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Welcome to the Sixth Grade Math homepage! In sixth grade, students continue to build upon the foundation laid in previous years, focusing on key concepts such as fractions, decimals, and percentages, while also venturing into more complex topics like ratios and proportions. Sixth graders engage with algebraic thinking, exploring variables and basic equations, which sets the stage for more advanced algebraic concepts in the future. Geometry becomes more intricate as sixth graders explore properties of shapes and study area, volume, and surface area. Across all units of study, sixth graders will continue to be challenged to think critically, make real-world connections, and apply problem-solving skills.

- Math
- 6th 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 Sixth Grade Pacing Guide.

In this unit, sixth graders learn to differentiate between different strategies and formulas to calculate the area of various polygons, such as rectangles, triangles, and parallelograms. Students also explore surface area, extending their understanding to three-dimensional shapes like rectangular prisms and cylinders, learning how to calculate the total surface area of these objects.

- Unit 1.1: Explore the meaning of area
- Unit 1.2: Decompose and compose polygons to find area
- Unit 1.3: Find the areas of polygons using decomposing, composing and rearranging, and subtracting
- Unit 1.4: Use the characteristics of a parallelogram to find the area of parallelograms
- Unit 1.5: Use the formula for area to find the area of any parallelogram
- Unit 1.6: Use parallelograms to find the area of triangles, identify base and corresponding height of a triangle
- Unit 1.7: Calculate the area of triangles using the area formula
- Unit 1.8: Use nets to calculate surface area of rectangular prisms
- Unit 1.9: Use nets to calculate surface area of triangular prisms
- Unit 1.10: Use nets to calculate surface area of rectangular and triangular prisms
- Unit 1.11: Explore volume of 3-dimensional figures
- Unit 1.12: Differentiate between volume and surface area

In this unit, students develop a solid understanding of ratios as a way to compare and relate quantities. They learn to express ratios in different forms (such as a:b, a to b, or a/b) and use them to solve various mathematical and real-life problems. Through real-world examples and visual representations, sixth graders gain the ability to interpret and analyze ratios, laying the groundwork for more complex proportional reasoning in higher grades.

- Unit 2.1: Use ratio language and notation to describe an association between two or more quantities
- Unit 2.2: Draw a diagram that represents a ratio and explain what the diagram means
- Unit 2.3: Write equivalent ratios and explain why two ratios are equivalent or not equivalent
- Unit 2.4: Use double number line diagrams to find and represent equivalent ratios
- Unit 2.5: Use equivalent ratios to find unit prices
- Unit 2.6: Use ratios and diagrams to understand how fast things move
- Unit 2.7: Use tables to find equivalent ratios
- Unit 2.8: Solve equivalent ratio problems by finding the rate per 1 in a table
- Unit 2.9: Solve word problems involving equivalent ratios
- Unit 2.10: Apply number lines, tables, and tape diagrams to solve problems about ratios

In this unit, students build on their study of ratios as they delve into the concept of unit rate. Students will discover how unit rate represents the relationship between two different quantities and how to calculate it to make meaningful comparisons. Additionally, they begin their journey into percentages, comprehending that percentages are ratios expressed out of 100 and learning how to convert between fractions, decimals, and percentages.

- Unit 3.1: Reason about ratios and solve problems using tape diagrams
- Unit 3.2: Explore approximate and relative sizes for standard units of length, volume, and weight or mass
- Unit 3.3: Use different units of measure to explore relative size
- Unit 3.4: Convert measurement units using double number lines and tables
- Unit 3.5: Compare speeds and prices by calculating rates per 1
- Unit 3.6: Calculate and use two different unit rates to solve problems
- Unit 3.7: Use unit rates to solve problems involving constant speed
- Unit 3.8: Understand percentages as rates per 100
- Unit 3.9: Use double number lines to calculate percentages
- Unit 3.10: Use tape diagrams to calculate percentages
- Unit 3.11: Relate the benchmark percentages of 10%, 25%, 50%, and 75% to fractions, and solve problems with benchmark percentages
- Unit 3.12: Solve percentage problems using multiplication and division

In this unit, students use models and equations to explore division in the arenas of both fractions and base ten. The unit opens with a thorough exploration of how to divide fractions first with models and pictures and then with equations. Then, students will explore how to use a number of strategies to multiply and divide decimals. Finally, students will use what they know to explore factors and multiples.

- Unit 4.1: Understand division with unit fractions
- Unit 4.2: Divide unit fractions in word problems
- Unit 4.3: Explore division with fractions
- Unit 4.4: Divide fractions in word problems
- Unit 4.5: Calculate sums, differences, and products of decimals in the context of money
- Unit 4.6: Add and subtract decimals
- Unit 4.7: Solve problems involving decimals
- Unit 4.8: Use different methods to find the product of decimals
- Unit 4.9: Use area diagrams to represent and justify how to find the product of two decimals
- Unit 4.10: Use the partial quotients method and the place value chart to divide
- Unit 4.11: Use the long division method to divide
- Unit 4.12: Use long division to divide whole numbers that result in a quotient with a decimal
- Unit 4.13: Divide decimals by whole numbers
- Unit 4.14: Divide decimals by decimal divisors
- Unit 4.15: Find the greatest common factor of two numbers
- Unit 4.16: Find the least common multiple of two numbers
- Unit 4.17: Solve word problems using common multiples and common factors

In this unit, students embark on a comprehensive journey through algebraic concepts. They learn to dissect, combine, and simplify expressions involving integers, fractions, and decimals, thereby strengthening their fluency in mathematical operations. Additionally, students explore the distributive property, laying a crucial foundation for more advanced algebraic manipulation.

- Unit 5.1: Use models to write equations and solve for unknown values
- Unit 5.2: Use given values to see if an equation is true or false
- Unit 5.3: Interpret and solve equations that represent the same situation
- Unit 5.4: Divide using fractions when solving equations in the form of px= q
- Unit 5.5: Create and solve an equation that represents a situation with an unknown amount by writing equations with variables
- Unit 5.6: Use equations to solve problems with percentages
- Unit 5.7: Use diagrams to differentiate between equal and equivalent expressions
- Unit 5.8: Use an area diagram to generate equivalent numerical expressions that are related by the distributive property
- Unit 5.9: Use an area diagram and the distributive property to write equivalent expressions with variables
- Unit 5.10: Use the distributive property to write equivalent expressions with variables
- Unit 5.11: Evaluate and write expressions with exponents that are equal to a given number
- Unit 5.12: Decide if expressions are equal by evaluating expressions and understanding what exponents mean
- Unit 5.13: Use the order of operations to evaluate expressions with exponents, multiplication, division, addition, and subtraction
- Unit 5.14: Evaluate expressions with a variable, an exponent and another operation, and determine whether a given value is a solution to an equation
- Unit 5.15: Create a table, graph, and equations to represent the relationship between quantities in a set of equivalent ratios
- Unit 5.16: Use graphs and equations to show different kinds of relationships involving area, volume, and exponents

In this unit, students learn how to make sense of positive and negative numbers in different situations, like temperature or elevation. They also become familiar with terms like “positive number,” “negative number,” “rational number,” “opposite,” and “absolute value.” They will explore the idea of opposites and absolute value by understanding that the absolute value of a number tells us how far it is from zero on the number line. Towards the end, students practice plotting pairs of positive and negative numbers on a graph, and they figure out how the signs of these numbers relate to where the point is located. They also use these coordinates to find out how far apart two points are horizontally or vertically.

- Unit 6.1: Explore positive and negative numbers
- Unit 6.2: Find absolute value and order rational numbers
- Unit 6.3: Use absolute value and inequalities to compare and interpret rational numbers
- Unit 6.4: Find and plot pairs of rational numbers on a 4-quadrant coordinate plane
- Unit 6.5: Use coordinates to find distances and reflections on the coordinate plane
- Unit 6.6: Plot points on the coordinate plane to make polygons, and solve problems about vertical and horizontal distance between points

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