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Grade 5 Math Lessons & Practice
Build Grade 5 skills in fractions, decimals, volume and the coordinate plane. Choose a topic lesson or skill quiz, then use practice to decide what to review next.
Fractions · Decimals · Volume
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Grade 5 Math Practice Tests
Choose a Grade 5 practice activity, then use the topics behind your missed questions to plan review. Check each activity’s directions for its timer, question count and calculator settings. These independent practice activities are separate from your state or school assessment.
Common Core Practice Test 1
Use a mixed practice set to find topics for review.
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Common Core Practice Test 2
Use another practice set after reviewing your missed topics.
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Common Core Practice Test 3
Check whether you can apply a reviewed method in mixed practice.
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Common Core Practice Test 4
Practice working through a set at a steady pace.
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Common Core Practice Test 5
Review a mixed set and note any recurring errors.
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Common Core Practice Test 6
Use your results to choose the next lesson or review session.
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Common Core Grade 5 Math Study Tools
Review a concept with the flashcards or formula sheet below. Then choose the same skill in the free Grade 5 worksheet collection for printable practice. Both review tools open right here.
Grade 5 Math Flashcards
Key formulas, vocabulary, and concepts. Flip, shuffle, and track what you know.
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Grade 5 Math Formula Review
Review expressions, decimals, fractions, volume and coordinate graphs, then return to the matching topic lesson.
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Common Core Grade 5 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.
Expressions & Patterns
A quick 10-question check on Expressions & Patterns with instant scoring and step-by-step solutions.
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Place Value & Decimals
A quick 10-question check on Place Value & Decimals with instant scoring and step-by-step solutions.
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Adding & Subtracting Fractions
A quick 10-question check on Adding & Subtracting Fractions with instant scoring and step-by-step solutions.
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Multiplying Fractions
A quick 10-question check on Multiplying Fractions with instant scoring and step-by-step solutions.
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Dividing Fractions
A quick 10-question check on Dividing Fractions with instant scoring and step-by-step solutions.
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Measurement & Line Plots
A quick 10-question check on Measurement & Line Plots with instant scoring and step-by-step solutions.
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Volume
A quick 10-question check on Volume with instant scoring and step-by-step solutions.
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Geometry & the Coordinate Plane
A quick 10-question check on Geometry & the Coordinate Plane with instant scoring and step-by-step solutions.
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Mixed Grade 5 Review
A quick 10-question check on Mixed Grade 5 Review with instant scoring and step-by-step solutions.
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Curriculum reference: Common Core Grade 5 mathematics overview. Use the general learning progression to plan math review. Your state’s current curriculum and classroom assignments determine local expectations.
Common Core Grade 5 Math Topics
Student-friendly Grade 5 math skills connected to the Common Core standards, each tagged with its Common Core standard code and a focused lesson.
Operations & Algebraic Thinking
- 5.OAUsing Parentheses, Brackets, and Braces in Numerical ExpressionsWorksheetsQuiz
- 5.OAEvaluating Numerical ExpressionsWorksheetsQuiz
- 5.OAWriting Simple Expressions from Verbal StatementsWorksheetsQuiz
- 5.OAInterpreting Numerical ExpressionsWorksheetsQuiz
- 5.OAComparing Expressions Without CalculatingWorksheetsQuiz
- 5.OAPatterns in the Number of Zeros in ProductsWorksheetsQuiz
- 5.OAPatterns in Decimal PlacementWorksheetsQuiz
- 5.OAUsing Patterns to Explain Repeated ReasoningWorksheetsQuiz
- 5.OAOrdered Pairs from Number PatternsWorksheetsQuiz
- 5.OAGraphing Number Patterns on the Coordinate PlaneWorksheetsQuiz
- 5.OAAnalyzing Relationships Between Two Numerical PatternsWorksheetsQuiz
Place Value, Decimals & Whole-Number Operations
- 5.NBTPowers of 10WorksheetsQuiz
- 5.NBTUnderstanding Place Value Through the ThousandthsWorksheetsQuiz
- 5.NBTReading and Writing DecimalsWorksheetsQuiz
- 5.NBTComparing DecimalsWorksheetsQuiz
- 5.NBTRounding DecimalsWorksheetsQuiz
- 5.NBTMultiplying Whole Numbers by Powers of 10WorksheetsQuiz
- 5.NBTDividing Whole Numbers by Powers of 10WorksheetsQuiz
- 5.NBTMultiplying Decimals by Powers of 10WorksheetsQuiz
- 5.NBTDividing Decimals by Powers of 10WorksheetsQuiz
- 5.NBTMulti-Digit Whole-Number MultiplicationWorksheetsQuiz
- 5.NBTWhole-Number Division with Two-Digit DivisorsWorksheetsQuiz
- 5.NBTAdding Decimals to HundredthsWorksheetsQuiz
- 5.NBTSubtracting Decimals to HundredthsWorksheetsQuiz
- 5.NBTMultiplying and Dividing with Decimal ReasoningWorksheetsQuiz
- 5.NBTSolving Word Problems with Whole Numbers and DecimalsWorksheetsQuiz
Fractions as Numbers (Addition & Subtraction)
- 5.NFUnderstanding Equivalent FractionsWorksheetsQuiz
- 5.NFFinding Common DenominatorsWorksheetsQuiz
- 5.NFAdding Fractions with Unlike DenominatorsWorksheetsQuiz
- 5.NFSubtracting Fractions with Unlike DenominatorsWorksheetsQuiz
- 5.NFAdding Mixed NumbersWorksheetsQuiz
- 5.NFSubtracting Mixed NumbersWorksheetsQuiz
- 5.NFEstimating Fraction Sums and DifferencesWorksheetsQuiz
- 5.NFSolving Word Problems with Fraction Addition and SubtractionWorksheetsQuiz
Multiplying Fractions
- 5.NFMultiplying a Fraction by a Whole NumberWorksheetsQuiz
- 5.NFMultiplying a Fraction by a FractionWorksheetsQuiz
- 5.NFMultiplying Mixed NumbersWorksheetsQuiz
- 5.NFUsing Area Models to Multiply FractionsWorksheetsQuiz
- 5.NFUnderstanding Fraction Products as ScalingWorksheetsQuiz
- 5.NFComparing the Size of ProductsWorksheetsQuiz
- 5.NFReal-World Problems with Fraction MultiplicationWorksheetsQuiz
Dividing Fractions
- 5.NFDividing Unit Fractions by Whole NumbersWorksheetsQuiz
- 5.NFDividing Whole Numbers by Unit FractionsWorksheetsQuiz
- 5.NFUsing Visual Models for Fraction DivisionWorksheetsQuiz
- 5.NFWriting Equations for Fraction DivisionWorksheetsQuiz
- 5.NFSolving Real-World Problems with Fraction DivisionWorksheetsQuiz
Measurement & Line Plots
Volume
- 5.MDUnderstanding Volume as an Attribute of Solid FiguresWorksheetsQuiz
- 5.MDUnit Cubes and Counting VolumeWorksheetsQuiz
- 5.MDFinding Volume with MultiplicationWorksheetsQuiz
- 5.MDVolume of Rectangular PrismsWorksheetsQuiz
- 5.MDVolume Formulas \(V = l times w times h\) and \(V = B times h\)WorksheetsQuiz
- 5.MDFinding Missing Dimensions from VolumeWorksheetsQuiz
- 5.MDAdditive Volume of Composite Solid FiguresWorksheetsQuiz
- 5.MDSolving Real-World Problems Involving VolumeWorksheetsQuiz
Geometry & The Coordinate Plane
- 5.GThe First Quadrant of the Coordinate PlaneWorksheetsQuiz
- 5.GPlotting Points with Ordered PairsWorksheetsQuiz
- 5.GInterpreting Points in Real-World and Mathematical ContextsWorksheetsQuiz
- 5.GUnderstanding Attributes of Two-Dimensional FiguresWorksheetsQuiz
- 5.GClassifying Quadrilaterals in a HierarchyWorksheetsQuiz
- 5.GClassifying Triangles by PropertiesWorksheetsQuiz
- 5.GUsing Venn Diagrams to Classify FiguresWorksheetsQuiz
Best Common Core Grade 5 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.
Common Core Grade 5 Math Made Ridiculously Simple
A Grade 5 math study guide for topic review and practice. Compare its contents with your child’s classwork and the skills they need to review.
- Structured Grade 5 topic review
- Pairs with Common Core flashcards and worksheets
- Use it before full timed practice tests
- Organized for students who need examples before drills
Step-by-step lessons
Short explanations show the move before the student practices it.
✍Worked examples
Examples connect the explanation to the steps in a math problem.
Targeted practice
Rebuild one skill at a time instead of jumping around.
Test-day bridge
After each topic, connect to formulas, flashcards, and practice questions.
How 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.
Choose the right Common Core Grade 5 math book
Common Core Grade 5 Math Made Ridiculously Simple
Start here to rebuild Common Core math from the ground up.
The Ultimate Middle School Math Bundle
This bundle covers Grades 6–8. Choose a Grade 5 title for current-grade review; consider this option when planning ahead.
Common Core Mathematics Workbook For Grade 5: Step-By-Step Guide to Preparing for the Common Core Math Test 2019
Repeated practice by topic when a student needs more reps.
7 Common Core Grade 5 Math Practice Tests
Use after topic review to build pacing and test stamina.
Common Core Grade 5 Math Standards
The official Common Core Grade 5 math standards, grouped by domain with the exact code and description for each expectation.
5.OA · Operations & Algebraic Thinking
- 5.OA.AWrite and interpret numerical expressions
- 5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols
- 5.OA.A.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them
- 5.OA.BAnalyze patterns and relationships
- 5.OA.B.3Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane
5.NBT · Number & Operations in Base Ten
- 5.NBT.AUnderstand the place value system
- 5.NBT.A.1Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left
- 5.NBT.A.2Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10
- 5.NBT.A.3Read, write, and compare decimals to thousandths
- 5.NBT.A.3aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)
- 5.NBT.A.3bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons
- 5.NBT.A.4Use place value understanding to round decimals to any place
- 5.NBT.BPerform operations with multi-digit whole numbers and with decimals to hundredths
- 5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm
- 5.NBT.B.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
- 5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used
5.NF · Number & Operations, Fractions
- 5.NF.AUse equivalent fractions as a strategy to add and subtract fractions
- 5.NF.A.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators
- 5.NF.A.2Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers
- 5.NF.BApply and extend previous understandings of multiplication and division to multiply and divide fractions
- 5.NF.B.3Interpret a fraction as division of the numerator by the denominator (a/b=a÷b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem
- 5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction
- 5.NF.B.4aInterpret the product (a/b) ×qasaparts of a partition ofqintobequal parts; equivalently, as the result of a sequence of operationsa×q÷b
- 5.NF.B.4bFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas
- 5.NF.B.5Interpret multiplication as scaling (resizing), by:
- 5.NF.B.5aComparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication
- 5.NF.B.5bExplaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalencea/b=(n × a)/(n × b)to the effect of multiplyinga/bby 1
- 5.NF.B.6Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem
- 5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions
- 5.NF.B.7aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients
- 5.NF.B.7bInterpret division of a whole number by a unit fraction, and compute such quotients
- 5.NF.B.7cSolve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem
5.MD · Measurement & Data
- 5.MD.AConvert like measurement units within a given measurement system
- 5.MD.A.1Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems
- 5.MD.BRepresent and interpret data
- 5.MD.B.2Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4,1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
- 5.MD.CGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition
- 5.MD.C.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement
- 5.MD.C.3aA cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume
- 5.MD.C.3bA solid figure which can be packed without gaps or overlaps usingnunit cubes is said to have a volume ofncubic units
- 5.MD.C.4Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units
- 5.MD.C.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume
- 5.MD.C.5aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication
- 5.MD.C.5bApply the formulasV=l×w×handV=b×hfor rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems
- 5.MD.C.5cRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems
5.G · Geometry
- 5.G.AGraph points on the coordinate plane to solve real-world and mathematical problems
- 5.G.A.1Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)
- 5.G.A.2Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation
- 5.G.BClassify two-dimensional figures into categories based on their properties
- 5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category
- 5.G.B.4Classify two-dimensional figures in a hierarchy based on properties
Standards: Michigan Academic Standards. Official source ↗
Common Core Grade 5 Math FAQ
How does Common Core relate to my child’s Grade 5 test?
Common Core is a set of learning standards. Your state or school determines the assessment. This page supports Grade 5 math review with independent lessons and practice; use the state links below to find the relevant learning Online Center.
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 5 Math by State
Choose your state to open its skill targets and available practice resources.
Make This Your Common Core Starting Point
Take a timed practice test, find your weakest topic, and study it with the linked lessons, worksheets, and the Common Core study guide.
Start a practice testA USEFUL NEXT STEP
Grade 5 Math: study questions
What topics should I review in Grade 5 math?
Work on fraction operations, place value and decimals, numerical expressions, measurement, volume, data and coordinate graphs. Choose a matching topic lesson and skill quiz from this page. The state links help you find the relevant learning Online Center.
Official source ↗Are Common Core and a state math test the same thing?
Common Core describes learning standards. Your state or school determines the assessment. The practice activities here are independent review; their settings do not establish official test rules.
Resources from Effortless Math · Editorial standards