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### 6.NS The Number System

- 6.NS.1 Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).
- 6.NS.2 Fluently divide multi-digit whole numbers using a standard algorithmic approach.
- 6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.
- 6.NS.4 Find common factors and multiples using two whole numbers.
- 6.NS.4.a Compute the greatest common factor (GCF) of two numbers both less than or equal to 100.
- 6.NS.4.b Compute the least common multiple (LCM) of two numbers both less than or equal to 12.
- 6.NS.4.c Express sums of two whole numbers, each less than or equal to 100, using the distributive property to factor out a common factor of the original addends.

- 6.NS.5 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.
- 6.NS.6 Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane.
- 6.NS.6.a Understand the concept of opposite numbers, including zero, and their relative locations on the number line.
- 6.NS.6.b Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane.
- 6.NS.6.c Recognize when ordered pairs are reflections of each other on the coordinate plane across one axis, both axes, or the origin.
- 6.NS.6.d Plot rational numbers on number lines and ordered pairs on coordinate planes.

- 6.NS.7 Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers.
- 6.NS.7.a Interpret statements using equal to (=) and not equal to (≠).
- 6.NS.7.b Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line.
- 6.NS.7.c Use concepts of equality and inequality to write and to explain real-world and mathematical situations.
- 6.NS.7.d Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to represent real-world situations.
- 6.NS.7.e Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases.

- 6.NS.8 Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers.
- 6.NS.8.a Plot points in all four quadrants to represent the problem.
- 6.NS.8.b Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates.
- 6.NS.8.c Relate finding the distance between two points in a coordinate plane to absolute value using a number line.

- 6.NS.9 Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100.

### 6.RP Ratios and Proportional Relationships

- 6.RP.1 Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole.
- 6.RP.2 Investigate relationships between ratios and rates.
- 6.RP.2.a Translate between multiple representations of ratios (i.e., a/b, a:b, a to b, visual models).
- 6.RP.2.b Recognize that a rate is a type of ratio involving two different units.
- 6.RP.2.c Convert from rates to unit rates.

- 6.RP.3 Apply the concepts of ratios and rates to solve real-world and mathematical problems.
- 6.RP.3.a Create a table consisting of equivalent ratios and plot the results on the coordinate plane.
- 6.RP.3.b Use multiple representations, including tape diagrams, tables, double number lines, and equations, to find missing values of equivalent ratios.
- 6.RP.3.c Use two tables to compare related ratios.
- 6.RP.3.d Apply concepts of unit rate to solve problems, including unit pricing and constant speed.
- 6.RP.3.e Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages.
- 6.RP.3.f Solve one-step problems involving ratios and unit rates (e.g., dimensional analysis).

### 6.EEI Expressions, Equations, and Inequalities

- 6.EEI.1 Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations.
- 6.EEI.2 Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers.
- 6.EEI.2.a Translate between algebraic expressions and verbal phrases that include variables.
- 6.EEI.2.b Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor.
- 6.EEI.2.c Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers.

- 6.EEI.3 Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions.
- 6.EEI.4 Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent.
- 6.EEI.5 Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.
- 6.EEI.6 Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the variable in the context of the situation.
- 6.EEI.7 Write and solve one-step linear equations in one variable involving non-negative rational numbers for real-world and mathematical situations.
- 6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations.
- 6.EEI.8.a Write an inequality of the form x > c or x < c and graph the solution set on a number line.
- 6.EEI.8.b Recognize that inequalities have infinitely many solutions.

- 6.EEI.9 Investigate multiple representations of relationships in real-world and mathematical situations.
- 6.EEI.9.a Write an equation that models a relationship between independent and dependent variables.
- 6.EEI.9.b Analyze the relationship between independent and dependent variables using graphs and tables.
- 6.EEI.9.c Translate among graphs, tables, and equations.

### 6.GM Geometry and Measurement

- 6.GM.1 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.
- 6.GM.2 Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (V = lwh, V = Bh) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems.
- 6.GM.3 Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations.
- 6.GM.3.a Given coordinates of the vertices, draw a polygon in the coordinate plane.
- 6.GM.3.b Find the length of an edge if the vertices have the same x-coordinates or same y-coordinates.

- 6.GM.4 Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problems.

### 6.DS Data Analysis and Statistics

- 6.DS.1 Differentiate between statistical and non-statistical questions.
- 6.DS.2 Use center (mean, median, mode), spread (range, interquartile range, mean absolute value), and shape (symmetrical, skewed left, skewed right) to describe the distribution of a set of data collected to answer a statistical question.
- 6.DS.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.DS.4 Select and create an appropriate display for numerical data, including dot plots, histograms, and box plots.
- 6.DS.5 Describe numerical data sets in relation to their real-world context.
- 6.DS.5.a State the sample size.
- 6.DS.5.b Describe the qualitative aspects of the data (e.g., how it was measured, units of measurement).

- 6.DS.5.c Give measures of center (median, mean).
- 6.DS.5.d Find measures of variability (interquartile range, mean absolute deviation) using a number line.
- 6.DS.5.e Describe the overall pattern (shape) of the distribution.
- 6.DS.5.f Justify the choices for measure of center and measure of variability based on the shape of the distribution.
- 6.DS.5.g Describe the impact that inserting or deleting a data point has on the measures of center (median, mean) for a data set.