Nys Common Core Mathematics Curriculum Answers Grade 6

Skills available for New York sixth-grade math standards

IXL's sixth-grade skills will be aligned to the Next Generation Learning Standards soon! Until then, you can view a complete list of sixth-grade standards below.

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

6.RP Ratios and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems.

  • 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

    • Write a ratio ( 6-R.1 )
    • Write a ratio: word problems ( 6-R.3 )
    • Which model represents the ratio? ( 6-R.4 )

  • 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.

    • Unit rates ( 6-R.9 )

  • 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.

    • 6.RP.3a 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.

      • Identify equivalent ratios ( 6-R.5 )
      • Write an equivalent ratio ( 6-R.6 )
      • Ratio tables ( 6-R.7 )
      • Equivalent ratios: word problems ( 6-R.8 )
      • Ratios and rates: complete a table and make a graph ( 6-R.11 )

    • 6.RP.3b Solve unit rate problems.

      • Compare rates: word problems ( 6-R.14 )
      • Ratios and rates: word problems ( 6-R.15 )
      • Unit prices ( 6-V.2 )

    • 6.RP.3c Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent.

      • What percentage is illustrated? ( 6-S.1 )
      • Understanding percents: strip models ( 6-S.2 )
      • Convert fractions to percents using grid models ( 6-S.3 )
      • Convert between percents, fractions, and decimals ( 6-S.4 )
      • Convert between percents, fractions, and decimals: word problems ( 6-S.5 )
      • Solve percent problems using grid models ( 6-S.8 )
      • Solve percent problems using strip models ( 6-S.9 )
      • Percents of numbers and money amounts ( 6-S.10 )
      • Percents of numbers: word problems ( 6-S.11 )
      • Percents of numbers: fractional and decimal percents ( 6-S.12 )
      • Find what percent one number is of another ( 6-S.13 )
      • Find what percent one number is of another: word problems ( 6-S.14 )
      • Find the total given a part and a percent ( 6-S.15 )
      • Solve percent problems ( 6-S.16 )
      • Solve percent word problems ( 6-S.17 )

    • 6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

      • Convert and compare customary units ( 6-T.3 )
      • Convert, compare, add, and subtract mixed customary units ( 6-T.4 )
      • Customary unit conversions involving fractions and mixed numbers ( 6-T.6 )
      • Convert and compare metric units ( 6-T.7 )
      • Convert between customary and metric systems ( 6-T.8 )

6.NS The Number System

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

  • 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

    • Reciprocals ( 6-L.2 )
    • Divide fractions by whole numbers in recipes ( 6-L.4 )
    • Divide fractions ( 6-L.5 )
    • Divide fractions and mixed numbers ( 6-L.7 )
    • Divide fractions and mixed numbers: word problems ( 6-L.8 )

• Compute fluently with multi-digit numbers and find common factors and multiples.

  • 6.NS.2 Fluently divide multi-digit numbers using a standard algorithm.

    • Division patterns with zeroes ( 6-C.2 )
    • Divide numbers ending in zeroes: word problems ( 6-C.3 )
    • Divide whole numbers - 2-digit divisors ( 6-C.5 )
    • Divide whole numbers - 3-digit divisors ( 6-C.6 )

  • 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.

    • Add and subtract decimal numbers ( 6-G.1 )
    • Add and subtract decimals: word problems ( 6-G.2 )
    • Complete the decimal addition or subtraction sentence ( 6-G.3 )
    • Maps with decimal distances ( 6-G.5 )
    • Multiply decimals ( 6-H.2 )
    • Divide decimals by whole numbers ( 6-H.4 )
    • Divide decimals by whole numbers: word problems ( 6-H.5 )
    • Multiply and divide decimals by powers of ten ( 6-H.6 )
    • Division with decimal quotients ( 6-H.8 )
    • Add, subtract, multiply, or divide two decimals ( 6-O.6 )
    • Add, subtract, multiply, or divide two decimals: word problems ( 6-O.7 )

  • 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100. 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 other than 1. Find the least common multiple of two whole numbers less than or equal to 12.

    • Identify factors ( 6-E.4 )
    • Find all the factor pairs of a number ( 6-E.5 )
    • Greatest common factor ( 6-E.8 )
    • Least common multiple ( 6-E.10 )
    • GCF and LCM: word problems ( 6-E.12 )
    • Factor numerical expressions using the distributive property ( 6-Y. )

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

  • 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

    • Understanding integers ( 6-M.1 )

  • 6.NS.6 Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.

    • 6.NS.6a 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, and that 0 is its own opposite.

      • Understanding opposite integers ( 6-M.4 )
      • Opposites of rational numbers ( 6-P.7 )
      • Rational numbers: find the sign ( 6-P.11 )

    • 6.NS.6b 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.

      • Quadrants ( 6-X.3 )
      • Reflect a point over an axis ( 6-X.4 )

    • 6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane.

      • Decimal number lines ( 6-F.8 )
      • Integers on number lines ( 6-M.2 )
      • Graph integers on horizontal and vertical number lines ( 6-M.3 )
      • Rational numbers on number lines ( 6-P.1 )
      • Objects on a coordinate plane ( 6-X.1 )
      • Graph points on a coordinate plane ( 6-X.2 )

  • 6.NS.7 Understand ordering and absolute value of rational numbers.

    • 6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line.

      • Compare integers ( 6-M.7 )

    • 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

      • Compare and order rational numbers using number lines ( 6-P.3 )
      • Compare rational numbers ( 6-P.4 )
      • Put rational numbers in order ( 6-P.5 )
      • Compare and order rational numbers: word problems ( 6-P.6 )
      • Compare temperatures above and below zero ( 6-T.9 )

    • 6.NS.7c 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.

      • Understanding absolute value ( 6-M.5 )
      • Absolute value ( 6-M.6 )
      • Absolute value and integers: word problems ( 6-M.10 )
      • Absolute value of rational numbers ( 6-P.8 )

    • 6.NS.7d Distinguish comparisons of absolute value from statements about order.

      • Integer inequalities with absolute values ( 6-M.9 )
      • Put rational numbers in order ( 6-P.5 )
      • Absolute value of rational numbers ( 6-P.8 )

  • 6.NS.8 Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

    • Coordinate planes as maps ( 6-X.5 )
    • Distance between two points ( 6-X.6 )
    • Follow directions on a coordinate plane ( 6-X.7 )

6.EE Expressions, Equations, and Inequalities

• Apply and extend previous understandings of arithmetic to algebraic expressions.

  • 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

    • Write multiplication expressions using exponents ( 6-D.1 )
    • Evaluate exponents ( 6-D.2 )
    • Write powers of ten with exponents ( 6-D.3 )
    • Find the missing exponent or base ( 6-D.4 )
    • Exponents with decimal bases ( 6-D.5 )
    • Exponents with fractional bases ( 6-D.6 )

  • 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

    • 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers.

      • Write variable expressions: one operation ( 6-Y.1 )
      • Write variable expressions: two operations ( 6-Y.2 )

    • 6.EE.2b Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor, and quotient); view one or more parts of an expression as a single entity.

      • Identify terms and coefficients ( 6-Y.8 )
      • Sort factors of variable expressions ( 6-Y.9 )

    • 6.EE.2c Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order (Order of Operations).

      • Evaluate numerical expressions one step at a time ( 6-O.3 )
      • Evaluate numerical expressions involving whole numbers ( 6-O.4 )
      • Identify mistakes involving the order of operations ( 6-O.5 )
      • Evaluate numerical expressions involving decimals ( 6-O.8 )
      • Evaluate numerical expressions involving fractions ( 6-O.11 )
      • Convert between Celsius and Fahrenheit ( 6-T.10 )
      • Evaluate variable expressions with whole numbers ( 6-Y.4 )
      • Evaluate multi-variable expressions ( 6-Y.5 )
      • Evaluate variable expressions with decimals, fractions, and mixed numbers ( 6-Y.6 )
      • Evaluate variable expressions: word problems ( 6-Y.7 )

  • 6.EE.3 Apply the properties of operations to generate equivalent expressions.

    • Multiply using the distributive property: area models ( 6-Y.13 )
    • Multiply using the distributive property ( 6-Y.14 )
    • Factor variable expressions: area models ( 6-Y. )
    • Factor variable expressions using the distributive property ( 6-Y.15 )
    • Write equivalent expressions using properties ( 6-Y.17 )

  • 6.EE.4 Identify when two expressions are equivalent.

    • Identify equivalent expressions using strip models ( 6-Y.10 )
    • Identify equivalent expressions I ( 6-Y.19 )
    • Identify equivalent expressions II ( 6-Y.20 )

• Reason about and solve one-variable equations and inequalities.

  • 6.EE.5 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.

    • Does x satisfy an equation? ( 6-Z.1 )
    • Which x satisfies an equation? ( 6-Z.2 )
    • Solutions to inequalities ( 6-AA.1 )

  • 6.EE.6 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.

    • Write variable expressions: word problems ( 6-Y.3 )

  • 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x – p = q; p x = q; and x/p = q for cases in which p, q and x are all nonnegative rational numbers.

    • Model and solve equations using algebra tiles ( 6-Z.5 )
    • Write and solve equations that represent diagrams ( 6-Z.6 )
    • Solve one-step addition and subtraction equations with whole numbers ( 6-Z.7 )
    • Solve one-step multiplication and division equations with whole numbers ( 6-Z.8 )
    • Solve one-step equations with whole numbers ( 6-Z.9 )
    • Solve one-step addition and subtraction equations with decimals and fractions ( 6-Z.10 )
    • Solve one-step multiplication and division equations with decimals and fractions ( 6-Z.11 )
    • Solve one-step addition and subtraction equations: word problems ( 6-Z.12 )
    • Solve one-step multiplication and division equations: word problems ( 6-Z.13 )
    • Write a one-step equation: word problems ( 6-Z.14 )
    • Solve one-step equations: word problems ( 6-Z.15 )

  • 6.EE.8 Write an inequality of the form x > c, x ≥ c, x ≤ c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line.

    • Graph inequalities on number lines ( 6-AA.2 )
    • Write inequalities from number lines ( 6-AA.3 )
    • Write and graph inequalities: word problems ( 6-AA.4 )

• Represent and analyze quantitative relationships between dependent and independent variables.

  • 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify 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.

    • Identify independent and dependent variables in tables and graphs ( 6-BB.2 )
    • Write an equation from a graph using a table ( 6-BB.3 )
    • Identify independent and dependent variables: word problems ( 6-BB.4 )
    • Find a value using two-variable equations ( 6-BB.5 )
    • Find a value using two-variable equations: word problems ( 6-BB.6 )
    • Solve word problems by finding two-variable equations ( 6-BB.7 )
    • Complete a table for a two-variable relationship ( 6-BB.8 )
    • Write a two-variable equation from a table ( 6-BB.9 )
    • Write a two-variable equation ( 6-BB.10 )
    • Identify the graph of an equation ( 6-BB.11 )
    • Complete a table and graph a two-variable equation ( 6-BB.12 )
    • Graph a two-variable equation ( 6-BB.13 )
    • Interpret a graph: word problems ( 6-BB.14 )

6.G Geometry

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

  • 6.G.1 Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.

    • Understanding area of a parallelogram ( 6-FF.3 )
    • Area of parallelograms ( 6-FF.4 )
    • Understanding area of a triangle ( 6-FF.5 )
    • Area of triangles ( 6-FF.6 )
    • Understanding area of a trapezoid ( 6-FF.7 )
    • Area of trapezoids ( 6-FF.8 )
    • Area of rhombuses ( 6-FF.9 )
    • Area of quadrilaterals ( 6-FF.10 )
    • Area of compound figures ( 6-FF.11 )
    • Area of compound figures with triangles ( 6-FF.12 )

  • 6.G.2 Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

    • Volume of cubes and rectangular prisms ( 6-FF.18 )
    • Volume of cubes and rectangular prisms with fractional side lengths ( 6-FF.19 )
    • Volume of cubes and rectangular prisms: word problems ( 6-FF.20 )

  • 6.G.3 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.

    • Area and perimeter of squares and rectangles on the coordinate plane ( 6-X.8 )
    • Graph triangles and quadrilaterals ( 6-CC.8 )

  • 6.G.4 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.

    • Nets of three-dimensional figures ( 6-EE.3 )
    • Surface area of cubes and rectangular prisms ( 6-FF.21 )
    • Surface area of triangular prisms ( 6-FF.23 )
    • Surface area of pyramids ( 6-FF.24 )

  • 6.G.5 Use area and volume models to explain perfect squares and perfect cubes.

6.SP Statistics and Probability

• Develop understanding of statistical variability.

  • 6.SP.1a Recognize that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers.

    • Identify statistical questions ( 6-HH.1 )

  • 6.SP.1b Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

    • Identify representative, random, and biased samples ( 6-HH.11 )

  • 6.SP.1c Understand that the method and sample size used to collect data for a particular question is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions.

  • 6.SP.2 Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

    • Create line plots ( 6-GG.4 )
    • Interpret stem-and-leaf plots ( 6-GG.21 )
    • Create stem-and-leaf plots ( 6-GG.22 )
    • Box plots ( 6-GG.23 )
    • Calculate quartiles and interquartile range ( 6-HH.7 )
    • Describe distributions in line plots ( 6-HH.10 )

  • 6.SP.3 Recognize that a measure of center for a quantitative 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.

    • Mean, median, mode, and range: find the missing number ( 6-HH.4 )

• Summarize and describe distributions.

  • 6.SP.4 Display quantitative data in plots on a number line, including dot plots and histograms.

    • Create line plots ( 6-GG.4 )
    • Create histograms ( 6-GG.15 )
    • Box plots ( 6-GG.23 )

  • 6.SP.5 Summarize quantitative data sets in relation to their context.

    • 6.SP.5a Report the number of observations.

      • Interpret line plots ( 6-GG.3 )
      • Interpret histograms ( 6-GG.14 )

    • 6.SP.5b Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.

      • Identify representative, random, and biased samples ( 6-HH.11 )

    • 6.SP.5c Calculate range and measures of center, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

      • Calculate mean, median, mode, and range ( 6-HH.2 )
      • Interpret charts and graphs to find mean, median, mode, and range ( 6-HH.3 )
      • Calculate mean absolute deviation ( 6-HH.6 )
      • Calculate quartiles and interquartile range ( 6-HH.7 )
      • Identify an outlier and describe the effect of removing it ( 6-HH.9 )
      • Describe distributions in line plots ( 6-HH.10 )

    • 6.SP.5d Relate the range and the choice of measures of center to the shape of the data distribution and the context in which the data were gathered.

• Investigate chance processes and develop, use, and evaluate probability models.

  • 6.SP.6 Understand that the probability of a chance event is a number between 0 and 1 inclusive, that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

    • Understanding probability ( 5-W.13 )
    • Find the probability ( 5-W.14 )
    • Probability of one event ( 6-II.2 )

  • 6.SP.7 Approximate the probability of a simple event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

  • 6.SP.8 Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

    • 6.SP.8a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.

      • Probability of one event ( 6-II.2 )

    • 6.SP.8b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Nys Common Core Mathematics Curriculum Answers Grade 6

Source: https://www.ixl.com/standards/new-york/math/grade-6

Posted by: jenkinsenswer.blogspot.com

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