Grade 5 Massachusetts End of Year Mixed Math Review

Skills available for Massachusetts sixth-grade math standards

IXL's 6th-course skills volition exist aligned to the Massachusetts Curriculum Frameworks before long! Until so, you can view a complete list of sixth-grade standards below.

Standards are in blackness and IXL math skills are in nighttime light-green. Agree 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

• 6.RP.A Understand ratio and charge per unit concepts and employ ratio and rate reasoning to solve problems.

  • 6.RP.A.1 Understand the concept of a ratio including the distinctions between part:part and part:whole and the value of a ratio; role/function and part/whole. Employ ratio language to describe a ratio relationship between ii quantities.

    • Write a ratio ( 6-R.one )
    • Write a ratio: give-and-take bug ( 6-R.3 )
    • Which model represents the ratio? ( 6-R.iv )

  • 6.RP.A.two Sympathize the concept of a unit charge per unit a/b associated with a ratio a:b with b ≠ 0, and utilise rate language in the context of a ratio relationship, including the utilise of units.

    • Unit of measurement rates ( half-dozen-R.9 )

  • 6.RP.A.3 Use ratio and rate reasoning to solve real-earth and mathematical problems, e.k., past reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

    • six.RP.A.iii.a Brand 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.

      • Place equivalent ratios ( 6-R.v )
      • Write an equivalent ratio ( 6-R.6 )
      • Ratio tables ( 6-R.7 )
      • Equivalent ratios: word bug ( 6-R.8 )
      • Ratios and rates: consummate a tabular array and make a graph ( 6-R.11 )

    • 6.RP.A.3.b Solve unit of measurement rate bug, including those involving unit pricing, and constant speed.

      • Compare rates: give-and-take problems ( six-R.14 )
      • Ratios and rates: word bug ( vi-R.15 )
      • Unit prices ( half-dozen-V.2 )

    • 6.RP.A.iii.c Find a percentage of a quantity as a rate per 100 (e.g., 30% of a quantity ways 30/100 times the quantity); solve problems involving finding the whole, given a office and the percent.

      • What pct is illustrated? ( half dozen-S.1 )
      • Understanding percents: strip models ( half-dozen-S.2 )
      • Convert fractions to percents using grid models ( 6-S.3 )
      • Catechumen between percents, fractions, and decimals ( half-dozen-S.4 )
      • Convert between percents, fractions, and decimals: word bug ( 6-Southward.5 )
      • Solve percent issues using grid models ( half-dozen-S.8 )
      • Solve percentage problems using strip models ( vi-S.9 )
      • Percents of numbers and coin amounts ( 6-S.10 )
      • Percents of numbers: word problems ( 6-Southward.xi )
      • Percents of numbers: fractional and decimal percents ( vi-S.12 )
      • Discover what percentage one number is of another ( vi-Southward.xiii )
      • Notice what percent one number is of some other: word issues ( half-dozen-S.xiv )
      • Find the total given a part and a percent ( 6-South.15 )
      • Solve percent bug ( 6-S.16 )
      • Solve percent word problems ( half dozen-Southward.17 )

    • vi.RP.A.iii.d Use ratio reasoning to convert measurement units within and between measurement systems; dispense and transform units appropriately when multiplying or dividing quantities.

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

    • 6.RP.A.3.e Solve problems that chronicle the mass of an object to its volume.

half-dozen.NS The Number System

• 6.NS.A Utilize and extend previous understandings of multiplication and division to divide fractions by fractions.

  • vi.NS.A.one Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, due east.chiliad., by using visual fraction models and equations to represent the problem.

    • Reciprocals ( 6-L.2 )
    • Divide fractions by whole numbers in recipes ( 6-50.4 )
    • Divide fractions ( 6-Fifty.5 )
    • Separate fractions and mixed numbers ( vi-L.7 )
    • Divide fractions and mixed numbers: give-and-take bug ( 6-L.viii )

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

  • 6.NS.B.2 Fluently carve up multi-digit numbers using the standard algorithm.

    • Partition patterns with zeroes ( half-dozen-C.2 )
    • Divide numbers ending in zeroes: word issues ( 6-C.three )
    • Divide whole numbers - 2-digit divisors ( 6-C.five )
    • Divide whole numbers - 3-digit divisors ( half-dozen-C.6 )

  • 6.NS.B.iii Fluently add together, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each functioning.

    • Add and subtract decimal numbers ( vi-G.1 )
    • Add and subtract decimals: word problems ( 6-Thousand.2 )
    • Consummate the decimal improver or subtraction sentence ( six-M.three )
    • Maps with decimal distances ( half dozen-M.5 )
    • Multiply decimals ( 6-H.2 )
    • Split decimals by whole numbers ( 6-H.4 )
    • Divide decimals by whole numbers: word problems ( half dozen-H.five )
    • Multiply and split up decimals by powers of 10 ( 6-H.6 )
    • Division with decimal quotients ( 6-H.viii )
    • Add, subtract, multiply, or divide two decimals ( 6-O.6 )
    • Add, decrease, multiply, or separate two decimals: word bug ( 6-O.seven )

  • 6.NS.B.4 Use prime factorization to find the greatest common factor of 2 whole numbers less than or equal to 100 and the to the lowest degree common multiple of 2 whole numbers less than or equal to 12. Apply the distributive property to limited a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two relatively prime numbers.

    • Identify factors ( 6-Eastward.iv )
    • Discover all the factor pairs of a number ( half-dozen-E.5 )
    • Greatest common factor ( vi-E.8 )
    • Least mutual multiple ( 6-E.10 )
    • GCF and LCM: word problems ( 6-East.12 )
    • Factor numerical expressions using the distributive property ( 6-Y. )

• six.NS.C Use and extend previous understandings of numbers to the organization of rational numbers.

  • 6.NS.C.5 Sympathize that positive and negative numbers are used together to describe quantities having contrary directions or values (e.g., temperature above/below nothing, tiptop to a higher place/below sea level, credits/debits, and positive/negative electric charge). Apply positive and negative numbers (whole numbers, fractions, and decimals) to stand for quantities in real-world contexts, explaining the pregnant of nil in each situation.

    • Understanding integers ( 6-M.1 )

  • 6.NS.C.six Understand a rational number every bit 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 aeroplane with negative number coordinates.

    • 6.NS.C.6.a Recognize reverse signs of numbers as indicating locations on contrary sides of 0 on the number line; recognize that the opposite of the contrary of a number is the number itself, due east.thousand., –(–3) = 3, and that zilch is its own opposite.

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

    • 6.NS.C.half dozen.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only past signs, the locations of the points are related by reflections across i or both axes.

      • Quadrants ( half dozen-Ten.three )
      • Reverberate a point over an axis ( six-10.iv )

    • 6.NS.C.6.c 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.

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

  • six.NS.C.7 Empathize ordering and accented value of rational numbers.

    • six.NS.C.seven.a Interpret statements of inequality equally statements about the relative positions of two numbers on a number line diagram.

      • Compare integers ( 6-M.7 )

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

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

    • half dozen.NS.C.7.c Empathize the absolute value of a rational number equally its altitude from 0 on the number line; interpret accented value as magnitude for a positive or negative quantity in a real-earth situation.

      • Understanding absolute value ( 6-M.5 )
      • Absolute value ( six-Chiliad.vi )
      • Absolute value and integers: give-and-take problems ( half dozen-M.10 )
      • Absolute value of rational numbers ( 6-P.viii )

    • 6.NS.C.7.d Distinguish comparisons of accented value from statements about guild.

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

  • 6.NS.C.8 Solve existent-globe and mathematical problems by graphing points in all 4 quadrants of the coordinate plane. Include apply of coordinates and absolute value to find distances between points with the same commencement coordinate or the same 2nd coordinate.

    • Coordinate planes as maps ( six-X.5 )
    • Distance between ii points ( half dozen-X.half-dozen )
    • Follow directions on a coordinate plane ( half-dozen-Ten.7 )

6.EE Expressions and Equations

• half dozen.EE.A Utilise and extend previous understandings of arithmetic to algebraic expressions.

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

    • Write multiplication expressions using exponents ( half-dozen-D.ane )
    • Evaluate exponents ( vi-D.two )
    • Write powers of 10 with exponents ( half dozen-D.3 )
    • Detect the missing exponent or base ( 6-D.iv )
    • Exponents with decimal bases ( 6-D.five )
    • Exponents with fractional bases ( 6-D.6 )

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

    • six.EE.A.ii.a Write expressions that record operations with numbers and with letters standing for numbers.

      • Write variable expressions: i operation ( vi-Y.1 )
      • Write variable expressions: two operations ( vi-Y.two )

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

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

    • 6.EE.A.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetics operations, including those involving whole-number exponents, in the conventional order when in that location are no parentheses to specify a particular order (Order of Operations).

      • Evaluate numerical expressions 1 pace at a time ( half dozen-O.3 )
      • Evaluate numerical expressions involving whole numbers ( half-dozen-O.4 )
      • Identify mistakes involving the order of operations ( 6-O.five )
      • Evaluate numerical expressions involving decimals ( 6-O.8 )
      • Evaluate numerical expressions involving fractions ( 6-O.11 )
      • Convert betwixt Celsius and Fahrenheit ( half-dozen-T.ten )
      • Evaluate variable expressions with whole numbers ( 6-Y.four )
      • Evaluate multi-variable expressions ( 6-Y.5 )
      • Evaluate variable expressions with decimals, fractions, and mixed numbers ( half dozen-Y.half-dozen )
      • Evaluate variable expressions: discussion issues ( 6-Y.7 )

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

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

  • 6.EE.A.4 Place when two expressions are equivalent (i.e., when the two expressions name the aforementioned number regardless of which value is substituted into them).

    • Identify equivalent expressions using strip models ( vi-Y.x )
    • Identify equivalent expressions I ( half dozen-Y.19 )
    • Identify equivalent expressions 2 ( 6-Y.20 )

• 6.EE.B Reason near and solve ane-variable equations and inequalities.

  • 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: Which values from a specified gear up, if whatsoever, make the equation or inequality true? Employ substitution to decide whether a given number in a specified ready makes an equation or inequality truthful.

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

  • 6.EE.B.six Apply variables to represent numbers and write expressions when solving a existent-world or mathematical problem; sympathize that a variable tin can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

    • Write variable expressions: word issues ( six-Y.3 )

  • half dozen.EE.B.7 Solve real-globe and mathematical problems by writing and solving equations of the form x + p = q and p x = q for cases in which p, q and x are all nonnegative rational numbers.

    • Model and solve equations using algebra tiles ( vi-Z.5 )
    • Model and solve equations using diagrams ( six-Z. )
    • Write and solve equations that represent diagrams ( 6-Z.6 )
    • Solve ane-stride improver and subtraction equations with whole numbers ( 6-Z.7 )
    • Solve one-step multiplication and sectionalisation equations with whole numbers ( half dozen-Z.viii )
    • Solve one-step equations with whole numbers ( 6-Z.9 )
    • Solve 1-step add-on and subtraction equations with decimals and fractions ( 6-Z.10 )
    • Solve one-footstep multiplication and division equations with decimals and fractions ( 6-Z.11 )
    • Solve one-step improver and subtraction equations: word bug ( half dozen-Z.12 )
    • Solve one-footstep multiplication and division equations: discussion problems ( 6-Z.xiii )
    • Write a one-stride equation: word problems ( vi-Z.14 )
    • Solve ane-step equations: word problems ( 6-Z.15 )

  • 6.EE.B.8 Write an inequality of the grade x > c or x < c to represent a constraint or condition in a existent-world or mathematical problem. Recognize that inequalities of the grade x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

    • Graph inequalities on number lines ( half-dozen-AA.ii )
    • Write inequalities from number lines ( 6-AA.3 )
    • Write and graph inequalities: give-and-take problems ( 6-AA.4 )

• six.EE.C Correspond and analyze quantitative relationships betwixt dependent and independent variables.

  • 6.EE.C.9 Use variables to represent two quantities in a existent-world problem that modify in relationship to one some other; write an equation to limited ane quantity, thought of every bit the dependent variable, in terms of the other quantity, idea of equally the independent variable. Clarify the human relationship betwixt the dependent and contained variables using graphs and tables, and relate these to the equation.

    • Identify independent and dependent variables in tables and graphs ( half dozen-BB.2 )
    • Write an equation from a graph using a table ( 6-BB.3 )
    • Identify independent and dependent variables: word problems ( six-BB.four )
    • Notice a value using two-variable equations ( six-BB.v )
    • Detect a value using 2-variable equations: word problems ( 6-BB.half-dozen )
    • Solve word problems by finding ii-variable equations ( half dozen-BB.seven )
    • Complete a tabular array for a 2-variable relationship ( 6-BB.viii )
    • Write a ii-variable equation from a table ( 6-BB.ix )
    • Write a two-variable equation ( 6-BB.10 )
    • Identify the graph of an equation ( 6-BB.eleven )
    • Consummate a tabular array and graph a 2-variable equation ( 6-BB.12 )
    • Graph a ii-variable equation ( 6-BB.13 )
    • Interpret a graph: word problems ( 6-BB.14 )

half dozen.G Geometry

• 6.G.A Solve real-globe and mathematical problems involving area, surface area, and volume.

  • 6.G.A.ane Detect the expanse of right triangles, other triangles, special quadrilaterals, and polygons past composing into rectangles or decomposing into triangles and other shapes; utilise these techniques in the context of solving real-world and mathematical issues.

    • Understanding area of a parallelogram ( 6-FF.3 )
    • Area of parallelograms ( 6-FF.4 )
    • Agreement area of a triangle ( 6-FF.v )
    • Area of triangles ( six-FF.6 )
    • Understanding surface area of a trapezoid ( half dozen-FF.7 )
    • Area of trapezoids ( 6-FF.8 )
    • Surface area of rhombuses ( vi-FF.ix )
    • Area of quadrilaterals ( 6-FF.x )
    • Area of compound figures ( 6-FF.xi )
    • Area of chemical compound figures with triangles ( six-FF.12 )

  • 6.G.A.two Discover the book of a right rectangular prism with partial edge lengths by packing it with unit cubes of the advisable unit fraction edge lengths, and bear witness that the book is the same equally would be found by multiplying the edge lengths of the prism. Employ the formulas Five =l w h and V = b h to find volumes of correct rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical bug.

    • Book 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 issues ( 6-FF.20 )

  • six.Thousand.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; utilize coordinates to find the length of a side joining points with the same first coordinate or the aforementioned 2nd coordinate. Use these techniques in the context of solving existent-globe and mathematical problems.

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

  • 6.G.A.4 Represent iii-dimensional figures using nets made up of rectangles and triangles, and use the nets to detect the surface areas of these figures. Utilize these techniques in the context of solving existent-world and mathematical problems.

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

6.SP Statistics and Probability

• 6.SP.A Develop understanding of statistical variability.

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

    • Identify statistical questions ( 6-HH.ane )

  • 6.SP.A.two Understand that a set of information collected to answer a statistical question has a distribution, which can be described by its center (median, hateful, and/or style), spread (range, interquartile range), and overall shape.

    • Create line plots ( six-GG.4 )
    • Interpret stem-and-foliage plots ( 6-GG.21 )
    • Create stem-and-leafage plots ( 6-GG.22 )
    • Box plots ( vi-GG.23 )
    • Calculate quartiles and interquartile range ( half dozen-HH.7 )
    • Depict distributions in line plots ( half dozen-HH.10 )

  • 6.SP.A.iii Recognize that a measure out of center for a numerical data fix 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: observe the missing number ( 6-HH.4 )
    • Interpret measures of center and variability ( 6-HH. )

• half-dozen.SP.B Summarize and describe distributions.

  • 6.SP.B.4 Display numerical information in plots on a number line, including dot plots, histograms, and box plots.

    • Create line plots ( six-GG.four )
    • Create histograms ( 6-GG.fifteen )
    • Box plots ( half-dozen-GG.23 )

    • half dozen.SP.B.four.a Read and interpret circumvolve graphs.

      • Interpret circle graphs ( half-dozen-GG.16 )

  • 6.SP.B.5 Summarize numerical data sets in relation to their context, such as past:

    • 6.SP.B.5.a Reporting the number of observations.

      • Translate line plots ( six-GG.3 )
      • Interpret histograms ( half-dozen-GG.14 )

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

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

    • half-dozen.SP.B.five.c Giving quantitative measures of centre (median, and/or mean) and variability (range and/or interquartile range), too as describing whatsoever overall pattern and any striking deviations from the overall blueprint with reference to the context in which the data were gathered.

      • Summate mean, median, style, and range ( 6-HH.2 )
      • Translate charts and graphs to find mean, median, fashion, and range ( 6-HH.3 )
      • Summate mean absolute deviation ( vi-HH.six )
      • Calculate quartiles and interquartile range ( 6-HH.seven )
      • Identify an outlier and describe the effect of removing it ( 6-HH.nine )
      • Depict distributions in line plots ( 6-HH.10 )

    • 6.SP.B.v.d Relating the selection of measures of middle and variability to the shape of the data distribution and the context in which the data were gathered.

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