Boundary Blueprint Homework
Standard NC.4.MD.3 NC Check-In Rigor
BOUNDARY BLUEPRINT
Real-World & Conceptual Area and Perimeter Investigations
Name:
Date: Score:
Formulas:
Area: \(A = l \times w\) | Perimeter: \(P = 2l + 2w\) or \(P = 2 \times (l + w)\)
Always label units!
1
Real-World: The Community Garden Project
Multi-Step
The Oak Grove Community Center is preparing a rectangular vegetable garden. The garden has an area of 108 square feet. The width of the garden is 9 feet.
Part A: What is the length of the rectangular garden? Show your equation.
Part B: The volunteers need to install chicken-wire fencing around the entire perimeter to keep rabbits out. How many feet of fencing do they need to purchase?
Garden Bed Area = 108 sq ft Length = ? ft Width = 9 ft
Blueprint sketch (not to scale)
Work for Part A (Length):
Length = feet
Work for Part B (Fencing / Perimeter):
Total Fencing = feet
2
Real-World: School Courtyard Renovation
Measurement & Cost
An elementary school is building a new rectangular courtyard with a length of 15 feet and a width of 8 feet.
Task A (Area): The entire interior floor will be covered in rubber safety tiles. How many square feet of tile must the school order?
Task B (Perimeter): A heavy-duty safety border costs $4 per foot. How much money will it cost to install the border along the entire perimeter?
Show Work for Task A (Tile Area):
Floor Tile Area = sq ft
Show Work for Task B (Perimeter & Total Cost):
Perimeter = Total Cost = $
NC Check-In Practice Series • Grade 4 Mathematics Continue to Page 2 for Problems 3, 4, and 5 → Page 1 of 2
BOUNDARY BLUEPRINT • Part II: Perimeter-to-Area Rigor & Conceptual Analysis
NC.4.MD.3 Check-In Page 2 of 2
3
Real-World: The Bark Park Enclosure
Two-Step Reasoning
The city park department built a rectangular dog run. The total perimeter is 64 meters and the length is 20 meters. The city needs to buy grass seed to cover the entire ground inside the fence. How many square meters of grass seed are needed?
Step 1: Find the missing width (\(w\))
Width = meters
Step 2: Calculate the area for grass seed
Total Area = sq meters
4
Concept: Same Perimeter, Different Area
NC Check-In Focus
Rectangle P has a length of 11 cm and a width of 5 cm.
Rectangle Q has the exact same perimeter as Rectangle P, but its length is 9 cm.
Rectangle P (11 cm \(\times\) 5 cm):
Perimeter: __________ cm
Area: __________ sq cm
Rectangle Q (\(l = 9\text{ cm}\)):
Width: __________ cm
Area: __________ sq cm
Comparison Conclusion:
Which rectangle has the greater area, and by how many square centimeters?
Greater Area: Rectangle _____
Difference: _____ sq cm
5
Concept Challenge: Multiplicative Dimensions
High Rigor
An artist designs a rectangular mosaic frame where the length is 3 times the width. The perimeter of the frame is 48 inches.
Hint: Think of the perimeter as \(2 \times (\text{width} + \text{length})\), or draw a tape model where length is 3 equal width units!
Dimension Ratio Model
w + w w w
Semi-Perimeter (\(l + w\)) = 24 in
Find Width:
Width = in
Find Length (\(3 \times w\)):
Length = in
Find Total Area (\(l \times w\)):
Area = sq in
Self-Check: I checked all units (ft, sq ft, etc.) | I proved my thinking with an equation
Page 2 of 2
Boundary Checkin Assessment
NC Check-In Practice Standard NC.4.MD.3
BOUNDARY CHECK-IN ASSESSMENT
Select the best answer for each question. Show any quick work in the margins.
Name:
Date: Score: / 4
1
Perimeter to Area Problem
Two-Step
A rectangular community playground has a perimeter of 42 yards. The width of the playground is 8 yards. What is the area, in square yards, of the playground?
A 52 square yards
B 104 square yards
C 272 square yards
D 336 square yards
2
Comparing Rectangular Dimensions
Conceptual Equivalence
Rectangle M has a length of 12 feet and a width of 4 feet.
Rectangle N has the same area as Rectangle M. Which could be the dimensions of Rectangle N?
A Length = 8 feet, Width = 6 feet
B Length = 10 feet, Width = 6 feet
C Length = 14 feet, Width = 2 feet
D Length = 16 feet, Width = 4 feet
3
Real-World Framing & Cost
Measurement Application
Elena makes a custom wooden picture frame for a rectangular photograph that is 14 inches long and 9 inches wide. The decorative wooden framing costs $3 per inch. How much will Elena spend on wood for the entire frame?
A $69
B $92
C $138
D $378
4
Multiplicative Dimension Challenge
High Rigor
A rectangular flowerbed has a width of 6 meters. The length is 4 times as long as the width. What is the perimeter of the flowerbed?
A 24 meters
B 48 meters
C 60 meters
D 144 meters
Strategy: Underline key words (area vs. perimeter) and double-check your calculations.
4.MD.3 Check-In
