Hampton School District
Math Competencies and Standards for Grade 6
THE NUMBER SYSTEM
▪ Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
▪ Apply and extend previous understandings of numbers to the system of rational numbers.
▪ Compute fluently with multi-digit numbers and find common factors and multiples.
▪ Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
▪ Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
▪ 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. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
▪ Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
▪ Fluently divide multi-digit numbers using the standard algorithm.
▪ Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
▪ Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
▪ Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
▪ Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
▪ 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.
▪ Understand ordering and absolute value of rational numbers.
▪ Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
▪ Understand the absolute value of a rational number as its distance from 0 on the number line.
RATIOS AND PROPORTIONAL RELATIONSHIPS
▪ Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.
▪ Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
▪ Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
▪ Understand ratio concepts and use ratio reasoning to solve problems.
▪ Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
▪ Use ratio and rate reasoning to solve real-world and mathematical problems.
▪ Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
EXPRESSIONS AND EQUATIONS
▪ Apply and extend previous understandings of arithmetic to algebraic expressions.
▪ Apply the properties of operations to generate equivalent expressions.
▪ Evaluate expressions at specific values for their variables.
▪ Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
▪ Identify when two expressions are equivalent.
▪ Reason about and solve one-variable equations and inequalities.
▪ Represent and analyze quantitative relationships between dependent and independent variables.
▪ 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? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
▪ Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
▪ Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
▪ Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
▪ Write and evaluate numerical expressions involving whole-number exponents.
▪ Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
▪ Write, read, and evaluate expressions in which letters stand for numbers.
▪ 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. Apply these techniques in the context of solving real-world and mathematical problems.
▪ Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
▪ Find the volume of a right rectangular prism with fractional edge lengths. Apply the formulas V = lwh and V = b*h to find volumes of right rectangular prisms with fractional edge lengths.
▪ Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
▪ Solve real-world and mathematical problems involving area, surface area, and volume.
STATISTICS AND PROBABILITY
▪ Develop understanding of statistical variability. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
▪ Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
▪ 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.
▪ Summarize and describe distributions.
▪ Summarize numerical data sets in relation to their context by describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
▪ Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
▪ Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
▪ Summarize numerical data sets in relation to their context by reporting the number of observations.
▪ Summarize numerical data sets in relation to their context.
▪ 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.
Hampton School District
Math Competencies and Standards for Grade 6
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