Number Blueprints Student Packet Number Blueprints
Integers & Rational Numbers
MS-MATH-01-P1
NAME: __________________________
DATE: __________________________
Phase 01: Integer Foundation
-15 + (-22) = ____
48 - (-12) = ____
-7 × 9 = ____
-56 ÷ (-8) = ____
12 + (-30) ÷ 5 = ____
(-4)² - 10 = ____
| -25 | + (-8) = ____
-3(4 - 9) = ____
-100 ÷ 5 × (-2) = ____
Phase 02: Rational Numbers
Convert 7/8 to a decimal and a percentage.
Decimal:
Percent:
Cut a 12.5 ft board into 1 1/4 ft pieces. How many pieces?
Final Count: ________________
Solve: \( -2.5 + \frac{3}{4} \times 8 = \) ________
Phase 03: Unit Rates
Printer Diagnostic Table
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k = _______ Eq: y = _______x
Competitive Bidding: Concrete Mixes
A: 5 bags for $82.50 -> $_______/bag
B: 8 bags for $128.00 -> $_______/bag
Architect's Choice & Reasoning:
Phase 04: Scale Factor
Scale 1" : 5'
Case Study: Master Bedroom (3 in x 4.5 in)
Actual W: ______ ft
Actual L: ______ ft
Total Area: ____________ sq ft
Map Redraw Task
Old Scale: 1 cm = 20 m (Trail = 8.5 cm). New Scale: 1 cm = 50 m.
New Map Length: ____________ cm
The Skyscraper Challenge
APEX TOWER PROJECT SPECS
• Height: 840 ft
• Floors: 60 (Equal)
• Scale: 1:120
• Bonus: +$750
Step 1: Rational Conversions
Tower height in inches? (1 ft = 12 in)
________ in
Step 2: Proportional Scaling
Model height in inches (at 1:120 scale)?
________ in
Step 3: Floor Height Analysis
Height of one real floor in feet? (Decimal)
________ feet
Step 4: The Project Budget (Integers)
Start $5000 | 3 Mistakes (-$250 ea) | 1 Bonus (+$750).
FINAL: $________________
Extension Vault
Challenge A: The Depths
Sub at 0 ft. Drops 12.5 ft/min for 8 min. Ascends 45.2 ft. Drops 100 ft. Final elevation?
Result: ________ ft
Challenge B: Ratio Riddle
Three numbers follow a 2:3:5 ratio. Their sum is 120. Find the values.
#1
#2
#3
NUMBER BLUEPRINTS UNIT TERMINATED MS-MATH-01
Number Blueprints Teacher Guide Foreman's Key
Emergency Kit: Number Blueprints
Version 2.0 • Authorized Guide
Time Management
Total: 90 Mins
Phases 1-4: 50 Mins
Task: 25 Mins
Exit: 10 Mins
Exit Ticket Key
1: -30 | 2: -25
3: 5 feet | 4: 25 mph
Key Focus
Integer Fluency
Rational Operations
Unit Rate Application
Phase 01: Integers
1: -37
6: 6
2: 60
7: 17
3: -63
8: 15
4: 7
9: 40
5: 6
Phase 02: Rationals
10: 0.875 | 87.5%
11: 10 pieces (12.5 / 1.25)
12: 3.5 (-2.5 + 6)
Phase 03: Unit Rates
13 Table: 1:2.5, 2:5, 10:25
k = 2.5 | Eq: y = 2.5x
14 Dealing: B is better ($16.00 vs $16.50)
Phase 04: Scale Factor
15 Study: 15' x 22.5' -> 337.5 sq ft
16 Redraw: 170m actual -> 3.4 cm
The Skyscraper Challenge
Step 1: 10,080 inches
Step 2: 84 inches
Step 3: 14.0 feet
Step 4: 5000 - 750 + 750 = $5,000
Extension Vault Solutions
A: The Depths
Result: -154.8 ft
B: Ratio Riddle
#1: 24 | #2: 36 | #3: 60
Unit MS-MATH-01 Master File Number Blueprints Teacher Authorization
Number Blueprints Exit Ticket Exit Ticket: Blueprint Basics
MS-MATH-01-ET
Name: __________________________
Score: ____ / 4
1. Evaluate: \( -18 + (-4) \times 3 \)
Ans: __________
2. \( 12.5 \div (-0.5) = \) ?
Ans: __________
3. Wall 15ft = 3in on map. Scale?
1 in = ____ ft
4. Unit Rate: 100 miles in 4 hours?
Rate: ____ mph
Reflection: One thing I learned today: _______________________________________________________
Exit Ticket: Blueprint Basics
MS-MATH-01-ET
Name: __________________________
Score: ____ / 4
1. Evaluate: \( -18 + (-4) \times 3 \)
Ans: __________
2. \( 12.5 \div (-0.5) = \) ?
Ans: __________
3. Wall 15ft = 3in on map. Scale?
1 in = ____ ft
4. Unit Rate: 100 miles in 4 hours?
Rate: ____ mph
Reflection: One thing I learned today: _______________________________________________________
Algebra Architects Student Packet Algebra Architects
Expressions & Equations
MS-MATH-02-P1
NAME: __________________________
DATE: __________________________
Phase 01: Expressions
5x + 3 - 2x + 10
3(4y - 5)
7(w + 2) - 4w
0.5(8k + 20)
12m - 2(3m - 4)
-3(a + 5) + 10a
Engineering Cost Model
A crane rental is a flat $1,200 fee + $150 per hour (h) of use.
Expression: ________________________
Phase 02: Equation Stability
x - 14 = -25
x = _______
4n + 8 = 40
n = _______
y/3 - 5 = 2
y = _______
2(p + 6) = 22
p = _______
-5g + 10 = -15
g = _______
Equation Word Problem
Total length of a beam is 60 ft. It consists of a 12 ft base and 6 equal support rods (r). Write and solve to find rod length.
Eq: _______________
r = _______ ft
Phase 03: Probability
Safety Kit #B4
P(Green Bolt) = _______
P(NOT Red Bolt) = _______
P(Yellow OR Red) = _______
Compound Probability (Independent)
Roll a 6-sided die AND flip a coin. What is the probability of rolling a 4 and flipping Heads?
P(4 & H) = ________
Sample Space Analysis
Choose 1 Hard Hat (Y, W) and 1 Safety Vest (O, L). List all possible combinations.
Total Combos: ________
Phase 04: Statistics
Construction Crew Ages: 24, 28, 35, 28, 42, 50, 31
MEAN
MEDIAN
MODE
RANGE
Box Plot Analysis: Crane Capacity (Tons)
10 25 40 55 80
IQR (Q3 - Q1) = ________
Engineering Vault
Challenge A: Algebra
2/3(x - 9) = 14
Algebra Architects Teacher Guide Lead Engineer's Key
Emergency Kit: Algebra Architects
Version 2.0 • Terminal Authorization
Pacing Guide
Phases 1-2: 45 Mins
Phases 3-4: 35 Mins
Exit Ticket: 10 Mins
Exit Ticket Key
1: 6x - 3 | 2: n = 10 | 3: x = -9
4: P = 0.6 (12/20)
Key Focus
Linear Modelling
Inverse Operations
Independent Probability
Phase 01: Expressions
1: 3x + 13 | 2: 12y - 15 | 3: 3w + 14
4: 4k + 10 | 5: 6m + 8 | 6: 7a - 15
7: 1200 + 150h
Phase 02: Equations
8: x = -11 | 9: n = 8 | 10: y = 21
11: p = 5 | 12: g = 5
13: 12 + 6r = 60 -> 6r = 48 -> r = 8 ft
Phase 03: Probability
14: 0.6 | 15: 0.75 | 16: 0.4
17: (1/6) * (1/2) = 1/12
18: {YO, YL, WO, WL} -> 4 total
Phase 04: Statistics
19: Mean: 34 | Median: 31
Mode: 28 | Range: 26
20: Q3(55) - Q1(25) = 30
Engineering Vault Solutions
A: Algebra Stability
2/3(x - 9) = 14 -> x - 9 = 21 -> x = 30
B: Mean Data Shift
Sum 5 = 100. New Sum = 150.
Added unit = 50
Unit MS-MATH-02 Secure Document Algebra Architects Teacher Authorization
Algebra Architects Exit Ticket Exit Ticket: Logic Check
MS-MATH-02-ET
Engineer: __________________________
Status: ____ / 4
1. Simplify: \( 10x + 5 - 4x - 8 \)
Ans: __________
2. Solve: \( 3n - 10 = 20 \)
n = __________
3. Solve: \( -2(x + 4) = 10 \)
x = __________
4. P(Green) in Bag {5R, 12G, 3Y}
P = __________
Analysis: Which phase (1-4) felt most secure today? ____________________________________________
Exit Ticket: Logic Check
MS-MATH-02-ET
Engineer: __________________________
Status: ____ / 4
1. Simplify: \( 10x + 5 - 4x - 8 \)
Ans: __________
2. Solve: \( 3n - 10 = 20 \)
n = __________
3. Solve: \( -2(x + 4) = 10 \)
x = __________
4. P(Green) in Bag {5R, 12G, 3Y}
P = __________
Analysis: Which phase (1-4) felt most secure today? ____________________________________________