Rate Raiders Slides Algebra II / Math 3
Rate Raiders
Differentiating between Growth Factors and Percent Change in Exponential Models.
v1.0.26
Warm-up: The Great Divide
Scenario A
\( b = 0.8 \)
A growth factor of 0.8
Scenario B
\( -20\% \)
A 20% decrease
"Are these two scenarios the same? Why or why not?"
The Tree Branch Dilemma
Watch from 6:00
Embedded media
Topic: Converting yearly models to monthly factors.
\( t = \text{years} \) \( 1 \text{ month} = 1/12 \text{ year} \)
Factor vs. Percent Change
Growth Factor (\( b \))
What you multiply by each step.
New Value = Old Value \(\times b\)
Percent Change (\( r \))
The relative increase/decrease .
\( b = 1 + r \) (as a decimal)
The Conversion Rule
To change the time unit from 1 to \( k \), calculate the new factor:
\( B = b^k \)
Where \( k \) is the number of original time units in the new time unit.
Factor vs. Percent Sort
1
Sort
Classify each card as "Growth Factor" or "Percent Change" based on the text.
2
Convert
Identify the current factor \( b \) and the relationship between time units.
3
Solve
Find the growth/decay factor for the new time model specified.
25 Minutes Remaining
Mission Complete
Exit Ticket
Convert a growth factor of 1.05 into a percentage change.
Hand in your paper before the bell rings!
Change Chasers Sort Activity Change Chasers Sort
Sorting Factors, Rates, and Units
Name:
Date:
Instructions
1. Cut out the 6 scenario cards on the following page.Growth Factor or Percent Change .
Card Category & Conversion Work New Factor (\( B \)) 1 2 3 4 5 6
Activity Cards: Cut Along the Dashed Lines
1
"The bacteria population decreases by 5% every 10 minutes."
Challenge:
Find the hourly growth/decay factor.
2
"The value of a rare coin is multiplied by 1.15 every year."
Challenge:
Find the monthly growth/decay factor.
3
"A forest loses 12% of its trees every decade."
Challenge:
Find the annual growth/decay factor.
4
"The number of users on a social app grows by a factor of 1.02 every week."
Challenge:
Find the daily growth/decay factor.
5
"A viral video's view count doubles every 3 hours."
Challenge:
Find the hourly growth/decay factor.
6
"A chemical substance decays by 2.5% every 20 minutes."
Challenge:
Find the growth/decay factor for an 8-hour period.
Teacher Tip: Provide scissors and glue sticks for the sort
Rate Reveal Exit Ticket Exit Ticket
Rate Reveal
Name:
Date:
Convert a growth factor of 1.05 into a percentage change.
Show your work & final answer:
Exit Ticket
Rate Reveal
Name:
Date:
Convert a growth factor of 1.05 into a percentage change.
Show your work & final answer:
Master Guide Teacher Resource Master Guide
Rate Raiders • Teacher Resource
Lesson Duration
45-50 min
Lesson Objective
Students will differentiate between growth factors and percent change in exponential contexts. They will learn to convert between these forms and adjust for unit changes using power rules (\( B = b^k \)), ensuring dimensional consistency in mathematical models.
Common Misconceptions
Unit Neglect: Students often plug time values directly into equations without checking if the units match the model's definition of \( t \).
Factor vs. Rate: Confusion between "grows by 5%" (\( b = 1.05 \)) and "grows by a factor of 5" (\( b = 5 \)).
Linear Thinking: Attempting to multiply the rate by time (e.g., 5% per 10 mins = 30% per hour) instead of using exponents.
Materials Needed
Rate Raiders Slides
Sort Activity Cards (1 per pair)
Recording Sheets (1 per student)
Exit Tickets (1 per student)
Scissors/Glue Sticks
Scientific Calculators
Pacing & Facilitation
05 MIN
Warm-up: The Great Divide
Discussion focused on whether a factor of 0.8 is the same as a 20% decrease. Highlight that \( 1 - 0.20 = 0.8 \).
10 MIN
Video Viewing: Tree Branch Problem
Show video from 6:00. Pause at 7:15 to ask: "A month is what fraction of a year?" Before the reveal, have students predict the monthly factor.
25 MIN
Main Activity: Change Chasers Sort
Students work in pairs. Encourage them to write the original model (\( b^t \)) before attempting the unit conversion.
05 MIN
Closure: Rate Reveal Exit Ticket
Individually assessed. Check for understanding of the \( b = 1 + r \) relationship.
Answer Key: Sorting Activity
# Classification Conversion Logic New Factor (\( B \)) 1 Percent Change \( r = -0.05 \rightarrow b = 0.95 \) 10 mins to 1 hr: \( k = 6 \) \( 0.95^6 \approx 0.7351 \) 2 Growth Factor \( b = 1.15 \) 1 yr to 1 month: \( k = 1/12 \) \( 1.15^{1/12} \approx 1.0117 \) 3 Percent Change
