Area Architects Slides Math Refresher
Area Architects
Mastering Complex Figures
Mystery Challenge
Can you find the total floor space of a room that isn't a simple rectangle? Let's solve the puzzle!
Today's Purpose
We are learning to find the area of rectilinear figures by splitting them into smaller rectangles.
Standard: 3.MD.C.7
Agenda
1
Strategy Blueprint
2
Modeling (2 I Dos)
3
Co-Design (2 We Dos)
4
Solo Build (4 You Dos)
The Area Architect Strategy
1. Split
Partition the shape into rectangles.
2. Eliminate Distractors
Cross out measurements you don't need!
3. Multiply
Find the area:
4. Add
Add the areas for the Total.
I Do 1: Example
Teacher Modeling
9 in 4 in 7 in 4 in 5 in 8 in
Eliminate Distractors
I cross out the 7 and the 4. They are distractors!
Box A: 5 × 8 = 40
Box B: 4 × 4 = 16
Total: 56 sq in
I Do 2: Example
Teacher Modeling
12 ft 3 ft 8 ft 5 ft 4 ft 8 ft
Watch Out!
The 8 and 5 are distractors. They don't help us measure the two rectangles we created!
Top: 4 × 8 = 32
Bottom: 8 × 3 = 24
Total: 56 sq ft
We Do 1: Collaborate
Practice Together
10 cm 3 cm 3 cm 3 cm 3 cm 4 cm 6 cm 6 cm
Architect Task
Point to the DISTRACTOR measurements!
___ + ___ = ?
We Do 2: Collaborate
Practice Together
6 m 4 m 6 m 4 m 12 m 8 m
Architect Task
Which numbers are the DISTRACTORS in this step-shaped room?
___ + ___ = ?
Solo Mission
Time for your 4 Solo Build problems! Eliminate the DISTRACTORS before you multiply.
Split
Distractors
Multiply
Add
Area Architects Slides Math Refresher
Area Architects
Mastering Complex Figures
Mystery Challenge
Can you find the total floor space of a room that isn't a simple rectangle? Let's solve the puzzle!
Our Purpose
We are learning to find the area of rectilinear figures by splitting them into smaller rectangles.
Objective: Split, Multiply, Add
Site Plan
1
Strategy Blueprint
2
Modeling (2 I Dos)
3
Co-Design (2 We Dos)
4
Solo Build (4 You Dos)
The Area Architect Strategy
1
Split
Partition the shape into smaller rectangles.
2
Eliminate Distractors
Cross out measurements you don't need!
3
Multiply
Find the area of each box:
4
Add
Add the areas for the Total Site Area.
I Do 1
Model
15 in 6 in 8 in 6 in 10 in 12 in
Step 2: Eliminate
I cross out the distractors. They don't represent a full side of my new rectangles!
Box A: 10 × 12 = 120
Box B: 5 × 6 = 30
Total: 150 sq in
Solo Build
Time for your Independent Practice! Remember to find your rectangles and eliminate the distractors.
Area Architects Exit Ticket Final Inspection
Exit Ticket: Area Architects
Architect Name
Date
Find the total area. Show your 4 steps: Split, Eliminate, Multiply, and Add.
6 in 3 in 3 in 2 in 2 in 4 in
Steps 1-3 (Split, Eliminate, Mult)
Step 4 (Total Area)
square inches
Area Architects Worksheet Area Architects
Blueprint Phase: Solo Build
Name:
Date:
1
Split shape
2
Eliminate Distractors
3
Multiply (L × W)
4
Add the areas
01
Find the area.
11 mm 4 mm 7 mm 4 mm 4 mm 8 mm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
sq mm
02
Find the area.
12 yd 5 yd 6 yd 7 yd 6 yd 12 yd
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
sq yd
Area Architects (Continued)
Page 2 of 2
03
Find the area.
10 cm 3 cm 3 cm 8 cm 4 cm 8 cm 3 cm 3 cm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
sq cm
04
Find the area.
6 ft 12 ft 12 ft 4 ft 2 ft 8 ft
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
sq ft
Area Architects Worksheet Area Architects
Blueprint Phase: Solo Build
Name:
Date:
1
Split
2
Eliminate
3
Multiply
4
Add
01
Drafting Site A
11 mm 4 mm 7 mm 3 mm 4 mm 8 mm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square mm
02
Drafting Site B
12 yd 5 yd 6 yd 7 yd 6 yd 12 yd
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square yards
Solo Build (Continued)
Page 2 of 2
03
Drafting Site C
10 cm 3 cm 3 cm 8 cm 4 cm 8 cm 3 cm 3 cm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square cm
04
Drafting Site D
6 ft 12 ft 12 ft 4 ft 2 ft 8 ft
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square feet
Area Architects Exit Ticket Final Inspection
Exit Ticket: Area Architects
Architect Name
Date
Find the total area. Show your 4 steps: Split, Eliminate, Multiply, and Add.
6 in 2 in 3 in 2 in 3 in 4 in
Steps 1-3 (Split, Eliminate, Mult)
Step 4 (Total Area)
square inches
Area Architects Teacher Guide Teacher Guide
Foundation Blueprints: Area Architects
Unit: Blueprint Builders
Day 1 of 3
Lesson Objective
Students will find the area of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the parts. Students must identify and eliminate distractor measurements that do not represent full side lengths of the partitioned boxes.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
The Area Architect Strategy
1
Split
(Partition Shape)
2
Eliminate
(Find Distractors)
3
Multiply
(Area of Parts)
4
Add
(Total Area)
Pacing & Facilitation
10 mins
Launch
Use the Slide 1 "Mystery Challenge". Ask: "How would we find the floor space of an L-shaped room?" Review area of a basic rectangle.
15 mins
I Do / We Do
Model the "Eliminate" step heavily. Explain that distractor numbers only represent part of a side or were the total side before we split the shape.
20 mins
Independent
Students work on the Solo Build Worksheet . Challenge them to split the shape in more than one way to verify their answer.
Full Answer Key
Worksheet: Solo Build
Problem 01 (Site A)
Distractors: 7, 3
32 + 28 = 60 sq mm
Problem 02 (Site B)
Distractors: 6, 7
72 + 30 = 102 sq yd
Problem 03 (Site C)
Distractors: 10, 3, 3
30 + 32 = 62 sq cm
Problem 04 (Site D)
Distractors: 4, 2
48 + 72 = 120 sq ft
Instructional Slides
I Do 1 (Modeling)
Distractors: 8, 6
120 + 30 = 150 sq in
Exit Ticket
Final Inspection
Distractors: 3, 2
12 + 6 = 18 sq in
Area Architects Teacher Guide Teacher Guide
Area Architects
A refresher lesson on partitioning complex rectilinear figures to find total area while eliminating distractor measurements.
Learning Objective
Students will find the area of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the parts. (3.MD.C.7d)
The 4-Step Strategy
1 Split: Partition the shape.
2 Eliminate Distractors: Cross out trick numbers!
3 Multiply: L × W for each part.
4 Add: Total area.
Full Answer Key
Slide Examples
I Do 1 (L-Shape)
Distractors: 7 in, 4 in
Part A (5x8) + Part B (4x4) = 56 sq in
I Do 2 (Reverse L)
Distractors: 8 ft, 5 ft
Part A (4x8) + Part B (8x3) = 56 sq ft
We Do 1 (T-Shape)
Distractors: 3, 3, 6, 6 cm
Part A (3x10) + Part B (6x4) = 54 sq cm
We Do 2 (Steps)
Distractors: 4 m, 6 m
Part A (6x8) + Part B (6x4) = 72 sq m
Independent Practice
You Do 1 (Room)
Distractors: 11, 8
32 + 28 = 60 sq mm
You Do 2 (Patio)
Distractors: 12, 12
72 + 30 = 102 sq yd
You Do 3 (Garden)
Distractors: 10, 3, 3
30 + 32 = 62 sq cm
You Do 4 (Hallway)
Distractors: 12, 12
48 + 72 = 120 sq ft
Exit Ticket Final Inspection
18 sq in
Area Architects Worksheet Area Architects
Blueprint Phase: Solo Build
Name:
Date:
1
Split
2
Eliminate
3
Multiply
4
Add
01
Drafting Site A
11 mm 4 mm 7 mm 3 mm 4 mm 8 mm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square mm
02
Drafting Site B
12 yd 5 yd 6 yd 7 yd 6 yd 12 yd
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square yards
Solo Build (Continued)
Page 2 of 2
03
Drafting Site C
10 cm 3 cm 3 cm 8 cm 4 cm 8 cm 3 cm 3 cm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square cm
04
Drafting Site D
6 ft 12 ft 12 ft 4 ft 2 ft 8 ft
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square feet
Area Architects Worksheet Area Architects
Blueprint Phase: Solo Build
Name:
Date:
1
Split
2
Eliminate
3
Multiply
4
Add
01
Drafting Site A
11 mm 4 mm 7 mm 4 mm 7 mm 8 mm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square mm
02
Drafting Site B
12 yd 5 yd 6 yd 5 yd 6 yd 10 yd
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square yards
Solo Build (Continued)
Page 2 of 2
03
Drafting Site C
10 cm 3 cm 3 cm 5 cm 4 cm 5 cm 3 cm 3 cm
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square cm
04
Drafting Site D
6 ft 12 ft 8 ft 4 ft 2 ft 8 ft
Cross out distractor measurements!
Calculations
Part A:
Part B:
Total Area
square feet
Blueprint Gaps Slides Blueprint Gaps
Finding Missing Measurements
Architect Training Day 2
The Mission
Today, we are NOT solving for area.
"We have gaps in our blueprints. We need the missing side lengths before we can build!"
We only need to find the missing side lengths .
12 m 10 m ? ?
The Blueprint Strategy
1
Find Partner Lines
Find lines going in the same direction (Horizontal or Vertical).
2
Add or Subtract?
Add if you have two small parts.Subtract if you have the long side and one part.
3
Solve
Calculate to find the missing length .
I Do
Missing Horizontal
15 in 6 in 7 in 10 in ?
1
Find Partners
Horizontal lines: 15 in (Long) and 7 in (Short).
2
Add or Subtract?
We have the long side and a part. We Subtract.
3
Solve
15 - 7 = 8 in
I Do
Missing Vertical
1
Find Partners
Vertical lines: 12 cm (Long) and 5 cm (Short).
2
Add or Subtract?
Subtract (Long - Short).
3
Solve
12 - 5 = 7 cm
12 cm 5 cm 8 cm ?
We Do
Collaborative Drafting
Target: Vertical Side (x)
10 ft 14 ft 4 ft 4 ft x
x = ____ ft
Target: Horizontal Side (y)
20 m 8 m y 12 m
y = ____ m
Strategy Recap
01
Find Partners
Lines in the same direction.
02
Add or Subtract?
Total vs Parts logic.
03
Solve
Find the missing length.
Ready for Independent Drafting?
Blueprint Masters!
You've successfully identified the missing measurements. Tomorrow, we put it all together to calculate the Full Site Area !
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Rule
Parallel sides must always balance! Look for lines going in the same direction (vertical or horizontal) to find your missing gap.
SHORT + SHORT = LONG
LONG - SHORT = SHORT
1
Blueprint A
16 m 11 m 8 m 6 m x y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft 6 ft 11 ft a b
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 22 cm 9 cm 12 cm 11 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in 20 in 24 in 8 in k m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m p 9 m 8 m q 11 m
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
18 ft 15 ft 18 ft r 6 ft s
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to check if the side is horizontal or vertical first?
Blueprint Gaps Exit Ticket Exit Ticket
Blueprint Gaps: Missing Measurements
Name:
1
Look at the blueprint below. Use the Parallel Rule to find the lengths of the missing sides x and y.
22 in 10 in x 14 in y 6 in
Solve for x (Horizontal):
x = ___________ in
Solve for y (Vertical):
y = ___________ in
Architect's Check-In
Which side was easier to find? Why?
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Rule
Parallel sides must always balance! Look for lines going in the same direction (vertical or horizontal) to find your missing gap.
SHORT + SHORT = LONG
LONG - SHORT = SHORT
1
Blueprint A
16 m 11 m 8 m 6 m x y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft 6 ft 11 ft a b
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 22 cm 9 cm 12 cm 11 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in 20 in 24 in 8 in k m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m p 9 m 8 m q 11 m
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
25 ft 12 ft 25 ft 20 ft s r
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to check if the side is horizontal or vertical first?
Blueprint Gaps Teacher Guide Teacher Guide
Blueprint Gaps: Missing Measurements
Unit: Blueprint Builders
Day 2 of 3
Lesson Objective
Students will identify and calculate missing side lengths in complex rectilinear figures by applying the Parallel Rule. Students will use the logic of adding or subtracting lengths of parallel sides to find unknown values without calculating area.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
Pacing & Facilitation
10 mins
Launch
Review parallel lines. Use the "Secret of Parallel Lines" slide to show that horizontal lines only interact with horizontal, and vertical with vertical.
15 mins
I Do / We Do
Model finding a missing horizontal side by identifying the 'Total' vs 'Parts'. Practice the 'Long - Short = Short' logic with students.
20 mins
Independent
Students complete the Blueprint Gaps Worksheet. Encourage them to use colored pencils to highlight parallel sides.
Architect's Alerts (Misconceptions)
Mixing Orientations
Students may try to add a vertical side to a horizontal side. Remind them: "Horizontal helps horizontal; Vertical helps vertical."
Ignoring Total Length
Students might add two numbers they see without checking if one is the "Long" side. Always identify the longest parallel side first.
Answer Key
Worksheet: Blueprint Gaps
Blueprint A x = 8 m, y = 5 m
Blueprint B a = 5 ft, b = 6 ft
Blueprint C w = 20 cm, z = 10 cm
Blueprint D k = 10 in, m = 12 in
Blueprint E p = 3 m, q = 16 m
Blueprint F r = 8 ft, s = 10 ft
Exit Ticket
Problem 1 - x (Horizontal)
22 - 10 = 12 in
Problem 1 - y (Vertical)
14 - 6 = 8 in
Reflection Notes
Students should explain that identifying orientation (vertical vs. horizontal) ensures they only compare sides that "match" or "balance."
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Rule
Parallel sides must always balance! Look for lines going in the same direction (vertical or horizontal) to find your missing gap.
SHORT + SHORT = LONG
LONG - SHORT = SHORT
1
Blueprint A
16 m 11 m 8 m 6 m x y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft 6 ft 11 ft a b
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 22 cm 9 cm 12 cm 11 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in 20 in 24 in 8 in k m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m p 9 m 8 m q 11 m
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
24 ft 20 ft 14 ft 12 ft s r
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to check if the side is horizontal or vertical first?
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Strategy
Step 1
Find all partner lines (lines going the same direction).
Step 2
Determine if we need to add or subtract.
Step 3
Solve to find the missing length.
1
Blueprint A
16 m 11 m 8 m 6 m x y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft 6 ft 11 ft a b
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 22 cm 9 cm 12 cm 11 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in 20 in 24 in 8 in k m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m p 9 m 8 m q 11 m
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
24 ft 14 ft s 12 ft 20 ft r
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to complete Step 1 (Find Partners) first?
Blueprint Gaps Exit Ticket Exit Ticket
Blueprint Gaps: Missing Measurements
Name:
1
Apply the Parallel Strategy to find the lengths of the missing sides x and y.
1. Find Partners
2. Add or Subtract?
3. Solve
22 in 10 in x 14 in y 6 in
Find x (Horizontal):
x = ___________ in
Find y (Vertical):
y = ___________ in
Architect's Check-In
How did checking for "Partner Lines" help you solve this problem?
Blueprint Gaps Teacher Guide Teacher Guide
Blueprint Gaps: Missing Measurements
Unit: Blueprint Builders
Day 2 of 3
Lesson Objective
Students will identify and calculate missing side lengths in complex rectilinear figures by applying the Parallel Strategy. Students will use the logic of adding or subtracting lengths of parallel sides to find unknown values without calculating area.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
The Parallel Strategy
1
Find Partner Lines
(Same direction)
2
Add or Subtract?
(Total vs Parts)
3
Solve
(Calculate missing)
Pacing & Facilitation
10 mins
Launch
Introduce the Parallel Strategy . Show students that horizontal lines only interact with horizontal lines, and vertical with vertical. Use colored highlighters to find "partners".
15 mins
I Do / We Do
Model the 3 steps explicitly. Focus on Step 2 : determining if we need to add (two parts) or subtract (total and one part). Use the "We Do" slide to let teams debate the operation before solving.
20 mins
Independent
Students work on the Blueprint Gaps Worksheet . Remind them to write out their Step 3 calculation in the provided space.
Architect's Alerts (Misconceptions)
Mixing Directions
Students may try to add a vertical side to a horizontal side. Remind them: "Step 1: Partners only! Only lines running the same way can play."
Wrong Operation
Students often default to addition. Stress Step 2 : If you have the total (longest line), you usually subtract the part you know.
Answer Key
Worksheet: Blueprint Gaps
Blueprint A x = 8 m, y = 5 m
Blueprint B a = 5 ft, b = 6 ft
Blueprint C w = 20 cm, z = 10 cm
Blueprint D k = 10 in, m = 12 in
Blueprint E p = 2 m, q = 16 m
Blueprint F r = 8 ft, s = 10 ft
Exit Ticket
Problem 1 - x (Horizontal)
22 - 10 = 12 in
Problem 1 - y (Vertical)
14 - 6 = 8 in
Reflection Notes
Students should describe that orientation (horizontal/vertical) prevents them from mixing incompatible side measurements.
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Strategy
Step 1
Find all partner lines (lines going the same direction).
Step 2
Determine if we need to add or subtract.
Step 3
Solve to find the missing length.
1
Blueprint A
16 m 11 m 8 m 6 m x y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft 6 ft 11 ft a b
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 22 cm 9 cm 12 cm 11 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in 20 in 24 in 8 in k m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m p 9 m 8 m q 11 m
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
24 ft 20 ft 14 ft 12 ft s r
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to complete Step 1 (Find Partners) first?
Blueprint Gaps Teacher Guide Scroll Teacher Guide
Blueprint Gaps: Missing Measurements
Unit: Blueprint Builders
Day 2 of 3
Lesson Objective
Students will identify and calculate missing side lengths in complex rectilinear figures by applying the Parallel Strategy.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
The Parallel Strategy
Step 1
Find all partner lines (same direction).
Step 2
Determine if we need to add or subtract.
Step 3
Solve to find the missing length.
Pacing & Facilitation
10 mins
Launch
Introduce the Parallel Strategy . Show students that horizontal lines only interact with horizontal lines. Use colored highlighters to find "partners".
15 mins
I Do / We Do
Model the 3 steps explicitly. Focus on Step 2 : determining the operation. If they have the total, subtract the part. If they have two parts, add to find the total.
20 mins
Independent
Students work on the Blueprint Gaps Worksheet . Check that students are writing out the Step 3 calculation.
Architect's Alerts (Misconceptions)
Direction Confusion
Students may try to subtract a vertical side from a horizontal side. Remind them: "Partners only!"
Default to Addition
Students often default to adding every number they see. Stress Step 2 : Is the missing piece a whole or a part?
Answer Key
Worksheet: Blueprint Gaps
A x = 8 m, y = 5 m
B a = 5 ft, b = 6 ft
C w = 20 cm, z = 10 cm
D k = 10 in, m = 12 in
E p = 3 m, q = 16 m
F r = 8 ft, s = 10 ft
Exit Ticket
x (Horizontal)
22 - 10 = 12 in
y (Vertical)
14 - 6 = 8 in
Reflection Notes
Students should note that finding partners ensures they are "comparing apples to apples" (same direction) and not mixing vertical/horizontal lengths.
Blueprint Gaps Exit Ticket Exit Ticket
Blueprint Gaps: Missing Measurements
Name:
1
Apply the Parallel Strategy to find the lengths of the missing sides x and y.
1. Find Partners
2. Add or Subtract?
3. Solve
22 in 10 in x 14 in y 6 in
Find x (Horizontal):
x = ___________ in
Find y (Vertical):
y = ___________ in
Architect's Check-In
How did checking for "Partner Lines" help you solve this problem?
Blueprint Gaps Teacher Guide Scroll Teacher Guide
Blueprint Gaps: Missing Measurements
Unit: Blueprint Builders
Day 2 of 3
Lesson Objective
Students will identify and calculate missing side lengths in complex rectilinear figures by applying the Parallel Strategy.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
The Parallel Strategy
Step 1
Find all partner lines (same direction).
Step 2
Determine if we need to add or subtract.
Step 3
Solve to find the missing length.
Pacing & Facilitation
10 mins
Launch
Introduce the Parallel Strategy . Show students that horizontal lines only interact with horizontal lines. Use colored highlighters to find "partners".
15 mins
I Do / We Do
Model the 3 steps explicitly. Focus on Step 2 : determining the operation. If they have the total, subtract the part. If they have two parts, add to find the total.
20 mins
Independent
Students work on the Blueprint Gaps Worksheet . Check that students are writing out the Step 3 calculation.
Architect's Alerts (Misconceptions)
Direction Confusion
Students may try to subtract a vertical side from a horizontal side. Remind them: "Partners only!"
Default to Addition
Students often default to adding every number they see. Stress Step 2 : Is the missing piece a whole or a part?
Answer Key
Worksheet: Blueprint Gaps
A x = 8 m, y = 5 m
B a = 5 ft, b = 6 ft
C w = 20 cm, z = 10 cm
D k = 10 in, m = 12 in
E p = 3 m, q = 16 m
F r = 8 ft, s = 10 ft
Exit Ticket
x (Horizontal)
22 - 10 = 12 in
y (Vertical)
14 + 6 = 20 in
Reflection Notes
Students should note that finding partners ensures they are "comparing apples to apples" (same direction) and not mixing vertical/horizontal lengths.
Blueprint Gaps Worksheet Blueprint Gaps
Finding Missing Measurements
Name:
Date:
Site
The Parallel Strategy
Step 1
Find all partner lines (same direction).
Step 2
Determine if we add or subtract.
Step 3
Solve to find the missing length.
1
Blueprint A
16 m 8 m x 11 m 6 m y
Calculation:
x = _________ m
Calculation:
y = _________ m
2
Blueprint B
12 ft 6 ft b 6 ft 11 ft a
Calculation:
a = _________ ft
Calculation:
b = _________ ft
3
Blueprint C
w 11 cm 9 cm 22 cm 12 cm z
Calculation:
w = _________ cm
Calculation:
z = _________ cm
4
Blueprint D
14 in k 24 in 20 in 8 in m
Calculation:
k = _________ in
Calculation:
m = _________ in
5
Blueprint E
7 m 9 m q 8 m 11 m p
Calculation:
p = _________ m
Calculation:
q = _________ m
6
Blueprint F
24 ft 14 ft s 12 ft 20 ft r
Calculation:
r = _________ ft
Calculation:
s = _________ ft
Architect's Reflection
When finding a missing side, why is it important to complete Step 1 (Find Partners) first?
Master Site Plan Slides Master Site Plan
Culminating Mission
Drafting & Calculating Total Area
The Full Process
Part 1: Fix the Blueprint
Use the Parallel Strategy to find the missing side length first!
Part 2: Area Architect
Once all sides are labeled, Split, Multiply, and Add to find the total area!
5 m 7 m 12 m 3 m ? 8 m
I Do 1
Modeling Phase
15 cm 6 cm 6 cm 4 cm x 10 cm
Phase 1: Fix Side x
x = 15 - 6 = 9 cm
Phase 2: Total Area
Split horizontally:
Top Box: 6 × 15 = 90
126 sq cm
I Do 2
Modeling Phase
Phase 1: Fix Side y
y = 5 + 3 = 8 ft
Phase 2: Total Area
Split vertically:
Left Box: 8 × 4 = 32
62 sq ft
4 ft 5 ft 6 ft y 10 ft 8 ft
Solo Build: Day 3
Open your Master Site Plan Worksheet. Complete the 2 Solo Build problems to earn your Architect Certification!
Master Site Plan Worksheet Master Site Plan
Phase 3: Solo Build
Architect:
Date:
Architect's Final Checklist
Phase 1
Find all Partner Lines to solve the missing side length.
Phase 2
Split the shape, eliminate distractors, and find total area.
01
Drafting Site Alpha
15 m 5 m 20 m 10 m 10 m k
Phase 1: Find k
k = ______________ m
Phase 2: Total Area
Total Area: __________ sq m
02
Drafting Site Beta
14 ft w 24 ft 10 ft 8 ft 18 ft
Phase 1: Find w
w = ____________ ft
Phase 2: Total Area
Total Area: __________ sq ft
Final Step Mastery: When partitioning your blueprint, always double-check your box dimensions. A distractor length is any number that represents a side before you split it or a total when you only need a part .
Master Site Plan Exit Ticket Final Inspection
Exit Ticket: Master Site Plan
Architect:
Your final certification task:missing side length (y) .total area of the site plan.
10 ft 20 ft 30 ft 16 ft 6 ft y
Phase 1: Find Side y
y = ____________ ft
Phase 2: Total Area
__________ sq ft
"I have verified this blueprint and it is ready for construction."
Architect Signature
Master Site Plan Exit Ticket Final Inspection
Exit Ticket: Master Site Plan
Architect:
Your final certification task:missing side length (y) .total area of the site plan.
10 ft 20 ft 30 ft 16 ft 6 ft y
Phase 1: Find Side y
y = ____________ ft
Phase 2: Total Area
__________ sq ft
"I have verified this blueprint and it is ready for construction."
Architect Signature
Master Site Plan Teacher Guide Teacher Guide
Day 3: Master Site Plan
Unit: Blueprint Builders
Day 3 of 3
Lesson Objective
Students will combine unit strategies to solve complex area problems. They must first calculate a missing side length using the Parallel Strategy, then partition and solve for total area using the Area Architect method.
Standards
CCSS.MATH.CONTENT.3.MD.C.7.D
The Architect's Certification Path
Phase 1: Parallel Secret
• Find Partner Lines (Same direction)
• Add or Subtract to solve missing
Phase 2: Area Architect
• Split into rectangles
• Eliminate Distractors
• Multiply & Add Areas
Pacing & Facilitation
10 mins
Launch
Review the "Double Mission" slide. Emphasize that finding the missing side is a requirement for finding the area, not an extra step.
15 mins
I Do / We Do
Model the transition from finding the side to splitting the shape. Warn students: "Don't use the old distractor numbers once you have your new side length!"
20 mins
Certification
Independent worksheet practice. Students must show work for both phases to earn their "Certification Signature" on the exit ticket.
Full Answer Key
Worksheet: Master Site Plan
01: Site Alpha
k (Vertical) = 10 + 10 = 20 m
Distractors: 15, 10
Area: (20 × 10) + (5 × 10) = 250 sq m
02: Site Beta
w (Horizontal) = 24 - 8 = 16 ft
Distractors: 10, 10
Area: (8 × 20) + (16 × 10) = 320 sq ft
Instructional Examples
I Do 1 (Modeling)
x = 9 cm. Area: 90 + 36 = 126 sq cm.
I Do 2 (Modeling)
y = 8 ft. Area: 20 + 48 = 68 sq ft.
Exit Ticket Certification
Phase 1: Side y
16 - 6 = 10 ft
Phase 2: Total Area
Box A: 10 × 16 = 160
Box B: 20 × 10 = 200
Total: 360 sq ft
Master Site Plan Exit Ticket Final Inspection
Exit Ticket: Master Site Plan
Architect:
Your final certification task:missing side length (y) .total area of the site plan.
10 ft 20 ft 30 ft 20 ft 12 ft y
Phase 1: Find Side y
y = ____________ ft
Phase 2: Total Area
__________ sq ft
"I have verified this blueprint and it is ready for construction."
Architect Signature
Master Site Plan Exit Ticket Final Inspection
Exit Ticket: Master Site Plan
Architect:
Your final certification task:missing side length (y) .total area of the site plan.
10 ft 20 ft 30 ft 16 ft 6 ft y
Phase 1: Find Side y
y = ____________ ft
Phase 2: Total Area
__________ sq ft
"I have verified this blueprint and it is ready for construction."
Architect Signature
Master Site Plan Worksheet Master Site Plan
Phase 3: Solo Build
Architect:
Date:
Architect's Final Checklist
Phase 1
Find all Partner Lines to solve the missing side length.
Phase 2
Split the shape, eliminate distractors, and find total area.
01
Drafting Site Alpha
15 m 5 m 20 m 10 m 10 m k
Phase 1: Find k
k = ____________ m
Phase 2: Total Area
Total: __________ sq m
02
Drafting Site Beta
14 ft w 24 ft 10 ft 8 ft 18 ft
Phase 1: Find w
w = ____________ ft
Phase 2: Total Area
Total: __________ sq ft
Final Step Mastery: When partitioning your blueprint, always double-check your box dimensions. A distractor length is any number that represents a side before you split it or a total when you only need a part .
