4th Grade Math Intervention Curriculum Map: Hands on Montessori Math Interventions

 4th Grade Math Intervention Curriculum Map:  Hands on Montessori Math Interventions

Addressing Post-COVID Learning Gaps through Concrete Manipulatives

Introduction

This curriculum map integrates traditional 4th grade Arizona State Standards with Montessori manipulatives to address learning gaps resulting from COVID-related disruptions. The sequence progresses from concrete to representational to abstract concepts, with allowances for revisiting earlier manipulatives when needed to strengthen conceptual understanding.

Overview of Learning Domains

The Arizona Mathematics Standards for 4th grade include five essential domains:

1. Operations and Algebraic Thinking (OA)
2. Number and Operations in Base Ten (NBT)
3. Number and Operations - Fractions (NF)
4. Measurement and Data (MD)
5. Geometry (G)

Montessori Materials for Remediation

The following Montessori materials are incorporated throughout the curriculum to address foundational gaps:

Quantity-Based Materials

• Golden Bead Material: Base-10 understanding, place value, operations
• Stamp Game: Place value and operations
• Bead Frame: Place value and operations
• Checkerboard: Multiplication and place value
• Bead Bars/Chains: Skip counting, multiplication tables

Fraction Materials

• Fraction Circles: Equivalence, comparisons, operations
• Fraction Skittles: Equivalence, comparisons, operations
• Fraction Insets: Fractions of a whole
• Fraction Charts: Fraction equivalences

Geometry Materials

• Geometric Cabinet: Plane figures, properties
• Constructive Triangles: Composition of shapes
• Geometry Sticks: Creating/measuring polygons
• Geometric Solids: 3D shapes and properties

Measurement Materials

• Measurement Materials: Length, volume, weight, area
• Clock Materials: Time concepts
• Money Materials: Decimal relationships

Annual Curriculum Map

Quarter 1 (August - October)

Weeks 1-3: Place Value Foundations

• Standards Focus: 4.NBT.A.1, 4.NBT.A.2
• Content: Understanding place value to 1,000,000; reading, writing, and comparing multi-digit numbers
• Montessori Materials:
• Golden Bead Material (remedial)
• Large Number Cards
• Hierarchical Material (thousand, million cubes)
• Activities:
• Place value identification with golden bead material
• Building large numbers with hierarchical materials
• Reading and writing large numbers in various forms
• "Bank Game" for representing large quantities

Weeks 4-6: Multi-digit Addition and Subtraction

• Standards Focus: 4.NBT.B.4
• Content: Fluently adding and subtracting multi-digit whole numbers
• Montessori Materials:
• Stamp Game
• Large Bead Frame
• Golden Bead Material (remedial)
• Activities:
• Static and dynamic addition with stamp game
• Multi-digit addition/subtraction with exchanges
• Problem-solving with real-world scenarios
• Recording work with paper/pencil alongside manipulatives

Weeks 7-9: Multiplication Concepts & Properties

• Standards Focus: 4.OA.A.1, 4.OA.A.2, 4.NBT.B.5
• Content: Interpreting multiplication equations; multiplicative comparison; properties
• Montessori Materials:
• Bead Bars
• Multiplication Board
• Multiplication Bead Box
• Bead Chains (remedial)
• Activities:
• Modeling multiplicative comparison
• Building multiplication arrays
• Exploring distributive property with bead bars
• Multiplying 2-digit numbers using area models

Quarter 2 (October - December)

Weeks 10-12: Multi-digit Multiplication

• Standards Focus: 4.NBT.B.5, 4.OA.A.3
• Content: Multiplying whole numbers up to 4 digits by 1 digit; multi-step problems
• Montessori Materials:
• Checkerboard
• Flat Bead Frame
• Bank Game (for word problems)
• Activities:
• Using the checkerboard for multi-digit multiplication
• Recording partial products
• Solving multi-step word problems with multiple operations
• Connecting concrete representations to standard algorithm

Weeks 13-15: Division Concepts and Strategies

• Standards Focus: 4.NBT.B.6, 4.OA.A.3
• Content: Division with remainders; interpreting remainders; multi-step problems
• Montessori Materials:
• Division Board
• Racks and Tubes Division
• Stamp Game (for division operations)
• Activities:
• Concrete division with remainders
• Division as equal sharing and equal grouping
• Multi-step problem-solving with division
• Recording division with remainders

Weeks 16-18: Patterns and Algebraic Thinking

• Standards Focus: 4.OA.C.5, 4.OA.A.3
• Content: Generating and analyzing patterns; number or shape patterns
• Montessori Materials:
• Colored Bead Bars
• Pegboard
• Number Cards
• Hundred Board
• Activities:
• Building and extending patterns
• Finding rules in pattern sequences
• Recording patterns and describing rules
• Creating patterns with operations

Quarter 3 (January - March)

Weeks 19-21: Fraction Concepts

• Standards Focus: 4.NF.A.1, 4.NF.A.2, 4.NF.B.3
• Content: Fraction equivalence; comparing fractions; decomposing fractions
• Montessori Materials:
• Fraction Circles
• Fraction Skittles
• Fraction Insets
• Fraction Charts
• Activities:
• Building equivalent fractions with materials
• Comparing fractions using common denominators
• Decomposing fractions into unit fractions
• Recording fraction operations with symbols

Weeks 22-24: Fraction Operations

• Standards Focus: 4.NF.B.3, 4.NF.B.4
• Content: Adding and subtracting fractions; multiplying fractions by whole numbers
• Montessori Materials:
• Fraction Circles
• Fraction Skittles
• Fraction Number Line
• Activities:
• Adding/subtracting fractions with like denominators
• Multiplying fractions by whole numbers
• Word problems with fraction operations
• Recording fraction operations

Weeks 25-27: Decimal Concepts

• Standards Focus: 4.NF.C.5, 4.NF.C.6, 4.NF.C.7
• Content: Decimals and fractions; comparing decimals
• Montessori Materials:
• Decimal Board
• Decimal Fraction Material
• Golden Bead Material (decimal connection)
• Money Material
• Activities:
• Relating fractions to decimals
• Reading and writing decimals
• Comparing decimal values
• Money problems with decimals

Quarter 4 (March - May)

Weeks 28-30: Measurement

• Standards Focus: 4.MD.A.1, 4.MD.A.2, 4.MD.A.3
• Content: Converting measurements; measurement problem solving; area and perimeter
• Montessori Materials:
• Measurement Tools
• Area Material
• Volume Material
• Constructive Triangles
• Activities:
• Converting between measurement units
• Measuring objects with different units
• Finding area and perimeter of figures
• Problem-solving with measurements

Weeks 31-33: Geometry

• Standards Focus: 4.G.A.1, 4.G.A.2, 4.G.A.3
• Content: Drawing/identifying lines and angles; classifying shapes
• Montessori Materials:
• Geometric Cabinet
• Constructive Triangles
• Geometry Sticks
• Geometric Solids
• Activities:
• Drawing lines, rays, angles with tools
• Classifying angles and shapes
• Building shapes with specific attributes
• Identifying symmetry in shapes

Weeks 34-36: Data Analysis and Review

• Standards Focus: 4.MD.B.4, Review of all domains
• Content: Line plots; interpreting data; cumulative review
• Montessori Materials:
• Graph Paper
• Colored Pencils/Markers
• Review of all previously used materials
• Activities:
• Creating line plots from measurement data
• Interpreting data from graphs
• Review stations with different Montessori materials
• End-of-year projects incorporating multiple domains

Assessment and Progress Monitoring

Diagnostic Assessment

• Pre-assessment using concrete materials to identify specific gaps
• Observation of student interactions with manipulatives
• Mathematical interviews to assess conceptual understanding

Formative Assessment

• Daily observation of student work with manipulatives
• Student presentations of mathematical thinking
• Math journals documenting process and understanding
• Small group conferences

Summative Assessment

• Concrete-to-abstract demonstrations of learning
• Performance tasks integrating multiple concepts
• Student portfolios showing progression
• End-of-unit assessments with manipulative and written components

Detailed Montessori Material Integration

Golden Bead Material

• Traditional Use: Primary grades for place value introduction
• Extended Use for 4th Grade: Review place value to thousands; extend to millions using hierarchical materials; connection to decimal system

Stamp Game

• Traditional Use: Primary/lower elementary operations
• Extended Use for 4th Grade: Multi-digit multiplication and division; algebraic thinking with unknown quantities

Fraction Materials

• Traditional Use: Sequential introduction in lower elementary
• Extended Use for 4th Grade: More complex equivalence; operations with unlike denominators; connection to decimals

Checkerboard

• Traditional Use: Elementary multiplication
• Extended Use for 4th Grade: Multi-digit multiplication; connecting to area models; distributive property exploration

Geometry Materials

• Traditional Use: Sensorial exploration to formal geometry
• Extended Use for 4th Grade: Properties of shapes; angle measurement; coordinate geometry connection

Differentiation Strategies

For Students with Significant Gaps

• Begin with lower-level Montessori materials (Golden Beads, Number Rods)
• Provide additional small-group time with concrete materials
• Pair visual and tactile experiences consistently

For On-Level Students

• Move more quickly from concrete to representational models
• Extend learning with problem-solving applications
• Peer teaching opportunities

For Advanced Students

• Connect multiple materials to explore relationships
• Challenge with pattern extension and generalization
• Independent projects applying concepts

Parent Connection

• Parent education sessions on using similar concrete models at home
• Math nights to demonstrate Montessori approach
• Weekly communication highlighting current materials and concepts
• Home extension activities using household items

Conclusion

This curriculum map addresses post-COVID learning gaps by systematically rebuilding mathematical foundations through concrete experiences. By integrating Montessori manipulatives with Arizona State Standards, students can develop strong conceptual understanding while progressing through grade-level content. The concrete-representational-abstract sequence ensures students develop number sense and computational fluency with meaningful understanding.