Tile Architects Worksheet Tile Architects
Lab Report: Area and Perimeter Modeling
STUDENT DATA
NAME:
DATE:
Blueprint Key: Tile Values
1 unit
Small Square
x units
Rectangle
x² units
Large Square
1
The Small House
Build a shape using 2 "x" tiles and 3 "1" tiles. Draw your shape in the space below.
Total Area
Total Perimeter
2
The Courtyard
Look at the tiles provided by your teacher. Write the Area expression for a shape with 1 large square (x²) and 4 rectangles (x).
Area Expression
3
Matching Dimensions
A rectangle has a length of x + 2 and a width of 3. Sketch this using your tiles below.
How many "x" tiles did you use?
How many "1" tiles did you use?
Architect's Conclusion
If we add one more Large Square (x²) to your drawing above, how would the Area expression change? Explain your thinking below.
TIER 3 SUPPORT
Manipulatives Recommended
Tile Mastery Slides Concept Lab: Lesson 1
TILE ARCHITECTS
Building the bridge between geometry and algebra.
Concrete Models
Variable Logic
Meet Your Materials
"1"
A tiny unit square.
"x"
The rectangle tile.
"x²"
The big square.
Area vs. Perimeter
PERIMETER
The distance AROUND the outside edges of the shape.
AREA
The TOTAL STUFF (tiles) inside the shape.
Model: 2x
Guided Build: Challenge 1
Build a shape with 1 large square and 2 unit squares.
What is the Area?
x² + 2
Let's Discuss
Why did we use x²?
How many ones did we add?
Tile Architects Teacher Guide Teacher Guide: Tile Architects
Lesson 1: Modeling Area & Perimeter | Tier 3 Intervention
Learning Objectives
Identify concrete tile values (1, x, x²).
Construct complex shapes based on verbal/written descriptions.
Differentiate between Area (total tiles) and Perimeter (outside edges).
Write basic algebraic expressions for modeled shapes.
Materials Needed
Physical Algebra Tile kits (enough for each student).
Tile Architects Worksheet.
Projector for Tile Mastery Slides.
Graph paper for extension sketches.
Tier 3 Scaffolding Strategies
Visual Anchors
Keep the "Blueprint Key" slide or worksheet reference visible at all times. Use physical color-coded tiles that match the digital colors (Yellow=1, Blue=x, Red=x²).
CRA Sequence (Concrete → Representational → Abstract)
Do not move to writing expressions (Abstract) until students can build the shape (Concrete) and draw it (Representational) with 90% accuracy.
Facilitation Questions
Check for Understanding
"If I put these two 'x' tiles together side-by-side, does the AREA change? Does the PERIMETER change?"
Error Correction
"I see you counted this edge twice where the tiles touch. Should we count that for perimeter if it's trapped on the inside?"
Abstraction Bridge
"If we have 'x' plus 'x' plus 'x', what is a faster way to write that total using a number and a letter?"
Common Misconceptions
Students often struggle with the "gap" in the perimeter where tiles touch. Explicitly teach that perimeter is the "fence" around the whole yard, and internal walls aren't part of the fence.
Elimination Puzzle Worksheet The Balance Lab
Intervention: Solving Systems by Elimination
STUDENT DATA
NAME:
DATE:
Lab Rule: The Golden Balance
If two scales are already balanced, we can combine them! If we add the left sides together and the right sides together, the new scale will still be balanced.
1
Visual Weight Puzzle
Scale A
B
5
=
15
Scale B
B
-
5
=
5
What happens if we stack Scale A on top of Scale B? Combine them below:
(B + 5) + (B - 5) = 15 + 5
Why did the "5" disappear?
What is the value of 1 "B"?
B = ___
2
The Elimination Challenge
System of Equations
\(x + y = 10\)
\(x - y = 4\)
A
ADD the two equations together. What variable cancels out?
Hint: +y and -y make zero!
B
Solve for X.
x = ___
Show work in the space below:
C
Now find Y. (Plug your X back into the top equation!)
y = ___
Pattern Tracker Worksheet Pattern Tracker
Lab Report: Growth and Decay Models
Lab Technician
NAME:
DATE:
Multiplication Explosion
In 5th grade, we learned patterns like 2, 4, 6, 8 (+2 each time).Concept Lab , we look at Multiplication Patterns like 2, 4, 8, 16 (x2 each time).
1
The Doubling Dish
A single bacteria cell doubles every hour. Fill in the pattern and draw the cells.
Start (Hour 0)
1 Cell
Hour 1
2 Cells
Hour 2
___ Cells
Hour 3
___ Cells
Growth Rule:
To find the next number, I must multiply the previous number by .
2
Exponential Decay (Shrinking)
A magic square loses half of its area every minute. Start with 16 squares.
16
8
___
___
Growth vs. Decay Summary
Scenario Is it Growing or Shrinking? The "Multiplier" A bank account doubles every year. Multiply by 2 A car's value is cut in half every 5 years. Shrinking (Decay) A population triples every decade.
Lab Reflection
How is "exponential growth" (multiplying) different from regular 5th grade counting (adding)?
Region Detective Worksheet Region Detective
Lab Report: Graphing Boundary Zones
Investigator
NAME:
DATE:
>
Greater Than
Dashed Line
<
Less Than
Dashed Line
1
The 1D Safe Zone
Find the "Safe Zone" where \(x > 3\). Use the number line below.
0
1
2
3
4
5
6
Test Point: 5
Is 5 greater than 3?
YES
NO
Test Point: 1
Is 1 greater than 3?
YES
NO
2
The 2D Region Investigation
Look at the graph. The boundary is the line \(y = 2x + 1\). We need to shade the region for \(y > 2x + 1\).
Step 1: Choose a Test Point
Let's try the origin (0,0). Plug it into \(y > 2x + 1\).
0 > 2(0) + 1
Step 2: Conclusion
Is 0 greater than 1? _____
Should we shade the side with (0,0)? (Yes / No)
