Step-by-Step Process for Solving 3648 ÷ 32 Using the Montessori Stamp Game

Step 1: Set up the dividend and divisor

1. Set up the dividend (3648) using the stamp game pieces:

   • 3 green thousand stamps
   • 6 blue hundred stamps
   • 4 red ten stamps
   • 8 blue unit stamps

2. Note the divisor (32) on a separate card

Step 2: Group and divide the first portion (3200 ÷ 32)

1. Group the 3 thousands with 2 hundreds to form 3200

   • This makes an easily divisible number (3200)
   • 3200 ÷ 32 = 100 with 0 remainder
   • Place 1 hundred stamp in the quotient

2. Note what's left:

   • 4 hundred stamps
   • 4 ten stamps
   • 8 unit stamps

Step 3: Group and divide the second portion (420 ÷ 32)

1. Group the 4 hundreds with 2 tens to form 420

   • 420 ÷ 32 = 13 with 4 remainder
   • Place 1 ten stamp and 3 unit stamps in the quotient

2. Note what's left:

   • 4 units (remainder from the division)
   • 2 ten stamps
   • 8 unit stamps

Step 4: Group and assess the final portion (28 ÷ 32)

1. Group the 2 tens, 8 units, and remainder 4 to form 28
   • 28 is less than 32, so we cannot continue division
   • We have completed the division process
   • The answer is complete with no remainder (the 28 has been accounted for in previous steps)

Step 5: Read the final answer

• Reading the quotient stamps: 1 hundred + 1 ten + 4 units = 114
• Therefore, 3648 ÷ 32 = 114

This simplified approach makes the division more intuitive by grouping numbers in ways that are easier to divide by 32. Instead of converting all thousands to hundreds, we work with the largest possible groups that can be evenly divided by 32, making the process more efficient and easier to understand.

The key difference in this approach is that we:

1. First divide 3200 by 32 (getting 100)
2. Then divide 420 by 32 (getting 13, with 4 remainder)
3. Finally check if 28 (including the remainder) can be divided by 32 (it cannot)

This method aligns better with how we think about division mentally, working with convenient groupings rather than strictly following place value conversions.

I'll create an educational resource that combines a word problem for dividing 3648 ÷ 32 with the "Read, Build, Draw, Write" problem-solving framework and Montessori principles.

The Tomato Garden Division: A "Read, Build, Draw, Write" Approach with the Montessori Stamp Game

I've created two complementary resources that showcase how to teach division using the Montessori stamp game with the "Read, Build, Draw, Write" problem-solving framework.

The Word Problem

The school garden produced 3,648 tomatoes this harvest. The gardening committee wants to package them equally into 32 boxes to sell at the farmer's market. How many tomatoes should be placed in each box?

The Four-Step RBDW Process for Teaching Division

1. READ

In this first step, students carefully read and analyze the problem:

• Identify the known information (3,648 tomatoes, 32 boxes)
• Determine what they need to find (tomatoes per box)
• Recognize that division is the appropriate operation
• Set up a verification method (multiplication check)

2. BUILD

Students use the Montessori stamp game materials to physically build the problem:

• Set up 3,648 using stamp pieces (3 thousands, 6 hundreds, 4 tens, 8 units)
• Place the divisor (32) on the left
• Use the strategic grouping method:
  • Group 3 thousands with 2 hundreds (3,200) and divide by 32 = 100
  • Group 4 hundreds with 2 tens (420) and divide by 32 = 13 with 4 remainder
  • Note that the remaining amount (28) is less than 32
• Create the quotient with physical stamps (1 hundred, 1 ten, 4 units = 114)

3. DRAW

Students create a visual representation of their concrete work:

• Draw the stamp pieces using colored representations
• Illustrate the grouping process with circles
• Show the division calculations beside each grouping
• Create a final drawing showing the answer (114)

4. WRITE

Students formalize their work with mathematical notation:

• Write the division equation: 3,648 ÷ 32 = 114
• Show the standard algorithm calculation
• Write a complete sentence answering the word problem: "Each box should contain 114 tomatoes."
• Verify the answer: 114 × 32 = 3,648

Classroom Implementation

This lesson integrates several powerful educational approaches:

• Montessori concrete materials provide hands-on experience with abstract math concepts
• Strategic grouping simplifies division by working with convenient numbers
• Visual representation bridges concrete and abstract understanding
• The Thinking Classroom approach encourages collaborative problem-solving and visible thinking
• Mathematical communication develops as students explain their reasoning

The lesson plan includes differentiation strategies, assessment methods, and extension activities to accommodate diverse learning needs while challenging all students.