The Colorado CMAS Grade 5 Math Worksheet Set — 49 Free Printable PDFs to Print and Hand Over

Fifth grade is where math quietly shifts. A student who has spent years adding, subtracting, and memorizing facts is now asked to make sense of decimals to the thousandths, find common denominators on the fly, multiply and divide fractions, measure volume with stacked unit cubes, and plot ordered pairs on a coordinate plane. None of those moves are arithmetic, they are ideas about numbers, and they reward steady, single-skill practice more than long packets.

These 49 worksheets were built to make fifth-grade math walkable, one skill at a time. Whether your fifth grader is in Denver, Colorado Springs, Aurora, or Boulder, each PDF gives them a single idea, a clear example, and enough practice to make it feel ordinary.

What’s on this page

Forty-nine single-skill PDFs, each aligned to the Colorado Mathematics Standards (Common Core-aligned) at Grade 5. Every file does one job. A student practicing decimal division is not also being quizzed on volume, and a student working through line plots is not getting pulled sideways into fractions. One skill, one page of practice, one clear focus.

Each PDF opens with a one-page Quick Review that explains the skill in plain language and walks through a fully worked example. Then come around 14-17 practice problems that build from easy to genuinely challenging, followed by word problems that put the skill in a real situation. The last page is a student-facing answer key, not bare answers, but short, friendly explanations a fifth grader can read alone and actually learn from.

Place Value and Number Sense

• Understanding Place Value, [5.NBT.A.1] name the value of every digit in a multi-digit number
• Multiplying and Dividing by Powers of 10, [5.NBT.A.2] shift the decimal point by 10, 100, or 1,000
• Reading and Writing Decimals to Thousandths, [5.NBT.A.3.A] say and write decimals out to the thousandths place
• Comparing and Ordering Decimals, [5.NBT.A.3.B] line up the place values to compare and order decimals
• Rounding Decimals, [5.NBT.A.4] round to the nearest whole, tenth, hundredth, or thousandth

Operations with Whole Numbers

• Multiplying Multi-Digit Whole Numbers, [5.NBT.B.5] the standard algorithm for multiplying large whole numbers
• Dividing by One-Digit Divisors, [5.NBT.B.6] long division with single-digit divisors
• Dividing by Two-Digit Divisors, [5.NBT.B.6] long division when the divisor has two digits
• Word Problems: Multiplication and Division, [5.NBT.B.6] turn a real situation into a multiplication or division problem

Numerical Expressions and Patterns

• Order of Operations, [5.OA.A.1] PEMDAS, the order that makes every expression have one answer
• Parentheses, Brackets, and Braces, [5.OA.A.1] grouping symbols and how they change the order of work
• Writing and Interpreting Numerical Expressions, [5.OA.A.2] turn a sentence into an expression, and read one back
• Prime Factorization, [4.OA.B.4] break a number down into a product of primes
• Numerical Patterns and Relationships, [5.OA.B.3] spot the rule and continue the pattern

Adding and Subtracting Fractions

• Finding Common Denominators, [5.NF.A.1] rewrite fractions so they share a denominator
• Adding Fractions with Unlike Denominators, [5.NF.A.1] find a common denominator, then add
• Subtracting Fractions with Unlike Denominators, [5.NF.A.1] find a common denominator, then subtract
• Adding and Subtracting Mixed Numbers, [5.NF.A.1] work with the whole and fraction parts, including regrouping
• Estimating with Benchmark Fractions, [5.NF.A.2] use 0, 1/2, and 1 to estimate a fraction sum or difference
• Word Problems: Adding and Subtracting Fractions, [5.NF.A.2] fraction word problems with realistic numbers

Multiplying Fractions

• Fractions as Division, [5.NF.B.3] a fraction is the numerator divided by the denominator
• Multiplying Fractions by Whole Numbers, [5.NF.B.4.A] scale a fraction up using a whole-number multiplier
• Multiplying Fractions by Fractions, [5.NF.B.4.A] multiply across the numerators and across the denominators
• Multiplying Mixed Numbers, [5.NF.B.4] rename as improper fractions, then multiply
• Multiplication as Scaling (Resizing), [5.NF.B.5] multiplying by less than 1 makes a number smaller, and why
• Word Problems: Multiplying Fractions, [5.NF.B.6] fraction-of-a-whole stories you have to set up

Dividing with Unit Fractions

• Dividing Unit Fractions by Whole Numbers, [5.NF.B.7.A] split a unit fraction into a whole number of equal pieces
• Dividing Whole Numbers by Unit Fractions, [5.NF.B.7.B] how many halves, thirds, or fourths fit in a whole number
• Word Problems: Dividing with Unit Fractions, [5.NF.B.7.C] set up a division word problem with unit fractions

Decimal Operations

• Adding Decimals, [5.NBT.B.7] line up the decimal points and add by place value
• Subtracting Decimals, [5.NBT.B.7] line up the decimal points and subtract, regrouping when needed
• Multiplying Decimals, [5.NBT.B.7] multiply like whole numbers, then count decimal places
• Dividing Decimals by Whole Numbers, [5.NBT.B.7] long division when the dividend has a decimal point
• Dividing Decimals by Decimals, [5.NBT.B.7] shift both decimals so the divisor becomes a whole number
• Word Problems with Decimals, [5.NBT.B.7] money, measurement, and other decimal word problems

Measurement and Data

• Converting Customary Units of Length, [5.MD.A.1] inches, feet, yards, miles, and how to switch between them
• Converting Customary Units of Weight and Capacity, [5.MD.A.1] ounces, pounds, cups, pints, quarts, gallons
• Converting Metric Units, [5.MD.A.1] millimeters, centimeters, meters, kilometers, same idea for grams and liters
• Line Plots with Fractions, [5.MD.B.2] graph fractional measurements and read the data

Volume

• Understanding Volume and Unit Cubes, [5.MD.C.3] what volume measures, and how unit cubes fill a solid
• Measuring Volume by Counting Unit Cubes, [5.MD.C.4] count the cubes in layers to find a solid’s volume
• Volume of Rectangular Prisms, [5.MD.C.5.B] length × width × height, and base × height
• Additive Volume (Composite Figures), [5.MD.C.5.C] break a complicated solid into prisms and add the volumes
• Word Problems with Volume, [5.MD.C.5] real-world volume problems with boxes, tanks, and rooms

Geometry and Coordinate Graphing

• Understanding the Coordinate Plane, [5.G.A.1] the x-axis, the y-axis, and how an ordered pair locates a point
• Graphing Points in the First Quadrant, [5.G.A.2] plot points and read coordinates in the first quadrant
• Properties of Two-Dimensional Figures, [5.G.B.3] name the properties that make a shape a shape
• Classifying Two-Dimensional Figures, [5.G.B.4] sort polygons into categories and subcategories
• Graphing Patterns on the Coordinate Plane, [5.OA.B.3] graph two related patterns and compare the lines

How to use these worksheets at home

The trick with fifth-grade math is sequence. Skills here come in families, and a worksheet lands much softer when the one before it set it up. Try Finding Common Denominators before Adding Fractions with Unlike Denominators, once a student is fluent at making the denominators match, the addition page feels like the same problem with one more step. Do Understanding Volume and Unit Cubes before Volume of Rectangular Prisms; the formula stops feeling like a rule to memorize and starts feeling like a description of what’s already happening in the box.

Keep the sessions short. Most of these PDFs take fifteen or twenty minutes, which is about as long as a fifth grader’s full attention lasts on a school night. Two afternoons a week, done steadily, will move a student further than a long Saturday session that nobody enjoys. Let them keep a pencil and scratch paper handy and resist the urge to correct mid-problem, the answer key is there for after.

One more habit worth building: when a worksheet goes well, do the next skill in the same family the following session, while the idea is still warm. When one goes badly, don’t pile on, set it aside and come back to that single page in a few days. A skill that felt impossible on Tuesday often feels merely tricky by Friday, and a fifth grader who experiences that shift a few times starts to trust the process. That trust is worth as much as any single skill on the list.

A note about CMAS at Grade 5

Colorado students take Colorado Measures of Academic Success, Mathematics in spring. CMAS is built on the Colorado Mathematics Standards (Common Core-aligned), the same framework these worksheets are aligned to, so the skills your student practices here and the skills the test asks about come from one source.

At Grade 5, CMAS expects students to read and write decimals to the thousandths, line up the decimal point to add and subtract, multiply and divide multi-digit numbers, find common denominators and operate on fractions (including unit-fraction division), convert measurement units, plot data on line plots, calculate the volume of rectangular prisms (including composite figures), and plot points in the first quadrant of the coordinate plane. Because each PDF on this page targets exactly one of those skills, the testing window doubles as a checklist. If your student is solid on volume but shaky on dividing fractions, you can see it plainly and spend your time only where it is needed.

A short closing

Fifth-grade math is a year of new ideas, but it is not a year a student has to face all at once. Bookmark this page, print one PDF tonight, and let your fifth grader start with a single skill. Colorado kids handle hard things well when the next step is clear, and a worksheet on the table is about as clear as it gets.

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Recommended EffortlessMath Books

For a workbook to pair with these printable practice pages, Mastering Grade 5 Math covers every fifth-grade topic with worked examples and practice sets. For the multi-step word problems and fraction work that fifth graders find hardest, see Mastering Grade 5 Math Word Problems.

Frequently Asked Questions

What math should a 5th grader know?

By the end of fifth grade, a student should add, subtract, multiply and divide decimals to hundredths, add and subtract fractions with unlike denominators, multiply fractions, and find the volume of rectangular prisms. In Colorado these skills come from the Colorado Academic Standards for grade 5. A quick check: can your child solve 2/3 + 1/4 = 11/12 and explain why 12 is the common denominator?

What is covered in 5th grade math?

Colorado fifth-grade math is organized into five areas: operations and algebraic thinking, number and operations in base ten, fractions, measurement and data, and geometry. In practice that means place value to thousandths, decimal and fraction operations, volume, line plots with fractions, and graphing points on a coordinate plane. CMAS questions mix these areas, so short practice in each one helps.

Can 5th graders use calculators?

In class it depends on the teacher and the lesson, but fifth graders are mostly expected to compute by hand. On the CMAS grade 5 math test, calculators are generally not part of the test unless a student has an approved accommodation; check the Colorado Department of Education’s current CMAS guidance. Practicing fraction and decimal work on paper, like 4.8 ÷ 0.6 = 8, is the safest plan.

Can 5th graders do algebra?

Yes, in an early form. Colorado grade 5 standards ask students to write and evaluate numerical expressions with parentheses, like 3 × (8 + 2) = 30, and to describe patterns that follow two rules, then graph the pairs on a coordinate plane. That is the groundwork for variables and equations in middle school, so a fifth grader who is comfortable with order of operations is already thinking algebraically.

What are the Colorado 5th grade math standards?

Colorado’s grade 5 math expectations are part of the Colorado Academic Standards, which are based on the Common Core for math. Key goals include fluent multi-digit multiplication, dividing with two-digit divisors, operations with decimals to hundredths, fraction addition, subtraction and multiplication, dividing with unit fractions, and understanding volume. The full document is on the Colorado Department of Education website.

How do you do 5th grade math worksheets?

Start with the Quick Review page, then work the example with your child before trying problems alone. Do the problems in order, since they get harder, and check each answer against the key right away instead of at the end. For a Colorado fifth grader, one worksheet of about 15 problems in 20 to 30 minutes is a good daily target.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to multiply and divide decimals
• Adding and subtracting fractions with unlike denominators
• How to find the volume of a rectangular prism
• Order of operations (PEMDAS)
• How to solve word problems