Skills available for Colorado sixth-grade math standards
Standards are in bold, followed by a list of the IXL math skills that are aligned to that standards. Students can practice these skills online at www.ixl.com.
6.1.1 Quantities can be expressed and compared using ratios and rates
6.1.1.a Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Write a ratio to describe objects in a picture (6-R.1)
6.1.1.b Apply the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship.
Unit rates and equivalent rates (6-R.7)
6.1.1.c Use ratio and rate reasoning to solve real-world and mathematical problems.
6.1.1.c.i. 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.
Identify equivalent ratios (6-R.3)
Ratio tables (6-R.5)
Objects on a coordinate plane (6-X.1)
6.1.1.c.ii. Use tables to compare ratios.
Ratio tables (6-R.5)
Compare ratios: word problems (6-R.8)
6.1.1.c.iii. Solve unit rate problems including those involving unit pricing and constant speed.
Unit rates and equivalent rates (6-R.7)
Unit prices with fractions and decimals (6-V.3)
Unit prices with customary unit conversions (6-V.4)
6.1.1.c.iv. Find a percent of a quantity as a rate per 100.
Percents of numbers and money amounts (6-S.4)
Percents of numbers: word problems (6-S.5)
Unit prices: which is the better buy? (6-V.2)
6.1.1.c.v. Solve problems involving finding the whole, given a part and the percent.
Sale prices: find the original price (7-M.8)
6.1.1.c.vi. Use common fractions and percents to calculate parts of whole numbers in problem situations including comparisons of savings rates at different financial institutions.
Compare percents and fractions: word problems (6-S.3)
Percents of numbers: word problems (6-S.5)
Unit prices: which is the better buy? (6-V.2)
6.1.1.c.vii. Express the comparison of two whole number quantities using differences, part-to-part ratios, and part-to-whole ratios in real contexts, including investing and saving.
Scale drawings: word problems (6-R.12)
Percents of numbers and money amounts (6-S.4)
Percents of numbers: word problems (6-S.5)
6.1.1.c.viii. Use ratio reasoning to convert measurement units.
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)
Unit prices with customary unit conversions (6-V.4)
6.1.2 Formulate, represent, and use algorithms with positive rational numbers with flexibility, accuracy, and efficiency
6.1.2.a Fluently divide multi-digit numbers using the standard algorithm.
Divisibility rules (6-C.1)
Division patterns with zeroes (6-C.2)
Divide numbers ending in zeroes: word problems (6-C.3)
Estimate quotients (6-C.4)
Divide whole numbers - 2-digit divisors (6-C.5)
Divide whole numbers - 3-digit divisors (6-C.6)
Add, subtract, multiply, or divide two whole numbers (6-O.1)
Add, subtract, multiply, or divide two whole numbers: word problems (6-O.2)
6.1.2.b Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Add and subtract decimal numbers (6-G.1)
Add and subtract decimals: word problems (6-G.2)
Estimate sums and differences of decimals (6-G.3)
Maps with decimal distances (6-G.4)
Estimate products of decimal numbers (6-H.1)
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.7)
Add, subtract, multiply, or divide two decimals (6-O.4)
Add, subtract, multiply, or divide two decimals: word problems (6-O.5)
6.1.2.c Find the greatest common factor of two whole numbers less than or equal to 100.
Identify factors (6-E.4)
Greatest common factor (6-E.7)
GCF and LCM: word problems (6-E.9)
6.1.2.d Find the least common multiple of two whole numbers less than or equal to 12.
Least common multiple (6-E.8)
GCF and LCM: word problems (6-E.9)
6.1.2.e 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.
Multiply using the distributive property (6-Y.9)
6.1.2.f Interpret and model quotients of fractions through the creation of story contexts.
Divide fractions and mixed numbers: word problems (6-L.8)
Add, subtract, multiply, or divide two fractions: word problems (6-O.8)
6.1.2.g Compute quotients of fractions.
Divide whole numbers by unit fractions using models (6-L.1)
Divide whole numbers and unit fractions (6-L.3)
Divide fractions (6-L.5)
Estimate quotients when dividing mixed numbers (6-L.6)
Divide fractions and mixed numbers (6-L.7)
Add, subtract, multiply, or divide two fractions (6-O.7)
6.1.2.h Solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Divide whole numbers by unit fractions using models (6-L.1)
Divide fractions and mixed numbers: word problems (6-L.8)
Add, subtract, multiply, or divide two fractions: word problems (6-O.8)
6.1.3 In the real number system, rational numbers have a unique location on the number line and in space
6.1.3.a Explain why positive and negative numbers are used together to describe quantities having opposite directions or values.
6.1.3.a.i. 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)
Compare temperatures above and below zero (6-T.9)
6.1.3.b Use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates.
6.1.3.b.i. Describe a rational number as a point on the number line.
Integers on number lines (6-M.3)
6.1.3.b.ii. Use opposite signs of numbers to indicate locations on opposite sides of 0 on the number line.
Integers on number lines (6-M.3)
Rational numbers: find the sign (6-P.6)
6.1.3.b.iii. Identify that the opposite of the opposite of a number is the number itself.
Integers on number lines (6-M.3)
6.1.3.b.iv. Explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Reflections: graph the image (6-DD.4)
6.1.3.b.v. Find and position integers and other rational numbers on a horizontal or vertical number line diagram.
Decimal number lines (6-F.9)
Integers on number lines (6-M.3)
Graph integers on horizontal and vertical number lines (6-M.4)
6.1.3.b.vi. Find and position pairs of integers and other rational numbers on a coordinate plane.
Objects on a coordinate plane (6-X.1)
Graph points on a coordinate plane (6-X.2)
Coordinate planes as maps (6-X.4)
Translations: graph the image (6-DD.3)
6.1.3.c Order and find absolute value of rational numbers.
6.1.3.c.i. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
Write inequalities from number lines (6-AA.3)
6.1.3.c.ii. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
Compare rational numbers (6-P.1)
Put rational numbers in order (6-P.2)
6.1.3.c.iii. Define the absolute value of a rational number as its distance from 0 on the number line and interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
Absolute value and opposite integers (6-M.2)
Absolute value of rational numbers (6-P.3)
6.1.3.c.iv. Distinguish comparisons of absolute value from statements about order.
Put rational numbers in order (6-P.2)
Absolute value of rational numbers (6-P.3)
6.1.3.d 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.
Objects on a coordinate plane (6-X.1)
Graph points on a coordinate plane (6-X.2)
Coordinate planes as maps (6-X.4)
6.2 Patterns, Functions, and Algebraic Structures
6.2.1 Algebraic expressions can be used to generalize properties of arithmetic
6.2.1.a Write and evaluate numerical expressions involving whole-number exponents.
Write multiplication expressions using exponents (6-D.1)
Evaluate exponents (6-D.2)
Find the missing exponent or base (6-D.3)
Exponents with decimal bases (6-D.4)
Exponents with fractional bases (6-D.5)
6.2.1.b Write, read, and evaluate expressions in which letters stand for numbers.
6.2.1.b.i. Write expressions that record operations with numbers and with letters standing for numbers.
Write variable expressions (6-Y.1)
Write variable expressions: word problems (6-Y.2)
Complete a table for a two-variable relationship (6-BB.5)
Write a two-variable equation (6-BB.6)
6.2.1.b.ii. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) and describe one or more parts of an expression as a single entity.
Identify terms and coefficients (6-Y.6)
6.2.1.b.iii. Evaluate expressions at specific values of their variables including expressions that arise from formulas used in real-world problems.
Write variable expressions: word problems (6-Y.2)
Solve word problems involving two-variable equations (6-BB.4)
6.2.1.b.iv. 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).
6.2.1.c Apply the properties of operations to generate equivalent expressions.
Properties of addition (6-Y.7)
Properties of multiplication (6-Y.8)
Write equivalent expressions using properties (7-R.11)
6.2.1.d Identify when two expressions are equivalent.
Add and subtract like terms (6-Y.13)
Identify equivalent expressions (6-Y.14)
Write equivalent expressions using properties (7-R.11)
6.2.2 Variables are used to represent unknown quantities within equations and inequalities
6.2.2.a Describe 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?
Write variable expressions: word problems (6-Y.2)
Which x satisfies an equation? (6-Z.2)
Solve one-step equations with whole numbers (6-Z.6)
Solve one-step inequalities (6-AA.4)
6.2.2.b 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)
Solutions to inequalities (6-AA.1)
6.2.2.c Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
6.2.2.c.i. Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Convert between Celsius and Fahrenheit (6-T.10)
Write variable expressions: word problems (6-Y.2)
Solve word problems involving two-variable equations (6-BB.4)
6.2.2.d 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.
Write an equation from words (6-Z.3)
Model and solve equations using algebra tiles (6-Z.4)
Write and solve equations that represent diagrams (6-Z.5)
Solve one-step equations with whole numbers (6-Z.6)
Solve one-step equations with decimals, fractions, and mixed numbers (6-Z.7)
6.2.2.e Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
Write inequalities from number lines (6-AA.3)
6.2.2.f Show that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Graph inequalities on number lines (6-AA.2)
Write inequalities from number lines (6-AA.3)
6.2.2.g Represent and analyze quantitative relationships between dependent and independent variables.
6.2.2.g.i. Use variables to represent two quantities in a real-world problem that change in relationship to one another.
Identify independent and dependent variables (6-BB.2)
6.2.2.g.ii. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.
Complete a table for a two-variable relationship (6-BB.5)
Write a two-variable equation (6-BB.6)
6.2.2.g.iii. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Complete a table for a two-variable relationship (6-BB.5)
Identify the graph of an equation (6-BB.7)
6.3 Data Analysis, Statistics, and Probability
6.3.1 Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge
6.3.1.a Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
Identify representative, random, and biased samples (6-HH.5)
6.3.1.b Demonstrate 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.
Create line plots (6-GG.4)
Stem-and-leaf plots (6-GG.18)
6.3.1.c Explain 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.
Calculate mean, median, mode, and range (6-HH.1)
Interpret charts to find mean, median, mode, and range (6-HH.2)
Mean, median, mode, and range: find the missing number (6-HH.3)
6.3.1.d Summarize and describe distributions.
6.3.1.d.i. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Interpret pictographs (6-GG.1)
Create pictographs (6-GG.2)
Create line plots (6-GG.4)
Create and interpret line plots with fractions (6-GG.5)
Create frequency tables (6-GG.6)
Interpret bar graphs (6-GG.7)
Create bar graphs (6-GG.8)
Interpret double bar graphs (6-GG.9)
Create double bar graphs (6-GG.10)
Interpret histograms (6-GG.11)
Create histograms (6-GG.12)
Circle graphs with fractions (6-GG.13)
Interpret line graphs (6-GG.14)
Create line graphs (6-GG.15)
Interpret double line graphs (6-GG.16)
Create double line graphs (6-GG.17)
Stem-and-leaf plots (6-GG.18)
Choose the best type of graph (6-GG.20)
Interpret box-and-whisker plots (7-BB.15)
6.3.1.d.ii. Summarize numerical data sets in relation to their context.
6.3.1.d.ii.1 Reporting the number of observations.
Create frequency tables (6-GG.6)
Create histograms (6-GG.12)
6.3.1.d.ii.2 Describing 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.5)
6.3.1.d.ii.3 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.
Calculate mean, median, mode, and range (6-HH.1)
Interpret charts to find mean, median, mode, and range (6-HH.2)
Mean, median, mode, and range: find the missing number (6-HH.3)
6.3.1.d.ii.4 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.
6.4 Shape, Dimension, and Geometric Relationships
6.4.1 Objects in space and their parts and attributes can be measured and analyzed
6.4.1.a Develop and apply formulas and procedures for area of plane figures.
6.4.1.a.i. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
Area of quadrilaterals (6-FF.5)
6.4.1.a.ii. Apply these techniques in the context of solving real-world and mathematical problems.
Area of quadrilaterals (6-FF.5)
6.4.1.b Develop and apply formulas and procedures for volume of regular prisms.
6.4.1.b.i. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.
Volume of cubes and rectangular prisms (6-FF.14)
Surface area of cubes and rectangular prisms (6-FF.15)
6.4.1.b.ii. Show that volume is the same as multiplying the edge lengths of a rectangular prism.
Volume of cubes and rectangular prisms (6-FF.14)
Surface area of cubes and rectangular prisms (6-FF.15)
6.4.1.b.iii. Apply the formulas V = l w h and V = b h to 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.14)
Surface area of cubes and rectangular prisms (6-FF.15)
6.4.1.c Draw polygons in the coordinate plan to solve real-world and mathematical problems.
6.4.1.c.i. Draw polygons in the coordinate plane given coordinates for the vertices.
Objects on a coordinate plane (6-X.1)
6.4.1.c.ii. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.
Objects on a coordinate plane (6-X.1)
6.4.1.d Develop and apply formulas and procedures for the surface area.
6.4.1.d.i. Represent three-dimensional figures using nets made up of rectangles and triangles.
Nets of three-dimensional figures (6-EE.3)
6.4.1.d.ii. Use nets to find the surface area of figures.
Nets of three-dimensional figures (6-EE.3)
6.4.1.d.iii. Apply techniques for finding surface area in the context of solving real-world and mathematical problems.
Volume of cubes and rectangular prisms (6-FF.14)
Surface area of cubes and rectangular prisms (6-FF.15)