Montessori Multiplication Task Card: 23 × 234

 Montessori Multiplication Task Card: 23 × 234

READ 📖

The Orchard Problem: Farmer Elena has 23 rows of apple trees in her orchard. Each row contains exactly 234 trees. How many apple trees does Farmer Elena have in total?

BUILD 🔨

Step 1: Set up the Multiplicand and Multiplier

• Place the multiplicand 234 at the top
  • 2 red hundreds stamps (200)
  • 3 blue tens stamps (30)
  • 4 green unit stamps (4)
• Place the multiplier 23 on the left
  • 2 blue tens stamps (20)
  • 3 green unit stamps (3)

Step 2: Create the Stamp Game Array

For each GREEN unit stamp (3):

• Place 2 red hundreds (600)
• Place 3 blue tens (90)
• Place 4 green units (12)

For each BLUE tens stamp (2):

• Place 2 thousands (4000)
• Place 3 hundreds (600)
• Place 4 tens (80)

Step 3: Combine the Stamps by Place Value

• Thousands: 4
• Hundreds: 12 (6 + 6)
• Tens: 17 (9 + 8)
• Units: 12

Step 4: Trade Stamps

• Trade 10 units → 1 ten (2 units remain)
• Add 1 ten to tens: 17 + 1 = 18 tens
• Trade 10 tens → 1 hundred (8 tens remain)
• Add 1 hundred to hundreds: 12 + 1 = 13 hundreds
• Trade 10 hundreds → 1 thousand (3 hundreds remain)
• Add 1 thousand to thousands: 4 + 1 = 5 thousands

Step 5: Final Result

• 5 thousands
• 3 hundreds
• 8 tens
• 2 units
• Answer: 5,382 apple trees

DRAW ✏️

STAMP GAME REPRESENTATION:

Initial Setup:
                    234
                     ↑
                     |
             2 hundreds (red)
             3 tens (blue)
             4 units (green)
    23 → 
    |
    ↓
 2 tens (blue)
 3 units (green)


Step 2: Building the Array

For 3 GREEN units:
[H][H][H][H][H][H] → 6 hundreds (red)
[T][T][T][T][T][T][T][T][T] → 9 tens (blue)
[U][U][U][U][U][U][U][U][U][U][U][U] → 12 units (green)

For 2 BLUE tens:
[Th][Th][Th][Th] → 4 thousands (green)
[H][H][H][H][H][H] → 6 hundreds (red)
[T][T][T][T][T][T][T][T] → 8 tens (blue)


Step 3: Combine by Place Value
Thousands: [Th][Th][Th][Th] → 4
Hundreds: [H][H][H][H][H][H][H][H][H][H][H][H] → 12
Tens: [T][T][T][T][T][T][T][T][T][T][T][T][T][T][T][T][T] → 17
Units: [U][U][U][U][U][U][U][U][U][U][U][U] → 12


Step 4: Trading
Units: [U][U][U][U][U][U][U][U][U][U] + [U][U] = 1 ten + 2 units
Tens: [T][T][T][T][T][T][T][T][T][T] + [T][T][T][T][T][T][T][T] + 1 = 1 hundred + 8 tens
Hundreds: [H][H][H][H][H][H][H][H][H][H] + [H][H][H] + 1 = 1 thousand + 3 hundreds
Thousands: [Th][Th][Th][Th] + 1 = 5 thousands

Final Result: 5,382

WRITE ✍️

Four Ways to Solve 23 × 234:

1. Standard Algorithm

    2 3 4
  ×   2 3
  -------
    7 0 2  (234 × 3)
  4 6 8 0  (234 × 20)
  -------
  5 3 8 2

2. Area Model

        200       30        4
    -------------------------
    |         |         |         |
 20 |  4000   |   600   |    80   |
    |         |         |         |
    -------------------------
    |         |         |         |
  3 |   600   |    90   |    12   |
    |         |         |         |
    -------------------------
    
    4000 + 600 + 80 + 600 + 90 + 12 = 5,382

3. Partial Products

23 × 234 =
  
20 × 234 = 4,680
 3 × 234 =   702
         = 5,382

4. Lattice Multiplication

    │2│3│4│
  ─┌─┬─┬─┐
  2│4│6│8│
   │/│/│/│
  3│6│9│1│
   │/│/│2│
  ─└─┴─┴─┘
    5│3│8│2

Response to the Problem:

Farmer Elena has a total of 5,382 apple trees in her orchard.