The Montessori Banking Game

Introduction

The Montessori Banking Game is an educational board game designed to teach students in grades 4-6 about mathematical operations, decimal fractions, and basic financial concepts. Based on the structure of the original Landlord's Game (predecessor to Monopoly), this game adapts the principles of the Montessori stamp game into an engaging board game format.

Game Components

Game board (square track with 40 spaces)
Montessori stamp materials (units, tens, hundreds, thousands)
Decimal fraction materials (tenths, hundredths, thousandths)
Property deed cards
Math Challenge cards (replacing Chance)
Community Learning cards (replacing Community Chest)
Player tokens
Dice (2)
Bank tray with compartments for different denominations
Property ownership markers

Game Setup

Place the board in the center of the play area.
Sort the stamp materials by denomination in the bank tray.
Shuffle the Math Challenge and Community Learning cards and place them face down on their designated spaces.
Appoint one student as the Banker who manages the bank resources.
Each player receives:
- 1,500 value in stamp materials:
  - 2 × 500 units
  - 2 × 100 units
  - 2 × 50 units
  - 6 × 20 units
  - 5 × 10 units
  - 5 × 5 units
  - 5 × 1 units
  - 2 × 0.5 units
  - 5 × 0.1 units
Each player chooses a token and places it on the "Begin Learning" space.

Game Objective

The objective is to be the last player with positive wealth after managing properties, solving math challenges, and navigating the game board.

Game Play

Players take turns rolling the dice and moving their tokens clockwise around the board.
Depending on the space a player lands on, they perform different actions:

Property Spaces

When landing on an unowned property:

The player may purchase it by paying the listed price to the bank
If they choose not to purchase it, no action is taken

When landing on another player's property:

The player must solve a math problem involving the operation associated with that property
The difficulty of the problem scales with the level of development on the property
If solved correctly, the player pays half the listed fee to the property owner
If solved incorrectly, the player pays the full fee to the property owner

Math Challenge and Community Learning Cards

When landing on these spaces:

Draw the top card from the respective deck
Follow the instructions on the card
Most cards involve solving math problems
Correct solutions may provide rewards, while incorrect solutions may incur penalties

Operation Corners

The four corners of the board represent the four mathematical operations:

Begin Learning (Addition Corner) - Collect 200 units when passing
Math Lab (Subtraction Corner) - Solve a subtraction challenge
Study Hall (Multiplication Corner) - Just visiting or serving detention
Assessment (Division Corner) - Pay 10% of your total wealth to the bank

Special Spaces

Math Tax: Pay 200 units to the bank
Learning Opportunity Fund: Pay 75 units to the bank
Go to Study Hall: Move directly to the Study Hall space

Property Groups and Values

Properties are grouped by mathematical concepts:

Numeric Properties (Brown)
- Number Line Avenue - Price: 60 units, Base fee: 2 units
- Place Value Boulevard - Price: 60 units, Base fee: 4 units Sample problem: "Write 3,254 in expanded form using place value"
Addition Properties (Light Blue)
- Commutative Way - Price: 100 units, Base fee: 6 units
- Associative Avenue - Price: 100 units, Base fee: 6 units
- Identity Street - Price: 120 units, Base fee: 8 units Sample problem: "Use the commutative property to rewrite 5.2 + 3.8"
Subtraction Properties (Pink)
- Difference Drive - Price: 140 units, Base fee: 10 units
- Minuend Road - Price: 140 units, Base fee: 10 units
- Subtrahend Street - Price: 160 units, Base fee: 12 units Sample problem: "Find the difference between 12.75 and 8.25"
Multiplication Properties (Orange)
- Factor Boulevard - Price: 180 units, Base fee: 14 units
- Product Place - Price: 180 units, Base fee: 14 units
- Multiple Avenue - Price: 200 units, Base fee: 16 units Sample problem: "Calculate 1.25 × 8"
Division Properties (Red)
- Quotient Quarter - Price: 220 units, Base fee: 18 units
- Dividend Drive - Price: 220 units, Base fee: 18 units
- Divisor Lane - Price: 240 units, Base fee: 20 units Sample problem: "Divide 56.7 by 7"
Decimal Properties (Yellow)
- Tenth Street - Price: 260 units, Base fee: 22 units
- Hundredth Avenue - Price: 260 units, Base fee: 22 units
- Thousandth Boulevard - Price: 280 units, Base fee: 24 units Sample problem: "Express 3/4 as a decimal"
Fraction Properties (Green)
- Numerator Road - Price: 300 units, Base fee: 26 units
- Denominator Drive - Price: 300 units, Base fee: 26 units
- Equivalent Fractions Place - Price: 320 units, Base fee: 28 units Sample problem: "Find three fractions equivalent to 2/5"
Advanced Properties (Blue)
- Percentage Plaza - Price: 350 units, Base fee: 35 units
- Ratio Road - Price: 400 units, Base fee: 50 units Sample problem: "Express 0.75 as a percentage"
Utilities (services)
- Calculator Company - Price: 150 units, Fee: Sum of dice × 0.4
- Measurement Utility - Price: 150 units, Fee: Sum of dice × 0.4 Sample problem: "Convert 2.5 meters to centimeters"
Transportation (mathematical tools)
- Number Line - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)
- Base Ten Blocks - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)
- Fraction Circles - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)
- Decimal Grid - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4) Sample problem: "Using a number line, show the distance between 1.25 and 3.75"

Property Development

Players can develop their properties by:

Owning all properties in a color group
Paying the development cost
Placing development markers on the property

Development levels and costs:

Level 1: Basic operations (addition/subtraction) - Cost: 50 units per property
Level 2: Intermediate operations (multiplication/division) - Cost: 150 units per property
Level 3: Advanced operations (decimals/fractions) - Cost: 300 units per property
Level 4: Master level (combined operations) - Cost: 500 units per property

As properties develop, the math problems associated with them become more complex, and the fees collected increase:

Level 1: Base fee
Level 2: 3× base fee
Level 3: 5× base fee
Level 4: 8× base fee

Development markers use Montessori geometric solids:

Level 1: Green triangular prism
Level 2: Blue rectangular prism
Level 3: Red square pyramid
Level 4: Yellow cube

Property Trading

Players may trade properties with each other by:

Proposing a trade including properties and/or stamp materials
Negotiating terms
Completing the transaction if both parties agree

Bankruptcy

If a player cannot pay a debt:

They must sell developments back to the bank at half price
If still unable to pay, they must transfer all assets to the creditor
The player is eliminated from the game

Game End

The game ends when:

Only one player remains solvent, or
After a predetermined time limit (e.g., 60 minutes)
The player with the highest wealth wins

Math Challenge Cards (Sample)

"Solve: 24.5 × 3.2. If correct, collect 78.4 units. If incorrect, pay 20 units."
"Calculate 15% of your current wealth. Collect this amount from the bank."
"Divide 1,250 by 2.5. Move forward that many spaces."
"Round 3.45 to the nearest whole number and multiply by 100. Pay this amount to the bank."
"Add the digits of all your property values. Collect this amount from the bank."
"Find the average of 12.5, 8.75, and 22.25. Pay this amount to the bank."
"Convert 3/4 to a decimal. Multiply by 100 and collect that amount."
"Subtract 1.35 from 4.2. Pay 10 times this amount to the bank."
"Calculate the product of the two dice numbers × 10. Collect this amount."
"Find the sum of all values on the board divisible by 5. Collect 1/10 of this amount."
"Solve: 1.75 ÷ 0.25. If correct, collect twice this amount. If incorrect, pay half this amount."
"Find the product of 0.8 × 0.7. Move backward this many spaces (rounded up)."
"Express 5/8 as a decimal and collect that many hundreds from the bank."
"Mental Math Challenge: Calculate 125 × 0.8 without writing. Collect this amount if correct."
"Calculate the perimeter of a rectangle with length 4.5 and width 2.25. Collect this amount."
"Convert 3.5 hours to minutes. Pay 1% of this amount to each player."
"Estimate the product of 9.7 × 5.1 (round to nearest whole). Collect this amount if within 1 unit."
"Express your current wealth as a percentage of the starting wealth (1,500). If it's over 100%, collect 50."
"Find the greatest common factor of 36 and 54. Collect 10 times this amount."
"Calculate the area of a square with side length 1.5 units. Pay this amount × 100 to the bank."

Community Learning Cards (Sample)

"Lead a math study group. Each player pays you 25 units."
"Tutor a struggling student. Collect 50 units from the bank."
"Made a calculation error in your homework. Pay 30 units to the bank."
"Won the mental math competition. Collect 100 units from the bank."
"Share your math manipulatives with the class. Collect 10 units from each player."
"Repair broken decimal materials. Pay 40 units to the bank."
"Your clear explanation of fractions helps everyone. Collect 25 units from each player."
"Create an innovative math project. Advance to Begin Learning and collect 200 units."
"Volunteer to clean the math lab. Collect 25 units from the bank."
"Help reorganize the Montessori materials. Each player gives you their smallest decimal piece."
"Present a decimal demonstration to younger students. All players give you 0.5 units as appreciation."
"Create a mathematics journal. Pay 100 units for supplies but collect 20 units from each player."
"School math competition! Roll the dice - highest roller collects 50 units from the bank."
"Discover a mathematical pattern. Move to any property space on the board."
"Help teacher prepare a new decimal fraction activity. Collect 75 units from the bank."
"Solve the daily problem correctly. Collect the digit sum of today's date in units."
"Organize a math game day. Collect 15 units from each player who participates."
"Explain a difficult concept to the class. You may exchange one of your properties for any one owned by another player."
"Made a mistake in your decimal placement. Pay 10× the wrong amount (minimum 10 units)."
"Assist with the annual math inventory. Go back 3 spaces but collect 25 units from the bank."

Board Layout

Starting from "Begin Learning" and moving clockwise:

Begin Learning (Addition Corner): Collect 200 units when passing
Number Line Avenue (Brown)
Community Learning
Place Value Boulevard (Brown)
Math Tax: Pay 200 units
Number Line (transportation)
Commutative Way (Light Blue)
Math Challenge
Associative Avenue (Light Blue)
Identity Street (Light Blue)
Math Lab (Subtraction Corner): Solve a subtraction challenge
Difference Drive (Pink)
Calculator Company (utility)
Minuend Road (Pink)
Subtrahend Street (Pink)
Base Ten Blocks (transportation)
Factor Boulevard (Orange)
Community Learning
Product Place (Orange)
Multiple Avenue (Orange)
Study Hall (Multiplication Corner): Just visiting or serving detention
Quotient Quarter (Red)
Math Challenge
Dividend Drive (Red)
Divisor Lane (Red)
Fraction Circles (transportation)
Tenth Street (Yellow)
Hundredth Avenue (Yellow)
Measurement Utility (utility)
Thousandth Boulevard (Yellow)
Assessment (Division Corner): Pay 10% of total wealth
Numerator Road (Green)
Denominator Drive (Green)
Community Learning
Equivalent Fractions Place (Green)
Decimal Grid (transportation)
Math Challenge
Percentage Plaza (Blue)
Learning Opportunity Fund: Pay 75 units
Ratio Road (Blue)

Using the Montessori Stamp Game Materials

The game integrates the Montessori stamp game by:

Using colored stamps/tiles representing different place values:
- Green: units (1)
- Blue: tens (10)
- Red: hundreds (100)
- Green with stripe: thousands (1000)
- Additional stamps for decimals:
  - Yellow: tenths (0.1)
  - Orange: hundredths (0.01)
  - Purple: thousandths (0.001)
All payments and collections require proper exchange of stamps:
- Players must correctly represent amounts using the fewest stamps possible
- Making change requires decimal understanding
- Addition and subtraction occur physically with the materials
- Players must verbalize their operations: "I need to pay 125.50 units, so I'll use 1 hundred stamp, 2 tens stamps, 5 unit stamps, and 5 tenth stamps"
Bank transactions follow Montessori principles:
- Always exchange for largest possible denominations
- When breaking larger units, players must correctly create equivalent amounts
- Example: To break a 100 stamp, receive 10 tens stamps
- To break a 1 unit stamp, receive 10 tenth stamps
For higher-level operations:
- Multiplication: repeated addition using stamps
- Division: fair sharing of stamps
- Decimals: proper placement of decimal stamps
- Verify operations by physically arranging stamps in place value columns
Banking procedures:
- The banker verifies all exchanges are mathematically correct
- Players must announce their current wealth when requested
- Banker may pose quick estimation challenges during transactions
- Players can audit each other's stamp collections to verify correct representation

Integrating Decimal Work

Students work with decimals by:

Using decimal stamps for payments less than 1 unit:
- Players must use the correct decimal stamps (tenths, hundredths, thousandths)
- Example: 0.35 = 3 tenth stamps + 5 hundredth stamps
Converting between units and decimals:
- Practice equivalencies (e.g., 0.5 = 5 tenths = 50 hundredths)
- Convert fractions to decimals (e.g., 3/4 = 0.75)
- Convert percentages to decimals (e.g., 25% = 0.25)
Performing operations with decimals:
- Addition: Combine like place values (units with units, tenths with tenths)
- Subtraction: Remove stamps from appropriate place values, with regrouping when needed
- Multiplication: Create arrays with decimal stamps or use repeated addition
- Division: Share decimal stamps equally among specified groups
Decimal challenges incorporated into gameplay:
- Comparing decimal values (greater than, less than, equal to)
- Ordering decimals from least to greatest
- Rounding decimals to nearest tenth, hundredth
- Converting between different representations (fractions, decimals, percentages)
Property-specific decimal work:
- Yellow properties (Tenth Street, Hundredth Avenue, Thousandth Boulevard) specifically focus on decimal operations
- Landing on these spaces requires solving increasingly complex decimal problems
- Development of these properties increases decimal complexity (e.g., Level 3: "Multiply 0.125 by 0.4")
Decimal exchange rates:
- Property purchases may require specific decimal exchanges
- Some Community Learning cards may award or penalize players with decimal amounts
- Math Challenge cards often involve decimal calculations
Special decimal zone (optional):
- Teachers can designate certain board sections as "decimal zones" where all values must be expressed with decimal notation
- Creates additional practice with decimal representation

Educational Outcomes

This game helps students:

Master the four operations with whole numbers and decimals
Understand place value concepts
Develop estimation and mental math skills
Learn financial concepts like saving, spending, and investing
Practice mathematical communication
Apply math in real-world contexts
Develop strategic thinking and planning skills

Game Variations

Simplified version: Use only whole numbers for younger students
Advanced version: Include negative numbers, percentages, ratios
Team play: Students work together to solve more complex problems
Time limit: Set a specific duration (30-60 minutes) for gameplay
Targeted practice: Focus on specific operations by modifying cards

Assessment Integration

Teachers can use the game for assessment by:

Observing student calculations and reasoning
Noting common errors or misconceptions
Tracking student progress in specific operation types
Using game outcomes to inform future instruction

Montessori Banking Game: Property Deed Cards

Sample Property Deed Card Format

DECIMAL PROPERTIES (Yellow)

TENTH STREET

PROPERTY DEED
TENTH STREET

Purchase Price: 260 units

Fees When Landed Upon:

Base Fee: 22 units
With Level 1 Development: 22 units + Solve simple decimal addition
With Level 2 Development: 66 units + Solve decimal multiplication
With Level 3 Development: 110 units + Solve mixed decimal operations
With Level 4 Development: 176 units + Solve complex decimal word problem

Development Costs:

Level 1 (Green Triangular Prism): 50 units
Level 2 (Blue Rectangular Prism): 150 units
Level 3 (Red Square Pyramid): 300 units
Level 4 (Yellow Cube): 500 units

Mathematical Concept: Tenths are the first decimal place to the right of the decimal point, representing fractions with denominators of 10.

Sample Problems by Level:

"Add 0.7 + 0.8"
"Multiply 0.9 × 7"
"Find 1/10 of 350"
"A container holds 2.4 liters of water. If 0.3 liters are poured into each of 5 cups, how much water remains in the container?"

Montessori Connection: Relates to the decimal board with tenths, golden bead units, and decimal fraction cards.

ADDITION PROPERTIES (Light Blue)

COMMUTATIVE WAY

PROPERTY DEED
COMMUTATIVE WAY

Purchase Price: 100 units

Fees When Landed Upon:

Base Fee: 6 units
With Level 1 Development: 6 units + Apply commutative property with whole numbers
With Level 2 Development: 18 units + Apply commutative property with decimals
With Level 3 Development: 30 units + Apply commutative property with fractions
With Level 4 Development: 48 units + Apply commutative property in multi-step problems

Development Costs:

Level 1 (Green Triangular Prism): 50 units
Level 2 (Blue Rectangular Prism): 150 units
Level 3 (Red Square Pyramid): 300 units
Level 4 (Yellow Cube): 500 units

Mathematical Concept: The commutative property states that changing the order of the operands does not change the result: a + b = b + a and a × b = b × a.

Sample Problems by Level:

"Show that 8 + 5 = 5 + 8 using stamps"
"Show that 1.5 × 4 = 4 × 1.5"
"Is subtraction commutative? Prove your answer with an example."
"Use the commutative property to find an easier way to calculate: 25 × 16 × 4"

Montessori Connection: Relates to the associative and commutative law materials and operations with bead materials.

DIVISION PROPERTIES (Red)

DIVISOR LANE

PROPERTY DEED
DIVISOR LANE

Purchase Price: 240 units

Fees When Landed Upon:

Base Fee: 20 units
With Level 1 Development: 20 units + Basic division with whole numbers
With Level 2 Development: 60 units + Division with decimal quotients
With Level 3 Development: 100 units + Division with decimal divisors
With Level 4 Development: 160 units + Complex division word problems

Development Costs:

Level 1 (Green Triangular Prism): 50 units
Level 2 (Blue Rectangular Prism): 150 units
Level 3 (Red Square Pyramid): 300 units
Level 4 (Yellow Cube): 500 units

Mathematical Concept: The divisor is the number by which another number (the dividend) is divided, and the result is the quotient.

Sample Problems by Level:

"Divide 72 ÷ 8"
"Divide 57 ÷ 5 and express the answer as a decimal"
"Calculate 24 ÷ 0.6"
"A recipe calls for 3.5 cups of flour to make 4 loaves of bread. How much flour is needed for each loaf?"

Montessori Connection: Relates to the division board, division charts, and division with bead materials.

FRACTION PROPERTIES (Green)

EQUIVALENT FRACTIONS PLACE

PROPERTY DEED
EQUIVALENT FRACTIONS PLACE

Purchase Price: 320 units

Fees When Landed Upon:

Base Fee: 28 units
With Level 1 Development: 28 units + Identify equivalent fractions
With Level 2 Development: 84 units + Convert between fractions and decimals
With Level 3 Development: 140 units + Operations with equivalent fractions
With Level 4 Development: 224 units + Multi-step fraction problems

Development Costs:

Level 1 (Green Triangular Prism): 50 units
Level 2 (Blue Rectangular Prism): 150 units
Level 3 (Red Square Pyramid): 300 units
Level 4 (Yellow Cube): 500 units

Mathematical Concept: Equivalent fractions are fractions that represent the same value, even though they may look different.

Sample Problems by Level:

"Find three fractions equivalent to 1/2"
"Convert 3/5 to a decimal"
"Add 1/4 + 2/8"
"Maria spent 3/8 of her money on books and 2/5 on art supplies. What fraction of her money does she have left?"

Montessori Connection: Relates to the fraction circles, equivalence materials, and fraction insets.

UTILITIES

CALCULATOR COMPANY

PROPERTY DEED
CALCULATOR COMPANY

Purchase Price: 150 units

Fees When Landed Upon:

Owning 1 Utility: Sum of dice × 0.4 units
Owning both Utilities: Sum of dice × 1.0 units

Mathematical Concept: Calculation tools enhance mathematical capacity but require understanding of underlying concepts.

Sample Problems:

"Use mental math to approximate 38 × 7, then verify with a calculator."
"Find the square root of 169 using estimation."
"Calculate the product of all the digits in your current wealth."

Montessori Connection: Relates to verification of work and the progression from concrete to abstract.

TRANSPORTATION

FRACTION CIRCLES

PROPERTY DEED
FRACTION CIRCLES

Purchase Price: 200 units

Fees When Landed Upon:

For 1 Mathematical Tool owned: 25 units
For 2 Mathematical Tools owned: 50 units
For 3 Mathematical Tools owned: 100 units
For all 4 Mathematical Tools owned: 200 units

Mathematical Concept: Fraction circles visually represent parts of a whole and allow for comparison of different fractional values.

Sample Problems:

"Use fraction circles to show that 3/6 = 1/2."
"Compare 2/3 and 3/5 using fraction circles."
"Show 1/4 + 1/2 using fraction circles."

Montessori Connection: Directly relates to the Montessori fraction circles material used for concrete fraction representation.

The Montessori Banking Game

Introduction

The Montessori Banking Game is an educational board game designed to teach students in grades 4-6 about mathematical operations, decimal fractions, and basic financial concepts. Based on the structure of the original Landlord's Game (predecessor to Monopoly), this game adapts the principles of the Montessori stamp game into an engaging board game format.

Game Components

Game board (square track with 40 spaces)

Montessori stamp materials (units, tens, hundreds, thousands)

Decimal fraction materials (tenths, hundredths, thousandths)

Property deed cards

Math Challenge cards (replacing Chance)

Community Learning cards (replacing Community Chest)

Player tokens

Dice (2)

Bank tray with compartments for different denominations

Property ownership markers

Game Setup

Place the board in the center of the play area.

Sort the stamp materials by denomination in the bank tray.

Shuffle the Math Challenge and Community Learning cards and place them face down on their designated spaces.

Appoint one student as the Banker who manages the bank resources.

Each player receives:

1,500 value in stamp materials:

2 × 500 units

2 × 100 units

2 × 50 units

6 × 20 units

5 × 10 units

5 × 5 units

5 × 1 units

2 × 0.5 units

5 × 0.1 units

Each player chooses a token and places it on the "Begin Learning" space.

Game Objective

The objective is to be the last player with positive wealth after managing properties, solving math challenges, and navigating the game board.

Game Play

Players take turns rolling the dice and moving their tokens clockwise around the board.

Depending on the space a player lands on, they perform different actions:

Property Spaces

When landing on an unowned property:

The player may purchase it by paying the listed price to the bank

If they choose not to purchase it, no action is taken

When landing on another player's property:

The player must solve a math problem involving the operation associated with that property

The difficulty of the problem scales with the level of development on the property

If solved correctly, the player pays half the listed fee to the property owner

If solved incorrectly, the player pays the full fee to the property owner

Math Challenge and Community Learning Cards

When landing on these spaces:

Draw the top card from the respective deck

Follow the instructions on the card

Most cards involve solving math problems

Correct solutions may provide rewards, while incorrect solutions may incur penalties

Operation Corners

The four corners of the board represent the four mathematical operations:

Begin Learning (Addition Corner) - Collect 200 units when passing

Math Lab (Subtraction Corner) - Solve a subtraction challenge

Study Hall (Multiplication Corner) - Just visiting or serving detention

Assessment (Division Corner) - Pay 10% of your total wealth to the bank

Special Spaces

Math Tax: Pay 200 units to the bank

Learning Opportunity Fund: Pay 75 units to the bank

Go to Study Hall: Move directly to the Study Hall space

Property Groups and Values

Properties are grouped by mathematical concepts:

Numeric Properties (Brown)

Number Line Avenue - Price: 60 units, Base fee: 2 units

Place Value Boulevard - Price: 60 units, Base fee: 4 units Sample problem: "Write 3,254 in expanded form using place value"

Addition Properties (Light Blue)

Commutative Way - Price: 100 units, Base fee: 6 units

Associative Avenue - Price: 100 units, Base fee: 6 units

Identity Street - Price: 120 units, Base fee: 8 units Sample problem: "Use the commutative property to rewrite 5.2 + 3.8"

Subtraction Properties (Pink)

Difference Drive - Price: 140 units, Base fee: 10 units

Minuend Road - Price: 140 units, Base fee: 10 units

Subtrahend Street - Price: 160 units, Base fee: 12 units Sample problem: "Find the difference between 12.75 and 8.25"

Multiplication Properties (Orange)

Factor Boulevard - Price: 180 units, Base fee: 14 units

Product Place - Price: 180 units, Base fee: 14 units

Multiple Avenue - Price: 200 units, Base fee: 16 units Sample problem: "Calculate 1.25 × 8"

Division Properties (Red)

Quotient Quarter - Price: 220 units, Base fee: 18 units

Dividend Drive - Price: 220 units, Base fee: 18 units

Divisor Lane - Price: 240 units, Base fee: 20 units Sample problem: "Divide 56.7 by 7"

Decimal Properties (Yellow)

Tenth Street - Price: 260 units, Base fee: 22 units

Hundredth Avenue - Price: 260 units, Base fee: 22 units

Thousandth Boulevard - Price: 280 units, Base fee: 24 units Sample problem: "Express 3/4 as a decimal"

Fraction Properties (Green)

Numerator Road - Price: 300 units, Base fee: 26 units

Denominator Drive - Price: 300 units, Base fee: 26 units

Equivalent Fractions Place - Price: 320 units, Base fee: 28 units Sample problem: "Find three fractions equivalent to 2/5"

Advanced Properties (Blue)

Percentage Plaza - Price: 350 units, Base fee: 35 units

Ratio Road - Price: 400 units, Base fee: 50 units Sample problem: "Express 0.75 as a percentage"

Utilities (services)

Calculator Company - Price: 150 units, Fee: Sum of dice × 0.4

Measurement Utility - Price: 150 units, Fee: Sum of dice × 0.4 Sample problem: "Convert 2.5 meters to centimeters"

Transportation (mathematical tools)

Number Line - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)

Base Ten Blocks - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)

Fraction Circles - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4)

Decimal Grid - Price: 200 units, Fee: 25 units (50 with 2, 100 with 3, 200 with all 4) Sample problem: "Using a number line, show the distance between 1.25 and 3.75"

Property Development

Players can develop their properties by:

Owning all properties in a color group

Paying the development cost

Placing development markers on the property

Development levels and costs:

Level 1: Basic operations (addition/subtraction) - Cost: 50 units per property

Level 2: Intermediate operations (multiplication/division) - Cost: 150 units per property

Level 3: Advanced operations (decimals/fractions) - Cost: 300 units per property

Level 4: Master level (combined operations) - Cost: 500 units per property

As properties develop, the math problems associated with them become more complex, and the fees collected increase:

Level 1: Base fee

Level 2: 3× base fee

Level 3: 5× base fee

Level 4: 8× base fee

Development markers use Montessori geometric solids:

Level 1: Green triangular prism

Level 2: Blue rectangular prism

Level 3: Red square pyramid

Level 4: Yellow cube

Property Trading

Players may trade properties with each other by:

Proposing a trade including properties and/or stamp materials

Negotiating terms

Completing the transaction if both parties agree

Bankruptcy

If a player cannot pay a debt:

They must sell developments back to the bank at half price

If still unable to pay, they must transfer all assets to the creditor

The player is eliminated from the game

Game End

The game ends when:

Only one player remains solvent, or

After a predetermined time limit (e.g., 60 minutes)

The player with the highest wealth wins

Math Challenge Cards (Sample)

"Solve: 24.5 × 3.2. If correct, collect 78.4 units. If incorrect, pay 20 units."

"Calculate 15% of your current wealth. Collect this amount from the bank."

"Divide 1,250 by 2.5. Move forward that many spaces."

"Round 3.45 to the nearest whole number and multiply by 100. Pay this amount to the bank."

"Add the digits of all your property values. Collect this amount from the bank."

"Find the average of 12.5, 8.75, and 22.25. Pay this amount to the bank."

"Convert 3/4 to a decimal. Multiply by 100 and collect that amount."

"Subtract 1.35 from 4.2. Pay 10 times this amount to the bank."

"Calculate the product of the two dice numbers × 10. Collect this amount."

"Find the sum of all values on the board divisible by 5. Collect 1/10 of this amount."

"Solve: 1.75 ÷ 0.25. If correct, collect twice this amount. If incorrect, pay half this amount."

"Find the product of 0.8 × 0.7. Move backward this many spaces (rounded up)."

"Express 5/8 as a decimal and collect that many hundreds from the bank."

"Mental Math Challenge: Calculate 125 × 0.8 without writing. Collect this amount if correct."

"Calculate the perimeter of a rectangle with length 4.5 and width 2.25. Collect this amount."

"Convert 3.5 hours to minutes. Pay 1% of this amount to each player."

"Estimate the product of 9.7 × 5.1 (round to nearest whole). Collect this amount if within 1 unit."

"Express your current wealth as a percentage of the starting wealth (1,500). If it's over 100%, collect 50."

"Find the greatest common factor of 36 and 54. Collect 10 times this amount."

"Calculate the area of a square with side length 1.5 units. Pay this amount × 100 to the bank."

Community Learning Cards (Sample)

"Lead a math study group. Each player pays you 25 units."

"Tutor a struggling student. Collect 50 units from the bank."

"Made a calculation error in your homework. Pay 30 units to the bank."

"Won the mental math competition. Collect 100 units from the bank."

"Share your math manipulatives with the class. Collect 10 units from each player."

"Repair broken decimal materials. Pay 40 units to the bank."

"Your clear explanation of fractions helps everyone. Collect 25 units from each player."

"Create an innovative math project. Advance to Begin Learning and collect 200 units."

"Volunteer to clean the math lab. Collect 25 units from the bank."

"Help reorganize the Montessori materials. Each player gives you their smallest decimal piece."

"Present a decimal demonstration to younger students. All players give you 0.5 units as appreciation."

"Create a mathematics journal. Pay 100 units for supplies but collect 20 units from each player."

"School math competition! Roll the dice - highest roller collects 50 units from the bank."

"Discover a mathematical pattern. Move to any property space on the board."

"Help teacher prepare a new decimal fraction activity. Collect 75 units from the bank."

"Solve the daily problem correctly. Collect the digit sum of today's date in units."

"Organize a math game day. Collect 15 units from each player who participates."

"Explain a difficult concept to the class. You may exchange one of your properties for any one owned by another player."

"Made a mistake in your decimal placement. Pay 10× the wrong amount (minimum 10 units)."

"Assist with the annual math inventory. Go back 3 spaces but collect 25 units from the bank."

Board Layout

Starting from "Begin Learning" and moving clockwise:

Begin Learning (Addition Corner): Collect 200 units when passing

Number Line Avenue (Brown)

Community Learning

Place Value Boulevard (Brown)

Math Tax: Pay 200 units

Number Line (transportation)

Commutative Way (Light Blue)

Math Challenge

Associative Avenue (Light Blue)

Identity Street (Light Blue)

Math Lab (Subtraction Corner): Solve a subtraction challenge

Difference Drive (Pink)

Calculator Company (utility)

Minuend Road (Pink)

Subtrahend Street (Pink)

Base Ten Blocks (transportation)

Factor Boulevard (Orange)

Community Learning

Product Place (Orange)

Multiple Avenue (Orange)

Study Hall (Multiplication Corner): Just visiting or serving detention

Quotient Quarter (Red)

Math Challenge

Dividend Drive (Red)

Divisor Lane (Red)

Fraction Circles (transportation)

Tenth Street (Yellow)

Hundredth Avenue (Yellow)

Measurement Utility (utility)

Thousandth Boulevard (Yellow)

Assessment (Division Corner): Pay 10% of total wealth

Numerator Road (Green)

Denominator Drive (Green)

Community Learning

Equivalent Fractions Place (Green)

Decimal Grid (transportation)

Math Challenge

Percentage Plaza (Blue)

Learning Opportunity Fund: Pay 75 units

Ratio Road (Blue)

Using the Montessori Stamp Game Materials

The game integrates the Montessori stamp game by:

Using colored stamps/tiles representing different place values:

Green: units (1)

Blue: tens (10)

Red: hundreds (100)

Green with stripe: thousands (1000)

Additional stamps for decimals:

Yellow: tenths (0.1)

Orange: hundredths (0.01)

Purple: thousandths (0.001)

All payments and collections require proper exchange of stamps:

Players must correctly represent amounts using the fewest stamps possible

Making change requires decimal understanding

Addition and subtraction occur physically with the materials

Players must verbalize their operations: "I need to pay 125.50 units, so I'll use 1 hundred stamp, 2 tens stamps, 5 unit stamps, and 5 tenth stamps"

Bank transactions follow Montessori principles:

Always exchange for largest possible denominations

When breaking larger units, players must correctly create equivalent amounts

Example: To break a 100 stamp, receive 10 tens stamps

To break a 1 unit stamp, receive 10 tenth stamps

For higher-level operations:

Multiplication: repeated addition using stamps

Division: fair sharing of stamps

Decimals: proper placement of decimal stamps

Verify operations by physically arranging stamps in place value columns

Banking procedures:

The banker verifies all exchanges are mathematically correct

Players must announce their current wealth when requested

Banker may pose quick estimation challenges during transactions

Players can audit each other's stamp collections to verify correct representation

Integrating Decimal Work

Students work with decimals by:

Using decimal stamps for payments less than 1 unit:

Players must use the correct decimal stamps (tenths, hundredths, thousandths)

Example: 0.35 = 3 tenth stamps + 5 hundredth stamps

Converting between units and decimals:

Practice equivalencies (e.g., 0.5 = 5 tenths = 50 hundredths)

Convert fractions to decimals (e.g., 3/4 = 0.75)

Convert percentages to decimals (e.g., 25% = 0.25)

Performing operations with decimals:

Addition: Combine like place values (units with units, tenths with tenths)

Subtraction: Remove stamps from appropriate place values, with regrouping when needed

Multiplication: Create arrays with decimal stamps or use repeated addition

Division: Share decimal stamps equally among specified groups

Decimal challenges incorporated into gameplay:

Comparing decimal values (greater than, less than, equal to)

Ordering decimals from least to greatest

Rounding decimals to nearest tenth, hundredth

Converting between different representations (fractions, decimals, percentages)

Property-specific decimal work:

Yellow properties (Tenth Street, Hundredth Avenue, Thousandth Boulevard) specifically focus on decimal operations

Landing on these spaces requires solving increasingly complex decimal problems

Development of these properties increases decimal complexity (e.g., Level 3: "Multiply 0.125 by 0.4")

Decimal exchange rates:

Property purchases may require specific decimal exchanges

Some Community Learning cards may award or penalize players with decimal amounts

Math Challenge cards often involve decimal calculations

Special decimal zone (optional):

Teachers can designate certain board sections as "decimal zones" where all values must be expressed with decimal notation

Creates additional practice with decimal representation

Classroom Implementation Guide

Preparation

Materials Assembly:

Print the game board on large format paper (at least 20" × 20")

Create property deed cards (laminated for durability)

Prepare Montessori stamp materials or create paper versions

Create development markers using colored geometric solids

Print and cut Math Challenge and Community Learning cards

Prepare player tokens (use Montessori materials like colored cylinders)

Create a bank tray with labeled compartments for each denomination

Teacher Preparation:

Review all mathematical concepts in the game

Practice sample transactions to model for students

Create a simple scoring rubric to assess student understanding

Prepare extension activities for advanced students

Create simplified rules for struggling students

Student Orientation:

Introduce Montessori stamp game materials before playing

Practice basic transactions (buying properties, paying fees)

Review decimal operations and conversions

Discuss financial literacy concepts (saving, spending, investing)

Model proper mathematical language during transactions

Game Facilitation

First Play Session:

Start with simplified rules (no development)

Focus on basic operations and transactions

Teacher acts as banker to model proper exchanges

Allow open discussion of mathematical thinking

Keep game time to 30 minutes

Progressive Complexity:

Introduce property development in subsequent sessions

Add decimal operations gradually

Increase mathematical discussion requirements

Reduce teacher intervention as students gain proficiency

Extend gameplay time to 45-60 minutes

Differentiation Strategies:

Advanced students: Add calculation time limits

Struggling students: Allow calculation aids

Mixed ability grouping: Assign student mentors

Create property-specific math challenge cards at different levels

Allow peer tutoring during gameplay

Assessment Opportunities

Observational Assessment:

Note student facility with mental calculation

Observe decimal operation proficiency

Track property management strategy development

Assess mathematical communication skills

Document growth in transaction speed and accuracy

Formal Assessment:

Create gameplay-based quiz questions

Develop student reflection questions

Design scenario-based assessment tasks

Implement peer assessment protocols

Create pre/post gameplay assessment

Portfolio Integration:

Students document their property acquisitions

Keep transaction logs with calculations

Record problem-solving strategies

Reflect on mathematical growth

Create student-designed challenge cards

Extension Activities

Game Modifications:

Students create new property spaces

Design advanced Math Challenge cards

Develop custom rules for specific math concepts

Add new development levels

Create additional mathematical tools spaces

Cross-Curricular Connections:

History: Research the origins of the Landlord's Game

Writing: Create mathematical story problems

Art: Design custom game tokens

Economics: Explore banking concepts

Social Studies: Discuss resource distribution

Home Connections:

Create a simplified version for home play

Design family math night activities

Develop parent education materials

Create homework challenges based on game concepts

Share game rules for family adaptation

Montessori Banking Game: Student Guidelines

Welcome, Mathematicians!

You are about to embark on a mathematical journey that combines strategy, calculation, and property management. The Montessori Banking Game helps you practice the four mathematical operations (addition, subtraction, multiplication, and division) with whole numbers and decimals in an exciting game format.

Quick Start Guide

Your Goal

Build your mathematical wealth by purchasing properties, solving math problems, and developing your properties to create a mathematical empire!

What You Need to Know

Starting Out

Choose a game token to represent you on the board

Receive your starting wealth: 1,500 units in stamp materials

Place your token on "Begin Learning"

Take turns rolling the dice and moving around the board

Managing Your Stamp Materials

Green stamps = units (1)

Blue stamps = tens (10)

Red stamps = hundreds (100)

Green with stripe = thousands (1000)

Yellow stamps = tenths (0.1)

Orange stamps = hundredths (0.01)

Purple stamps = thousandths (0.001)

On Your Turn

Roll both dice

Move your token clockwise the number of spaces shown

Follow the instructions on the space you land on

Solve any required math problems

Make any payments or collect any earnings

End your turn

Mathematical Tips and Tricks

Addition Strategies

When adding decimals, line up the decimal points

Look for combinations that make 10 to simplify mental math

Example: 7.5 + 2.5 = 10

Subtraction Strategies

When making change, count up from the smaller number

For regrouping with decimals, remember that 1 unit = 10 tenths

Example: 5 - 2.7 = 2.3 (borrow 1 unit to make 10 tenths)

Multiplication Strategies

Use known facts and place value

Double and halve to find equivalent calculations

Example: 25 × 4 = 50 × 2 = 100

Division Strategies

For division with decimals, move the decimal point to create a whole number divisor

Use known multiplication facts to estimate quotients

Example: 36 ÷ 0.4 = 360 ÷ 4 = 90

Property Management Guide

When to Buy Properties

Buy properties whenever you can afford them

Focus on completing color groups to allow development

Properties with higher values are more expensive but earn more

Development Strategy

Look at these factors when deciding which properties to develop:

Probability of others landing on the space

Development cost vs. potential earnings

Your mathematical strengths (if you're good at multiplication, develop multiplication properties)

Trading Tips

When trading with other players:

Offer trades that benefit both players

Consider the value of completing a color group

Calculate the long-term value, not just the immediate costs

Mathematical Challenge Guide

Math Challenge Cards

When you draw a Math Challenge Card:

Read the problem carefully

Consider estimation first before calculating

Show your work using stamp materials when helpful

Double-check your answer before finalizing

Property Challenges

When landing on another player's property:

The owner will present a math problem

Solve it correctly to pay only half the fee

If incorrect, pay the full fee

The difficulty depends on the property's development level

Game Etiquette

As a Montessori mathematician:

Be honest about your calculations

Help others understand mathematical concepts

Use proper mathematical language

Be gracious whether winning or losing

Keep your stamp materials organized by place value

Listen carefully when others explain their mathematical thinking

Mathematical Vocabulary

Term Definition

Addend A number being added to another

Minuend The number from which another is subtracted

Subtrahend The number being subtracted

Factor A number that divides another number without a remainder

Product The result of multiplication

Quotient The result of division

Dividend The number being divided

Divisor The number by which the dividend is divided

Decimal A number expressed in the base-ten system with a decimal point

Fraction A number representing part of a whole

Equivalent Having the same value

Term	Definition
Addend	A number being added to another
Minuend	The number from which another is subtracted
Subtrahend	The number being subtracted
Factor	A number that divides another number without a remainder
Product	The result of multiplication
Quotient	The result of division
Dividend	The number being divided
Divisor	The number by which the dividend is divided
Decimal	A number expressed in the base-ten system with a decimal point
Fraction	A number representing part of a whole
Equivalent	Having the same value

Reflection Questions

After playing, ask yourself:

Which mathematical operation did I find easiest? Most challenging?

What strategies helped me calculate more efficiently?

How did I use decimal knowledge to make good decisions?

What mathematical concept do I want to practice more?

How did managing stamp materials help me understand place value?

Remember, the journey through mathematics is as important as reaching the destination. Enjoy the game and grow your mathematical mind!

Montessori Banking Game Board Design

Board Layout Visualization

The Montessori Banking Game board is designed as a square track with 40 spaces. The track runs around the perimeter of the board with each space representing a property or action space.

┌─────────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬─────────────┐
│ ASSESSMENT  │ NUMERATOR│DENOMINATOR│COMMUNITY │EQUIVALENT│ DECIMAL  │   MATH   │PERCENTAGE│ LEARNING │  RATIO   │    BEGIN    │
│ (DIVISION)  │   ROAD   │  DRIVE   │ LEARNING │FRACTIONS │  GRID    │CHALLENGE │  PLAZA   │OPPORTUNITY│  ROAD    │  LEARNING   │
│  Pay 10%    │  (Green) │ (Green)  │          │ (Green)  │          │          │  (Blue)  │   FUND   │  (Blue)  │ (ADDITION)  │
│             │          │          │          │          │          │          │          │ Pay 75   │          │Collect 200  │
├─────────────┼──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴─────────────┤
│ THOUSANDTH  │                                                                                                   │ NUMBER LINE │
│  BOULEVARD  │                                                                                                   │   AVENUE    │
│  (Yellow)   │                                                                                                   │  (Brown)    │
├─────────────┤                                                                                                   ├─────────────┤
│ MEASUREMENT │                                                                                                   │  COMMUNITY  │
│   UTILITY   │                                                                                                   │  LEARNING   │
│             │                                                                                                   │             │
├─────────────┤                                                                                                   ├─────────────┤
│  HUNDREDTH  │                                                                                                   │ PLACE VALUE │
│   AVENUE    │                                                                                                   │  BOULEVARD  │
│  (Yellow)   │                                                                                                   │  (Brown)    │
├─────────────┤                                                                                                   ├─────────────┤
│   TENTH     │                                                                                                   │  MATH TAX   │
│   STREET    │                              MONTESSORI BANKING GAME                                              │  Pay 200    │
│  (Yellow)   │                                                                                                   │             │
├─────────────┤                                                                                                   ├─────────────┤
│  FRACTION   │                         [Center Area Contains:]                                                   │ NUMBER LINE │
│   CIRCLES   │                         - Math Challenge Cards                                                    │             │
│             │                         - Community Learning Cards                                                │             │
├─────────────┤                         - Bank Tray with Stamp Materials                                          ├─────────────┤
│  DIVISOR    │                         - Development Markers                                                     │ COMMUTATIVE │
│    LANE     │                         - Dice                                                                    │    WAY      │
│   (Red)     │                                                                                                   │ (Light Blue)│
├─────────────┤                                                                                                   ├─────────────┤
│  DIVIDEND   │                                                                                                   │    MATH     │
│   DRIVE     │                                                                                                   │  CHALLENGE  │
│   (Red)     │                                                                                                   │             │
├─────────────┤                                                                                                   ├─────────────┤
│   MATH      │                                                                                                   │ ASSOCIATIVE │
│  CHALLENGE  │                                                                                                   │   AVENUE    │
│             │                                                                                                   │ (Light Blue)│
├─────────────┤                                                                                                   ├─────────────┤
│  QUOTIENT   │                                                                                                   │  IDENTITY   │
│  QUARTER

Sunday, May 4, 2025