Our fully accredited 5th Grade Math course, aligned with the Common Core standards, is expertly designed to build upon the robust foundations laid down in our 4th Grade course. This comprehensive course empowers students to master the standard algorithms for multiplication, division, and arithmetic involving fractions and decimals. Beyond computations, students will delve deeper into vital mathematical concepts, including numerical expressions, negative numbers, units of measurement, exponents, number patterns, and geometry. Finally, the course requires students to apply their knowledge across varying contexts, fostering a holistic understanding of mathematics and its practical applications.

## Content

In this engaging and comprehensive course, students will achieve mastery of the standard algorithms for multi-digit multiplication and division. After mastering these fundamental techniques, students will extend their understanding to solving problems involving multi-digit decimals.

The course enables students to deepen their knowledge and computational fluency in fractions and mixed number operations. Students will achieve proficiency in fraction addition and subtraction with unlike denominators and fraction multiplication and division.

As part of their journey, students will delve deeper into algebra fundamentals. This includes exploring negative numbers, constructing numerical expressions, an introduction to exponents, and further developing their understanding of number patterns.

Throughout the course, students will apply their mathematical understanding to various real-world scenarios, geometric contexts, and mathematical problems, reinforcing the practical application of the skills they have learned.

Upon successful completion of the course, students will have attained the necessary skills and knowledge to seamlessly progress to our Prealgebra course. This is a critical stepping stone towards our rigorous high-school math curriculum, setting students on a path toward mathematical confidence and success.

Upon successful completion of this course, students will have mastered the following:
• Constructing and evaluating numerical expressions, including cases with multiple parentheses.
• Understanding and representing negative numbers on a number line, comparing negative numbers, and understanding absolute value.
• Mastery of multiplication involving single and multi-digit numbers.
• Proficiency in dividing whole numbers, including interpreting remainders and dividing by two-digit numbers using various strategies.
• Adding and subtracting fractions and mixed numbers with unlike denominators, explaining these operations using concrete models, and solving related word problems.
• Mastery of fraction multiplication concepts, including multiplying mixed numbers.
• The ability to divide fractions by whole numbers and other fractions, understand and apply the concept of reciprocals, and solve related problems in context.
• Understand and apply the place value system with decimals, reading and writing decimals in various forms, comparing and rounding decimals, and understanding significant figures.
• The capability to estimate, add, and subtract decimals, including handling unequal numbers of decimals.
• Multiply and divide decimals using various strategies, including the standard algorithms.
• Estimate products and quotients in decimal multiplication and division problems.
• Understand exponents, and evaluate expressions containing exponents with whole number, fractional, and decimal bases.
• Convert units of measurement within the metric and customary systems.
• Represent and interpret data using line plots and fractions.
• Understand and use coordinates to solve real-world problems and represent locations on maps.
• Identify, describe, and compare number patterns and relationships in data.
• Calculate the volume of right rectangular prisms using unit cubes and formulas, and solve real-world problems involving volume and classification of 2D shapes.
• Classify quadrilaterals according to a hierarchical structure.
1.
The Number System
9 topics
1.1. Numerical Expressions
 1.1.1. Evaluating Whole Number Expressions 1.1.2. Evaluating Whole Number Expressions Containing Parentheses 1.1.3. Creating and Interpreting Numerical Expressions 1.1.4. Using Terminology to Create Expressions 1.1.5. Working With Numerical Expressions: Multiplication and Division 1.1.6. Working With Numerical Expressions: Addition and Subtraction
1.2. Introduction to Negative Numbers
 1.2.1. Negative Numbers 1.2.2. Comparing Negative Numbers 1.2.3. Absolute Value
2.
Multiplying & Dividing Whole Numbers
18 topics
2.3. Multiplying Whole Numbers
 2.3.1. Multiplying Whole Numbers by Powers of Ten Using Place Value 2.3.2. Two-Digit by One-Digit Multiplication Using the Standard Algorithm 2.3.3. Multiplying Three and Four-Digit Numbers By One-Digit Numbers 2.3.4. Multiplying Five and Six-Digit Numbers By One-Digit Numbers 2.3.5. Two-Digit by Two-Digit Multiplication Using the Standard Algorithm 2.3.6. Multi-Digit by Two-Digit Multiplication Using the Standard Algorithm 2.3.7. Three-Digit by Three-Digit Multiplication Using the Standard Algorithm
2.4. Dividing Whole Numbers
 2.4.1. Two-Digit by One-Digit Division Using the Standard Algorithm 2.4.2. Three-Digit by One-Digit Division Using the Standard Algorithm 2.4.3. Four-Digit by One-Digit Division Using the Standard Algorithm 2.4.4. Using Fractions to Represent Division of Whole Numbers 2.4.5. Dividing Numbers by One-Digit Numbers With Rounding 2.4.6. Dividing Numbers by One-Digit Numbers: Interpreting the Remainder 2.4.7. Dividing by Two-Digit Numbers by Connecting Multiplication and Division 2.4.8. Dividing by Two-Digit Numbers With Remainders by Connecting Multiplication and Division 2.4.9. Dividing Numbers by Two-Digit Numbers Using Box Models 2.4.10. Three-Digit by Two-Digit Division Using the Standard Algorithm 2.4.11. Four-Digit by Two-Digit Division Using the Standard Algorithm
3.
14 topics
3.5. Adding and Subtracting Fractions and Whole Numbers
 3.5.1. Adding Fractions and Whole Numbers Using Models 3.5.2. Adding Fractions and Whole Numbers 3.5.3. Subtracting Fractions and Whole Numbers Using Models 3.5.4. Subtracting Fractions and Whole Numbers
 3.6.1. Estimating Sums and Differences of Fractions Using Benchmarks 3.6.2. Adding Fractions With Unlike Denominators Using Models 3.6.3. Subtracting Fractions With Unlike Denominators Using Models 3.6.4. Adding Fractions With Unlike Denominators 3.6.5. Subtracting Fractions With Unlike Denominators 3.6.6. Adding and Subtracting Fractions With Unlike Denominators: Word Problems
3.7. Adding and Subtracting Mixed Numbers
 3.7.1. Adding Mixed Numbers With Unlike Denominators 3.7.2. Subtracting Mixed Numbers With Unlike Denominators 3.7.3. Subtracting Mixed Numbers With Unlike Denominators Using Improper Fractions 3.7.4. Adding and Subtracting Mixed Numbers With Unlike Denominators: Word Problems
4.
Multiplying & Dividing Fractions
26 topics
4.8. Multiplying Fractions
 4.8.1. Multiplying Fractions by Unit Fractions Using Models 4.8.2. Multiplying Fractions Using Models 4.8.3. Multiplying Fractions 4.8.4. Multiplying Fractions: Word Problems 4.8.5. Strategies to Simplify Fraction Multiplication 4.8.6. Multiplying Mixed Numbers by Whole Numbers 4.8.7. Multiplying Mixed Numbers by Fractions 4.8.8. Multiplying Mixed Numbers 4.8.9. Multiplying Mixed Numbers: Word Problems 4.8.10. Connecting Fraction Multiplication and Area 4.8.11. Finding Areas Using Fraction Multiplication 4.8.12. Fraction Multiplication Number Sense
4.9. Dividing Fractions
 4.9.1. Interpreting Fraction Division Using Area Models 4.9.2. Dividing Whole Numbers by Unit Fractions Using Models 4.9.3. Dividing Whole Numbers by Unit Fractions 4.9.4. Dividing Unit Fractions by Whole Numbers Using Models 4.9.5. Dividing Unit Fractions by Whole Numbers 4.9.6. Reciprocals 4.9.7. Dividing Whole Numbers by Fractions Using Models: Whole Number Results 4.9.8. Dividing Whole Numbers by Fractions Using Models: Fractional Results 4.9.9. Dividing Whole Numbers by Fractions 4.9.10. Dividing Fractions by Whole Numbers Using Models 4.9.11. Dividing Fractions by Whole Numbers 4.9.12. Dividing Fractions and Whole Numbers: Word Problems 4.9.13. Dividing Fractions Using Models 4.9.14. Dividing Fractions
5.
Decimals
18 topics
5.10. Decimals
 5.10.1. The Place Value System With Decimals 5.10.2. Comparing Place Values With Decimals 5.10.3. Reading and Writing Decimals Written in Words 5.10.4. Converting From Standard Form to Expanded Form With Decimals 5.10.5. Converting From Expanded Form to Standard Form With Decimals 5.10.6. Equivalent Decimals 5.10.7. Comparing Decimals Using Place Value 5.10.8. Rounding Down Decimals 5.10.9. Rounding Up Decimals 5.10.10. Significant Figures 5.10.11. Significant Figures With Decimals
 5.11.1. Estimating Decimal Addition and Subtraction 5.11.2. Adding Decimals 5.11.3. Decimal Addition With Unequal Numbers of Decimals 5.11.4. Subtracting Decimals 5.11.5. Decimal Subtraction With Unequal Numbers of Decimals 5.11.6. Estimating Decimal Addition With Benchmarks 5.11.7. Estimating Decimal Subtraction With Benchmarks
6.
Multiplying & Dividing Decimals
17 topics
6.12. Multiplying Decimals
 6.12.1. Multiplying Decimals by Powers of Ten Using Place Value 6.12.2. Multiplying Decimals by Powers of Ten Using Decimal Point Placement 6.12.3. Estimating Decimal Multiplication 6.12.4. Multiplying a Decimal by a One-Digit Whole Number 6.12.5. Multiplying a Decimal by a Multi-Digit Whole Number 6.12.6. Multiplying Two-Digit Decimals 6.12.7. Multiplying Two-Digit Decimals by Three-Digit Decimals 6.12.8. Multiplying Three-Digit Decimals
6.13. Dividing Decimals
 6.13.1. Dividing Decimals by Powers of Ten Using Place Value 6.13.2. Dividing Decimals by Powers of Ten Using Decimal Point Placement 6.13.3. Estimating Decimal Division 6.13.4. Dividing Decimals Using Strategies Based on Place Value 6.13.5. Division of Whole Numbers With Decimal Quotients 6.13.6. Division of Whole Numbers With Decimal Quotients and Rounding 6.13.7. Dividing Decimals Using the Standard Algorithm 6.13.8. Dividing Three-Digit Decimals by Two-Digit Decimals 6.13.9. Dividing Four-Digit and Five-Digit Decimals
7.
Exponents
10 topics
7.14. Exponents
 7.14.1. Powers of Ten With Exponents 7.14.2. Multiplying a Whole Number by a Power of Ten With Exponents 7.14.3. Multiplying a Decimal Number by a Power of Ten With Exponents 7.14.4. Introduction to Exponents 7.14.5. Evaluating Exponents 7.14.6. Evaluating Larger Exponents 7.14.7. Evaluating Exponents With Fractional Bases 7.14.8. Evaluating Exponents With Decimal Bases 7.14.9. Comparing Exponents 7.14.10. Evaluating Whole Number Expressions Containing Exponents
8.
Measurement & Data
12 topics
8.15. Units and Data
 8.15.1. Converting Metric Units of Length to Larger Units 8.15.2. Converting Customary Units of Length to Larger Units 8.15.3. Converting Units of Volume to Larger Units 8.15.4. Converting Units of Mass to Larger Units 8.15.5. Converting Units of Time to Larger Units 8.15.6. Operations on Fractions With Line Plots
8.16. Coordinates
 8.16.1. Describing the Coordinate Plane 8.16.2. Solving Real World Problems Using Coordinates 8.16.3. Coordinate Planes as Maps
8.17. Patterns and Relationships
 8.17.1. Connecting Patterns 8.17.2. Comparing Patterns 8.17.3. Graphing Patterns
9.
Geometry
7 topics
9.18. Volume
 9.18.1. Understanding Volume Using Unit Cubes 9.18.2. Volumes of Right Rectangular Prisms 9.18.3. Volumes of Right Rectangular Prisms: Word Problems
9.19. 2D Shapes
 9.19.1. Polygons 9.19.2. Quadrilaterals 9.19.3. Rectangles, Rhombuses, and Squares 9.19.4. Classifying Quadrilaterals