6.RP Ratios & Proportional Relationships
6.RP.A Understand ratio concepts and use ratio reasoning to solve problems
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6.RP.A.1Understand the concept of a ratio and describe ratio relationships between two quantities. -
6.RP.A.2Understand the concept of a unit rate and use rate language in context. -
6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems. -
6.RP.A.3.AMake tables of equivalent ratios, find missing values, and use tables to compare ratios. -
6.RP.A.3.CFind a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent. -
6.RP.A.3.DUse ratio reasoning to convert measurement units; manipulate and transform units appropriately.
6.NS The Number System
6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions
6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples
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6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm. -
6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. -
6.NS.B.4Find the GCF of two whole numbers ≤ 100 and the LCM of two whole numbers ≤ 12. Use the distributive property to express a sum of two whole numbers 1–100.
6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers
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6.NS.C.5Understand that positive and negative numbers describe quantities having opposite directions or values; use them in real-world contexts. -
6.NS.C.6Understand a rational number as a point on the number line. Extend number line and coordinate axes to represent negative numbers. -
6.NS.C.6.ARecognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. -
6.NS.C.6.BUnderstand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. -
6.NS.C.6.CFind and position integers and other rational numbers on a number line diagram and coordinate plane. -
6.NS.C.7Understand ordering and absolute value of rational numbers. -
6.NS.C.7.AInterpret statements of inequality as statements about relative position on a number line. -
6.NS.C.7.BWrite, interpret, and explain statements of order for rational numbers in real-world contexts. -
6.NS.C.7.CUnderstand the absolute value of a rational number as its distance from 0 on the number line. -
6.NS.C.7.DDistinguish comparisons of absolute value from statements about order. -
6.NS.C.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use absolute value to find distances between points.
6.EE Expressions & Equations
6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions
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6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents. -
6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers. -
6.EE.A.2.AWrite expressions that record operations with numbers and with letters standing for numbers. -
6.EE.A.2.BIdentify 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. -
6.EE.A.2.CEvaluate expressions at specific values of their variables, including expressions arising from formulas. Perform arithmetic operations in the conventional order. -
6.EE.A.3Apply the properties of operations to generate equivalent expressions. -
6.EE.A.4Identify when two expressions are equivalent.
6.EE.B Reason about and solve one-variable equations and inequalities
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6.EE.B.5Understand solving an equation or inequality as a process of finding which values from a specified set make the equation or inequality true. -
6.EE.B.6Use variables to represent numbers and write expressions when solving real-world or mathematical problems. -
6.EE.B.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for nonnegative rational numbers. -
6.EE.B.8Write an inequality of the form x > c or x < c to represent a constraint or condition. Represent solutions on number line diagrams.
6.EE.C Represent and analyze quantitative relationships between dependent and independent variables
6.SP Statistics & Probability
6.SP.A Develop understanding of statistical variability
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6.SP.A.1Recognize a statistical question as one that anticipates variability in the data. -
6.SP.A.2Understand that a set of data has a distribution which can be described by its center, spread, and overall shape. -
6.SP.A.3Recognize that a measure of center summarizes all values with a single number, while a measure of variation describes how values vary.
6.SP.B Summarize and describe distributions
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6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots. -
6.SP.B.5Summarize numerical data sets in relation to their context. -
6.SP.B.5.AReport the number of observations. -
6.SP.B.5.BDescribe the nature of the attribute under investigation, including how it was measured and its units of measurement. -
6.SP.B.5.CGive 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. -
6.SP.B.5.DRelate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
6.G Geometry
6.G.A Solve real-world and mathematical problems involving area, surface area, and volume
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6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into known shapes. -
6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths. Apply the formulas V = lwh and V = Bh. -
6.G.A.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side. -
6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find surface area.