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5th Grade Math

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.

Getting Started

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.

5th Grade Math Unit Materials

Unit 1: Place Value with Decimals

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.

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Unit 2: Base Ten Operations

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.

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Unit 3: Add and Subtract Fractions

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.

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Unit 4: Multiply and Divide Fractions

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.

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Unit 5: Area and Volume

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.

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Unit 6: The Coordinate Plane

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.

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