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
standard.
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 (Sixth grade - AA.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 (Sixth grade - AA.8)
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.
Coordinate graphs review (Sixth grade - Q.1)
Ratio tables (Sixth grade - AA.2)
Equivalent ratios (Sixth grade - AA.4)
6.1.1.c.ii. Use tables to compare ratios.
Ratio tables (Sixth grade - AA.2)
Compare ratios: word problems (Sixth grade - AA.6)
6.1.1.c.iii. Solve unit rate problems including those involving unit pricing and constant speed.
Unit prices with fractions and decimals (Sixth grade - G.3)
Unit prices with customary unit conversions (Sixth grade - G.4)
Unit rates and equivalent rates (Sixth grade - AA.8)
6.1.1.c.iv. Find a percent of a quantity as a rate per 100.
Unit prices: which is the better buy? (Sixth grade - G.2)
Percents of numbers and money amounts (Sixth grade - AA.14)
Percents of numbers: word problems (Sixth grade - AA.15)
6.1.1.c.v. Solve problems involving finding the whole, given a part and the percent.
Sale prices: find the original price (Seventh grade - L.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.
Unit prices: which is the better buy? (Sixth grade - G.2)
Compare percents and fractions: word problems (Sixth grade - AA.13)
Percents of numbers: word problems (Sixth grade - AA.15)
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 (Sixth grade - AA.10)
Percents of numbers and money amounts (Sixth grade - AA.14)
Percents of numbers: word problems (Sixth grade - AA.15)
6.1.1.c.viii. Use ratio reasoning to convert measurement units.
Unit prices with customary unit conversions (Sixth grade - G.4)
Convert and compare customary units (Sixth grade - Y.3)
Convert, compare, add, and subtract mixed customary units (Sixth grade - Y.4)
Customary unit conversions involving fractions and mixed numbers (Sixth grade - Y.6)
Convert and compare metric units (Sixth grade - Y.7)
Convert between customary and metric systems (Sixth grade - Y.8)
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 (Sixth grade - L.1)
Division patterns with zeroes (Sixth grade - L.2)
Divide numbers ending in zeroes: word problems (Sixth grade - L.3)
Add, subtract, multiply, and divide decimals (Sixth grade - X.4)
Add, subtract, multiply, and divide decimals: word problems (Sixth grade - X.5)
6.1.2.c Find the greatest common factor of two whole numbers less than or equal to 100.
Identify factors (Sixth grade - N.4)
Greatest common factor (Sixth grade - N.7)
GCF and LCM: word problems (Sixth grade - N.9)
6.1.2.d Find the least common multiple of two whole numbers less than or equal to 12.
Least common multiple (Sixth grade - N.8)
GCF and LCM: word problems (Sixth grade - N.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.
Distributive property (Sixth grade - P.19)
6.1.2.f Interpret and model quotients of fractions through the creation of story contexts.
Divide fractions and mixed numbers: word problems (Sixth grade - W.8)
Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Sixth grade - X.7)
6.1.2.g Compute quotients of fractions.
Divide whole numbers by unit fractions using models (Sixth grade - W.1)
Divide fractions (Sixth grade - W.5)
Estimate quotients when dividing mixed numbers (Sixth grade - W.6)
Divide fractions and mixed numbers (Sixth grade - W.7)
Add, subtract, multiply, and divide fractions and mixed numbers (Sixth grade - X.6)
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 (Sixth grade - W.1)
Divide fractions and mixed numbers: word problems (Sixth grade - W.8)
Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Sixth grade - X.7)
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 (Sixth grade - C.1)
Working with temperatures above and below zero (Sixth grade - Y.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 (Sixth grade - C.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 (Sixth grade - C.3)
6.1.3.b.iii. Identify that the opposite of the opposite of a number is the number itself.
Integers on number lines (Sixth grade - C.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 (Sixth grade - Z.18)
6.1.3.b.v. Find and position integers and other rational numbers on a horizontal or vertical number line diagram.
Decimal number lines (Sixth grade - B.9)
Integers on number lines (Sixth grade - C.3)
6.1.3.b.vi. Find and position pairs of integers and other rational numbers on a coordinate plane.
Coordinate graphs review (Sixth grade - Q.1)
Graph points on a coordinate plane (Sixth grade - Q.2)
Coordinate graphs as maps (Sixth grade - Q.3)
Translations: graph the image (Sixth grade - Z.17)
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.
Inequalities on number lines (Sixth grade - P.22)
6.1.3.c.ii. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
Compare rational numbers (Sixth grade - D.1)
Put rational numbers in order (Sixth grade - D.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 (Sixth grade - C.2)
Absolute value of rational numbers (Sixth grade - D.3)
6.1.3.c.iv. Distinguish comparisons of absolute value from statements about order.
Put rational numbers in order (Sixth grade - D.2)
Absolute value of rational numbers (Sixth grade - D.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.
Coordinate graphs review (Sixth grade - Q.1)
Graph points on a coordinate plane (Sixth grade - Q.2)
Coordinate graphs as maps (Sixth grade - Q.3)
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 (Sixth grade - E.1)
Evaluate exponents (Sixth grade - E.2)
Exponents: solve for the variable (Sixth grade - E.3)
Exponents with decimal bases (Sixth grade - E.4)
Exponents with fractional bases (Sixth grade - E.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 to represent word problems (Sixth grade - P.1)
Complete a function table (Sixth grade - P.10)
Write linear functions (Sixth grade - P.11)
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, coefficients, and monomials (Sixth grade - P.16)
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 to represent word problems (Sixth grade - P.1)
Solve word problems involving two-variable equations (Sixth grade - P.3)
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).
Evaluate variable expressions with whole numbers (Sixth grade - P.2)
6.2.1.c Apply the properties of operations to generate equivalent expressions.
Properties of addition (Sixth grade - I.3)
Properties of multiplication (Sixth grade - K.9)
Simplify variable expressions using properties (Seventh grade - Y.3)
6.2.1.d Identify when two expressions are equivalent.
Add and subtract like terms (Sixth grade - P.17)
Simplify variable expressions using properties (Seventh grade - Y.3)
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 to represent word problems (Sixth grade - P.1)
Solve one-step equations with whole numbers (Sixth grade - P.6)
Solve one-step linear inequalities (Sixth grade - P.24)
6.2.2.b Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Solutions to variable inequalities (Sixth grade - P.23)
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.
Write variable expressions to represent word problems (Sixth grade - P.1)
Solve word problems involving two-variable equations (Sixth grade - P.3)
Convert between Celsius and Fahrenheit (Sixth grade - Y.10)
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.
Solve one-step equations with whole numbers (Sixth grade - P.6)
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.
Inequalities on number lines (Sixth grade - P.22)
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.
Inequalities on number lines (Sixth grade - P.22)
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.
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 function table (Sixth grade - P.10)
Write linear functions (Sixth grade - P.11)
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 function table (Sixth grade - P.10)
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 (Sixth grade - S.4)
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.
Stem-and-leaf plots (Sixth grade - R.3)
Create line plots (Sixth grade - R.5)
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 (Sixth grade - S.1)
Interpret charts to find mean, median, mode, and range (Sixth grade - S.2)
Mean, median, mode, and range: find the missing number (Sixth grade - S.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 (Sixth grade - R.1)
Create pictographs (Sixth grade - R.2)
Stem-and-leaf plots (Sixth grade - R.3)
Create line plots (Sixth grade - R.5)
Create frequency tables (Sixth grade - R.7)
Interpret bar graphs (Sixth grade - R.8)
Create bar graphs (Sixth grade - R.9)
Interpret double bar graphs (Sixth grade - R.10)
Create double bar graphs (Sixth grade - R.11)
Create histograms (Sixth grade - R.13)
Circle graphs with fractions (Sixth grade - R.14)
Interpret line graphs (Sixth grade - R.15)
Create line graphs (Sixth grade - R.16)
Interpret double line graphs (Sixth grade - R.17)
Create double line graphs (Sixth grade - R.18)
Choose the best type of graph (Sixth grade - R.20)
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 (Sixth grade - R.7)
Create histograms (Sixth grade - R.13)
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 (Sixth grade - S.4)
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 (Sixth grade - S.1)
Interpret charts to find mean, median, mode, and range (Sixth grade - S.2)
Mean, median, mode, and range: find the missing number (Sixth grade - S.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 (Sixth grade - Z.23)
6.4.1.a.ii. Apply these techniques in the context of solving real-world and mathematical problems.
Area (Sixth grade - Z.23)
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 (Sixth grade - Z.36)
Surface area of cubes and rectangular prisms (Sixth grade - Z.37)
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 (Sixth grade - Z.36)
Surface area of cubes and rectangular prisms (Sixth grade - Z.37)
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 (Sixth grade - Z.36)
Surface area of cubes and rectangular prisms (Sixth grade - Z.37)
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.
Coordinate graphs review (Sixth grade - Q.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.
Coordinate graphs review (Sixth grade - Q.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 3-dimensional figures (Sixth grade - Z.35)
6.4.1.d.ii. Use nets to find the surface area of figures.
Nets of 3-dimensional figures (Sixth grade - Z.35)
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 (Sixth grade - Z.36)
Surface area of cubes and rectangular prisms (Sixth grade - Z.37)