New Hampshire NH SAS Grade 4 Math Free Worksheets: Printable Standards-Aligned Practice with Answers

If third-grade math is a set of tools, fourth-grade math is the year a child starts using them on bigger jobs. The numbers grow — into the hundred-thousands and past — and have to be read, rounded, and compared without hesitation. Multiplication is no longer a single recalled fact; it is a procedure with several steps that each have to land correctly. Division begins to leave remainders, and those remainders carry meaning a student has to explain. The work gets longer because the reasoning behind it deepens.

Fractions take a real turn this year. They stop being a picture of a pizza and become numbers with rules of their own — finding equivalents, comparing, adding and subtracting with like denominators, working with mixed numbers, multiplying a fraction by a whole number. The first decimals arrive, alongside angles, area and perimeter, line plots, and multi-step word problems that ask a child to plan first and compute second. It is a foundational year, and it goes best in small, deliberate steps.

These worksheets were built for exactly that pace. Whether your fourth grader is in Manchester, Nashua, Concord, or Dover, each PDF isolates one skill and gives it enough practice to make it stick.

What’s on this page

There are 43 single-skill PDFs on this page, each aligned to the New Hampshire Mathematics Standards at Grade 4. Every file stays on one skill, so a student working on multi-digit multiplication is not also being quizzed on angle types, and a student practicing equivalent fractions is not pulled sideways into decimal place value.

Each PDF opens with a one-page Quick Review that lays out the skill in plain words and works an example through from start to finish. Then come 20 practice problems that rise gradually from easy to harder, followed by 4 word problems that set the skill in a real situation. The final page is a student-facing answer key, written so a fourth grader can check their own work and trace exactly where an answer went off track.

Place Value & Multi-Digit Numbers

• Understanding Place Value Relationships — [4.NBT.A.1] each place is ten times the one to its right
• Reading and Writing Multi-Digit Numbers — [4.NBT.A.2] standard form, word form, and expanded form
• Comparing and Ordering Multi-Digit Numbers — [4.NBT.A.2] use place value and the symbols >, <, and =
• Rounding Multi-Digit Numbers — [4.NBT.A.3] round to any place from tens to hundred-thousands

Multi-Digit Arithmetic

• Adding Multi-Digit Whole Numbers — [4.NBT.B.4] the standard addition algorithm, with regrouping
• Subtracting Multi-Digit Whole Numbers — [4.NBT.B.4] the standard subtraction algorithm, including across zeros
• Multiplying by a One-Digit Number — [4.NBT.B.5] multiply up to four digits by a single digit
• Multiplying Two Two-Digit Numbers — [4.NBT.B.5] the area model and the standard algorithm side by side
• Dividing with Remainders — [4.NBT.B.6] divide and name the leftover as a remainder
• Finding Factors and Multiples — [4.OA.B.4] list every factor of a number and its first multiples
• Prime and Composite Numbers — [4.OA.B.4] exactly two factors means prime; more means composite

Operations & Problem Solving

• Multiplicative Comparisons — [4.OA.A.1] read ‘4 times as many’ as a multiplication statement
• Multiplicative Comparison Word Problems — [4.OA.A.2] solve ‘times as many’ stories with multiplication or division
• Multi-Step Word Problems — [4.OA.A.3] two or more operations in one real-world problem
• Interpreting Remainders — [4.OA.A.3] decide what the leftover means — round up, drop it, or use it
• Number and Shape Patterns — [4.OA.C.5] follow a rule and find the next terms in a pattern

Fractions

• Equivalent Fractions — [4.NF.A.1] the same amount written with different numbers
• Comparing Fractions — [4.NF.A.2] compare fractions with unlike denominators using benchmarks
• Adding Fractions with Like Denominators — [4.NF.B.3a] add the numerators, keep the denominator
• Subtracting Fractions with Like Denominators — [4.NF.B.3a] subtract the numerators, keep the denominator
• Decomposing Fractions — [4.NF.B.3b] break a fraction into a sum of unit fractions
• Adding and Subtracting Mixed Numbers — [4.NF.B.3c] work with the whole and fraction parts, including regrouping
• Multiplying a Fraction by a Whole Number — [4.NF.B.4b] repeated addition of a fraction, written as multiplication
• Fraction Word Problems — [4.NF.B.3d] real-world stories that call for adding or subtracting fractions

Decimals

• Fractions with Denominators 10 and 100 — [4.NF.C.5] rename tenths as hundredths and add the two
• Decimal Notation for Fractions — [4.NF.C.6] write tenths and hundredths as decimals, and back
• Comparing Decimals to Hundredths — [4.NF.C.7] line up the place values and compare with >, <, =
• Adding Decimal Fractions — [4.NF.C.5] add decimals to the hundredths place

Measurement & Data

• Converting Measurement Units — [4.MD.A.1] change from a larger unit to a smaller one
• Measurement Word Problems — [4.MD.A.2] length, weight, volume, and time in real situations
• Area of Rectangles — [4.MD.A.3] length times width — the space inside a rectangle
• Perimeter of Rectangles — [4.MD.A.3] the distance all the way around a rectangle
• Area and Perimeter Word Problems — [4.MD.A.3] decide whether a problem needs area or perimeter
• Line Plots with Fractions — [4.MD.B.4] read and use a line plot of fraction measurements

Angles

• Angles as Fractions of a Circle — [4.MD.C.5] a full turn is 360 degrees — find a fraction of it
• Measuring Angles with a Protractor — [4.MD.C.6] name angles acute, right, or obtuse by their measure
• Drawing Angles with Given Measures — [4.MD.C.6] know what a given degree measure should look like
• Adding and Subtracting Angles — [4.MD.C.7] an angle split into parts — find the missing part

Geometry

• Points, Lines, Rays, and Angles — [4.G.A.1] the building blocks of geometry and how to tell them apart
• Parallel and Perpendicular Lines — [4.G.A.1] lines that never meet, and lines that cross at a square corner
• Classifying Triangles — [4.G.A.2] sort triangles by their angles and their sides
• Classifying Quadrilaterals — [4.G.A.2] name four-sided shapes by their sides and angles
• Lines of Symmetry — [4.G.A.3] find the lines that fold a shape onto itself

How to use these worksheets at home

Keep each session short and lean on the regularity instead. Fifteen minutes is the right amount of time for a nine- or ten-year-old, and a calm quarter hour does more good than a long, tense one. Pick one PDF, sit nearby, and let your child do the work while you stay available for the moments they get stuck.

The most reliable trick is running related skills back to back so each one reinforces the last. Try “Adding Multi-Digit Whole Numbers” one afternoon and “Subtracting Multi-Digit Whole Numbers” the next — the second feels like a familiar relative instead of something new. The same pairing works for “Equivalent Fractions” before “Comparing Fractions,” or “Area of Rectangles” right before “Perimeter of Rectangles.” When skills travel in pairs, the connection between them does part of the teaching.

Hold the answer key until the work is done, then go through it together. In a home in Concord or a classroom in Dover, that review step is where the learning actually settles — not in a flawless first attempt, but in seeing clearly why a method works. Ask your child to explain one problem back to you in their own words; if they can do that, the skill has genuinely taken hold.

Finally, do not feel you have to move quickly through the whole set. Some weeks a single PDF will be all you manage, and that is fine — at this age, steady wins over fast. A fourth grader who finishes the year having truly understood place value, multi-digit multiplication, and the start of real fraction work is in a much better position than one who raced through every sheet without the ideas sticking.

A note about NH SAS at Grade 4

New Hampshire fourth graders take the NH SAS — the New Hampshire Statewide Assessment System — in Mathematics in the spring. It is built on the New Hampshire Mathematics Standards, which are aligned to the Common Core, so the skills these worksheets practice and the skills the test measures are drawn from the same place.

At Grade 4, NH SAS asks for reasoning rather than bare recall. Students round and compare large whole numbers, perform multi-digit multiplication and division, reason about factors and multiples, compare and combine fractions, work with decimals to the hundredths, and solve multi-step word problems where the first job is choosing the operation. Because each PDF here targets a single standard, the list works neatly as a checklist: if your child is shaky on one skill, you can see it plainly and work just that one rather than reviewing the whole year.

A short closing

Fourth-grade math grows quickly, but it grows in a sensible order, each skill resting on the one before it. Bookmark this page, print a single PDF tonight, and let your child start somewhere small. New Hampshire kids handle big new things well when the next step is clear — and a worksheet on the kitchen table is about as clear as a next step gets.

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