VERMONTTHE GREEN MOUNTAIN STATEVermont VTCAP Grade 6 Math Prep Online Center
Everything Vermont 6th graders need to master the VTCAP math test β practice tests, lessons, worksheets, and step-by-step answer explanations.
Start With a VTCAP Practice Test
Six full, timed Vermont VTCAP Grade 6 math practice tests β 40 questions each, instant scoring, a topic-by-topic breakdown, and full step-by-step solutions. Each one opens right here in a popup. Calculator: Scientific calculator (on part).
VTCAP Practice Test 1
A full diagnostic across every Vermont Grade 6 math topic.
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VTCAP Practice Test 2
Fresh questions and problem types to build accuracy.
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VTCAP Practice Test 3
New problems to add speed and confidence on every skill.
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VTCAP Practice Test 4
Another complete, timed exam to build pacing and stamina.
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VTCAP Practice Test 5
A brand-new mixed set to test your readiness.
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VTCAP Practice Test 6
A final full-length simulation to confirm you are ready.
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Jump into Vermont Grade 6 Math
Vermont Grade 6 Math Study Tools
A few minutes of quick review β flip through flashcards or scan every key formula. Both open right here.
Grade 6 Math Flashcards
Key formulas, vocabulary, and concepts. Flip, shuffle, and track what you know.
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Grade 6 Math Formula Review
Every key Grade 6 formula on one page β ratios, percents, geometry, statistics, and more.
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Vermont Grade 6 Math Skill Quizzes
Short, focused quizzes β pick one skill, answer 10 questions, get instant scoring and full solutions, then jump to the matching lesson. Each opens right here.
Ratios, Rates & Proportions
A quick 10-question check on Ratios, Rates & Proportions with instant scoring and step-by-step solutions.
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Fractions & Decimals
A quick 10-question check on Fractions & Decimals with instant scoring and step-by-step solutions.
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Integers & the Coordinate Plane
A quick 10-question check on Integers & the Coordinate Plane with instant scoring and step-by-step solutions.
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Factors, Multiples & Percents
A quick 10-question check on Factors, Multiples & Percents with instant scoring and step-by-step solutions.
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Expressions, Equations & Inequalities
A quick 10-question check on Expressions, Equations & Inequalities with instant scoring and step-by-step solutions.
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Geometry: Area, Surface Area & Volume
A quick 10-question check on Geometry: Area, Surface Area & Volume with instant scoring and step-by-step solutions.
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Statistics & Data
A quick 10-question check on Statistics & Data with instant scoring and step-by-step solutions.
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Mixed Grade 6 Review
A quick 10-question check on Mixed Grade 6 Review with instant scoring and step-by-step solutions.
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Join students who study with a clearer path
This state grade math hub is part of the Effortless Math library for Vermont VTCAP Grade 6 Math Center. We connect lessons, worksheets, practice tests, books, and tools so students can study with a clearer next step.
Effortless Math is an independent educational publisher. Test names, state exams, standards names, and trademarks are used only to identify the relevant study topic; their owners do not sponsor, endorse, or approve this page.
Vermont VTCAP Grade 6 Math Snapshot
Vermont Grade 6 Math Topics
Student-friendly Grade 6 math skills connected to the Vermont standards β each tagged with its VTCAP standard code and a focused lesson.
VTCAP standard codes
Ratios And Proportional Relationships
The Number System β Fractions
- 6.NS.B.4Simplifying FractionsQuiz
- 6.NS.A.1Adding Fractions with Unlike DenominatorsQuiz
- 6.NS.A.1Subtracting Fractions with Unlike DenominatorsQuiz
- 6.NS.B.3Adding and Subtracting Mixed NumbersQuiz
- 6.NS.A.1Multiplying FractionsQuiz
- 6.NS.B.4Multiplying Mixed NumbersQuiz
- 6.NS.A.1Dividing FractionsQuiz
- 6.NS.A.1Dividing Mixed NumbersQuiz
The Number System β Decimals
- 6.NS.B.3Decimal Place ValueQuiz
- 6.NS.C.7Comparing and Ordering DecimalsQuiz
- 6.NS.B.3Adding and Subtracting DecimalsQuiz
- 6.NS.B.3Multiplying DecimalsQuiz
- 6.NS.B.4Dividing Decimals by Whole NumbersQuiz
- 6.NS.B.3Dividing Decimals by DecimalsQuiz
- 6.NS.A.1Converting Fractions to DecimalsQuiz
- 6.NS.A.1Converting Decimals to FractionsQuiz
The Number System β Integers And The Coordinate Plane
The Number System β Factors And Multiples
Ratios And Percents
Expressions And Equations
- 6.EE.A.2Writing Algebraic ExpressionsQuiz
- 6.EE.A.2Evaluating Algebraic ExpressionsQuiz
- 6.EE.A.2cOrder of OperationsQuiz
- 6.EE.A.4The Distributive PropertyQuiz
- 6.EE.A.3Combining Like TermsQuiz
- 6.EE.B.7Writing Equations from Word ProblemsQuiz
- 6.EE.B.7Solving One-Step Addition and Subtraction EquationsQuiz
- 6.NS.A.1Solving One-Step Multiplication and Division EquationsQuiz
- 6.EE.B.8Writing and Graphing InequalitiesQuiz
- 6.EE.B.8Solving One-Step InequalitiesQuiz
Geometry β Area
Geometry β 3D Figures, Surface Area, And Volume
Best Vermont VTCAP Grade 6 Math Books
Each book has a job: start from scratch, drill weak skills, or build pacing with full tests. All of them pair with the free tools on this page.
Vermont VTCAP Grade 6 Math Made Ridiculously Simple
A step-by-step VTCAP Grade 6 math book that rebuilds every tested skill clearly and in order β built to match the Vermont standards.
- Best starting point for the VTCAP math test
- Pairs with Vermont flashcards and worksheets
- Use it before full timed practice tests
- Organized for students who need examples before drills
πStep-by-step lessons
Short explanations show the move before the student practices it.
βοΈWorked examples
Examples translate VTCAP-style wording into clear math steps.
π―Targeted practice
Rebuild one skill at a time instead of jumping around.
πTest-day bridge
After each topic, connect to formulas, flashcards, and practice questions.
πΊοΈHow to use it
- Read one lesson and copy the worked example.
- Do a short worksheet set on the same topic.
- Review the matching flashcards or formulas.
- Try a mixed quiz and mark every miss.
πPair it with free tools
Choose the right Vermont Grade 6 math book
Vermont VTCAP Grade 6 Math Made Ridiculously Simple
Start here to rebuild VTCAP math from the ground up.
Vermont VTCAP Grade 6 Math Preparation Bundle
The full prep library β study guide, workbook, and practice tests together.
7 Vermont VTCAP Grade 6 Math Practice Tests
Use after topic review to build pacing and test stamina.
Vermont Grade 6 Math Standards
The official Vermont Grade 6 math standards, grouped by domain with the exact code and description for each expectation.
6.RP Β· Ratios & Proportional Relationships
- 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities
- 6.RP.A.2Understand the concept of a unit ratea/bassociated with a ratio a:b withbβ 0, and use rate language in the context of a ratio relationship
- 6.RP.A.3Use 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
- 6.RP.A.3aMake 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. Use tables to compare ratios
- 6.RP.A.3bSolve unit rate problems including those involving unit pricing and constant speed
- 6.RP.A.3cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means30/100times the quantity); solve problems involving finding the whole, given a part and the percent
- 6.RP.A.3dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities
6.NS Β· The Number System
- 6.NS.A.1Interpret 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
- 6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm
- 6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation
- 6.NS.B.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 1β100 with a common factor as a multiple of a sum of two whole numbers with no common factor
- 6.NS.C.5Understand that 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
- 6.NS.C.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.C.6aRecognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., β(β3) = 3, and that 0 is its own opposite
- 6.NS.C.6bUnderstand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes
- 6.NS.C.6cFind and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane
- 6.NS.C.7Understand ordering and absolute value of rational numbers
- 6.NS.C.7aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram
- 6.NS.C.7bWrite, interpret, and explain statements of order for rational numbers in real-world contexts
- 6.NS.C.7cUnderstand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation
- 6.NS.C.7dDistinguish comparisons of absolute value from statements about order
- 6.NS.C.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 first coordinate or the same second coordinate
6.EE Β· Expressions & Equations
- 6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents
- 6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers
- 6.EE.A.2aWrite expressions that record operations with numbers and with letters standing for numbers
- 6.EE.A.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity
- 6.EE.A.2cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 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.EE.A.3Apply the properties of operations to generate equivalent expressions
- 6.EE.A.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them)
- 6.EE.B.5Understand 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
- 6.EE.B.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.B.7Solve real-world and mathematical problems by writing and solving equations of the formx+p=qandpx=qfor cases in whichp,qandxare all nonnegative rational numbers
- 6.EE.B.8Write an inequality of the formx>corx<cto represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the formx>corx<chave infinitely many solutions; represent solutions of such inequalities on number line diagrams
- 6.EE.C.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 Β· Geometry
- 6.G.A.1Find 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
- 6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulasV=l w handV=b hto find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems
- 6.G.A.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 first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems
- 6.G.A.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 Β· Statistics & Probability
- 6.SP.A.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.A.2Understand 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
- 6.SP.A.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.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots
- 6.SP.B.5Summarize numerical data sets in relation to their context, such as by:
- 6.SP.B.5aReporting the number of observations
- 6.SP.B.5bDescribing the nature of the attribute under investigation, including how it was measured and its units of measurement
- 6.SP.B.5cGiving 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
- 6.SP.B.5dRelating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
Standards: Vermont Common Core. Official source β
Vermont VTCAP Grade 6 Math FAQ
What is the VTCAP Grade 6 math test?
The VTCAP (Vermont Comprehensive Assessment Program) is Vermont's Grade 6 mathematics assessment. These free practice tests mirror its format with 40 questions and full solutions.
Can I use a calculator?
A no-calculator section plus a calculator section using an embedded scientific (Desmos) calculator at grade 7.
How long is each practice test?
Each test has a 100-minute timer and auto-submits at 0:00, then shows your score, a topic breakdown, and step-by-step solutions.
Is it free?
Yes β all six tests, lessons, and worksheets are free with no login. 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.
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Make This Your Vermont VTCAP Starting Point
Take a timed practice test, find your weakest topic, and study it with the linked lessons, worksheets, and the VTCAP study guide.