Gizmos for Colorado - Mathematics: 6th Grade (2020 Academic Standards adopted 2018)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

1: Number and Quantity

MA.6.RP.A: Ratios & Proportional Relationships: Understand ratio concepts and use ratio reasoning to solve problems.

MA.6.RP.A.1: Students can: Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

MA.6.RP.A.2: Students can: Apply the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

MA.6.RP.A.3: Students can: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MA.6.NS.A: The Number System: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

MA.6.NS.A.1: Students can: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

MA.6.NS.B: The Number System: Compute fluently with multi-digit numbers and find common factors and multiples.

MA.6.NS.B.2: Students can: Fluently divide multi-digit numbers using the standard algorithm.

MA.6.NS.B.3: Students can: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

MA.6.NS.B.4: Students can: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. 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.

MA.6.NS.C: The Number System: Apply and extend previous understandings of numbers to the system of rational numbers.

MA.6.NS.C.5: Students can: Explain why positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

MA.6.NS.C.6: Students can: Describe a rational number as 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 plane with negative number coordinates.

MA.6.NS.C.7: Students can: Order and find absolute value of rational numbers.

MA.6.NS.C.8: Students can: 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.

2: Algebra and Functions

MA.6.EE.A: Expressions & Equations: Apply and extend previous understandings of arithmetic to algebraic expressions.

MA.6.EE.A.1: Students can: Write and evaluate numerical expressions involving whole-number exponents.

MA.6.EE.A.2: Students can: Write, read, and evaluate expressions in which letters stand for numbers.

MA.6.EE.A.3: Students can: Apply the properties of operations to generate equivalent expressions.

MA.6.EE.A.4: Students can: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

MA.6.EE.B: Expressions & Equations: Reason about and solve one-variable equations and inequalities.

MA.6.EE.B.5: Students can: 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? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

MA.6.EE.B.6: Students can: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

MA.6.EE.B.7: Students can: 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.

MA.6.EE.B.8: Students can: Write an inequality of the form x > c, x is greater than or equal to c, x < c, or x is less than or equal to c to represent a constraint or condition in a real-world or mathematical problem. Show that inequalities of the form x > c, x is greater than or equal to c, x < c, or x is less than or equal to c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

3: Data, Statistics, and Probability

MA.6.SP.A: Statistics & Probability: Develop understanding of statistical variability.

MA.6.SP.A.1: Students can: Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

MA.6.SP.A.2: Students can: Demonstrate that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread, and overall shape.

MA.6.SP.A.3: Students can: 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.

MA.6.SP.B: Statistics & Probability: Summarize and describe distributions.

MA.6.SP.B.4: Students can: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

MA.6.SP.B.5: Students can: Summarize numerical data sets in relation to their context, such as by:

4: Geometry

MA.6.G.A: Geometry: Solve real-world and mathematical problems involving area, surface area, and volume.

MA.6.G.A.1: Students can: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

MA.6.G.A.3: Students can: 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.

MA.6.G.A.4: Students can: 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.

Correlation last revised: 3/30/2026

Colorado - Mathematics: 6th Grade

2020 Academic Standards | Adopted: 2018

1: Number and Quantity

2: Algebra and Functions

3: Data, Statistics, and Probability

4: Geometry