Ratio Rebels Teacher Guide Ratio Rebels Teacher Guide
Grades 6-8 • Proportional Reasoning
Real-world math through the lens of culinary arts, cartography, and commerce.
Learning Objectives
• Use ratio and rate reasoning to solve real-world problems.
• Scale quantities up and down while maintaining proportions.
• Interpret map scales to determine actual distances.
• Compare unit rates to find the "best buy" in shopping scenarios.
MA Standards
6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., tables of equivalent ratios, unit rates).
7.RP.A.2: Recognize and represent proportional relationships between quantities.
7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems (e.g., tax, gratuities, commissions, scale drawings).
Lesson Roadmap
1
The Hook (10 mins)
Present the "Pancake Fiasco": A recipe for 4 people that was scaled for 20 by only adding 16 to every number instead of multiplying. Ask: "Why does the giant pancake taste like baking soda?"
2
Ratio Rebels Lab: Collaborative (30 mins)
Students work in pairs or trios to fix the recipe and navigate a city map using scale factors. Facilitate by asking: "If the ratio is 2 to 3, what happens if we have 6 of the first item?"
3
Price Patrol: Individual (15 mins)
Students solve "best buy" problems independently to practice unit rate calculations. This serves as a formative assessment.
Scaffolding Entry Points
• Provide double number lines or ratio tables for recipe scaling.
• Use visual counters or manipulatives for simple 1:2 or 1:3 ratios.
• Focus on "halving" and "doubling" before moving to odd scale factors.
Extension Challenges
• Non-integer scaling: Scaling a recipe by a factor of 2.75.
• Currency Conversion: Apply ratio reasoning to exchange rates for international shipping.
• 3D Scaling: How does scaling side lengths affect volume?
Quick Answer Key
Recipe Scaling (Factor of 5)
Flour: 2 cups → 10 cups
Milk: 1.5 cups → 7.5 cups
Eggs: 2 → 10
Map Navigation
Scale: 1 in = 4 miles
3.5 inches → 14 miles
20 miles → 5 inches
Inquiry Facilitation Tips
The "Wait Time" Strategy
During the hook, wait at least 10 seconds before calling on anyone. Let students debate why "adding 16" failed. Guide them toward the idea of multiplicative vs additive reasoning.
Prompting Questions
"If you double the flour, what happens to the consistency if you don't double the milk?"
"How can we use a unit rate to find the price of any amount of flour?"
Ratio Rebels Slides Ratio Rebels
Mastering Proportions in the Real World
The Pancake Fiasco
Original (Serves 4)
Flour 2 cups
Milk 1.5 cups
Baking Soda 1 tsp
The Failure (Serves 20)
Flour 18 cups
Milk 17.5 cups
Baking Soda 17 tsp
Wait... why does it taste like soap? What went wrong?
How do things scale up without losing their "essence"?
Is the relationship about adding or multiplying ?
The Chef's Challenge
Lab Task 1
The original recipe is for 4 people . You need to serve 20 people .
Think-Pair-Share:
What is the "Scale Factor"? How many batches of 4 fit into 20?
x?
4
20
The Cartographer's Code
Lab Task 2
A map is just a scaled-down version of reality!
1 inch = 4 miles
If your destination is 3.5 inches away on the map, how long is the actual bike ride?
The Savvy Shopper
Stores use unit rates to show you which item is actually cheaper.
Instead of looking at the total price, look at the price per ounce or price per item .
Box A: 10oz $5.00
Box B: 24oz $9.60
Go Forth, Rebels!
Grab your Lab Sheet. Work with your team to solve the three missions of the city.
1. Scale the Recipe
2. Decode the Map
3. Find the Best Buy
Ratio Rebels Lab Activity Ratio Rebels Lab
Mission: Restore Balance to the City
Team Name
Team Members
Mission 1: The Chef's Redemption
The "Pancake Fiasco" happened because the chef added instead of multiplying . Fix the recipe by scaling it from serves 4 to serves 20 .
Original Size
4 People
Target Size
20 People
Scale Factor
How many times larger is the target?
Ingredient Original (4) New (20) All-Purpose Flour 2 cups Whole Milk 1.5 cups Large Eggs 2 Baking Soda 1 tsp
The "Why":
Explain why multiplying the ingredients keeps the recipe tasting the same, while adding ingredients (like the fiasco) ruins it.
Mission 2: Map to the Market
The grocery store is across town. Use the map scale to calculate your journey.
MAP SCALE: 1 inch = 4 miles
Avg. Speed
8 miles / hour
Q1: From the kitchen to the market is 3.5 inches on the map. What is the actual distance?
miles
Q2: How long will the bike ride take to get there?
hours
REBEL STRETCH: THE EXTREME SCALE
A competitor restaurant serves 120 people using the same base recipe. What is the scale factor from the original serves 4 to this new monster batch?
Calculations:
New Flour Total
? cups
Ratio Rebels Solo Practice Ratio Rebels: Solo Mission
Agent Name
Unit Rate: Finding the "Best Buy"
Option A: Mini-Pack
12 oz
$3.60
Unit Rate ($ per oz)
Option B: Mega-Tub
30 oz
$7.50
Unit Rate ($ per oz)
Verdict: Which is the "Best Buy" and why?
Conceptual Check-In
1. If two quantities are in a proportional relationship, what must be true about their ratio as they grow?
The difference between them stays the same (e.g., both add 5).
The ratio (fraction) between them stays equivalent.
They both get larger by adding the same whole number.
2. Give a real-life example of a relationship that is NOT proportional.
(Hint: Think of things that grow, but not at a constant rate, like your height over your age.)
Reflect:
What is the most important thing to remember when scaling a drawing or a recipe?
Self-Check
