Array Architect Slides Array Architects
Mastering the Distributive Property
Architect Certification Course
01 Too Big to Build?
Sometimes, a project is just too large to finish in one day.
"If you can't build the whole thing at once, break it into smaller pieces!"
\( 6 \times 8 \) is a big build!
02 The Distributive Property
Break it apart
Split a large factor into two smaller numbers.
Build and Add
Multiply the smaller parts and add the answers.
Architect's Formula
\( 6 \times 8 \)
becomes...
\( (6 \times 5) + (6 \times 3) \)
Drafting Example: \( 4 \times 7 \)
Step 1: Multiply First Piece
\( 4 \times 5 = 20 \)
Step 2: Multiply Second Piece
\( 4 \times 2 = 8 \)
Step 3: Combine!
\( 20 + 8 = 28 \)
Ready to Build?
Grab your blueprints! It's time to head to the drafting table and use the distributive property to complete your certification.
Next Step
Project: Blueprint v.3.0
Array Architect Teacher Guide Teacher Guide
Lesson: Array Architects
Target Grade
Grade 3
Learning Objectives
Understand that a large multiplication problem can be broken into two smaller problems.
Apply the distributive property using arrays as a visual model.
Represent decomposition of factors using parentheses and addition equations.
Pacing & Materials
Total Time: 45-60 minutes
Materials:
Array Architect Slides
Array Architect Worksheet (1 per student)
Rulers or straight-edges (optional)
Blue markers/colored pencils
Instructional Flow
1
The Hook (Slides 1-2)
Introduce the concept of "Array Architects." Explain that when a building project is too big, architects break it into phases. Display the \( 6 \times 8 \) array. Ask students: "Is it easier to count all 48 squares or solve two smaller facts like \( 6 \times 5 \) and \( 6 \times 3 \)? Why?"
2
Direct Instruction (Slides 3-4)
Introduce the term Distributive Property . Use Slide 4 to model the process. Emphasize that the first factor (number of rows) stays the same, while the second factor (total columns) is broken into two parts that add up to the original.
3
Guided Practice (Worksheet Page 1)
Work through "Example 01" together. Have students trace the dotted line. Ask: "How many columns are in the first part? (5) How many in the second? (3) Does \( 5 + 3 = 8 \)? Yes!" Fill in the equation blanks together.
Answer Key
Example 01 (\( 3 \times 8 \)):
\( (3 \times 5) + (3 \times 3) \)
Project 02 (\( 5 \times 6 \)):
Common split (5 and 1 or 3 and 3):
\( (5 \times 3) + (5 \times 3) \)
Project 03 (\( 4 \times 9 \)):
Common split (5 and 4):
\( (4 \times 5) + (4 \times 4) \)
Challenge (\( 7 \times 8 \)):
Accept any valid split.
Differentiation
Support
Encourage students to always split the second factor at "5" to make use of easier multiplication facts. Provide physical counters to build the arrays before splitting.
Extension
Ask students to find a different way to split the same array (e.g., split the rows instead of the columns). Ask: "Does the property still work if we split vertically or horizontally?"
Array Architect Exit Ticket Project Inspection
Exit Ticket: Distributive Property
Architect:
Date:
1. Look at this array. Fill in the blanks to show how it was split.
\( 3 \times 7 = (3 \times \text{____}) + (3 \times \text{____}) \)
\( 3 \times 7 = \text{____} + \text{____} \)
\( 3 \times 7 = \text{____} \)
2. Solve \( 4 \times 6 \) by breaking it into two smaller pieces. Show your equation below.
Drafting Space
\( 4 \times 6 = (\text{____} \times \text{____}) + (\text{____} \times \text{____}) = \text{____} \)
How confident are you in your "architect" skills today?
1
2
3
Array Architect Worksheet Ink Saver Array Architect
Project: The Distributive Property
Architect Name:
Date:
The Architect's Method
Architects break large blueprints into smaller sections to make them easier to handle. In math, we use the distributive property to break large arrays into two smaller ones. Solve each section, then add the totals together!
\( 4 \times 7 = (4 \times 5) + (4 \times 2) \)
Phase 1: Foundation Break
Example 01
Break this \( 3 \times 8 \) array at the dashed line. Then complete the blueprint equation below.
\( 3 \times 8 = (3 \times \text{____}) + (3 \times \text{____}) \)
\( 3 \times 8 = \text{____} + \text{____} \)
\( 3 \times 8 = \text{____} \)
Phase 2: Independent Practice
Project 02
Draw a vertical line to split this \( 5 \times 6 \) array. Then complete the calculations below.
\( 5 \times 6 = (5 \times \text{____}) + (5 \times \text{____}) \)
\( 5 \times 6 = \text{____} + \text{____} \)
\( 5 \times 6 = \text{____} \)
Phase 3: Final Build
Project 03
Architect's Choice! Split this \( 4 \times 9 \) array however you like.
\( 4 \times 9 = (4 \times \text{____}) + (4 \times \text{____}) \)
\( 4 \times 9 = \text{____} + \text{____} \)
\( 4 \times 9 = \text{____} \)
Final Challenge
Solve \( 7 \times 8 \) using the distributive property. Show your work or draw a helpful array below!
Array Architect Worksheet Ink Saver Final Array Architect
Project: The Distributive Property
Plan v12.0
Architect Name:
Date:
The Architect's Method
Architects break large blueprints into smaller sections. In math, we use the distributive property to break large arrays into two smaller ones. Solve each section, then add the totals together!
\( 4 \times 7 = (4 \times 5) + (4 \times 2) \)
Example 01
Phase 1: Foundation Break
Break this \( 3 \times 8 \) array at the dashed line. Then complete the blueprint equation below.
\( 3 \times 8 = (3 \times \text{____}) + (3 \times \text{____}) \)
\( 3 \times 8 = \text{____} + \text{____} \)
\( 3 \times 8 = \text{____} \)
Project 02
Phase 2: Independent Practice
Draw a vertical line to split this \( 5 \times 6 \) array. Then complete the calculations below.
\( 5 \times 6 = (5 \times \text{____}) + (5 \times \text{____}) \)
\( 5 \times 6 = \text{____} + \text{____} \)
\( 5 \times 6 = \text{____} \)
Project 03
Phase 3: Final Build
Architect's Choice! Split this \( 4 \times 9 \) array however you like. Then finish the plan below.
\( 4 \times 9 = (4 \times \text{____}) + (4 \times \text{____}) \)
\( 4 \times 9 = \text{____} + \text{____} \)
\( 4 \times 9 = \text{____} \)
Final Challenge
Solve \( 7 \times 8 \) using the distributive property. Show your work or draw a helpful array in the space below.
