Blueprint Slides Unit: Ratios & Proportions
BLUEPRINT
BUILDERS
Constructing Understanding through Ratios
Scale
Rate
Proportion
MISSION BRIEFING
As Blueprint Builders, you are responsible for designing the new community center. To do this, you must master:
Ratio Relationships: Comparing different quantities like cement and water.
Unit Rates: Finding the cost for a single unit of material.
Scaling: Using maps and blueprints to build real-sized structures.
Vocabulary Check
Ratio
A comparison of two quantities (a:b, a to b, or a/b).
Rate
A ratio comparing two different units (e.g., miles per hour).
Unit Rate
A rate where the second quantity is 1.
TOOL 1: TAPE DIAGRAMS
Concrete Mixing
A standard concrete mix uses 3 parts sand to 2 parts gravel.
If we use 15 buckets of sand, how much gravel do we need?
Sand:
5
5
5
= 15 buckets
Gravel:
5
5
= 10 buckets
Architect's Tip: In a tape diagram, every box represents the same value! Dividing the total amount of sand (15) by the number of boxes (3) gives us the value per box (5).
TOOL 2: RATIO TABLES
Scaling Blueprints
"On our scale drawing, 2 inches represents 5 feet of the actual building."
Use the table to find the actual length of a room that is 10 inches on the blueprint.
1
Identify the starting ratio.
2
Multiply or divide both quantities by the same factor.
Blueprint (in) Actual (ft) 2 5 4 10 6 15 10 25
TOOL 3: DOUBLE NUMBER LINES
Procurement & Pricing
Lumber costs $12 for every 3 planks.
What is the unit rate (cost per plank)? How much for 5 planks?
Cost ($)
0
4
8
12
16
Planks
0
1
2
3
4
Find Unit Rate:
$12 ÷ 3 planks = $4 per plank
Predicting 5 Planks:
5 planks × $4/plank = $20 total
BUILDER'S CHALLENGE
Wait! The client changed the order. We need 800 sq ft of tiles for every 5 rooms.
How many square feet are needed for 12 rooms?
A
1,600 sq ft
B
1,920 sq ft
C
2,400 sq ft
Hint: Find the unit rate (sq ft per 1 room) first!
Architects Toolkit Notes Field Notes: Architects
ARCHITECT'S TOOLKIT
Project Lead
Date
1. Site Foundations (Vocabulary)
Ratio
Example: 3 : 2
Rate
Example: 60 miles per 2 hours
Unit Rate
Example: 30 miles per 1 hour
2. Tool #1: Tape Diagrams
"Concrete Mix Scenario: 3 parts sand to 2 parts gravel."
Sand
?
?
?
= 15 buckets
Gravel
?
?
= ______ buckets
Working Steps: 15 buckets ÷ 3 boxes = ______ per box. Fill each box with this number.
3. Tool #2: Ratio Tables
"Blueprint Scale: 2 inches = 5 actual feet."
Ratio tables allow us to scale up or scale down by multiplying or dividing both sides by the ________ ___________.
The Goal:
Find the actual feet for 10 blueprint inches.
Blueprint (in) Actual (ft) 2 5 4 _____ 6 _____ 10 _____
4. Tool #3: Double Number Lines
"Pricing: $12 for 3 planks of cedar."
COST ($)
0
____
____
$12
PLANKS
0
1
2
3
Unit Rate: Divide total cost ($12) by total planks (3) to find the cost per one plank.
Unit Rate = $_______ / plank
FINAL SPEC CHECK
800 sq ft for 5 rooms. How many for 12 rooms?
Your Calculation
Scaling Success Worksheet Work Order: #402-RP
SCALING SUCCESS
Project: Community Center Build-Out
Site Engineer
Shift Date
Project Brief
The city has approved the new Horizon Community Center. As the Lead Architect, you must solve these three scaling challenges to ensure the building is constructed safely and within budget. Use the tools provided in your toolkit!
1
Challenge 1: Map Navigation (NCSCOS 6.RP.3)
On the master site plan, 3 centimeters on the map represents 50 meters in the real world.
Task: Complete the ratio table to find the actual distance for a 12 cm map measurement.
Map Distance (cm) Actual Distance (m) 3 50 6 9 12
Show your scaling logic here:
2
Challenge 2: Unit Price Comparison (NCSCOS 6.RP.2)
We need to order bulk nails. Vendor A sells 4 lbs for $14. Vendor B sells 6 lbs for $18.
Vendor A (4 lbs for $14)
Unit Rate Calculation ($ per 1 lb):
$_________ / lb
Vendor B (6 lbs for $18)
Unit Rate Calculation ($ per 1 lb):
$_________ / lb
Which Vendor is the "Better Buy" (Cheaper Unit Rate)?
Vendor A
Vendor B
3
Challenge 3: Concrete Ratios (NCSCOS 6.RP.1)
High-strength concrete uses a ratio of 2 bags of cement to 5 bags of crushed stone.
Draw a Tape Diagram to represent this ratio:
Cement
Stone
The Scenario:
If the crew uses 15 bags of crushed stone, how many bags of cement do they need?
Calculations:
Answer: ________ bags of cement
4
Challenge 4: Wiring the Center (NCSCOS 6.RP.3)
The electricians use 24 feet of wire for every 3 light fixtures.
Wire (ft)
0
24 ft
Fixtures
0
3
A. Find the unit rate (wire per 1 fixture):
Answer: ________ feet per fixture
B. How much wire for 10 fixtures?
Answer: ________ feet of wire
Architect Certification
"I certify that all ratios have been verified for safety and structural integrity."
Project Manager Guide Instructional Blueprint
PROJECT MANAGER GUIDE
Lesson: Blueprint Builders (Ratios & Proportions)
Standards Alignment
NCSCOS 6.RP.1-3
Phase 1: Groundbreaking (Intro)
Hook (5 min): Ask students: "If you want to build a real skyscraper but only have a map that fits on your desk, how do you know how big to make the real walls?" Introduce the role of the Architect and the necessity of ratios.
Direct Instruction (15 min): Use the Blueprint Slides . Guide students through the three primary visual models:
Tape Diagrams: Best for "part-to-part" comparisons (e.g., sand to gravel).Ratio Tables: Best for scaling up or down in multiple steps.Double Number Lines: Best for rates involving different units (e.g., cost per item).
Phase 2: Construction (Practice)
Guided Practice (10 min): Complete the Architect's Toolkit Notes together during the presentation. Focus on identifying the "Scale Factor" in tables and the "Unit Value" in tape diagram boxes.
Independent Practice (20 min): Students work on the Scaling Success Worksheet . This includes map scaling, unit price comparison (the "Better Buy"), and concrete mix calculations.
Phase 3: Inspection (Assessment)
Exit Ticket / Check for Understanding:
"A blueprint uses a scale where 5 inches = 20 feet. If a wall is 45 feet long, how many inches will it be on the blueprint?"
Answer: 11.25 inches
Strategy: Unit rate is 4 ft per inch
Misconceptions
Additive Thinking: Students may try to add the same number to both sides of a ratio rather than multiplying (e.g., 2:5 becomes 3:6 by adding 1). Remind them that ratios are multiplicative.
Unit Rate Direction: Choosing the wrong divisor when finding unit rates (e.g., finding items per dollar instead of dollars per item). Always ask: "What are we finding the cost of one of?"
Materials Needed
• Architect's Toolkit Notes (1 per student)
• Scaling Success Worksheet
• Rulers (optional for map scale visual)
• Calculators (for unit price division)
MASTER SPECIFICATIONS (KEY)
Internal Use Only
Challenge 1: Map Navigation
