Area Arrays Guide Day 1 Doc Area Arrays Guide
Day 1: Teacher Instruction
Time 25 Min
Teacher Script
TEACHER NOTE: Use grid paper. Have students duplicate models from screen to paper.
Step 1: Rows are Groups Area . Every plan is made of Rows . A row goes across (left to right) like a line of bricks. Rows are our Groups . Look at Problem 1. Identify the rows (groups). There are 4 rows."
Step 2: Items in each Group ONE row? A column identifies each row. The number of squares in just ONE row tells us how many items are in each row. In Problem 1, there are 4 squares in each row. So we have 4 groups of 4. Our equation is 4 × 4."
Step 3: Modeling Rows × Items = Area ."
Step 4: Units for Area units ! If the blueprint says feet, our area is in square feet . If there are no specific units, we use sq units to label your answer."
Foundation: FULLY TILED
Blueprint #001
Rows: __________
Items/Row: __________
____ × ____ = ____
Foundation: FULLY TILED
Blueprint #002
Rows: __________
Items: __________
____ × ____ = ____
Foundation: FULLY TILED
Blueprint #003
Rows: __________
Items: __________
____ × ____ = ____
Foundation: FULLY TILED
Blueprint #004
Rows: __________
Items: __________
____ × ____ = ____
Challenge: PARTIALLY TILED
Phase 2: STAAR Strategy
Teacher Script
Step 1: Side Column = Groups side column on the left . This column identifies each row. The number of squares in this column tells us the total number of Rows (Groups) ."
Step 2: Top Row = Items top row . The number of squares across the top tells us the number of Squares in each row (Items) ."
Step 3: Multiply Rows × Items = Area ."
Construction Challenge
Blueprint #101
Use the partial tiling on the top row and left side column to find the total area.
Rows (Groups): ________
Items/Row: ________
____ × ____ = ____
Construction Challenge
Blueprint #102
Rows (Groups): ________
Items/Row: ________
____ × ____ = ____
Area Inspection
STAAR Check • Day 1
Name:
Date:
1. Avalon draws a shaded rectangle on a grid, as shown. What is the area of Avalon's shaded rectangle in square centimeters?
= 1 square centimeter
A. 50
B. 26
C. 30
D. 36
2. Each square shown has an area of 1 square inch. Which rectangles have an area of 24 square inches?
3. A rectangular rug has 10 rows of tiles. There are 6 tiles in each row. Which expression can be used to find the total area of the rug in square units?
10 + 6
10 × 6
10 + 10
6 + 6 + 6
Area Architects Guide Day 2 Doc Area Architects
Day 2: Application Problems (RDW)
Time Limit 25 Min
Teacher Script
The RDW Strategy: Architects who turn word problems into our own models using RDW ."
Step 1: Read Read the problem to understand the situation. We think about what the problem is asking us to find."
Step 2: Draw Draw a model or representation. We visualize the rows (groups) and the items in each row. We label our model so we can see the math."
Step 3: Write Write an equation and a sentence to answer the question. Rows × Items = Area ."
Architect's Portfolio
Case Study #001
Modeling
"A hallway in the library has 5 shelves for books. Each shelf has 12 books sitting in a row. What is the total area taken up by the books?"
Model or Representation:
(Model 5 rows of 12)
Equation:
____________________
Sentence Answer:
The total area is ____________________
Architect's Portfolio
Case Study #002
A garden plot is built in a rectangular shape. The gardener planted 7 rows of seeds. There were 4 seeds in each row. What is the area of the garden plot in square units?
Model or Representation:
Blueprint Workspace
Write Equation:
____ × ____ = ____
Area: ________________
Architect's Portfolio
Case Study #003
An architect is designing a tray for cupcakes. The tray has 3 horizontal rows. Each row fits 8 cupcakes. What is the total area of the tray in square units?
Model or Representation:
(Visualize 3 groups of 8)
Equation:
____________________
Total: ____________________
Architect's Portfolio
Case Study #004
A brick wall has 10 horizontal rows. There are 6 bricks in each row. What is the area of the wall section in square units?
Model or Representation:
Blueprint Workspace
Write Equation:
____ × ____ = ____
Area: ________________
Master Architect
Perimeter Paths Guide Day 3 Doc Perimeter Instruction
Day 3: Part 1 - Finding the Border
Time Limit 10 Min
Teacher Script
The Fence Analogy: Perimeter is the distance around the outside edge of a shape. Imagine putting up a fence around a yard. To find the total length, we add up every single side."
The Add-All Rule: every single side . If a shape has 4 sides, we add 4 numbers. If it has 6 sides, we add 6 numbers."
Foundation Practice
Blueprint #001: Site Alpha
15 m 8 m ? ?
Step 1: Label missing sides.
Perimeter Calculation:
P = __________ m
Foundation Practice
Blueprint #002: Site Beta
7 in.
A regular hexagon has 6 equal sides .
Equation:
7 × 6 = ____
P = __________ in.
Missing Measures
Day 3: Part 2 - Finding the Missing Link
Time Limit 15 Min
Teacher Script
The Missing Side Mystery: total perimeter (the whole fence), but one piece is missing! We have to work backward to solve the puzzle."
Step 1: Know the Total
Step 2: Add what you know are labeled. This tells us how much of the fence is already there."
Step 3: Subtract to solve missing side length !"
Mystery Case Files
Case #101: The Window Frame
A rectangular window has a total perimeter of 18 feet. The length of the window is 6 feet. What is the width (w )?
6 ft w ? w
Draw a model or representation of all 4 sides.
1. Sum of 2 lengths:
6 + 6 = ________
2. Perimeter - Sum:
18 - ____ = ________
3. Divide for width (w):
w = _______ ft
Mystery Case Files
Case #102
The Square Sandbox
Boundary Masters Check Day 5 Doc Boundary Masters
Cumulative STAAR Assessment
Ref 3.6C • 3.7B
Master Builder Name:
Date of Inspection:
Expert Certification
"Demonstrate your mastery of Area and Perimeter by completing this final construction check."
1
Area Operations
A rectangular rug is shown below. Square tiles were used to cover the entire rug. What is the area of the rug in square units?
A. 10
B. 20
C. 24
D. 12
2
Area Operations
A rectangular floor is being covered with square tiles. Only some of the tiles have been placed. What is the total area of the floor in square units?
F. 13
G. 26
H. 40
J. 48
3
Missing Measures
The perimeter of the triangular garden shown below is 36 feet. What is the length of side n in feet?
12 ft 12 ft n
A. 10
B. 12
C. 24
D. 18
4
Boundary Analysis
An L-shaped patio is shown below. What is the total perimeter of the patio in meters?
14 m 10 m 6 m 4 m ?
Record Perimeter:
meters
Use this area for your model or representation.
Master Builder Reflection
"Explain the difference between finding the Area of a shape and finding its Perimeter."
Builder Seal
Inspector Sign
Boundary Builders Key Doc Answer Key & Teacher Guide
Boundary Builders: Rigorous Intervention Sequence
Area Mastery (3.6C)
Day 1 Foundation & Challenges:
1: 4 × 4 = 16 sq units
2: 10 × 2 = 20 sq units
3: 5 × 5 = 25 sq units
4: 4 × 7 = 28 sq units
Challenge #101: 9 × 5 = 45 sq units
Challenge #102: 6 × 8 = 48 sq units
Day 1 Exit Ticket:
1: D. 30 sq cm (6 wide × 5 high)
2: Choice 1 (8x3) and Choice 2 (12x2)
3: 10 × 6 = 60
Day 2 Application (RDW):
CS1: 5 × 12 = 60 sq units
CS2: 7 × 4 = 28 sq units
CS3: 3 × 8 = 24 sq units
CS4: 10 × 6 = 60 sq units
Day 2 Exit Ticket:
1: 8 × 5 = 40 sq units
2: 4 × 6 = 24 sq units
3: 2 × 10 (Expression B)
Perimeter Mastery (3.7B)
Day 3 (Combined Skills):
P1: 15+8+15+8 = 46 m
P2: 7 × 6 = 42 in.
P3 (L): 12+10+6+6+8+4 = 46 ft
P4 (Tri): 9+9+14 = 32 m
M1 (Rect): 18-(6+6)=6; 6/2=3 ft
M2 (Square): 36/4 = 9 m
Day 3 Exit Ticket:
1: C. 74 ft | 2: 32 cm | 3: 36 inches
Day 4 Application (RDW):
CS1: 9+6+9+6 = 30 in.
CS2: 45-(15+15) = 15 yd
CS3: 28 / 4 = 7 m
Day 4 Exit Ticket:
1: 24-(4+4)=16; 16/2=8 yd
2: 30-(6+6+7+7)=4; side=4 in.
3: 9+6+9+6 (Addition choice)
Day 5: Cumulative Master Check
Section 1 & 2:
1. C (8 × 5 = 40 sq units)
2. G (12 + 12 + 12 = 36; side n = 12)
Section 3 & 4:
3. C (Area is 40 sq ft because 8 × 5 = 40)
4. 48 meters (14+10+6+6+8+4)
Intervention Scaffolding
Rows vs Columns
Always anchor Rows as horizontal groups. Use the phrase: "Rows go across, like seats in a movie theater." Trace rows left-to-right to anchor the first factor.
Model or Representation
Enforce the creation of a model or representation for every application problem. A model with labels transforms abstract words into manageable calculations.
The Perimeter Path
For missing measures, remind students that rectangles have two pairs of equal sides. Labeling all 4 sides immediately prevents the common error of only adding two sides.
Perimeter Architects Guide Day 4 Doc Perimeter Architects
Day 4: Perimeter Application (RDW)
Time Limit 25 Min
Teacher Script
The RDW Strategy: RDW to solve real-world perimeter puzzles."
Step 1: Read Read the problem. We visualize the situation and think about the story. Are we putting a border around something? Are we measuring a fence? We determine if we are finding the total perimeter or if we are solving for a missing piece of the boundary."
Step 2: Draw Draw a model or representation. We sketch the shape and label every side we know. If the total perimeter is given, we write 'P = ___' inside the shape."
Step 3: Write Write our math sentence and a sentence answer. Remember: Sum of all sides = Perimeter ."
Architect's Portfolio
Case Study #101
Modeling
"Evelyn makes a rectangular birthday card. The card has a length of 9 inches and a width of 6 inches. What is the perimeter of Evelyn's card in inches?"
Model or Representation:
Draw the rectangle and label all 4 sides!
Equation:
____________________
Sentence Answer:
The perimeter is ____________________
Architect's Portfolio
Case Study #102
A crew is building a fence around a triangular yard. The total perimeter is 45 yards. Two sides are 15 yards each. What is the length of the third side?
Model or Representation:
Blueprint Workspace
Step 1: Sum of Known
15 + 15 = ____
Step 2: Subtract from P
45 - ____ = ____
Side = ________________
Architect's Portfolio
Case Study #103
A square patio has a total perimeter of 28 meters. What is the length of one side of the patio?
Model or Representation:
Draw a square and divide the total by 4!
Equation:
28 ÷ 4 = ____
Side = ________________
Missing Link
STAAR Check • Day 4
Name:
Date:
1. A rectangular garden has a perimeter of 24 yards. The width of the garden is 4 yards. What is the length of the garden?
