California Mathematics — Grade 4
Comprehensive Course Syllabus
Course Overview
Our California Grade 4 Mathematics course is designed around the California Common Core State Standards for Mathematics and the 2023 California Mathematics Framework. Students develop stronger skills in multi-digit arithmetic, multiplication and division, fractions, decimals, measurement, angles, geometry, data, and mathematical problem solving.
Grade 4 places major emphasis on understanding multi-digit whole numbers, performing multi-digit operations, developing fraction equivalence and comparison, connecting fractions to decimals, and solving measurement and geometry problems. Students also build mathematical reasoning and explain how they arrive at their solutions.
Multi-Digit Numbers & Place Value
Numbers to 1,000,000
Students read, write, compare, and represent multi-digit whole numbers up to 1,000,000 using standard, word, and expanded forms.
Place Value Relationships
Students understand how the value of a digit changes from one place to the next and recognize the relationship between adjacent place values.
Comparing Multi-Digit Numbers
Students compare large numbers using place-value reasoning and symbols such as greater than, less than, and equal to.
Rounding Whole Numbers
Students round multi-digit numbers to different place values and use estimation to make reasonable mathematical judgments.
Estimation & Number Sense
Students use place value, rounding, and estimation to approximate quantities and determine whether mathematical answers are reasonable.
Multi-Digit Addition, Subtraction, Multiplication & Division
Multi-Digit Addition & Subtraction
Students develop fluency with adding and subtracting multi-digit whole numbers using standard algorithms and place-value reasoning.
Multiplication by One-Digit Numbers
Students multiply numbers with up to four digits by one-digit numbers using place-value strategies, equations, and visual models.
Multiplication of Two-Digit Numbers
Students multiply two two-digit numbers using area models, rectangular arrays, equations, and standard strategies.
Multi-Digit Division
Students divide multi-digit numbers by one-digit numbers and interpret remainders in the context of real-world problems.
Operation Strategies & Properties
Students use properties of operations and relationships between multiplication and division to calculate efficiently and explain their strategies.
Multi-Step Arithmetic Problems
Students solve problems involving multiple operations and learn to identify the correct sequence of steps before calculating.
Multiplication, Division & Algebraic Thinking
Multiplicative Comparison
Students solve problems that compare quantities using multiplication and division and distinguish multiplicative comparisons from additive comparisons.
Factors & Multiples
Students identify factors and multiples of whole numbers and use these relationships to solve mathematical problems.
Prime & Composite Numbers
Students identify prime and composite numbers and explore how numbers can be represented through their factors.
Patterns & Rules
Students identify patterns generated by a mathematical rule and use tables to organize and analyze relationships.
Number Relationships
Students examine relationships between numbers and operations to identify missing values and predict future terms in a pattern.
Equations & Unknown Values
Students solve simple equations with unknown quantities and learn to determine values that make mathematical statements true.
Fractions & Decimal Numbers
Equivalent Fractions
Students recognize and generate equivalent fractions using visual models, number lines, and multiplication or division reasoning.
Comparing Fractions
Students compare fractions with different numerators and denominators by using common denominators, common numerators, visual models, and benchmark fractions.
Fraction Addition & Subtraction
Students add and subtract fractions and mixed numbers with common denominators and apply these skills to real-world problems.
Fractions & Whole Numbers
Students understand fractions greater than one and represent them using mixed numbers and improper fractions.
Multiplying Fractions by Whole Numbers
Students understand multiplication of a fraction by a whole number using visual models and real-world situations.
Decimals as Fractions
Students understand that decimals can represent fractions with denominators of 10 or 100 and connect decimal notation to fractional representations.
Comparing Decimals
Students compare decimal numbers to hundredths using place-value reasoning and symbols such as >, <, and =.
Measurement, Data & Angles
Measurement Unit Conversion
Students solve problems involving conversions between larger and smaller units of length, mass, weight, volume, and time.
Measurement Word Problems
Students apply measurement concepts to real-world problems involving distances, quantities, time intervals, and other measurable values.
Line Plots
Students create and interpret line plots using measurements expressed as fractions of a unit.
Angles & Angle Measurement
Students understand angles as geometric figures and measure them using degrees and appropriate tools.
Angle Relationships
Students identify and analyze angles and understand relationships involving angles that combine to form larger angles.
Unknown Angles
Students use addition and subtraction of angle measurements to determine missing angles in geometric figures and real-world situations.
Geometry & Shape Classification
Lines & Line Relationships
Students identify parallel, perpendicular, and intersecting lines and describe relationships between lines in geometric figures.
Angles in Shapes
Students identify and classify shapes based on the presence and size of their angles.
Classifying Two-Dimensional Figures
Students classify triangles and quadrilaterals according to their sides, angles, and other defining properties.
Special Quadrilaterals
Students explore squares, rectangles, rhombuses, parallelograms, and trapezoids and compare their characteristics.
Symmetry
Students identify lines of symmetry in two-dimensional figures and draw lines that divide shapes into matching parts.
Geometric Reasoning
Students use properties of lines, angles, and shapes to analyze figures and explain why a shape belongs to a particular category.
Mathematical Problem Solving & Reasoning
Multi-Step Word Problems
Students solve real-world problems requiring multiple operations and learn to organize information before choosing a solution strategy.
Mathematical Models
Students use diagrams, equations, number lines, tables, area models, and other representations to model mathematical situations.
Estimation & Reasonableness
Students estimate solutions, check calculations, and explain whether an answer is reasonable based on the original problem.
Patterns & Mathematical Relationships
Students analyze numerical and geometric patterns and use rules to identify relationships and predict unknown values.
Strategy Selection
Students learn to select appropriate strategies such as drawing a model, creating a table, working backward, estimating, or using an equation.
Mathematical Communication
Students explain their mathematical thinking clearly using numbers, equations, diagrams, mathematical vocabulary, and written reasoning.
Teaching Methodology
Our Grade 4 Mathematics classes focus on conceptual understanding, procedural fluency, mathematical reasoning, problem solving, and real-world application.
Students learn through:
Learning Outcomes
By the end of Grade 4, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: