Dog Groomer Dilemma Slides
Multi-Step Problem Solving
Real-World Rates & Multi-Step Math
The Dog Groomer Dilemma
Step-by-step strategy guide: unpacking workdays, daily rates, dog counts, and weekly earnings differences.
3 Structured Steps
Checkpoint Answers
Extension Challenges
PROBLEM LAUNCH
Unpack the Sticky Problem
Read & Annotate Key Facts
"Dana and Monique are dog groomers. Dana's workday is 10 hours and Monique's workday is 8 hours. Dana and Monique each work 40 hours per week. On Monday, Dana groomed 15 dogs in 10 hours and Monique groomed 10 dogs in 8 hours. They each earn $12.75 for each dog groomed. Assuming that for the rest of the week Dana and Monique groom the same number of dogs per workday as they did on Monday, what will be the difference between their weekly earnings?"
Dana's Given Info
- Workday length: 10 hours/day
- Total schedule: 40 hours/week
- Monday output: 15 dogs/day
Monique's Given Info
- Workday length: 8 hours/day
- Total schedule: 40 hours/week
- Monday output: 10 dogs/day
STEP 1
How Many Days Does Each Person Work?
Sub-Question 1 of 3
Guiding Question: If both work 40 total hours per week, how many workdays does each person work to reach 40 hours?
Dana's Days 10-hr shifts
Divide weekly hours by shift length:
\( 40 \text{ hours} \div 10 \text{ hrs/day} = \) 4 days
Dana works 4 days per week
Monique's Days 8-hr shifts
Divide weekly hours by shift length:
\( 40 \text{ hours} \div 8 \text{ hrs/day} = \) 5 days
Monique works 5 days per week
Checkpoint 1 Summary
Dana works 4 days • Monique works 5 days
Verified ✓
STEP 2
How Many Dogs Does Each Groom Weekly?
Sub-Question 2 of 3
Guiding Question: Multiply each groomer's workdays per week by the number of dogs groomed per workday.
Dana's Weekly Dogs 15 dogs/day
\( 4 \text{ workdays} \times 15 \text{ dogs/day} \)
= 60 dogs
Monique's Weekly Dogs 10 dogs/day
\( 5 \text{ workdays} \times 10 \text{ dogs/day} \)
= 50 dogs
Checkpoint 2 Summary
Dana grooms 60 dogs • Monique grooms 50 dogs → Difference = 10 dogs
60 vs 50 Dogs
STEP 3
Find Difference in Weekly Earnings
Rate: $12.75 / dog
METHOD A Calculate Both & Subtract
Dana: \( 60 \times \$12.75 = \mathbf{\$765.00} \)
Monique: \( 50 \times \$12.75 = \mathbf{\$637.50} \)
\( \$765.00 - \$637.50 = \mathbf{\$127.50} \)
Standard calculation: find each total first.
METHOD B (FAST) Difference in Dogs × Rate
Dog Difference: \( 60 - 50 = \mathbf{10 \text{ dogs}} \)
Multiply by Rate: \( 10 \times \$12.75 \)
\( = \mathbf{\$127.50} \)
Shortcut: Distributive property \( 12.75(60 - 50) \)
Final Answer Checkpoint
Dana earns $127.50 more than Monique per week.
$127.50
PROBLEM SOLVING MOVES
Why Was This Problem "Sticky"?
Strategy Debrief
1
Trap: Assuming 5-Day Weeks
Students often multiply both by 5 days. You had to calculate 40 ÷ 10 = 4 days for Dana first!
2
Trap: Hourly vs Daily Rates
Dana grooms 1.5 dogs/hr, Monique grooms 1.25 dogs/hr. Calculating by day was simpler than finding decimals per hour.
3
Pro Move: Distributive Property
Finding the difference in dogs (\(10\)) before multiplying by \(\$12.75\) saved time and avoided multi-digit arithmetic errors.
Rule of Thumb: When rates per unit are identical, find the difference in total units first!
EARLY FINISHERS
Extension & Challenge Variations
Test Your Math Grit
Challenge 1: Overtime Twist
Suppose Monique works an extra 8-hour workday on Saturday at the same grooming rate (10 dogs).
Question: Who earns more for that week, and by how much?
Hint: Recalculate Monique's total dogs for 6 days.
Challenge 2: Effective Hourly Pay
Since both Dana and Monique worked exactly 40 hours in the original week:
Question: What was Dana's effective hourly rate versus Monique's effective hourly rate?
Hint: Divide each person's total weekly earnings by 40 hours.
Ready to check challenge solutions with your partner?
Challenge 1: Monique ($0 diff - tied!) • Challenge 2: $19.125/hr vs $15.9375/hr
