MassachusettsMassachusetts 6th Grade Math Curriculum
Video lessons and practice for every 6th grade math topic. Aligned to the Massachusetts Mathematics Curriculum Framework standards.
Massachusetts 6th Grade Math Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. |
6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. |
6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems. |
6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. |
6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. |
6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. |
6.NS.B.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. |
6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. |
6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. |
6.NS.7 | Understand ordering and absolute value of rational numbers. |
6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. |
6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. |
6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. |
6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. |
6.EE.A.4 | Identify when two expressions are equivalent. |
6.EE.A.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? |
6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. |
6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. |
6.EE.B.8 | Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. |
6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. |
6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. |
6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths. |
6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. |
6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. |
6.SP.A.1 | Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. |
6.SP.A.2 | Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. |
6.SP.A.3 | Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. |
6.SP.B.4 | Display numerical data in plots on a number line, including dot plots, histograms, and box plots. |
6.SP.B.5 | Summarize numerical data sets in relation to their context. |
Massachusetts 6th Grade Math: Key Topics and Skills
In 6th grade, Massachusetts students make a major leap in mathematical thinking. The Massachusetts Mathematics Curriculum Framework introduces concepts that lay the groundwork for algebra, geometry, and data analysis in middle school and beyond. StudyPug covers every standard with clear video lessons and focused practice problems.
Ratios, Rates, and Proportional Reasoning
Students learn to understand and use ratios and unit rates to describe relationships between quantities. They apply ratio and rate reasoning to solve real-world problems, including problems involving percentages and proportional relationships. These skills connect directly to later work in 7th grade proportional reasoning.
The Number System
6th graders extend their number knowledge to include negative numbers and rational numbers. Topics include placing rational numbers on number lines, understanding absolute value, ordering rational numbers, and graphing points in all four quadrants of the coordinate plane. Students also practice fluent division of multi-digit numbers and all four operations with multi-digit decimals.
Expressions and Equations
A major focus of 6th grade math is algebraic thinking. Students write and evaluate numerical expressions with exponents, use variables to represent unknown quantities, apply properties of operations to generate equivalent expressions, and solve one-step equations and inequalities. Understanding the relationship between dependent and independent variables is introduced here.
Geometry
Students find areas of triangles, quadrilaterals, and polygons by composing and decomposing shapes. They calculate volumes of rectangular prisms with fractional edge lengths, draw polygons on the coordinate plane, and use nets to find the surface areas of three-dimensional figures.
Statistics and Probability
6th graders are introduced to statistical thinking — recognizing statistical questions, understanding data distributions, and summarizing data using measures of center (mean, median, mode) and measures of variation. They display data using dot plots, histograms, and box plots.
- Ratios and unit rates
- Fraction division and multi-digit decimal operations
- Integers and rational numbers on the number line
- Coordinate plane graphing in all four quadrants
- Algebraic expressions, equations, and inequalities
- Area, volume, and surface area
- Statistical questions, data displays, and data summaries
StudyPug video lessons walk through each of these topics step by step, making it easy for Massachusetts students to follow along, practice, and build lasting understanding.