Base Camp Lesson Plan Base Camp Lesson Plan
Subject: Algebra 1 | Topic: Exponent Rules with Different Bases
Grade Level: 9-10
Duration: 45 Minutes
Learning Objective
Students will apply exponent rules to numbers with different bases by identifying common bases and converting them into power-of-prime form.
Materials
Power Up Practice Worksheet
Base Camp Anchor Chart
Exponent Expedition Slides
Projector & Internet (for video)
Key Vocabulary
Common Base Prime Factor Product Rule Power of a Power
Lesson Procedure
1
Warm-up: Power Detection (5 min)
Engage students with a rapid-fire prime factorization drill.
Distribute the Power Up Practice Worksheet.
Students rewrite numbers (4, 8, 9, 16, 25, 27) as powers of prime numbers.
Key Check: Ensure they recognize 8 as \(2^3\) and 27 as \(3^3\).
2
Video Briefing (10 min)
Conceptual bridge using the "Multiplying and Dividing Monomials" video.
Play the video from 6:56 to 9:05.
Pause Point (7:53): Stop before the narrator reveals how to convert base 4 to \(2^2\). Ask: "Does anyone see a way to make the bases match?"
Highlight the two methods shown: (1) Common Base vs. (2) Common Exponent.
3
The Ascent: Collaborative Practice (20 min)
Students work in pairs/trios to solve multi-base problems.
Groups solve tasks like \(3^2 \cdot 9^2\) and \(5^3 \cdot 25\) on their worksheets.
Rule of the Trail: Every step must show the base conversion.
Teacher circulates to check for the common error: multiplying the bases instead of exponents (e.g., \(2^3 \cdot 4^2 \neq 8^5\)).
4
The Summit: Closure (10 min)
Synthesizing the learning through discussion.
Discussion Prompt: "When do we add exponents, and when are we allowed to multiply the bases? Why is converting bases the safer strategy?"
Refer to the Base Camp Anchor Chart to solidify the rules.
Exit Ticket: Solve \(2^5 \cdot 8^1\).
Mountain Guide: Differentiation
Support (Scaffolding)
Provide a 'Prime Power Cheat Sheet' (e.g., \(4 = 2^2\), \(8 = 2^3\)) for students struggling with basic conversions. Focus on single-variable problems before numerical bases.
Extension (Peak Climbers)
Introduce problems with variables in the exponent (e.g., \(4^x \cdot 2^3 = 2^{13}\)) or divisions with different bases (e.g., \(27^4 / 9^2\)).
Base Camp Anchor Chart Base Camp
Mastering Different Bases
!
The Golden Rule
You can only add exponents if the
Bases are Identical
The Expedition Strategy
1
Detection
Identify a Common Base (usually a prime number like 2, 3, or 5).
4 = 22 27 = 33
2
Replacement
Substitute the original number with its power-form.
25 • (22)3
3
Power of a Power
Multiply the inside exponent by the outside exponent.
25 • 26
4
Summit
Now that bases match, ADD the exponents!
211
Exponent Expedition
Stay at the base, or climb to the power.
Exponent Expedition Slides Exponent Expedition
Climbing Different Bases
Base Camp 01
Algebra I
Power Detection
5 MINUTES
Rewrite each number as a Power of a Prime Number:
4
\(?^?\)
8
\(?^?\)
9
\(?^?\)
16
\(?^?\)
25
\(?^?\)
27
\(?^?\)
Expert Briefing
Embedded media
Watch closely from 6:56 - 9:05
Watch For:
How \(4\) becomes \(2^2\).
The "Power of a Power" rule.
Why we need common bases.
Trail Analysis
Challenge Problem:
25 • 43
Q Why can't we add exponents yet?
The bases (2 and 4) are not identical!
A What is the move?
Convert the 4 into a power of 2.
The Ascent
Collaborative Problem Solving
Mission 1
32 • 92
Hint: 9 is 3 squared.
Mission 2
53 • 25
Hint: 25 is 5 squared.
Climb together! Compare steps with your group. Showing work is mandatory.
Reached the Peak
Discussion Anchor:
"Why do we add exponents, but we multiply the bases when converting? Why is the base the most important part of the climb?"
Power Up Practice Worksheet Power Up Practice
Exponent Expedition: Base Camp 01
Hiker Name:
Date:
Phase 1: Power Detection (Warm-up)
Identify the prime power for each number. Example: 4 = 22
8 =
9 =
16 =
25 =
27 =
49 =
Phase 2: The Ascent (Collaborative Practice)
Show every step! Convert to a common base, apply the power-of-a-power rule, then find the final answer.
32 • 92
Target Base: 3
Your Trail Work
53 • 25
Target Base: 5
Your Trail Work
24 • 82
Target Base: 2
Your Trail Work
163 ÷ 44
Target Base: 4 or 2
Your Trail Work
Phase 3: The Summit (Exit Ticket)
Climb the Final Peak:
Simplify to a single power: 25 • 81
Ready for base camp? Submit your worksheet to the trail lead.
