Square Squad Worksheet Square Squad Worksheet
Project: Initial Area Survey | Standard: 3.MD.C.7a
Name: __________________________
Date: ___________________________
Architect's Rule: Area is the number of unit squares that cover a shape without gaps or overlaps.
Model Problems: The Foreman Explains
1
Count the unit squares to find the area of this rectangular floor plan.
Thinking: I count 1, 2, 3, 4 squares on the top row and 5, 6, 7, 8 squares in total.Area = 8 square units.
2
Does this shape have gaps or overlaps? Can we find its area by counting squares?
Thinking: No! The squares are not lined up correctly. There are gaps and overlaps . We cannot measure area this way.
3
Shade exactly 6 unit squares to create a rectangle with an area of 6.
Thinking: I could color 2 rows of 3 squares, or 3 rows of 2 squares. As long as I color 6 total, the area is 6.
We Do: The Crew Works Together
4
Find the area by counting the square units. Label each square as you count!
Area = ________ square units
5
Count the unit squares. Which rectangle is larger?
Plan A
Area: ______
Plan B
Area: ______
Plan ______ is larger.
6
Draw a shape with an area of 5 units on the grid below.
You Do: Solo Construction
7
What is the area of this square window?
Area = ________ units2
8
Find the area of the shaded shape.
Area = ________ units2
9
Critical Thinking
Can a rectangle with an area of 12 square units have more squares than a rectangle with an area of 10 square units? Why or why not?
Square Squad Exit Ticket Square Squad Exit Ticket
Job Site: Exit Survey | Day 1
Architect ID
1
Count the squares to find the area of this tile pattern.
Area = square units
2
Which shape has an area of 8 square units ? Circle it.
Shape A
Shape B
Shape C
Architect's Note
How do we know if we have measured the area correctly? (Hint: Think about gaps and overlaps!)
Square Squad Slides Square Squad
The Foundation of Area
Standard 3.MD.C.7a: Tiling & Counting
Today's Blueprint
I can define area as the space covered by a flat surface.
I can measure area by tiling with unit squares.
I can count squares to find the total area without gaps or overlaps.
What is Area?
"Area is the amount of 2D space inside a boundary."
Examples of Area:
📏 Floor in a room
🎨 Paint on a wall
👕 Fabric for a shirt
AREA
The Architect's Golden Rule
To find area, squares must be tiled:
NO GAPS
NO OVERLAPS
Model 1: Counting Units
Foreman Check
1
2
3
4
5
6
7
8
9
10
11
12
Step 1: Verify no gaps.
Step 2: Verify no overlaps.
Step 3: Count every square.
Total = 12 Units
The Crew Works Together
Look at your worksheet (Problem #4). Let's count these together!
Area: ?
Grid Growth Worksheet Grid Growth Worksheet
Project: Area Formula Discovery | Standard: 3.MD.C.7b
Name: __________________________
Date: ___________________________
Architect's Shortcut: You can find the area of a rectangle by multiplying the number of squares in each row by the number of rows.
Model Problems: Multiplication Tool
1
Find the area of this grid using multiplication.
← 5 Units Wide →
Thinking: There are 3 rows. Each row has 5 squares.Equation: 3 x 5 = 15.Area: 15 square units.
2
Relate addition to multiplication for this 4x4 floor plan.
Addition: 4 + 4 + 4 + 4 = 16
Multiplication: 4 x 4 = 16
Both ways give the same area!
3
Label the side lengths and write the area equation.
?
?
Thinking: I see 4 rows and 2 columns.Equation: 4 x 2 = 8 square units.
We Do: Calculating Together
4
Write a multiplication equation for the area of this wall.
______ x ______ = ______
Area = ________ units2
5
Draw a rectangle with side lengths of 3 and 7. What is its area?
Equation: __________________________
6
An architect has a 5x4 tile pattern. They add one more row. What is the new area?
Old Area: 5 x 4 = 20
New Area: (5 + 1) x 4 = ______
You Do: Formula Mastery
7
Write the side lengths and the equation for this shape.
Length: ______ Width: ______
Equation: ____________________
Total Area: ______ units2
8
A rug is 6 feet long and 3 feet wide. Draw the grid and find the area.
Area = ________ square feet
9
Explain why you can use multiplication to find the area of a rectangle.
Grid Growth Slides Grid Growth
From Counting to Calculating
Standard 3.MD.C.7b: Multiplication & Area
The Architect's Discovery
Counting 100 squares takes a long time!
What if we could find the area in seconds ?
"Rectangles are just Arrays of unit squares!"
3 Rows of 5
The Area Formula
L x W = A
Length x Width = Area
Length = Number of Rows
Width = Squares in each row
Model: Using the Formula
Job Site Demo
Length = 3 Width = 6
Calculation:
3 x 6 = 18
Area = 18 Square Units
"It matches counting, but it's much faster!"
Adding it Up
We can also use Repeated Addition :
4 + 4 + 4 + 4 + 4
Is the same as...
5 x 4
Grid Growth Exit Ticket Grid Growth Exit Ticket
Job Site: Formula Check | Day 2
Architect ID
1
Write a multiplication equation to find the area of this tiled floor.
Equation: ______ x ______ = ______
Area = ________ units2
2
Draw a rectangle with side lengths of 5 units and 2 units . What is its area?
Area = ________ units2
3
How is repeated addition like multiplication when finding area?
Site Specs Worksheet Site Specs Worksheet
Project: Real-World Specifications | Standard: 3.MD.C.7b
Name: __________________________
Date: ___________________________
Architect's Tip: Use side lengths to solve area problems even when the grid isn't visible!
Model Problems: Solving Specs
1
A rectangular garden is 8 feet long and 4 feet wide. What is its area?
8 ft
4 ft
Thinking: I identify the side lengths (8 and 4).Equation: 8 x 4 = 32.Area: 32 square feet.
2
Find the area of a square playground that is 7 meters on each side.
7 m
7 m
Thinking: Since it's a square, both sides are the same.Equation: 7 x 7 = 49.Area: 49 square meters.
3
Compare the areas of two rooms. Room A: 3m x 10m. Room B: 5m x 6m.
Room A
3 x 10 = 30 m2
Room B
5 x 6 = 30 m2
Even though they have different side lengths, they have the SAME area!
We Do: Analyzing Specs Together
4
The master bedroom is 9 feet by 7 feet. Draw the floor plan and calculate the area.
Area = ______ x ______ = ________ sq. feet
5
Which shape has an area of 24 square units? Label each side and calculate.
4 by 6
Area: ________
8 by 3
Area: ________
Hint: Could both be right?
6
Solve the word problem: A construction worker is laying tile. Each tile is 1 square foot. If the room is 5 feet long and 12 feet wide, how many tiles are needed?
Tiles needed = Area of the room
Equation: __________________________
Total Tiles: ________
You Do: Blueprint Finalization
7
Find the area of these three shapes. Circle the one with the smallest area.
A: 6m x 6m
Area: ______
B: 9m x 3m
Area: ______
C: 5m x 8m
Area: ______
8
A mural is painted on a wall that is 10 feet wide and 8 feet tall. Draw a diagram and calculate the area.
Equation: ____________________ Area = ________ sq. feet
9
Critical Thinking: An architect says a rectangle with side lengths of 4 and 6 has the same area as one with 3 and 8. Is this correct? Prove it with multiplication.
Site Specs Exit Ticket Site Specs
Exit Ticket • Day 3
Project: Blueprint Builders
Architect:
Date:
Complete the site specifications below to finalize the floor plans. Show your work for each calculation.
1
The Breakroom Floor
The breakroom floor is a rectangle that is 9 feet long and 7 feet wide. What is the total area of the floor?
9 ft 7 ft
Area:
square feet
2
The Lobby Rug
A rectangular rug for the lobby covers 48 square feet. If the length of the rug is 8 feet, what is its width?
Width:
feet
3
Office Expansion
An architect is drawing two different office spaces. Both offices have an area of 24 square feet. Draw and label the side lengths of two different rectangles that could represent these offices.
Office A (Area = 24 sq ft)
Office B (Area = 24 sq ft)
Master Map Worksheet Master Map Worksheet
Project: Complex Floor Plans | Standard: 3.MD.C.7d
Name: __________________________
Date: ___________________________
Architect's Secret: You can find the area of complex shapes by splitting them into smaller rectangles and adding the areas together!
Model Problems: Decomposing Shapes
1
Split this L-shaped room into two rectangles and find the total area.
A B 6 units 4 units
Step 1: Split the shape (Rectangle A and B).
Step 2: Area A = 6 x 4 = 24
Step 3: Area B = 10 x 6 = 60
Step 4: Total = 24 + 60 = 84 units2
2
Can we split this shape a different way? (Vertical vs Horizontal)
Yes! You can split shapes vertically OR horizontally. As long as you add all the pieces, you will get the same total area.
3
Label the missing side length to help split the shape.
Part A
4
6
10
Thinking: If the total width is 10 and the top part is 4, the missing part must be 6.
We Do: Splitting the Site Together
4
Find the area of this T-shaped platform by decomposing it.
Area of Top: ______ x ______ = ______
Area of Bottom: ______ x ______ = ______
Total Area: ________
5
Draw a line to split this shape into two rectangles. Then find the area.
Area 1: ________
Area 2: ________
Total Area: ________
6
Word Problem: A deck has a square section (5ft x 5ft) and a connected rectangular section (4ft x 10ft). What is the total area of the deck?
Equation: (____ x ____) + (____ x ____) = ________
You Do: Master Map Completion
7
Find the total area of this complex floor plan.
4m 4m 6m 6m 10m
Area 1: ________
Area 2: ________
Total Area: ________ sq. meters
8
Draw a shape that is made of two rectangles with a total area of 20 square units.
9
Why must the rectangles be "non-overlapping" when finding total area?
Master Map Exit Ticket Master Map Exit Ticket
Job Site: Final Inspection | Day 4
Architect ID
1
Split this shape and find the total area.
7m 10m 3m 10m
Area 1: ________
Area 2: ________
Total: ________ m2
2
Which expression shows the total area of the shape below?
A (2x3)
B (4x3)
(2 + 3) + (4 + 3)
(2 x 3) + (4 x 3)
(2 x 4) + (3 x 3)
Final Blueprint Check
What was the most challenging part of finding area this week?
