Grade 6 Math South Dakota Standards

Write and evaluate numerical expressions involving whole-number exponents, including those with parentheses.

Analyze the relationship between the dependent and independent variables in an equation using tables and graphs, relating these to the equation.

Translate verbal descriptions into algebraic expressions and evaluate them for given values.

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient, variable, constant) and view one or more parts of an expression as a single entity.

Evaluate expressions at specific values of their variables, including expressions with whole number exponents and those from formulas in real-world problems. Explain how the structure of an expression affects its value by justifying each step using the order of operations and properties of operations.

Apply properties of operations (distributive, commutative, associative) to generate equivalent expressions.

Use substitution to determine if a given value in a specified set makes an equation or inequality true. Include the following inequality symbols: <, >, ≤, ≥, ≠.

Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.

Write, solve, and graph one-step inequalities in real-world and mathematical problems, involving positive rational numbers and zero.

Understand an equation with two variables as a statement expressing a relationship between two quantities, and recognize that this relationship can often be represented as a function, where one variable depends on the other.

Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing to solve real-world problems.

Find the volume of right rectangular prisms with fractional edge lengths by packing and relate it to multiplication.

Draw polygons in the coordinate plane when given coordinates for the vertices.

Use coordinates to calculate vertical and horizontal distances between points with the same 𝑥𝑥-coordinate or the same 𝑦𝑦-coordinate to solve real-world and mathematical problems.

Construct nets of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid, using the nets to find the surface area of these prisms and pyramids.

Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in realworld and mathematical problems.

Understand that signs of a coordinate pair indicate locations in a quadrant of the coordinate plane, opposite signs indicate reflections across one or both axes.

Use ratio reasoning to convert measurement units within the U.S. Customary and metric measuring systems.

Understand a ratio as a comparison of two quantities.

Solve word problems involving division of fractions by fractions.

Compare rational numbers, using inequalities (<, >, ≤, ≥, ≠) and order on a number line.

Find the greatest common factor of two whole numbers less than or equal to 100.

Find the least common multiple of two whole numbers less than or equal to 12.

Use the distributive property to rewrite the sum of two whole numbers 1-100 using its greatest common factor.

Fluently divide multi-digit numbers using various strategies, including but not limited to the standard algorithm.

Fluently add, subtract, multiply, and divide multi-digit decimals and fractions using various strategies, including but not limited to the standard algorithm.

Classify numbers (integers, fractions, decimals) as rational numbers.

Explain positive and negative integers as being opposite (inverse) values or directions from zero. Also, explain zero as its own opposite.

Understand the meaning of zero in a real-world context.

Understand the absolute value of rational numbers to be its distance from zero on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Determine the absolute value of a rational number by finding its distance from zero on a number line in real-world situations; recognize that the opposite of the opposite of a number is the number itself.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Use visual models (e.g., area models, number lines) to explore and explain why dividing by a fraction is equivalent to multiplying by its reciprocal.

Use visual models (e.g., area models, number lines) to explain, justify, and apply the process of dividing fractions by fractions in real-world contexts.

Write ratios, rates, and unit rates. Determine the units of a unit rate.

Use ratio and rate reasoning to solve real-world and mathematical problems including making ratio tables, solving unit rate problems, and using percentages.

Solve unit rate problems including those involving unit pricing and constant speed.

Find a percent of a quantity as a rate per 100.

Understand the four components of the statistical process (question formulation, data collection, data analysis, interpretation).

Recognize that data sets collected to answer a statistical question can be analyzed by their distributions.

Represent numerical data on a number line, histogram, and box plot.

Interpret a box plot to answer statistical questions about a data set.

Distinguish between a measure of center (mean, medium, and mode) and measure of variation (range and/or mean absolute deviation).

Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.

Determine which measure of center (mean or median) is more appropriate to describe the center of data; justify the choice.

Compare and interpret range and interquartile range (IQR) to describe how data varies in a distribution.

Calculate and interpret the measure of variation (range, interquartile range (IQR), and/or mean absolute deviation) of a numerical data set.

Algebra

Geometry

Measurement

Coordinate Plane System

Rational Numbers

Rational Number Operations

Common Factors and Multiples

Numerical Data

Measures of Center

Statistical and Nonstatistical

Mathematical Fluency

Equations and Inequalities

Conversions

Area, Volume, and Surface Area

Expressions

Ratio and Rates

Measures of Variation

Numbers Concepts and Computations

Proportional Relationships

Statistics and Probability

Write and evaluate numerical expressions involving whole-number exponents (e.g. parentheses, brackets, or braces).

Write, read, and evaluate expressions in which letters stand for numbers.

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.

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. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 +7) as both a single entity and a sum of two terms.

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.

Perform arithmetic operations following the order of operations with and without parentheses, including those involving whole-number exponents.

Apply the properties of operations to generate equivalent expressions with an emphasis on the distributive property.

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Understand solving an equation or inequality is a process in which you determine values from a set that make an 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.

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.

Write an inequality of the form x > c, x ≥ c, x < c or x ≤ c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams.

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. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Find the 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 by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

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.

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.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (¾) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (¾) = 8/9 because ¾ of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many ¾-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length ¾ mi and area ½ square mi?

Fluently divide multi-digit numbers using an algorithm including but not limited to the standard algorithm.

Fluently add, subtract, multiply, and divide multi-digit decimals using an algorithm including but not limited to the standard algorithm for each operation.

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.

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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.

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.

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.

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.

Understand ordering and absolute value of rational numbers.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Distinguish comparisons of absolute value from statements about order.

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 the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For examples, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

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?

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.

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

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.

Recognize that a measure of center (mean and/or median) for a numerical data set summarizes all of its values with a single number, while a measure of variation (such as mean absolute deviation and/or range) summarizes data points' distances from the mean or each other.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context, such as by:

Reporting the number of observations.

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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 were gathered.

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Apply and extend previous understands of numbers to the system of rational numbers.

Represent and analyze quantitative relationships between dependent and independent variables.

The Number System

Standards for Mathematical Practice

Apply and extend previous understandings of numbers to the system of rational numbers.

Statistics and Probability

Understand ratio concepts and use ratio reasoning to solve problems.

Geometry

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Develop understanding of statistical variability.

Reason about and solve one-variable equations and inequalities.

Expressions and Equations

Solve real-world and mathematical problems involved area, surface area, and volume.

Ratios and Proportional Relationships