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# Sixth Grade Math

## Ratios and Proportional Relationships

6.RP.1

Intro to Ratios

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.2

Unit Rates and Unit Prices

Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.

6.RP.3.a

Ratio Tables

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.

6.RP.3.b

Unit Rates and Unit Prices

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

6.RP.3.c.i

Percent of a Quantity

Find the part of a whole, given the percent of a quantity.

6.RP.3.c.ii

Percent of a Quantity

Solve for the whole when given a part and the percent.

6.RP.3.d

Using Ratios to Convert Units

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

## The Number System

6.NS.1

Dividing Fractions

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.

6.NS.2

Divide Multi-Digit Numbers

Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3

Operations with Decimals

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.4

Common Multiples & Factors

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.

6.NS.5

Positive and Negative Numbers

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.

6.NS.6.a

Opposites of Numbers

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.

6.NS.6.b

Graphing in the Coordinate Plane

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.

6.NS.6.c

Opposites of Numbers

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.

6.NS.7.c

Absolute Value

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.

6.NS.8

Graphing in the Coordinate Plane

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.

## Expressions and Equations

6.EE.1

Expressions with Exponents

Write and evaluate numerical expressions involving whole-number exponents.

6.EE.2.a

Writing Expressions

Write expressions that record operations with numbers and with letters standing for numbers.

6.EE.2.c

Expressions with Exponents

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

6.EE.3

Equivalent Expressions

Apply the properties of operations to generate equivalent expressions.

6.EE.4

Equivalent Expressions

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

6.EE.6

Writing Expressions

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.

6.EE.7

Solve One Variable Equations

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.

## Statistics and Probability

6.SP.1

Intro to Statistics

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

6.SP.2

Center, Spread and Shape

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.

6.SP.3

Measures of Center and Variation

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.SP.4

Displaying Data

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

6.SP.5.a

Summarizing Data Sets

Reporting the number of observations.

6.SP.5.b

Summarizing Data Sets

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

6.SP.5.c

Summarizing Data Sets

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.

6.SP.5.d

Summarizing Data Sets

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.