New Jersey Mathematics — Grade 4
Comprehensive Course Syllabus
Course Overview
Our New Jersey Grade 4 Mathematics course is designed around the New Jersey Student Learning Standards for Mathematics (NJSLS-M). Grade 4 develops strong mathematical reasoning through multi-digit arithmetic, factors and multiples, fractions, decimals, measurement, geometry, data, and multi-step problem solving.
Students move from basic computation toward more advanced mathematical thinking, estimation, modeling, and real-world applications.
Place Value & Multi-Digit Numbers
Place Value
Students understand the value of digits in multi-digit whole numbers and use place-value relationships to compare and represent numbers.
Reading & Writing Large Numbers
Students read, write, and represent whole numbers using standard, word, and expanded forms.
Comparing Whole Numbers
Students compare multi-digit numbers using symbols such as >, <, and = and explain their reasoning.
Rounding Whole Numbers
Students round multi-digit whole numbers to appropriate place values and use rounding to estimate results.
Number Patterns
Students identify and explain patterns created by place value, multiplication, and repeated operations.
Multi-Digit Addition & Subtraction
Multi-Digit Addition
Students add multi-digit whole numbers accurately using place-value strategies and standard algorithms.
Multi-Digit Subtraction
Students subtract multi-digit whole numbers using regrouping and place-value reasoning.
Estimation
Students estimate sums and differences and use estimation to determine whether answers are reasonable.
Addition & Subtraction Word Problems
Students solve real-world problems involving multiple quantities, unknown values, and different types of situations.
Multi-Step Problems
Students solve problems requiring two or more operations and explain the strategy used.
Multiplication & Division
Multi-Digit Multiplication
Students multiply multi-digit numbers using place-value strategies, area models, partial products, and standard algorithms.
Multiplication by Multiples of 10
Students use place-value relationships to multiply numbers by 10, 100, 1,000, and related multiples.
Multi-Digit Division
Students divide larger whole numbers using place-value reasoning, models, strategies, and standard procedures.
Quotients & Remainders
Students interpret remainders in real-world situations and determine what a remainder means within a problem.
Multiplication & Division Word Problems
Students apply multiplication and division to solve multi-step and real-world problems.
Factors, Multiples & Number Relationships
Factors
Students identify factors of whole numbers and understand how factors relate to multiplication.
Multiples
Students identify multiples of whole numbers and use them to solve mathematical problems.
Prime & Composite Numbers
Students classify numbers as prime or composite based on their factors.
Factor Pairs
Students identify factor pairs and use them to analyze numerical relationships.
Patterns in Multiples
Students identify patterns in multiples and use those patterns to solve problems efficiently.
Fractions
Understanding Fractions
Students represent fractions as numbers and understand their relationship to whole quantities.
Equivalent Fractions
Students generate and recognize equivalent fractions using visual models, number lines, and multiplication relationships.
Comparing Fractions
Students compare fractions with different numerators and denominators using common denominators, common numerators, benchmarks, and visual models.
Fractions on Number Lines
Students locate and represent fractions on number lines and understand their relative positions.
Decomposing Fractions
Students understand that fractions can be broken into sums of smaller fractions with the same denominator.
Fraction Operations
Adding Fractions
Students add fractions with the same denominator using visual models and numerical strategies.
Subtracting Fractions
Students subtract fractions with the same denominator and explain their reasoning.
Mixed Numbers
Students work with mixed numbers and understand the relationship between whole numbers and fractional parts.
Fraction Word Problems
Students solve real-world problems involving addition and subtraction of fractions.
Fraction Multiplication Concepts
Students develop an introductory understanding of multiplying a fraction by a whole number using models and repeated addition.
Decimal Numbers
Decimal Notation
Students understand decimals as representations of fractions and identify tenths and hundredths.
Comparing Decimals
Students compare decimals to hundredths using place value, symbols, and number lines.
Decimal Number Lines
Students represent tenths and hundredths on number lines and relate them to fractions.
Fractions & Decimals
Students connect fractions with denominators of 10 and 100 to their decimal representations.
Decimal Applications
Students apply decimal concepts to money, measurement, and other real-world situations.
Measurement & Unit Conversion
Measurement Units
Students work with standard units for length, mass, weight, liquid volume, and time.
Unit Conversion
Students convert between larger and smaller units within the same measurement system.
Measurement Word Problems
Students solve problems involving measurement quantities, comparisons, and conversions.
Time & Elapsed Time
Students solve problems involving time intervals, schedules, and elapsed time.
Money & Decimal Applications
Students apply decimal and measurement skills to money-related situations and real-world calculations.
Geometry
Points, Lines & Angles
Students identify points, line segments, rays, lines, and angles and use appropriate geometric vocabulary.
Angle Measurement
Students understand angles as geometric figures and measure them using degrees and appropriate tools.
Classifying Angles
Students identify acute, right, obtuse, and straight angles.
Classifying Shapes
Students classify two-dimensional figures based on their properties, including sides, angles, and parallel or perpendicular lines.
Symmetry
Students identify and create lines of symmetry in geometric shapes and designs.
Area, Perimeter & Geometry Applications
Area of Rectangles
Students calculate the area of rectangles using multiplication and understand why the formula works.
Perimeter
Students calculate the perimeter of polygons and solve real-world perimeter problems.
Area & Perimeter Relationships
Students compare area and perimeter and explore how changing dimensions affects each measurement.
Composite Figures
Students break complex shapes into simpler parts to calculate area or perimeter.
Real-World Geometry
Students apply geometry, measurement, area, and perimeter to practical situations involving spaces, objects, and designs.
Data & Mathematical Reasoning
Data Collection
Students collect and organize data using surveys, measurements, observations, and other simple methods.
Line Plots
Students create and interpret line plots using fractional measurement units.
Tables & Graphs
Students interpret tables and graphs and use the information to answer mathematical questions.
Data-Based Problem Solving
Students solve multi-step problems involving information represented in charts, tables, and graphs.
Mathematical Reasoning
Students explain mathematical ideas, justify solutions, compare strategies, and use evidence to support conclusions.
Mathematical Modeling & Enrichment
Multi-Step Problem Solving
Students solve complex problems involving multiple operations and determine an efficient strategy.
Mathematical Models
Students use drawings, diagrams, equations, tables, graphs, number lines, and physical models to represent mathematical situations.
Estimation & Reasonableness
Students estimate solutions and use mathematical reasoning to determine whether answers are reasonable.
Math Puzzles & Challenges
Students solve age-appropriate mathematical puzzles involving patterns, numbers, logic, geometry, and operations.
Real-World Mathematics Projects
Students apply arithmetic, fractions, decimals, measurement, geometry, and data skills to practical projects.
Teaching Methodology
Our Grade 4 Mathematics classes focus on conceptual understanding, computational fluency, mathematical reasoning, problem solving, modeling, and real-world applications. Students learn through:
Learning Outcomes
By the end of Grade 4, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: