Ratio Rangers Field Guide pocket version
Ratio Rangers
Field Guide: Activity 1 (20 mins)
Ranger ID:
Date:
1. The Table Test
The ratio of \(y/x\) must be:
2. The Graph Check
Must hit the origin:
( 0 , 0 )
3. The Equation Form
\(y = kx\)
\(k\) stands for:
4. Unit Rate Point
Identify this specific point:
( 1 , \(r\) )
Visual Scouting: Which line is proportional?
Line A
Line B Line C
My Choice:
Evidence & Justification:
Activity 2: Representation (20 mins)
Challenge 1: The Gear Rental Log
<table class="w-full text-center text-xs border border-stone-300 rounded-lg overflow-hidden"><tbody><tr class="bg-stone-100 font-bold border-b border-stone-300"><td class="p-2 border-r border-stone-300 uppercase text-[9px]">Days (\(x\))</td><td class="p-2 uppercase text-[9px]">Cost (\(y\))</td></tr><tr class="border-b border-stone-200"><td class="p-2 border-r border-stone-200">3</td><td class="p-2">$51</td></tr><tr class="border-b border-stone-200"><td class="p-2 border-r border-stone-200">7</td><td class="p-2">$119</td></tr><tr><td class="p-2 border-r border-stone-200">10</td><td class="p-2">$170</td></tr></tbody></table>
Constant (\(k\)):
Equation:
Show Work:
Challenge 2: Mapping the Trail
Fill table for: \(y = 4x\)
| Hours (\(x\)) | Miles (\(y\)) |
|---|
| 1 | |
| 2 | |
| 3 | |
Hours (x)
Miles (y)
Activity 3: Unit Rate Climb (20 mins)
Challenge 1: The Steep Trail
Ranger Alex climbs \(\frac{2}{3}\) of a mile in every \(\frac{1}{4}\) hour. Find the unit rate in miles per hour.
Workspace (Setup ratios):
Final Rate:
_______ mph
Challenge 2: Rescue Pacing
Which drone is faster? Find the unit rate for each.
Drone Alpha
\(\frac{3}{5}\) mile in \(\frac{1}{10}\) hour.
Rate: _______ mph
Drone Beta
\(\frac{5}{8}\) mile in \(\frac{1}{4}\) hour.
Rate: _______ mph
Faster Drone:
Activity 4: Percent Summit (20 mins)
Challenge 1: Expedition Gear
New gear costs $160.00. Discount: 25%. Sales Tax: 6%.
1. Price after Discount
2. Final with 6% Tax
Total Cost:
$
Challenge 2: The Outpost Cafe
Mug Supply Cost: $8.00. Markup: 60%. Tip: 15%.
1. Retail Price (Markup)
2. Retail + 15% Tip
Total Paid:
$
Challenge 3: Ranger Sales
Sam earns 5.5% commission on $2,400 in sales. Total commission:
$
Ratio Rangers Answer Key
Answer Key: Ratio Rangers
Mission Pack • Activities 1-4 & Mastery Quiz
TEACHER KEY
Activity 1: The Toolkit
1. Table Test:
The ratio of \(y\) to \(x\) (\(y/x\)) is constant for all rows.
2. Graph Check:
Passes through the Origin (0,0).
3. Equation \(y = kx\):
\(k\) = Constant of Proportionality / Unit Rate.
4. Unit Rate Point:
On a graph, this is point (1, r).
Visual Test Result:
Line A. It is the only straight line that passes through (0,0). Line B does not hit the origin. Line C is a curve.
Activity 2: Representation
Challenge 1: Gear Rental Log
Proof: \(51/3 = 17\), \(119/7 = 17\), \(170/10 = 17\).
\(k = 17\) | Equation: \(y = 17x\)
Challenge 2: Mapping the Trail (\(y = 4x\))
Table values: (1, 4), (2, 8), (3, 12). Graph should be a straight line through (0,0) and these three points.
Activity 3: Unit Rate Climb
Challenge 1: Steep Trail (\(2/3 \div 1/4\))
\(\frac{2}{3} \times \frac{4}{1} = \frac{8}{3} = \mathbf{2\frac{2}{3}}\) mph (or approx 2.67 mph).
Challenge 2: Rescue Pacing
Drone Alpha:
\(\frac{3/5}{1/10} = \frac{3}{5} \times 10 = \mathbf{6}\) mph
Drone Beta:
\(\frac{5/8}{1/4} = \frac{5}{8} \times 4 = \mathbf{2.5}\) mph
Winner: Drone Alpha
Activity 4: Percent Summit
Challenge 1: Expedition Gear ($160, 25%, 6%)
Discounted: \(160 \times 0.75 = 120\). Tax: \(120 \times 1.06 = \mathbf{\$127.20}\).
Challenge 2: Outpost Cafe ($8, 60%, 15%)
Retail: \(8 \times 1.60 = 12.80\). Total: \(12.80 \times 1.15 = \mathbf{\$14.72}\).
Challenge 3: Commission ($2400, 5.5%)
Commission: \(2400 \times 0.055 = \mathbf{\$132.00}\).
Mastery Quiz Answers
1. Visual Scouting
Correct Answer: D (Straight line through origin).
2. Constant Tracker (Elk Table)
Proof: \(32/4 = 8, 56/7 = 8, 96/12 = 8\).
Constant \(k = 8\) | Equation: \(y = 8x\)
3. Rapid Unit Rate (\(4/5 \div 1/8\))
\(\frac{4}{5} \times \frac{8}{1} = \frac{32}{5} = \mathbf{6.4}\) mph.
4. Summit Challenge ($250, 30%, 5%)
Discount: \(250 \times 0.70 = 175\). Shipping: \(175 \times 0.05 = 8.75\).
Ratio Rangers Slides
Ratio Rangers
The 4-Mission Challenge
Mission Roadmap
1
Toolkit
Visual Identification
2
Relate
Tables & Graphs
3
Climb
Complex Unit Rates
4
Summit
Percent Challenges
Mission 1: The Visual Test
Which line is proportional?
- Is it straight?
- Goes through (0,0)?
Line A
Line B
Line C
Mission 2: Representation
The Rental Equation
\(y = 17x\)
Every 1 day costs exactly $17.
Check the Ratios:
\(51 \div 3\)
17
\(119 \div 7\)
17
The ratio is constant!
Mission 3: Unit Rate Climb
Complex Fractions Strategy
\(\frac{2/3}{1/4}\)
\(\frac{2}{3} \times \frac{4}{1}\)
\(2\frac{2}{3}\)
"Keep the first, flip the second, and multiply!"
Mission 4: Percent Summit
Multi-Step Flow
1
Calculate Discount/Markup
2
Find New Subtotal
3
Apply Tax or Tip
Expedition Result
Discounted:$120.00
Plus 6% Tax:$7.20
$127.20
Mission Success
Rangers, you have successfully mastered the 7.RP standard and conquered the summit!
Mastery Level Achieved
Ratio Rangers Quiz
Ranger Mastery Quiz
Assessment: Standard 7.RP
Ranger:
1
Visual Scouting
Which description represents a proportional relationship? (Circle one)
A
A straight line graph passing through (2, 5) and (0, 1).
B
A table where the ratio of \(y\) to \(x\) varies per row.
C
An equation written in the form \(y = 3x + 2\).
D
A straight line graph passing through the origin (0, 0).
2
The Constant Tracker
| Hours (\(x\)) | Miles (\(y\)) |
|---|
| 4 | 32 |
| 7 | 56 |
| 12 | 96 |
Constant (\(k\)):
Equation:
3
Rapid Unit Rate
A drone travels \(\frac{4}{5}\) mile in \(\frac{1}{8}\) hour. Find the unit rate.
Final Rate:
_______ mph
4
The Summit Challenge
Binoculars cost $250.00. Government Discount: 30%. Shipping Fee: 5% (on the discounted price). What is the total?
1. Price with Discount
2. Total with Shipping
Final Total Cost:
$
