Patterns to Products Lesson Plan Day 1 of 2 • Tiered Intervention
Patterns to Products Lesson Plan
Target Audience: Grades 6–7 Intervention (Operating at Grades 3–4 Level) • Duration: 45 Minutes
Structural Bridge
Essential Question
How do counting patterns and repeated addition build the foundation for multiplication arrays?
Learning Targets
Represent equal groups using skip counting sequences and repeated addition sentences.Model repeated addition as a rectangular grid (array) with rows and columns.Translate fluently between verbal descriptions, visual sets, and multiplication expressions.
45-Minute Instructional Arc
8 Min
Hook & Pattern Diagnostic (Launchpad):
Present the "Rhythm of Numbers" prompt on Slide 1. Students identify missing intervals in sequences (+3, +4, +6). Connect auditory and visual counting to physical equal hops on a number line.
12 Min
Explicit Modeling: Groups to Grids:
Demonstrate moving from loose items to bundled equal groups, then organizing bundles into rectangular arrays (e.g., 4 rows of 6 items = 6 + 6 + 6 + 6 = \(4 \times 6 = 24\)). Explicitly label rows (horizontal) and columns (vertical).
18 Min
Tiered Guided & Independent Practice:
Students transition into assigned tiers based on warm-up diagnostics. Teacher conducts a 10-minute targeted small-group clinic with Tier 1 students while Tiers 2 & 3 work on scaffolded challenge sets.
7 Min
Synthesis & Exit Check:
Students complete the 3-question Patterns Exit Ticket. Whole-class debrief: "Why is an array faster to count than scattered dots?"
Tiered Differentiation Matrix
Tier 1: High Support Gr 3 Entry
Focus: Equal group circles & structured number line jumps.
Provides pre-drawn containers and dot arrays. Students write repeated addition statements before matching multiplication equations.
Tier 2: Core Bridge Gr 3–4 Solid
Focus: Array grids & row/column equivalence.
Students construct rectangular arrays on dot grids, demonstrating that \(3 \times 5 = 5 \times 3\) using the commutative property.
Tier 3: Extension Gr 4+ Bridge
Focus: Decomposing arrays & word problems.
Students partition large arrays (e.g., \(6 \times 7\) broken into \(5 \times 7 + 1 \times 7\)) to prepare for Day 2 area models.
Number Bridges Sequence • Day 1 Guide Page 1 of 2
Instructional Delivery & Intervention Protocols
Day 1: Teacher Scripting, Misconception Diagnostics, and Small-Group Strategy
Facilitator Playbook
Teacher Dialogue & Guiding Prompts
Framing the Bridge (Minutes 1–3): "Today we aren't just memorizing facts from a table. We are going to look at multiplication as an architect looks at a building plan. When you skip count by 4s—4, 8, 12, 16—what are you really doing? You are adding another layer of bricks. Let's see how our addition shortcuts build high-level math speed."
Connecting Equal Groups to Arrays (Minutes 9–12): "Look at these 18 counter circles scattered randomly. Counting by ones takes forever and makes it easy to lose your place. But watch what happens when I align them into 3 rows of 6. How does our eye instantly know the total? Who can read the addition sentence? Now, how do we write that in multiplication code?"
Critical Misconceptions & Real-Time Corrections
Misconception 1: Confusing Factor with Sum (\(4 \times 3 = 7\))
The Root: Defaulting to single-step addition when seeing the multiplication symbol.
Immediate Move: Have the student read "\(4 \times 3\)" aloud as "4 groups of 3" . Draw 4 physical circles and place 3 tally marks inside each. "Do we have 7 tallies or 12 tallies?"
Misconception 2: Inverting Rows and Columns
The Root: Not distinguishing between horizontal horizontal sets (rows) and vertical stacks (columns).
Immediate Move: Use the "Row like a boat across water (side to side)" and "Column like a Roman pillar standing tall (up and down)" mnemonic. Emphasize that while orientation flips the factors, the total area remains identical.
Small-Group Clinic Protocol (10-Minute Intensive Table)
Step 1 (2 min): Physical build: Place two-color counters in rows of 4. Have students tap and chant the skip sequence: "4... 8... 12... 16."
Step 2 (4 min): Dual representation: Students write "\(4 + 4 + 4 + 4\)" on their mini-whiteboards directly underneath their physical counters, followed by "\(4 \times 4 = 16\)".
Step 3 (4 min): Independent release to Tier 1 worksheet problems 1–3 with explicit check before returning to independent seating.
Number Bridges Sequence • Day 1 Guide Page 2 of 2
Patterns to Products Slides Number Bridges • Day 1 Intervention Workshop
Patterns to Products
Cracking multiplication through rhythm, equal groups, and architectural grids.
Launch Challenge: Find the Rhythm
4 → 8 → 12 → ? → 20
Focus: Counting → Addition → Multiplication Slide 1 of 6
Concept 01 Connecting Hops to Totals
Skip Counting is Repeated Addition
Imagine 5 equal jumps of 4 along the number track:
Jump 1 +4 (Total: 4)
Jump 2 +4 (Total: 8)
Jump 3 +4 (Total: 12)
Jump 4 +4 (Total: 16)
Jump 5 +4 (Total: 20)
4 + 4 + 4 + 4 + 4 = 20 5 groups of 4 = 20
Key Insight: Adding the same number repeatedly creates predictable jumps. Slide 2 of 6
Concept 02 Visual Organization
Organizing Loose Counts into Arrays
Scattered Items
Hard to count quickly. High risk of losing your place!
12 scattered dots
Organized Array
Instant recognition! 3 neat rows with 4 dots each.
3 rows × 4 in each row = 12 total
Architectural rule: Rows run horizontally (→), Columns stand vertically (↑). Slide 3 of 6
Concept 03 The Multiplication Formula
The Anatomy of an Array
Rows (Horizontal) 4
Number of equal rows
× "groups of"
Columns (Vertical) 6
Items inside each row
Repeated Addition: 6 + 6 + 6 + 6
Total Product = 24
Turn & Talk: Does 4 × 6 give the exact same total as 6 × 4? Why? Slide 4 of 6
Practice Stations Choose Your Launchpad
Today's Tiered Practice Mission
Tier 1: Group Builders
Equal Circles & Tracks
Use pre-built group circles and number line hops to write addition and multiplication pairs.
Guided Clinic at Table 1
Tier 2: Grid Architects
Array Construction
Draw rectangular arrays on dot grids and prove the commutative flip rule (\(A \times B = B \times A\)).
Independent / Partner Pod
Tier 3: Pattern Masters
Array Deconstruction
Split complex arrays into friendly components (5s and 2s) to solve larger multiplication puzzles.
Challenge Station
Grab your tiered handout and begin your first 3 problems now. Slide 5 of 6
Exit Debrief Day 1 Reflection
Equal Groups Tiered Practice Worksheet Day 1 Practice Handout • Tiered Problem Set CODE: NB-101
Equal Groups & Array Grids
Connecting counting rhythm, repeated addition, and rectangular arrays.
Name:
Date:
Tier 1
Track Builders: Number Lines & Equal Groups
Foundational Bridge
1. Trace the hops of 3 on the number line to reach the target total.
0 ··· 3 ··· 6 ··· 9 ··· 12 ··· 15 ··· 18
Repeated Addition Equation:
Multiplication Sentence (\(\text{Hops} \times \text{Size}\)):
2. Look at the 4 containers below. Each container holds 5 tokens.
Number of groups:
Items per group:
Total items:
Tier 2
Grid Architects: Constructing Rectangular Arrays
Core Intervention
3. On the grid on the left, shade an array of 3 rows with 6 columns . On the right, shade 6 rows with 3 columns .
Array A: 3 rows × 6 columns
Equation:
Array B: 6 rows × 3 columns
Equation:
Explain why both arrays have the exact same total:
Number Bridges • Lesson 1 Student Handout Page 1 of 2
Equal Groups & Array Grids (Continued)
Decomposition & Applications
Tier 3
Pattern Masters: Splitting Arrays with Friendly Numbers
Extension & Pre-Algebra Bridge
4. When facing a harder fact like \(6 \times 7\), we can split 6 into \(5 + 1\).
Study the decomposed model below: Part A is \(5 \times 7\), and Part B is \(1 \times 7\).
Part A: 5 rows of 7 \(5 \times 7 = \text{___}\)
Part B: 1 row of 7 \(1 \times 7 = \text{___}\)
=
Total Product \(6 \times 7 = \text{___}\)
Now, use this strategy to solve \(7 \times 8\) by splitting 7 into \(5 + 2\):
Friendly Part 1: \(5 \times 8\)
Friendly Part 2: \(2 \times 8\)
Combined Total:
Real-World Architectural Challenge
The School Auditorium Scenario: The middle school stage crew is arranging chairs for an assembly. They set up 8 rows with 9 chairs in each row .
Draw or sketch an array box model of the chairs:
Show your calculation (Repeated addition or decomposed multiplication):
Total number of chairs arranged:
Self-Assessment & Reflection
Patterns Exit Ticket Exit Ticket
Day 1: Patterns to Products Check
Name:
Period:
1. A frog takes 4 equal hops of 6 on a number line. Complete the models:
Repeated Addition Equation:
Multiplication Equation:
2. Look at the array grid below. Write the matching multiplication fact:
Rows: Columns:
Equation:
3. Why is using an array (\(4 \times 8\)) faster and less error-prone than counting 32 scattered dots one by one?
Today's Comfort: [ ] 1: Shaky [ ] 2: OK [ ] 3: Solid [ ] 4: Expert Teacher Score: _____ / 3
Cut along dashed line for 2 tickets per sheet
Exit Ticket
Day 1: Patterns to Products Check
Name:
Period:
1. A frog takes 4 equal hops of 6 on a number line. Complete the models:
Repeated Addition Equation:
Multiplication Equation:
2. Look at the array grid below. Write the matching multiplication fact:
Rows: Columns:
Equation:
3. Why is using an array (\(4 \times 8\)) faster and less error-prone than counting 32 scattered dots one by one?
Today's Comfort: [ ] 1: Shaky [ ] 2: OK [ ] 3: Solid [ ] 4: Expert Teacher Score: _____ / 3
Equal Groups Answer Key Teacher Reference • Answer Key & Guide MATCHES: NB-101
Equal Groups & Array Grids Answer Key
Day 1 Solutions, Scaffolding Notes, and Misconception Interventions.
Day 1 Material
Tier 1 Key
Track Builders: Number Lines & Equal Groups
Foundational Solutions
1. Number Line Hops of 3 to Reach 18:
0 → 3 3 → 6 6 → 9 9 → 12 12 → 15 15 → 18
Students trace 6 individual hops of length 3 ending precisely at 18.
Repeated Addition Equation: 3 + 3 + 3 + 3 + 3 + 3 = 18 (Six 3s summed together)
Multiplication Sentence: 6 × 3 = 18 (Also accept \(3 \times 6 = 18\))
2. 4 Containers with 5 Tokens Each:
Number of groups: 4
Items per group: 5
Total items: 20
Teacher Coaching Note: Verify students see this as 4 groups of 5 (\(5 + 5 + 5 + 5 = 20\)), not 5 groups of 4.
Tier 2 Key
Grid Architects: Constructing Rectangular Arrays
Array Equivalence
3. Array Grid Shading & Commutative Equivalence:
Array A (3 rows × 6 cols):
Equation: 3 × 6 = 18
3 horizontal rows, each containing 6 shaded blocks.
Array B (6 rows × 3 cols):
Equation: 6 × 3 = 18
6 horizontal rows, each containing 3 shaded blocks.
Exemplar Explanation (Why totals match):
"Both arrays contain exactly 18 squares because rotating the shape does not add or remove any blocks. By the commutative property of multiplication, \(3 \times 6 = 6 \times 3 = 18\)."
Number Bridges Sequence • Day 1 Practice Key Page 1 of 2
Equal Groups & Array Grids Key (Continued)
Decomposition & Applications Key
Tier 3 Key
Pattern Masters: Splitting Arrays with Friendly Numbers
Distributive Bridge
4. Decomposed Model Solutions:
Part A: Solving \(6 \times 7\) decomposed as \((5 \times 7) + (1 \times 7)\)
Part A (\(5 \times 7\)) 35
Part B (\(1 \times 7\)) 7
Total (\(35 + 7\)) 42
Part B: Solving \(7 \times 8\) decomposed as \((5 \times 8) + (2 \times 8)\)
Friendly 1 (\(5 \times 8\)) 40
Friendly 2 (\(2 \times 8\)) 16
Total (\(40 + 16\)) 56
Real-World Auditorium Scenario Solution
Problem Context: 8 rows with 9 chairs in each row.
Expected Sketch:
A rectangular box with
Patterns Exit Ticket Key Teacher Reference • Formative Check Key CODE: NB-102-KEY
Patterns Exit Ticket Answer Key
Exemplar responses, 3-point scoring criteria, and Day 2 placement rubric.
Day 1 Exit Check
Model Solution Layout Standard 3-Point Rubric
1. Number Line Hops (4 hops of 6) 1.0 Point
Repeated Addition Equation: 6 + 6 + 6 + 6 = 24
Multiplication Equation: 4 × 6 = 24
Award 0.5 for correct repeated addition and 0.5 for multiplication equation.
2. Array Grid Dimensions & Equation 1.0 Point
Rows: 3
Columns: 7
Equation: 3 × 7 = 21
Also accept \(7 \times 3 = 21\) if the student noted 7 columns of 3.
3. Conceptual Reasoning: Why use an array? 1.0 Point
Exemplar Student Response: "An array organizes the dots into equal rows and columns so you can multiply (\(4 \times 8 = 32\)) or skip count by 8s. Counting 32 scattered dots one by one takes much longer, and it's easy to lose count or count the same dot twice."
Full credit requires stating that arrays create equal groups/rows or allow multiplication instead of slow 1-by-1 counting.
Day 2 Student Placement Guide (Based on Exit Score)
Score: 0 – 1 Pathway A
Assign to Guided Clinic Table . Provide physical two-color counters and focus on friendly 5s decomposition before introducing multi-digit area models.
Score: 2 Pathway B
Assign to Core Intervention Pod . Good grasp of rows and columns; ready to construct 1-digit by teen area models (\(4 \times 16\)).
Score: 3 Pathway C
Assign to Challenge Station . High fluency with array structures; ready for multi-zone floor plan architecture and error analysis tasks.
Quick Feedback Comments for Student Tickets
• "Great job labeling your rows and columns accurately!"
• "Remember: rows go across horizontally (→); columns stand tall (↑)."
• "Strong mathematical reasoning on why arrays are faster!"
• "Watch out: make sure to multiply, not add, the row and column numbers."
Number Bridges Sequence • Day 1 Exit Key Page 1 of 1
Arrays to Action Lesson Plan Day 2 of 2 • Tiered Intervention
Arrays to Action Lesson Plan
Target Audience: Grades 6–7 Intervention (Operating at Grades 3–4 Level) • Duration: 45 Minutes
Area Model Bridge
Essential Question
How does decomposing large arrays into "friendly chunks" (5s and 10s) unlock fast mental multiplication?
Day 2 Learning Targets
Decompose difficult multiplication facts into two friendlier sub-products using the distributive property.Construct rectangular area models representing partial products.Solve multi-step real-world word problems using array models and mathematical reasoning.
45-Minute Lesson Timeline
7 Min
Warm-up & Friendly 5s Diagnostic:
Quick choral counting by 5s and 10s. Present Slide 1 & 2: "The 7 × 8 Wall." Ask: "Who knows 5 × 8? Who knows 2 × 8? What happens when we put them together?"
13 Min
Direct Instruction: The Array Splitter & Area Model:
Introduce the area model (Slides 3 & 4). Model how a \(6 \times 14\) garden plot splits into \(6 \times 10 = 60\) and \(6 \times 4 = 24\), summing to 84. Highlight how this replaces rote memorization with spatial logic.
15 Min
Tiered Workshop Stations:
Students work in tiered pathways (Level A: Scaffolds with 5s; Level B: Decomposing tens; Level C: Multi-step layout challenge). Teacher facilitates targeted Table Clinic for Tier A.
10 Min
Cumulative Mastery Check:
Students independently complete the Multiplication Mastery Assessment, synthesizing Days 1 & 2 skills across counting, arrays, and word problems.
Tiered Practice Pathways
Pathway A Intensive
Focus: Splitting facts with 2s and 5s.
Uses color-coded physical blocks and pre-split array diagrams. Students calculate each half before combining.
Pathway B Target Intervention
Focus: 1-digit × teens area models.
Expands numbers like 13 into \((10 + 3)\). Students draw box models and sum partial products accurately.
Pathway C Challenge
Focus: Multi-step real-world problem solving.
Students analyze floor plans and error-analysis tasks, justifying which decomposition strategy is most efficient.
Number Bridges Sequence • Day 2 Guide Page 1 of 2
Station Coaching & Progress Diagnostics
Day 2: Teacher Dialogue, Common Obstacles, and Remediation Benchmarks
Arrays to Action Slides Number Bridges • Day 2 Intervention Workshop
Arrays to Action
Splitting big numbers into friendly chunks and mastering rectangular area models.
The Question: Can You Solve \(7 \times 8\) in 5 Seconds?
Don't memorize it in panic. Split it into numbers you already own!
Focus: Arrays → Decomposing → Area Models Slide 1 of 6
Strategy 01 The Power of Friendly Numbers
The Array Splitter: Break \(7 \times 8\)
7 rows of 8 can feel overwhelming. So we slice 7 into 5 + 2 :
Friendly Chunk 1 5 rows of 8 \(5 \times 8 = 40\)
Friendly Chunk 2 2 rows of 8 \(2 \times 8 = 16\)
Total: 40 + 16 \(7 \times 8 = 56\)
Rule: Always look for 5s, 10s, and 2s to break apart tough numbers. Slide 2 of 6
Strategy 02 The Area Model Blueprint
Moving to Area Models: \(6 \times 14\)
Instead of drawing 84 individual dots, draw a rectangle partitioned by place value:
6
Top: 10 \(6 \times 10\) = 60
Top: 4 \(6 \times 4\) = 24
Total Area = 60 + 24 = 84
Notice: Length (10 + 4 = 14) times Width (6) equals the total area. Slide 3 of 6
Application Engineering Challenge
Real-World Case: Maker Space Workbenches
The STEM lab has 8 workbenches . Each bench needs 12 3D-printer filament spools .
Step 1: Partition 12
12 = 10 + 2
10 is the friendliest number in math!
Step 2: Multiply & Combine
\(8 \times 10 = 80\)
\(8 \times 2 = 16\)
\(80 + 16 = 96\) spools
Turn & Talk: How would you solve this if there were 15 workbenches? Slide 4 of 6
Workshop Stations Station Directives
Today's Tiered Workshop Pathways
Pathway A
Friendly 5s Splitter
Use visual split cards to solve facts between 6 and 9 by breaking them into 5s and 2s.
Guided Clinic Table
Pathway B
Area Model Builders
Construct 2-digit by 1-digit area models by partitioning tens and ones.
Partner Work Station
Pathway C
Master Architects
Solve multi-step floor plan challenges and find the hidden errors in complex models.
Independent Challenge Station
Work hard for the next 15 minutes. Mastery Assessment begins at minute 35! Slide 5 of 6
Arrays Tiered Challenge Worksheet Day 2 Practice Handout • Tiered Pathways CODE: NB-201
Arrays to Action: Decomposing & Area Models
Unlocking multi-digit multiplication using friendly chunks and geometric area boxes.
Name:
Date:
Pathway A
Friendly 5s Splitter: Fact Decomposition
Scaffolded Support
Break the first factor into (5 + something) to calculate faster. Complete each scaffolded box:
1. Solve \(7 \times 6\) by splitting 7 into \(5 + 2\):
Step 1: Multiply with 5 \(5 \times 6 =\)
Step 2: Multiply with 2 \(2 \times 6 =\)
Step 3: Add Partial Products Total \(7 \times 6 =\)
2. Solve \(8 \times 7\) by splitting 8 into \(5 + 3\):
Friendly Part: \(5 \times 7\)
Remaining Part: \(3 \times 7\)
Final Combined Total:
Pathway B
Area Model Blueprinting: Multiplying Tens and Ones
Core Intervention
3. A community garden plot has an area of \(4 \text{ ft} \times 16 \text{ ft}\) . Split 16 into 10 + 6 on the area model:
4
Length: 10 ft \(4 \times 10 = \text{____}\)
Length: 6 ft \(4 \times 6 = \text{____}\)
Add both partial areas:
Total area in square feet:
Number Bridges • Lesson 2 Student Challenge Page 1 of 2
Arrays to Action (Continued)
Engineering & Reasoning
Pathway C
Master Architects: Multi-Zone Floor Plan
Extension Challenge
4. Middle School Maker Lab Design:
An architect is designing an 8-meter-wide lab with two sections: a Coding Zone (12 meters long) and a Robotics Arena (8 meters long) .
Width: 8 m
Zone 1: Coding Length: 12 m
Zone 2: Robotics Length: 8 m
Area of Coding Zone (\(8 \times 12\)):
Area of Robotics Zone (\(8 \times 8\)):
Total Floor Area of the entire Maker Lab:
Math Detective: Spot the Blunder
Devon's Claim: "To solve \(5 \times 14\), I split 14 into 10 and 4. Then I did \(5 \times 10 = 50\), and added 4 to get 54!"
What mistake did Devon make?
Show the correct calculation and true product:
Strategy Evaluation
Which strategy feels easiest for you when multiplying large numbers: repeated addition, skip counting, or splitting with an area model? Why?
Mastery Check Assessment Number Bridges Sequence • Cumulative Assessment Total Points: / 10
Multiplication Mastery Check
Demonstrating the bridge from skip counting and repeated addition to arrays and area models.
Name:
Period:
Part 1
Skip Counting & Repeated Addition (2 Points)
1. Fill in the missing numbers in the skip counting sequence:
6, 12, , 24, , 36
2. Write the sequence above as a repeated addition sentence that totals 30:
Part 2
Interpreting Rectangular Arrays (3 Points)
3. Look at the array of solar panels below:
Rows across:
Columns down:
Multiplication Equation:
4. If the solar panel technician rotates this array 90 degrees, how many panels will there be in total? Explain why.
Part 3
Decomposing Factors & Area Models (3 Points)
5. Solve \(7 \times 14\) by splitting 14 into 10 + 4 inside the area model:
Box 1: \(7 \times 10\)
Box 2: \(7 \times 4\)
Total Sum:
Part 4
Real-World Architectural Challenge (2 Points)
6. A basketball arena has 6 seating sections . Each section has 15 rows with 10 seats in each row .
How many seats are in ONE section? Then, how many total seats are in all 6 sections combined? Show your work:
Work for 1 Section (\(15 \times 10\)):
Total for all 6 Sections:
Number Bridges Sequence • Cumulative Assessment Page 1 of 2
Facilitator Resource • Confidential
Answer Key & Assessment Rubric
Scoring Guide (10 Total Points)
Part 1: Skip Counting & Repeated Addition 2 Points
1. Missing numbers: 18 and 30 (Sequence: 6, 12, 18 , 24, 30 , 36). [1 pt]2. Repeated addition sentence: \(6 + 6 + 6 + 6 + 6 = 30\) (Accept 5 groups of 6, or \(5 \times 6 = 30\)). [1 pt]
Part 2: Interpreting Rectangular Arrays 3 Points
3. Rows across = 3 ; Columns down = 8 ; Equation: \(3 \times 8 = 24\). [2 pts]4. Rotating gives \(8 \times 3 = 24\) panels. Explanation must cite the commutative property (rotating changes row/column orientation but total area remains unchanged). [1 pt]
Part 3: Decomposing Factors & Area Models 3 Points
Arrays Challenge Answer Key Teacher Reference • Answer Key & Guide MATCHES: NB-201
Arrays Tiered Challenge Answer Key
Day 2 Solutions, Decomposed Area Models, and Error Analysis Rubrics.
Day 2 Material
Pathway A Key
Friendly 5s Splitter: Fact Decomposition
Scaffolded Solutions
1. Solution for \(7 \times 6\) (splitting 7 into \(5 + 2\)):
Step 1 (\(5 \times 6\)) 30 Friendly count by 5s
Step 2 (\(2 \times 6\)) 12 Double fact (6 + 6)
Step 3 (\(30 + 12\)) 42 Final product = 42
2. Solution for \(8 \times 7\) (splitting 8 into \(5 + 3\)):
Friendly (\(5 \times 7\)) 35
Remaining (\(3 \times 7\)) 21
Total (\(35 + 21\)) 56
Alternate Valid Split: Some students may split 7 instead: \((8 \times 5) + (8 \times 2) = 40 + 16 = 56\). Award full credit for either decomposition!
Pathway B Key
Area Model Blueprinting: Multiplying Tens & Ones
Core Intervention
3. Garden Plot Area (\(4\text{ ft} \times 16\text{ ft}\) with 16 split into \(10 + 6\)):
Left Sub-Area: \(4 \times 10\) 40 sq ft
Right Sub-Area: \(4 \times 6\) 24 sq ft
Sum of Partial Areas: 40 + 24 = 64
Total Garden Area: 64 square feet
Number Bridges Sequence • Day 2 Challenge Key Page 1 of 2
Arrays Tiered Challenge Key (Continued)
Engineering & Reasoning Key
Pathway C Key
Master Architects: Multi-Zone Floor Plan
Extension Solutions
4. Maker Lab Multi-Zone Floor Plan (Width = 8 m):
Coding Zone Calculation:
\(8\text{ m} \times 12\text{ m} = (8 \times 10) + (8 \times 2)\)
Robotics Arena Calculation:
\(8\text{ m} \times 8\text{ m} = \mathbf{64\text{ m}^2}\)
Total Maker Lab Floor Area:
Method 1 (Sum of Zones): \(96\text{ m}^2 + 64\text{ m}^2 = \mathbf{160\text{ m}^2}\)
Method 2 (Combined Length): \(8\text{ m} \times (12 + 8\text{ m}) = 8\text{ m} \times 20\text{ m} = \mathbf{160\text{ m}^2}\)
Highlight Method 2 during whole-class debrief as the most elegant architectural shortcut.
Math Detective Solution: Spotting Devon's Blunder
Devon's Work: \(5 \times 14 = (5 \times 10) + 4 = 50 + 4 = 54\)
Devon's Exact Error:
Devon split 14 into \(10 + 4\), but forgot to multiply 4 by 5 . He simply added 4 to the product of \(5 \times 10\). Under the distributive property, the multiplier 5 must distribute to
