Pengi Math (Grade 5) is a fifth-grade mathematics textbook covering the full range of core math concepts students need at this level. The curriculum spans place value and powers of 10, multi-digit multiplication and division, decimal and fraction operations, numerical expressions, measurement and volume, the coordinate plane, geometry with two-dimensional figures, pattern analysis, and data representation using dot plots. Together, these topics build a strong foundation in number sense, algebraic thinking, and geometric reasoning aligned with Grade 5 expectations.

Pengi Math (Grade 5) textbook table of contents

Chapter 1: Palace Value and Powers of 10

Lesson 1: Extending Place Value to DecimalsLearn Practice
Lesson 2: Representing Numbers Using Powers of 10Learn Practice
Lesson 3: Multiplying and Dividing Whole Numbers by Powers of 10Learn Practice
Lesson 4: Representing Decimals in Multiple FormsLearn Practice
Lesson 5: Equivalent, Comparing, and Ordering DecimalsLearn Practice
Lesson 6: Rounding Decimals to Any PlaceLearn Practice

Chapter 2: Multi-Digit Multiplication and Division with Place Value

Lesson 1: Estimating Products Using Rounding and Compatible NumbersLearn Practice
Lesson 2: Modeling Multiplication with Area Models and Partial ProductsLearn Practice
Lesson 3: Connecting Partial Products to the Standard AlgorithmLearn Practice
Lesson 4: Understanding Division as Finding a Missing FactorLearn Practice
Lesson 5: Dividing Multi-Digit Numbers Using Area Models and Partial QuotientsLearn Practice
Lesson 6: Applying Division Algorithms and Interpreting RemaindersLearn Practice

Chapter 3: Decimal Operations and Estimation

Lesson 1: Mental Addition Strategies with DecimalsLearn Practice
Lesson 2: Mental Subtraction Strategies with DecimalsLearn Practice
Lesson 3: Decimal Addition with RegroupingLearn Practice
Lesson 4: Decimal Subtraction with RegroupingLearn Practice
Lesson 5: Estimation and Reasonableness ChecksLearn Practice
Lesson 6: Multi-Step Decimal ProblemsLearn Practice

Chapter 4: Decimal Multiplication and Division

Lesson 1: Estimating Decimal Products to Check ReasonablenessLearn Practice
Lesson 2: Multiplying Decimals by Whole Numbers Using ModelsLearn Practice
Lesson 3: Multiplying Two Decimals Using Area and Partial ProductsLearn Practice
Lesson 4: Decimal Multiplication Algorithms and Decimal PlacementLearn Practice
Lesson 5: Dividing Decimals Using Models and AlgorithmsLearn Practice
Lesson 6: Dividing Decimals by DecimalsLearn Practice
Lesson 7: Solving Multi-Step Problems with Decimal OperationsLearn Practice

Chapter 5: Add & Subtract Fractions and Mixed Numbers

Lesson 1: Estimate Fraction Sums and DifferencesLearn Practice
Lesson 2: Finding Equivalent Fractions Using a Common DenominatorLearn Practice
Lesson 3: Add & Subtract Fractions with Unlike DenominatorsLearn Practice
Lesson 4: Add Mixed Numbers with Unlike DenominatorsLearn Practice
Lesson 5: Subtract Mixed Numbers with Unlike DenominatorsLearn Practice
Lesson 6: Solve Multi-step Fraction ProblemsLearn Practice

Chapter 6: Multiplying and Dividing Fractions

Lesson 1: Fractions as DivisionLearn Practice
Lesson 2: Multiplying a Fraction by a Whole NumberLearn Practice
Lesson 3: Multiplying Fractions Using Area ModelsLearn Practice
Lesson 4: The Standard Algorithm for Fraction MultiplicationLearn Practice
Lesson 5: Multiplying Mixed NumbersLearn Practice
Lesson 6: Division of Unit Fractions by Whole NumbersLearn Practice
Lesson 7: Division of Whole Numbers by Unit FractionsLearn Practice
Lesson 8: Solving Fraction Word Problems with Multiplication and DivisionLearn Practice

Chapter 7: Numerical Expressions and Problem Solving

Lesson 1: Order of OperationsLearn Practice
Lesson 2: Writing and Reading Numerical ExpressionsLearn Practice
Lesson 3: Solving Word Problems with ExpressionsLearn Practice

Chapter 8: Measurement — Volume & Unit Conversions

Lesson 1: Convert Measurement UnitsLearn Practice
Lesson 2: Solve Measurement Word Problems with ConversionsLearn Practice
Lesson 3: Introduction to Volume and Cubic UnitsLearn Practice
Lesson 4: Measure Volume with Unit Cubes, Layers, and Shape ComparisonsLearn Practice
Lesson 5: Volume Formulas and Equivalent ExpressionsLearn Practice
Lesson 6: Volume of Composite SolidsLearn Practice
Lesson 7: Solve Multi-Step Word Problems Using VolumeLearn Practice

Chapter 9: The Coordinate Plane

Lesson 1: Coordinate Plane and Ordered PairsLearn Practice
Lesson 2: Solving Problems on the Coordinate PlaneLearn Practice

Chapter 10: Analyze Patterns and Relationships

Lesson 1: Comparing and Classifying Numerical PatternsLearn Practice
Lesson 2: Representing Pattern Relationships with Tables and GraphsLearn Practice

Chapter 11: Geometry — Classifying and Understanding Two-Dimensional Figures

Lesson 1: Classifying Triangles by Sides and AnglesLearn Practice
Lesson 2: Defining and Identifying QuadrilateralsLearn Practice
Lesson 3: Rectangles and SquaresLearn Practice
Lesson 4: Quadrilateral Hierarchy and RelationshipsLearn Practice

Chapter 12: Representing and Solving Problems with Dot Plots

Lesson 1: Create and Interpret Dot PlotsLearn Practice
Lesson 2: Solve Word Problems Using Dot PlotsLearn Practice

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Pengi Math (Grade 5) — Lessons, Skills & Practice | Pengi