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Utah Standards

Utah 6th Grade Math Standards

All 37 Utah math standards for 6th grade, each explained in plain English. The official wording is in Utah State Board of Education's document, linked at the end of this page.

37 standards

Mathematical Practices

8 standards
6.MP.1
Analyze what a problem gives and asks, plan a path, keep asking whether the work makes sense, and check answers another way, like testing a ratio table answer with a unit rate.
6.MP.2
Move between real situations and algebra, like writing 4h for 4 hours of pay at h dollars, work with the symbols, then explain what the result means in the situation.
6.MP.3
Use definitions and known facts to make and test claims, like whether two ratios are equivalent, justify conclusions, and question and critique the reasoning of others.
6.MP.4
Apply math to everyday problems, like using a ratio table to scale a recipe, make sensible assumptions, interpret results in context, and revise the model if it falls short.
6.MP.5
Choose tools wisely, like tape diagrams, double number lines, graph paper, calculators, or online resources, knowing what each can and cannot show, and use them to explore ideas.
6.MP.6
Use exact definitions and say what each symbol means, label units and axes, calculate accurately, and round answers to a precision that fits, like money to the cent.
6.MP.7
Look for structure, like seeing 3x + 6 as 3 groups of x + 2 or a polygon as triangles and rectangles, and use it to simplify the work.
6.MP.8
Notice when calculations repeat, like finding unit rates over and over, and turn them into general methods or shortcuts while keeping track of the details.

Ratios and Proportional Relationships

3 standards
6.RP.1
Explain what a ratio is and describe how two quantities relate with ratio language, like for every 3 dogs at the shelter there are 2 cats.
6.RP.2
Explain the unit rate that goes with a ratio and describe it with rate language, like $60 for 12 tickets being $5 per ticket, using simple fractions.
6.RP.3
Solve ratio and rate problems with ratio tables, tape diagrams, and double number lines, covering graphing ratio pairs, unit price, speed, percents, and converting units.

The Number System

8 standards
6.NS.1
Divide fractions by fractions with models, equations, and the link to multiplication, explain what the quotient means, and solve real-world problems, like 1/3-cup servings in 3/4 cup.
6.NS.2
Divide multi-digit numbers with standard long division, quickly and accurately.
Common Core 6.NS.2
6.NS.3
Add, subtract, multiply and divide multi-digit decimals with the standard written method for each.
Common Core 6.NS.3
6.NS.4
Find the greatest common factor of two numbers up to 100 and the least common multiple of two numbers up to 12, and rewrite a sum like 36 + 8 as 4 (9 + 2).
Common Core 6.NS.4
6.NS.5
Use positive and negative numbers for opposite quantities in real life, like temperatures above and below zero or deposits and withdrawals, and explain what zero means in each.
6.NS.6
Place positive and negative numbers on a number line, know that -(-3) = 3, and plot points with negative coordinates in all four quadrants.
Common Core 6.NS.6
6.NS.7
Order positive and negative numbers, like -3 is warmer than -7, and read absolute value as distance from 0, so a balance of -30 is a debt of 30.
Common Core 6.NS.7
6.NS.8
Solve problems by plotting points in all four quadrants, and use coordinates and absolute value to tell how far apart two points are when they share an x- or y-coordinate.

Expressions and Equations

9 standards
6.EE.1
Write and work out expressions with whole-number exponents, like 5³ = 125.
Common Core 6.EE.1
6.EE.2
Write, read, and evaluate expressions with letters for numbers, name parts like terms, factors, and coefficients, and plug values into formulas, following the order of operations with exponents.
6.EE.3
Use the properties of operations to rewrite an expression in an equivalent form, like 3 (2 + x) as 6 + 3x.
Common Core 6.EE.3
6.EE.4
Tell when two expressions are equivalent because they give the same value for any number, like 4x and x + x + x + x.
6.EE.5
See solving an equation or inequality as finding which values from a set make it true, and substitute numbers to check, like testing 2, 3, and 4 in x + 5 > 8.
6.EE.6
Use a letter for an unknown or changing number when writing an expression for a real problem.
Common Core 6.EE.6
6.EE.7
Write and solve one-step equations like x + a = b and ax = b with nonnegative rational numbers to answer real-world and math problems, like 4x = 18.
6.EE.8
Write an inequality like x > 5 for a real condition, know it has infinitely many solutions, and show them on a number line.
Common Core 6.EE.8
6.EE.9
Write an equation for two quantities that change together, like d = 65t for distance and time, and show the relationship in a table and a graph.
Common Core 6.EE.9

Geometry

4 standards
6.G.1
Work out areas of triangles, trapezoids, parallelograms, and other polygons by cutting them into or combining them from rectangles and triangles, including in real-world problems.
6.G.2
Find the volume of a rectangular prism with fractional edges by packing it with unit-fraction cubes, show it matches multiplying the edges, and use V = lwh and V = Bh in problems.
6.G.3
Draw polygons on the coordinate plane from vertex coordinates, and find side lengths between points sharing an x- or y-coordinate, including in real-world problems.
6.G.4
Unfold a 3D shape into a net of rectangles and triangles and use the net to find its surface area.
Common Core 6.G.4

Statistics and Probability

5 standards
6.SP.1
Tell a statistical question, one with varied answers like how old are the students in my school, from one with a single answer.
Common Core 6.SP.1
6.SP.2
Explain that data collected for a statistical question has a distribution described by its center, spread, and overall shape, like most values clustering near 10.
6.SP.3
Know that a measure of center, like the mean or median, sums up a data set in one number, while a measure of spread tells how much the values vary.
Common Core 6.SP.3
6.SP.4
Show numerical data on a number line with dot plots, histograms, and box plots, and choose the plot that fits the data best.
6.SP.5
Summarize a data set in its context, reporting how many values there are, what was measured, the mean or median, the spread and the overall shape.
Common Core 6.SP.5

The official Utah documents

The plain-English lines on this page are EMStudio's own explanations of Utah's standards, not the official wording, which Utah State Board of Education publishes in the documents above. Codes and strand names identify each standard.