1}{2}\)).
🛞 Blown Tire Spot: \(1\frac{1}{2}\)
Blown rubber! Must spend next turn in pit; skip turn unless you roll an EVEN roll .
⛽ Fuel Leak Spot: \(2\frac{1}{3}\)
Engine sputter! Lose speed and slip back -\(\frac{2}{6}\) (-\(\frac{1}{3}\)) to Milestone 2.0.
🚧 Debris Field Spot: \(2\frac{5}{6}\)
Yellow flag hazard! On your following turn, your jump is capped at +\(\frac{1}{6}\) max.
Race Telemetry Math Work Record
Pit Crew Track Log & Math Calculations
Target Finish
3.00 (Checkered Flag)
Pit Stop Equivalence Tuning (Find Common Denominators) Remember: Both Thirds and Sixths share sixths!
1 Third equals \(\frac{1}{3} = \frac{2}{6}\)
2 Thirds equals \(\frac{2}{3} = \frac{4}{6}\)
3 Thirds equals \(\frac{3}{3} = \frac{6}{6} = 1\)
Pro Tip: When adding fractions with unlike denominators, convert thirds into sixths first! Example: \(1\frac{1}{3} + \frac{1}{6} = 1\frac{2}{6} + \frac{1}{6} = 1\frac{3}{6}\) (\(1\frac{1}{2}\))
Lap-by-Lap Calculation Log
Each driver records their turns below:
Turn
Driver
Start Spot
Die Roll
Fraction Math Equation
New Spot
Demo
Racer 1
0
Roll 1 \(\rightarrow +\frac{1}{3}\)
\(0 + \frac{1}{3} = \frac{1}{3}\) (\(=\frac{2}{6}\))
\(\frac{1}{3}\)
1
2
3
4
5
6
7
8
9
10
Official Race Marshall Regulations
Overshoot Rule: If you are on \(2\frac{5}{6}\) and roll an ODD (min. jump \(\frac{1}{3} = \frac{2}{6}\)), you would reach \(3\frac{1}{6}\). You must STAY put! Only a roll of 2 (+\(\frac{1}{6}\)) wins!Hazard Priority: Complete your move forward first. If you land exactly on a hazard space, apply the penalty immediately.
Champion's Post-Race Check
When a driver lands on 3, all racers check their Pit Crew equations. If all math checks out, award them the Fraction GP Trophy !
Grand Prix Winner:
Fuel Burn Subtraction Game Version 2 • Reverse Burn Subtraction From 4 to 0
Fuel Burn GP: Countdown to Zero
Driver / Team
Date
Reverse Gearbox: Subtract Fuel on Every Roll
WIN CONDITION: Subtract down to EXACTLY 0 !
Roll
ODD
SUBTRACT THIRDS (\(-\frac{1}{3}\)) Rolls 1, 3, 5
Roll 1 : \(-\frac{1}{3}\) Roll 3 : \(-\frac{2}{3}\) Roll 5 : \(-\frac{3}{3}\) (-1)
Roll
EVEN
SUBTRACT SIXTHS (\(-\frac{1}{6}\)) Rolls 2, 4, 6
Roll 2 : \(-\frac{1}{6}\) Roll 4 : \(-\frac{2}{6}\) Roll 6 : \(-\frac{3}{6}\)
Engine Stall Rule: If your roll would subtract below 0 (negative), your engine stalls! Stay at your current spot and forfeit the turn. Example: At \(\frac{1}{6}\), rolling 1 (\(-\frac{1}{3}\)) overshoots past 0 (Stall! Stay at \(\frac{1}{6}\)).
1 Lap 1: High-Speed Start (4.0 down to 3.0) Hazard: Oil Slick at \(3\frac{2}{3}\)
START: 4 \(3\frac{2}{3}\) \(3\frac{1}{3}\) Mile 3
⚠️
4.0 \(3\frac{5}{6}\) \(3\frac{4}{6}\) (=\(3\frac{2}{3}\)) \(3\frac{3}{6}\) (=\(3\frac{1}{2}\)) \(3\frac{2}{6}\) (=\(3\frac{1}{3}\)) \(3\frac{1}{6}\) 3.0
2 Lap 2: Midfield Burn (3.0 down to 2.0) Hazard: Blown Tire at \(2\frac{1}{6}\)
Mile 3 \(2\frac{2}{3}\) \(2\frac{1}{3}\) Mile 2
🛞
3.0 \(2\frac{5}{6}\) \(2\frac{4}{6}\) (=\(2\frac{2}{3}\)) \(2\frac{3}{6}\) (=\(2\frac{1}{2}\)) \(2\frac{2}{6}\) (=\(2\frac{1}{3}\)) \(2\frac{1}{6}\) 2.0
3 Lap 3: Danger Zone Straightaway (2.0 down to 1.0) Hazard: Fuel Leak at \(1\frac{1}{3}\)
Mile 2 \(1\frac{2}{3}\) \(1\frac{1}{3}\) Mile 1
⛽
2.0 \(1\frac{5}{6}\) \(1\frac{4}{6}\) (=\(1\frac{2}{3}\)) \(1\frac{3}{6}\) (=\(1\frac{1}{2}\)) \(1\frac{2}{6}\) (=\(1\frac{1}{3}\)) \(1\frac{1}{6}\) 1.0
4 Lap 4: Final Sprint to Empty (1.0 down to 0.0) Finish Target: Exactly 0.0
Mile 1 \(\frac{2}{3}\) \(\frac{1}{3}\) WINNER: 0!
🚧
1.0 \(\frac{5}{6}\) \(\frac{4}{6}\) (=\(\frac{2}{3}\)) \(\frac{3}{6}\) (=\(\frac{1}{2}\)) \(\frac{2}{6}\) (=\(\frac{1}{3}\)) \(\frac{1}{6}\) 0.0 FINISH
Official Pit Stop Hazard Rulebook (Landing Exactly on Hazard Triggers Penalty) Play with classroom counters or game pawns
⚠️ Oil Slick Spot: \(3\frac{2}{3}\)
Tires slide! Move backward +\(\frac{1}{6}\) fuel (back up to \(3\frac{5}{6}\))!
🛞 Blown Tire Spot: \(2\frac{1}{6}\)
Emergency pit stop! Miss next turn unless you roll an EVEN roll to repair.
⛽ Fuel Siphon Spot: \(1\frac{1}{3}\)
Tank penalty! Add +\(\frac{2}{6}\) (\(+\frac{1}{3}\)) back to your tank (up to \(1\frac{2}{3}\))!
🚧 Debris Field Spot: \(\frac{1}{2}\)
Caution flag speed limit! Next turn jump is capped at \(-\frac{1}{6}\) max.
Telemetry Sheet Fraction Subtraction Work
Fuel Burn Subtraction Log & Regrouping
Starting Fuel / Finish
Start 4.0 \(\rightarrow\) Finish 0.0
Pit Stop Regrouping Guide: How to Subtract from Wholes and Mixed Numbers Equivalence: \(\frac{1}{3} = \frac{2}{6}\), \(\frac{2}{3} = \frac{4}{6}\), \(1 = \frac{6}{6}\)
Strategy A: Decomposing a Whole \(4 - \frac{1}{3} = 3\frac{3}{3} - \frac{1}{3} = \mathbf{3\frac{2}{3}}\) Borrow 1 whole as \(\frac{3}{3}\) or \(\frac{6}{6}\)
Strategy B: Common Denominator (6) \(3\frac{1}{3} - \frac{1}{6} = 3\frac{2}{6} - \frac{1}{6} = \mathbf{3\frac{1}{6}}\) Rewrite thirds as sixths first!
Strategy C: Mixed Regrouping \(2\frac{1}{6} - \frac{2}{3} = 1\frac{7}{6} - \frac{4}{6} = \mathbf{1\frac{3}{6}}\) Regroup 1 whole as \(\frac{6}{6}\) when needed
Lap-by-Lap Subtraction Calculation Table
Record starting position, die roll, equation, and new spot:
Turn
Driver
Start Fuel
Die Roll
Subtraction Math Equation
New Fuel Spot
Demo
Racer 1
4.0
Roll 1 \(\rightarrow -\frac{1}{3}\)
\(4 - \frac{1}{3} = 3\frac{3}{3} - \frac{1}{3} = 3\frac{2}{3}\)
\(3\frac{2}{3}\) (Oil Slick!)
1
2
3
4
5
6
7
8
9
Sub-Zero Marshall Regulations
Stall Rule: Must hit EXACTLY 0 . If your subtraction results in less than zero, you cannot move! Turn is skipped.Hazard Order: Execute subtraction first; if your car lands on an active hazard marker, apply penalty immediately.
Fuel Champion Signoff
The first racer to reach exactly 0.0 fuel with verified telemetry equations claims the Fuel Burn Cup !
Cup Winner:
Overdrive Fraction Racing Game 4-Mile Endurance Circuit Extended Addition: 0 to 4
Overdrive GP: The 4-Mile Endurance Dash
Driver / Team
Date
Endurance Gearbox: Roll Die to Advance
WIN CONDITION: Land EXACTLY on 4.0 !
Roll
ODD
THIRDS GEAR (\(\frac{1}{3}\)s) Rolls 1, 3, 5
Roll 1 : +\(\frac{1}{3}\) Roll 3 : +\(\frac{2}{3}\) Roll 5 : +\(\frac{3}{3}\) (1)
Roll
EVEN
SIXTHS GEAR (\(\frac{1}{6}\)s) Rolls 2, 4, 6
Roll 2 : +\(\frac{1}{6}\) Roll 4 : +\(\frac{2}{6}\) Roll 6 : +\(\frac{3}{6}\)
Overshoot Rule: If your jump exceeds 4.0, your car spins out! Stay at your current spot and forfeit the turn. Example: At \(3\frac{5}{6}\), jumping \(\frac{1}{3}\) (\(\frac{2}{6}\)) lands past 4.0 (Stay at \(3\frac{5}{6}\)).
1 Lap 1: Grandstand Straightaway (0 to 1) Hazard: Crosswind at \(\frac{2}{3}\) (\(\frac{4}{6}\))
START: 0 \(\frac{1}{3}\) \(\frac{2}{3}\) Mile 1 (\(\frac{3}{3}\))
🌪️
0 \(\frac{1}{6}\) \(\frac{2}{6}\) (=\(\frac{1}{3}\)) \(\frac{3}{6}\) (=\(\frac{1}{2}\)) \(\frac{4}{6}\) (=\(\frac{2}{3}\)) \(\frac{5}{6}\) Mile 1.0
2 Lap 2: Midfield Chicanes (1 to 2) Hazard: Hydroplane at \(1\frac{5}{6}\)
Mile 1 \(1\frac{1}{3}\) \(1\frac{2}{3}\) Mile 2
🌧️
1.0 \(1\frac{1}{6}\) \(1\frac{2}{6}\) (=\(1\frac{1}{3}\)) \(1\frac{3}{6}\) (=\(1\frac{1}{2}\)) \(1\frac{4}{6}\) (=\(1\frac{2}{3}\)) \(1\frac{5}{6}\) Mile 2.0
3 Lap 3: Radar Alley (2 to 3) Hazard: Radar Trap at \(2\frac{1}{3}\) (\(2\frac{2}{6}\))
Mile 2 \(2\frac{1}{3}\) \(2\frac{2}{3}\) Mile 3
⚡
2.0 \(2\frac{1}{6}\) \(2\frac{2}{6}\) (=\(2\frac{1}{3}\)) \(2\frac{3}{6}\) (=\(2\frac{1}{2}\)) \(2\frac{4}{6}\) (=\(2\frac{2}{3}\)) \(2\frac{5}{6}\) Mile 3.0
4 Lap 4: Final Overdrive Sprint (3 to 4) Victory Goal: Exactly 4.0
Mile 3 \(3\frac{1}{3}\) \(3\frac{2}{3}\) WINNER: 4!
🧊
3.0 \(3\frac{1}{6}\) \(3\frac{2}{6}\) (=\(3\frac{1}{3}\)) \(3\frac{3}{6}\) (=\(3\frac{1}{2}\)) \(3\frac{4}{6}\) (=\(3\frac{2}{3}\)) \(3\frac{5}{6}\) 4.0 FINISH
Endurance Hazard Guide: Brand-New Hazards on the 4-Mile Track Play with coins, counters, or game pawns
🌪️ Crosswind Spot: \(\frac{2}{3}\)
Headwind gust! Blown backward -\(\frac{2}{6}\) (-\(\frac{1}{3}\)) back to Milestone \(\frac{2}{6}\) (\(\frac{1}{3}\)).
🌧️ Hydroplane Spot: \(1\frac{5}{6}\)
Deep puddle! Car loses traction; skip next turn unless you roll an ODD roll to recover.
⚡ Radar Trap Spot: \(2\frac{1}{3}\)
Speed limit penalty! Forced pit lane detour: slide back -\(\frac{1}{6}\) to Milestone \(2\frac{1}{6}\).
🧊 Black Ice Spot: \(3\frac{1}{2}\)
Zero grip near the finish! Car slides backward -\(\frac{2}{6}\) (-\(\frac{1}{3}\)) down to \(3\frac{1}{6}\)!
Telemetry Sheet 4-Mile Addition Work
Overdrive Telemetry Log: Race to 4.0
Starting Spot / Finish
Start 0.0 \(\rightarrow\) Finish 4.0
Endurance Telemetry Tuning: Adding Thirds and Sixths Across 4 Wholes Golden Rule: Convert Thirds to Sixths (\(\frac{1}{3} = \frac{2}{6}\))
Equivalence Tuning \(\frac{1}{3} = \frac{2}{6}\) | \(\frac{2}{3} = \frac{4}{6}\) Use common denominator 6 for easy addition
Crossing into Next Whole \(1\frac{5}{6} + \frac{2}{6} = 1\frac{7}{6} = \mathbf{2\frac{1}{6}}\) Regroup \(\frac{6}{6}\) as 1 additional whole
Exact 4.0 Victory Check \(3\frac{4}{6} + \frac{2}{6} = 3\frac{6}{6} = \mathbf{4.0}\) Must equal exactly 4; overshoots stay put!
Lap-by-Lap Addition Calculation Table
Record start, die roll, math equation, and new spot:
Turn
Driver
Start Spot
Die Roll
Addition Math Equation
New Spot
Demo
Driver 1
\(1\frac{1}{3}\)
Roll 3 \(\rightarrow +\frac{2}{3}\)
\(1\frac{1}{3} + \frac{2}{3} = 1\frac{3}{3} = 2.0\)
\(2.0\) (Mile 2 Checkpoint)
1
2
3
4
5
6
7
8
9
Endurance Marshall Regulations
Finish Line: Must reach EXACTLY 4.0 . If your jump overshoots past 4, you stay put!Hazard Priority: Move forward to your calculated spot first. If that spot has a hazard icon, apply penalty immediately!
Endurance Trophy Verification
The first racer to land on 4.0 with verified telemetry addition wins the Overdrive GP Trophy !
Endurance Champion:
