PA 6th Grade Math Curriculum

PA 6th Grade Math Curriculum

• 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
  • What is ratio?
  • Ratios
• 6.RP.A.2Understand 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.
  • Converting among ratios, fractions and decimals
  • Rates
• 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems.
  • Rates with fractions
  • Proportions
• 6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
  • Dividing fractions and mixed numbers
  • Applications of fraction operations
• 6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.
  • Dividing multi-digit numbers
  • Dividing decimals
• 6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  • Adding and subtracting decimals
  • Multiplying decimals
• 6.NS.B.4Find 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.
  • Determining common factors
  • Greatest common factors (GCF)
  • Least common multiple (LCM)
  • Determining common multiples
• 6.NS.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.
  • Introduction to integer addition
• 6.NS.6Understand 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.
  • Adding integers
• 6.NS.7Understand ordering and absolute value of rational numbers.
  • Introduction to integer subtraction
• 6.NS.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
  • Cartesian plane
• 6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.
  • Using exponents to describe numbers
  • Introduction to exponents
• 6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.
  • Writing expressions with variables
  • Evaluating algebraic expressions
• 6.EE.A.3Apply the properties of operations to generate equivalent expressions.
  • Combining like terms
  • Order of operations (PEMDAS)
• 6.EE.A.4Identify when two expressions are equivalent.
  • Equivalent expressions
  • Patterns
• 6.EE.A.5Understand 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?
  • Introduction to linear equations
• 6.EE.B.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
  • Introduction to nonlinear equations
• 6.EE.B.7Solve 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.
  • Special case of linear equations: Horizontal lines
  • Model and solve one-step linear equations: ax = b, x/a = b
  • Solving one - step equations: x + a = b
• 6.EE.B.8Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
  • Express linear inequalities graphically and algebraically
  • Solving one-step linear inequalities
• 6.EE.C.9Use 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.
  • Representing patterns in linear relations
  • Reading linear relation graphs
  • Solving linear equations by graphing
• 6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
  • Area and perimeter of triangles
  • Area and perimeter of rectangles
  • Area and perimeter of parallelograms
• 6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.
  • Introduction to volume
  • Volume of prisms
• 6.G.A.3Draw 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.
  • Draw on coordinate planes
• 6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
  • Surface area of prisms
  • Introduction to surface area of 3-dimensional shapes
  • Nets of 3-dimensional shapes
• 6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
  • Median and mode
• 6.SP.A.2Understand 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.
  • Mean
• 6.SP.A.3Recognize 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.
  • Range and outliers
• 6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • Reading and drawing histograms
  • Reading and drawing bar graphs
  • Box-and-whisker plots and scatter plots
  • Frequency tables and dot plots
• 6.SP.B.5Summarize numerical data sets in relation to their context.
  • Application of averages
  • Advantages and disadvantages of different graphs
  • Misleading graphs
  • Critiquing data presentation