6th Grade Math (Massachusetts Curriculum Frameworks)

Ratios and Proportional Relationships (6.RP)

• 6.RP.A.1 Understand ratios (part to part and part to whole) and use ratio language to describe them.
• 6.RP.A.2 Understand a unit rate a/b linked to a ratio a:b (b not 0) and use rate language.
• 6.RP.A.3 Use ratio and rate reasoning with tables, tape diagrams, number lines or equations to solve problems.
  • a. Make tables of equivalent ratios with whole numbers, find missing values, plot the pairs and compare ratios.
  • b. Solve unit rate problems, including unit pricing and constant speed.
  • c. Treat a percent as a rate per 100: find a percent of an amount and the whole from a part and its percent.
  • d. Use ratio reasoning to convert units within and between measurement systems.
  • e. Solve problems linking an object's mass and its volume.

The Number System (6.NS)

• 6.NS.A.1 Divide fractions by fractions and solve word problems about it with visual models and equations.
• 6.NS.B.2 Divide multi-digit whole numbers accurately and efficiently with the standard algorithm.
• 6.NS.B.3 Do all four operations with multi-digit decimals accurately and efficiently using standard methods.
• 6.NS.B.4 Find the GCF of two numbers up to 100 and the LCM of two up to 12, including by prime factorization; know relatively prime numbers.
• 6.NS.C.5 Use positive and negative numbers for opposite quantities in real life and explain what 0 means in each case.
• 6.NS.C.6 Treat rational numbers as points on a number line and extend lines and axes to show negative numbers.
  • a. Read opposite signs as opposite sides of 0; the opposite of the opposite is the number itself and 0 is its own opposite.
  • b. Use signs of coordinates to tell the quadrant and see sign changes as reflections across axes.
  • c. Place integers and other rational numbers on number lines and ordered pairs on the coordinate plane.
• 6.NS.C.7 Order rational numbers and understand their absolute value.
  • a. Read an inequality as a statement about where two numbers sit on a number line.
  • b. Write, interpret and explain orderings of rational numbers in real contexts such as temperatures.
  • c. Understand absolute value as distance from 0 and as the size of a positive or negative quantity.
  • d. Tell comparisons of absolute value apart from statements about order, e.g. with debts.
• 6.NS.C.8 Solve problems by plotting points in all four quadrants, using coordinates and absolute value to find distances on a horizontal or vertical line.

Expressions and Equations (6.EE)

• 6.EE.A.1 Write and evaluate numerical expressions with whole-number exponents.
• 6.EE.A.2 Write, read and evaluate expressions that use letters for numbers.
  • a. Write expressions that record operations using numbers and letters for numbers.
  • b. Name parts of an expression (sum, term, product, factor, quotient, coefficient) and see a part as a single quantity.
  • c. Evaluate expressions and formulas for given values using the order of operations.
• 6.EE.A.3 Use properties of operations to write equivalent expressions.
• 6.EE.A.4 Recognize when two expressions are equivalent whatever number is substituted.
• 6.EE.B.5 Understand solving an equation or inequality as finding values from a set that make it true, using substitution.
• 6.EE.B.6 Use variables for an unknown number or for any number in a set when solving problems.
• 6.EE.B.7 Write and solve equations like x + p = q and px = q (p, q, x non-negative rationals) for problems.
• 6.EE.B.8 Write inequalities x > c or x < c for real-world limits and show their infinitely many solutions on a number line.
• 6.EE.C.9 Use variables for two quantities that change together, write an equation for the dependent one and analyze it with tables and graphs.

Geometry (6.G)

• 6.G.A.1 Find areas of triangles, special quadrilaterals and polygons by composing them into or decomposing them into rectangles and triangles.
• 6.G.A.2 Find volumes of rectangular prisms with fractional edges by packing unit-fraction cubes and by formula.
• 6.G.A.3 Draw polygons on the coordinate plane from vertices and find side lengths of sides with a shared coordinate.
• 6.G.A.4 Use nets made of rectangles and triangles to represent solids and find their surface area.

Statistics and Probability (6.SP)

• 6.SP.A.1 Recognize a statistical question as one that expects variability in the answers.
• 6.SP.A.2 Know a distribution is described by its center (median, mean, mode), spread (range, IQR) and shape.
• 6.SP.A.3 Know a measure of center sums up data with one number, while a measure of variation describes spread.
• 6.SP.B.4 Show numerical data in dot plots, histograms and box plots.
  • a. Read and interpret circle graphs.
• 6.SP.B.5 Describe numerical data sets in a way that fits their context.
  • a. Give the number of observations.
  • b. Describe the attribute studied, how it was measured and its units.
  • c. Give measures of center and of variability (range and/or IQR) and describe overall pattern and deviations.
  • d. Link the choice of center and variability measures to the shape of the data and its context.