LEARN · PRACTICE · EXPLORE

Utah Grade 6 Math

Utah Grade 6 Math: explore grade-level lessons, worksheets, and learning references. Check the curriculum source and choose practice for your next skill.

Focused lessons · Useful practice · Clear next steps

Standards source: Utah Core Standards, Utah State Board of Education.

Utah Grade 6 Math Skill Quizzes

Short, focused quizzes, pick one skill, answer 10 questions, get instant scoring and full solutions, then jump to the matching lesson. Each opens right here.

Utah RISE Grade 6 Math Snapshot

RISEReadiness Improvement Success Empowerment
6full practice tests
100minute timer each
Scientificcalculator policy

Utah Grade 6: connect practice to a classroom target

Use Utah curriculum source to check the expectation your class is studying. The topic directory provides general lessons; it is not a complete state alignment. These selected learning references give you more precise ideas to compare with an assignment. Common Core-style codes are Common Core references, and other codes come from the existing planning reference. Confirm current state wording and placement before treating either as an official local requirement.

6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every two wings there was one beak." "For every vote candidate A received, candidate C received nearly three votes."
6.NS.1
Interpret and compute quotients of fractions
6.EE.1
Write and evaluate numerical expressions involving whole-number exponents
6.G.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into rectangles, triangles and/or other shapes; apply these techniques in the context of solving real-world and mathematical problems
6.SP.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers

Choose practice from the explanation

Ask the student to explain one of the ideas above with a drawing, model, table, or short calculation. If the explanation is unclear, open the related lesson before assigning a mixed test. If the idea is understood but the calculation is unreliable, choose a focused worksheet and review the strategy afterward.

Keep the classroom target, the resource used, and the next step together in a study note. A topic quiz can guide review; its score is not an official state performance level. Revisit the skill in a new context after a few days.

Utah Grade 6 Math Topics

Student-friendly Grade 6 math skills connected to the Utah standards, each tagged with its RISE standard code and a focused lesson.

RISE standard codes

Utah Grade 6 Math Standards

The official Utah Grade 6 math standards, grouped by domain with the exact code and description for each expectation.

6.RP · Ratios & Proportional Relationships

  • 6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every two wings there was one beak." "For every vote candidate A received, candidate C received nearly three votes."
  • 6.RP.2Understand 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. The following are examples of rate language: "This recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (In sixth grade, unit rates are limited to non-complex fractions.)
  • 6.RP.3Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems

6.NS · The Number System

  • 6.NS.1Interpret and compute quotients of fractions
  • 6.NS.2Fluently divide multi-digit numbers using the standard algorithm
  • 6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation
  • 6.NS.4Find 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 to 100 with a common factor as a multiple of a sum of two whole numbers with no common factor
  • 6.NS.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, 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 zero in each situation
  • 6.NS.6Understand 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
  • 6.NS.7Understand ordering and absolute value of rational numbers
  • 6.NS.8Solve 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 x-coordinate or the same y-coordinate

6.EE · Expressions & Equations

  • 6.EE.1Write and evaluate numerical expressions involving whole-number exponents
  • 6.EE.2Write, read, and evaluate expressions in which letters represent numbers
  • 6.EE.3Apply the properties of operations to generate equivalent expressions
  • 6.EE.4Identify when two expressions are equivalent
  • 6.EE.5Understand solving an equation or inequality as a process of answering the 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
  • 6.EE.6Use 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
  • 6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + a = b and ax = b for cases in which a, b and x are all non-negative rational numbers
  • 6.EE.8Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams
  • 6.EE.9Use variables to represent two quantities in a real-world problem that change in relationship to one another; 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. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation

6.G · Geometry

  • 6.G.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into rectangles, triangles and/or other shapes; apply these techniques in the context of solving real-world and mathematical problems
  • 6.G.2Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (for example, 3½ x 2 x 6), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams.)
  • 6.G.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x coordinate or the same y coordinate. Apply these techniques in the context of solving real-world and mathematical problems
  • 6.G.4Represent 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

6.SP · Statistics & Probability

  • 6.SP.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
  • 6.SP.2Understand that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread/range and overall shape
  • 6.SP.3Recognize 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
  • 6.SP.4Display numerical data in plots on a number line, including dot plots, histograms and box plots. Choose the most appropriate graph/plot for the data collected
  • 6.SP.5Summarize numerical data sets in relation to their context, such as by:

Standards: Utah Core Standards. Official source ↗

Utah RISE Grade 6 Math FAQ

What is the RISE Grade 6 math test?

The RISE (Readiness Improvement Success Empowerment) is Utah's Grade 6 mathematics assessment. The linked activities are independent Grade 6 practice. Their question count, timer, scoring, and item types may differ from the official assessment. Use the directions inside each activity.

Can I use a calculator?

Calculator rules depend on the grade, assessment, test segment, and approved accommodations. Follow the current assessment guidance and ask your school which rules apply. A tool available in independent practice does not establish permission on the official test.

How long is each practice test?

Read the timer and question count shown in the practice activity you open. These are practice settings, not a statement of the official assessment’s duration or scoring.

Is it free?

The linked general practice and topic resources are available separately from optional books. Check each activity’s directions and access requirements. The study guide and bundle are optional next steps.

Grade 6 Math in Other States

Explore Grade 6 math standards, practice tests, and worksheets for every state.

Make This Your Utah RISE Starting Point

Take a timed practice test, find your weakest topic, and study it with the linked lessons, worksheets, and the RISE study guide.

Start a practice test

A USEFUL NEXT STEP

Utah Grade 6 Math: study questions

How should I choose a Grade 6 math study target?

Choose a current classroom target, find the matching learning reference, and use a lesson or available practice resource to check understanding. State documents control local wording and placement; shared reference codes are not a certified crosswalk.

Official source ↗
Are these activities official state assessments?

These are independently published learning resources. A practice score does not predict or replace an official state score. Use the directions in each activity and consult your school for official testing and accommodation rules.

Resources from Effortless Math · Editorial standards