Root Runner Teacher Guide
Root Runner
Teacher Facilitation Guide
Radical Equations
Activity Overview
The Root Runner Scavenger Hunt is a self-pacing "Around the Room" activity. Students solve a radical equation at one station, and their answer leads them to the next station. If they solve all 15 problems correctly, they will complete a full loop and return to where they started.
Learning Objectives
- Solve radical equations with a single radical term.
- Solve radical equations with radicals on both sides.
- Isolate radicals and square both sides to find solutions.
- Identify the correct sequence of operations.
15
Stations
60
Minutes
Looping
Structure
Setup & Pacing
Prep Work
- 1 Print the 15 Problem Posters. Laminate them if you plan to reuse the activity.
- 2 Hang the posters randomly around the room. Do not hang them in alphabetical order; the path should jump across the room.
- 3 Print a Recording Sheet for every student.
During the Activity
- Starter: Students can begin at any station. Have them write the letter of their starting station in the first box of their recording sheet.
- The Flow: Students solve the "Current Challenge" at the bottom of the poster. They find their answer at the top of a different poster.
- Scaffolding: If a student can't find their answer on any poster, they've made a calculation error. Encourage them to check their work!
ROOT RUNNER ACTIVITY PAGE 1 OF 2
MASTER TRACKER
Correct Sequence and Solutions
| Station | Equation | Answer (Leads to...) |
|---|
| Station A | \[\sqrt{x+5} = 9\] | 76 |
| Station B | \[\sqrt{2x-4} = \sqrt{x+6}\] | 10 |
| Station C | \[4\sqrt{x} = 20\] | 25 |
| Station D | \[\sqrt{x-3} + 4 = 11\] | 52 |
| Station E | \[\sqrt{3x+4} = \sqrt{5x-8}\] | 6 |
| Station F | \[2\sqrt{x+1} = 12\] | 35 |
| Station G | \[\sqrt{x/2 + 5} = 8\] | 118 |
| Station H | \[\sqrt{7x-3} = \sqrt{4x+12}\] | 5 |
| Station I | \[\sqrt{x-10} = 3\] | 19 |
| Station J | \[5 + \sqrt{2x} = 13\] | 32 |
| Station K | \[\sqrt{4x+1} = \sqrt{x+10}\] | 3 |
| Station L | \[\sqrt{x-8} = 2\] | 12 |
| Station M | \[\sqrt{10x-4} = \sqrt{2x+60}\] | 8 |
| Station N | \[3\sqrt{x-2} = 15\] | 27 |
| Station O | \[\sqrt{6x-2} = \sqrt{x+43}\] | 9 |
Teacher Shortcut Tip:
The sequence is alphabetical! A → B → C → D → E → F → G → H → I → J → K → L → M → N → O → A. This makes it easy for you to check student progress without the key in hand.
ROOT RUNNER ACTIVITY ANSWER KEY
Root Runner Posters
Previous Answer
9
A
Solve the Equation
\[\sqrt{x+5} = 9\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
76
B
Solve the Equation
\[\sqrt{2x-4} = \sqrt{x+6}\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
10
C
Solve the Equation
\[4\sqrt{x} = 20\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
25
D
Solve the Equation
\[\sqrt{x-3} + 4 = 11\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
52
E
Solve the Equation
\[\sqrt{3x+4} = \sqrt{5x-8}\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
6
F
Solve the Equation
\[2\sqrt{x+1} = 12\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
35
G
Solve the Equation
\[\sqrt{\frac{x}{2} + 5} = 8\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
118
H
Solve the Equation
\[\sqrt{7x-3} = \sqrt{4x+12}\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
5
I
Solve the Equation
\[\sqrt{x-10} = 3\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
19
J
Solve the Equation
\[5 + \sqrt{2x} = 13\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
32
K
Solve the Equation
\[\sqrt{4x+1} = \sqrt{x+10}\]
Solve this to find the next station's top number!
Root Runner
Previous Answer
Root Runner Recording Sheet Final
Root Runner
Radical Equation Scavenger Hunt
Name
Date
Start at any station. Record the letter, show your work below, and find your solution at the top of a new station to continue the path!
Challenge 1
Station:
My Answer:
Challenge 2
Station:
My Answer:
Challenge 3
Station:
My Answer:
Challenge 4
Station:
My Answer:
Challenge 5
Station:
My Answer:
Challenge 6
Station:
My Answer:
Challenge 7
Station:
My Answer:
Challenge 8
Station:
My Answer:
Challenge 9
Station:
My Answer:
Challenge 10
Station:
My Answer:
Challenge 11
Station:
My Answer:
Challenge 12
Station:
My Answer:
Challenge 13
Station:
My Answer:
Challenge 14
Station:
My Answer:
Challenge 15
Station:
My Answer:
Runner Status
Did you return to your starting station? If yes, your path forms a perfect loop! Check your work and turn in your runner log.
Loop Complete
Work Checked
"The only way to learn mathematics is to do mathematics." — Paul Halmos
