Welcome to the Fifth Grade Math homepage! In fifth grade, students delve into multi-digit operations and mastering advanced concepts in multiplication and division. Through rigorous spiraled practice, they become increasingly fluent and accurate with complex mathematical procedures. A significant portion of the year is dedicated to fractions, where students explore topics such as comparing, ordering, and manipulating fractions using both models and equations. Students also apply their knowledge of operations to add, subtract, multiply, and divide fractions and they will continue to investigate equivalent and improper fractions along with mixed numbers. Moreover, fifth graders explore the intricate relationship between decimals, fractions, and place value. They learn to translate between these forms and apply their understanding to real-world situations. Throughout the year, they are challenged to think critically and apply problem-solving skills, honing their abilities for both academic success and real-world application.

- Math
- 5th Grade

Please review the CityTutor DC Lesson Overview and terms of use before using CTDC lessons.

To support alignment with common DC curricula, please review the 5th Grade Pacing Guide.

In this unit, fifth graders will explore the relationships between place values and delve into decimal operations. They’ll learn to express numbers in scientific notation and name decimal fractions in various forms. With a focus on arithmetic, students will master addition, subtraction, multiplication, and division of decimals, utilizing their understanding of place value to ensure accuracy. They’ll also compare decimals, round them, and check multiplication answers using estimation techniques. By the end of the unit, students will have a solid grasp of decimal operations and their connections to place value, laying the foundation for further mathematical exploration.

- Unit 1.1: Explain the relationships between the place values
- Unit 1.2: Write numbers in scientific notation using place value
- Unit 1.3: Name decimal fractions in different forms
- Unit 1.4: Compare decimals
- Unit 1.5: Round decimals
- Unit 1.6: Add decimals
- Unit 1.7: Subtract decimals
- Unit 1.8: Multiply decimals by whole numbers
- Unit 1.9: Check multiplication answers with estimation
- Unit 1.10: Divide decimals using the place value chart
- Unit 1.11: Divide decimals with remainders
- Unit 1.12: Divide decimals with remainders in the smallest place

In this unit, fifth graders will master multiplying multi-digit whole numbers and decimal fractions using various techniques, including the standard algorithm and place value understanding. They’ll also explore connections between visual models, the distributive property, and multiplication strategies. Later, students will delve into division operations, tackling tasks such as dividing multi-digit dividends by multiples of 10 and two-digit divisors. By the end of the unit, students will fluently solve multi-step word problems and confidently express equivalent measurements using both whole number and decimal multiplication.

- Unit 2.1: Multiply multi-digit whole numbers and multiples of 10
- Unit 2.2: Estimate multi-digit products by rounding factors
- Unit 2.3: Write and interpret numerical expressions, and compare expressions
- Unit 2.4: Connect visual models and the distributive property to partial products of the standard algorithm without renaming
- Unit 2.5: Connect area models and the distributive property to partial products of the standard algorithm with renaming
- Unit 2.6: Fluently multiply multi-digit whole numbers using the standard algorithm
- Unit 2.7: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems
- Unit 2.8: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products
- Unit 2.9: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem
- Unit 2.10: Reason about the product of a whole number and a decimal with hundredths
- Unit 2.11: Use whole number multiplication to express equivalent measurements
- Unit 2.12: Use fraction and decimal multiplication to express equivalent measurements
- Unit 2.13: Use basic facts to approximate quotients with two-digit divisors
- Unit 2.14: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients
- Unit 2.15: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients
- Unit 2.16: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point
- Unit 2.17: Use basic facts to approximate decimal quotients with two-digit divisors
- Unit 2.18: Divide decimal dividends by two-digit divisors

Throughout this unit, fifth graders will explore a variety of strategies for making equivalent fractions and performing operations with fractions. They’ll use visual models such as the number line and area models to understand and create equivalent fractions. Students will also learn strategies for adding and subtracting fractions with unlike units, focusing on creating equivalent fractions to facilitate the operations. Additionally, they’ll practice adding and subtracting fractions from whole numbers, honing their skills in using equivalence and the number line as problem-solving tools. By the end of the unit, students will be proficient in solving multi-step word problems involving fractions, assessing the reasonableness of their solutions using fraction benchmark numbers.

- Unit 3.1: Make equivalent fractions with the number line, the area model, and numbers
- Unit 3.2: Make equivalent fractions with sums of fractions with like denominators
- Unit 3.3: Add fractions with unlike units using the strategy of creating equivalent fractions
- Unit 3.4: Add fractions with sums between 1 and 2
- Unit 3.5: Subtract fractions with unlike units using the strategy of creating equivalent fractions
- Unit 3.6: Subtract fractions from numbers between 1 and 2
- Unit 3.7: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies
- Unit 3.8: Add fractions making like units numerically
- Unit 3.9: Add fractions with sums greater than 2
- Unit 3.10: Subtract fractions making like units numerically
- Unit 3.11: Subtract fractions greater than or equal to 1
- Unit 3.12: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations
- Unit 3.13: Strategize to solve multi-term problems
- Unit 3.14: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers

In this unit, fifth graders will master essential concepts and operations with fractions and decimals. They’ll interpret fractions as division, find fractions of sets, and fluently multiply decimals. Students will explore fraction multiplication and division using tape diagrams, comparing the size of products to factors and solving word problems. They’ll also delve into decimal operations, including division by tenths and hundredths, and fluently use all four decimal operations.

- Unit 4.1: Interpret fractions as division
- Unit 4.2: Find a fraction of a set
- Unit 4.3: Multiply whole numbers by fractions using tape diagrams
- Unit 4.4: Relate multiplying fractions to repeated addition
- Unit 4.5: Compare the size of a product to the size of its factors
- Unit 4.6: Compare expressions with fraction multipacation
- Unit 4.7: Multiply unit fractions by unit fractions
- Unit 4.8: Multiply unit fractions by non-unit fractions
- Unit 4.9: Multiply non-unit fractions by non-unit fractions
- Unit 4.10: Relate decimal and fraction multipacation
- Unit 4.11: Multiply decimals fluently
- Unit 4.12: Solve word problems using fraction and decimal multipacation
- Unit 4.13: Divide a unit fraction by a whole number
- Unit 4.14: Divide a whole number by a unit fraction
- Unit 4.15: Solve problems involving fraction division
- Unit 4.16: Divide by 1 tenth and 1 hundredth as a fraction and decimal
- Unit 4.17: Divide decimals by decimals
- Unit 4.18: Fluently use all four decimal operations

In this unit, fifth graders will explore various methods for finding the volume of right rectangular prisms and the area of rectangles with mixed side lengths. They’ll begin by understanding volume as the result of packing cubic units into prisms and using multiplication to calculate it. Students will then progress to composing and decomposing right rectangular prisms into layers, allowing them to find the total volume of solid figures composed of multiple prisms. Additionally, they’ll apply their understanding of area to solve real-world problems involving figures with fractional side lengths, using visual models and equations. By the end of the unit, students will be proficient in finding volume and area using a combination of methods such as packing, tiling, drawing, and multiplication.

- Unit 5.1: Find the volume of a right rectangular prism by packing with cubic units and counting.
- Unit 5.2: Compose and decompose right rectangular prisms using layers.
- Unit 5.3: Use multiplication to calculate volume.
- Unit 5.4: Find the total volume of solid figures composed of two non-overlapping rectangular prisms.
- Unit 5.5: Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.
- Unit 5.6: Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by tiling, record by drawing, and relate to fraction multiplication.
- Unit 5.7: Multiply mixed number factors, and relate to the distributive property and the area model.
- Unit 5.8: Solve real-world problems involving area of figures with fractional side lengths using visual models and/or equations.

In this unit, fifth graders will explore the coordinate plane. They’ll learn to find and write coordinate pairs, plot points following specific rules, and compare the graphs of addition and multiplication equations. Additionally, students will gain proficiency in writing equations for parallel lines, enhancing their understanding of geometric relationships. By the end of the unit, students will be equipped with essential skills in coordinate geometry and algebraic reasoning.

- Unit 6.1: Find and write coordinate pairs
- Unit 6.2: Find patterns for points on a line
- Unit 6.3: Plot and generate points that follow a rule
- Unit 6.4: Compare the graphs of addition equations and multiplication equations
- Unit 6.5: Write equations for parallel lines

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