Fourth Grade Math: Advanced Mastery Curriculum
Excel in advanced fourth-grade mathematics through comprehensive lessons covering multi-digit multiplication and division, fraction operations and equivalence, decimal fractions, geometric measurement with angles, unit conversions, and multi-step problem-solving. Our standards-aligned curriculum develops computational excellence and deep mathematical reasoning.
Why Fourth Grade Math Is Transformative
Fourth grade represents a critical turning point in mathematical development. Students transition from concrete manipulatives to more abstract thinking, building fluency with multi-digit operations, understanding fractions as numbers (not just parts), and applying geometric concepts with precision. This year's foundations directly predict success in algebra and advanced mathematics.
Our curriculum aligns with Common Core and state standards across four critical areas: multi-digit multiplication and division operations, fraction and decimal understanding and operations, geometric shape analysis and angle measurement, and multi-step problem-solving using all four operations. Each topic builds systematically through multiple representations and real-world applications.
Whether your student needs foundational skill development, targeted practice with specific concepts, or enrichment to deepen understanding, these expertly-designed resources provide comprehensive support grounded in research-based instructional methods and proven classroom best practices.
Comprehensive Fourth Grade Math Topics
Place Value to Millions
Master place value extending to millions: millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, ones. Write numbers in standard form (\(1,234,567\)), word form, and expanded form (\(1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7\)). Compare and order large numbers using place value understanding.
Multi-Digit Addition
Fluently add multi-digit whole numbers using the standard algorithm. Compute \(3,456 + 2,789\) by aligning place values and adding from right to left with regrouping. Check answers using estimation: \(3,500 + 2,800 \approx 6,300\). Solve word problems involving addition in real-world contexts.
Multi-Digit Subtraction
Fluently subtract multi-digit whole numbers using the standard algorithm with regrouping. Subtract \(5,000 - 2,347\) by regrouping: \(5,000 - 2,347 = 2,653\). Use place value understanding and check using addition: if \(5,000 - 2,347 = 2,653\), then \(2,347 + 2,653\) should equal \(5,000\).
Multi-Digit Multiplication
Master multiplication of multi-digit numbers. Compute \(234 × 5 = 1,170\) and \(23 × 14 = (23 × 10) + (23 × 4) = 230 + 92 = 322\). Use the standard multiplication algorithm with regrouping. Understand area models showing \(23 × 14\) as a rectangle decomposed into smaller rectangles representing \(20 × 10\), \(20 × 4\), \(3 × 10\), and \(3 × 4\).
Multi-Digit Division
Divide multi-digit numbers by one-digit divisors using long division. Solve \(456 ÷ 3\) step-by-step: divide \(4 ÷ 3 = 1\) R\(1\), bring down 5 to make 15, \(15 ÷ 3 = 5\), bring down 6, \(6 ÷ 3 = 2\). Answer: 152. Interpret remainders in context and verify using multiplication: if \(456 ÷ 3 = 152\), then \(3 × 152 = 456\).
Multi-Step Problem Solving
Solve multi-step word problems using all four operations strategically. Example: "Sarah buys 3 books for \$12.50 each and gets a \$5.00 discount. If she pays with \$50, how much change?" Solution: \((3 × 12.50) - 5.00 = 37.50 - 5.00 = 32.50\); change = \(50 - 32.50 = 17.50\).
Fraction Equivalence and Operations
Understand fraction equivalence: \(1/2 = 2/4 = 4/8\). Find equivalent fractions by multiplying: \(1/3 × 2/2 = 2/6\). Compare fractions using common denominators: \(1/2\) vs \(1/3\) becomes \(3/6\) vs \(2/6\). Add and subtract fractions: \(1/2 + 1/4 = 2/4 + 1/4 = 3/4\). Multiply fractions by whole numbers: \(1/4 × 3 = 3/4\).
Data and Line Plots
Create and interpret line plots with data involving fractions. Plot heights at intervals like \(4 1/4\), \(4 1/2\), \(4 3/4\) inches. Analyze data by counting frequency and identifying modes and ranges. Answer questions: "How many students are between 4 1/4 and 4 1/2 inches?" Compare datasets and draw conclusions.
Patterns and Sequences
Generate numerical patterns following given rules. Pattern: start with 2, add 3 repeatedly: \(2, 5, 8, 11, 14, ...\). Analyze two related patterns and find relationships. Example: input/output table where output = input × 2 + 1. Extend patterns and explain rules using function notation.
Money and Decimals
Solve real-world money problems involving decimals. Add: \(\$3.45 + \$2.78 = \$6.23\). Subtract: \(\$10.00 - \$4.35 = \$5.65\). Multiply: \(3 items × \$2.50 = \$7.50\). Make change and solve comparison problems. Understand that \(\$3.75 = 3\) dollars and \(75\) cents or \(375\) cents.
Units of Measurement
Convert measurements from larger to smaller units: \(1 \text{ foot} = 12 \text{ inches}\); \(1 \text{ meter} = 100 \text{ centimeters}\); \(1 \text{ kilogram} = 1000 \text{ grams}\); \(1 \text{ liter} = 1000 \text{ milliliters}\). Solve word problems: "How many inches in \(3\) feet?" \(3 × 12 = 36\) inches. Estimate and measure using appropriate tools.
Time and Elapsed Time
Solve elapsed time problems: "An event starts at 2:15 p.m. and lasts \(1\) hour \(45\) minutes. When does it end?" \(2:15 + 1:45 = 4:00\) p.m. Convert between time units: \(1 \text{ hour} = 60 \text{ minutes}\), \(1 \text{ minute} = 60 \text{ seconds}\). Use number lines and clocks to visualize time intervals. Tell time to the nearest minute.
Geometry and Shapes
Classify shapes by their properties. Rectangles have four right angles (\(90°\)) and opposite sides equal. Rhombuses have four equal sides. Trapezoids have one pair of parallel sides. Triangles are classified by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). Identify lines of symmetry in shapes.
Geometric Measurement
Measure angles using protractors and identify degrees. Calculate area of rectangles: \(\text{Area} = \text{length} × \text{width}\). A \(5 \text{ cm} × 3 \text{ cm}\) rectangle has area \(15 \text{ cm}^2\). Calculate perimeter by adding side lengths: perimeter = \(2 × \text{length} + 2 × \text{width}\) for rectangles. Solve real-world problems involving area and perimeter.
Logical Reasoning
Develop critical thinking through complex multi-step logic problems and mathematical puzzles. Use systematic reasoning to solve problems. Make and test predictions. Explain why solutions are correct using mathematical justification. Develop persistence and flexible problem-solving approaches.
Probability Concepts
Analyze probability of events in simple experiments. List all possible outcomes systematically. Predict likely outcomes and conduct experiments to test predictions. Compare experimental results to theoretical predictions. Understand that some events are certain, impossible, or likely.
Fourth Grade Math Mastery Goals
Multi-Digit Fluency
Fluently multiply and divide multi-digit numbers using standard algorithms and strategic reasoning.
Fraction Mastery
Understand fraction equivalence, compare, and perform operations with fractions and decimals.
Geometric Excellence
Classify shapes, measure angles, calculate area and perimeter, and identify geometric properties.
Unit Conversions
Convert measurements between units and solve real-world problems involving time and distance.