problem solving for grade 3 math

35 math problems for 3 rd graders

In 3rd grade, students are introduced to important math concepts that become the building blocks for future mathematical learning. Let’s practice those concepts with this list of math problems for 3rd graders.

Author Katie Wickliff

Published September 25, 2023

• Key takeaways
• In 3rd grade math, students develop a deeper understanding of multiplication and division, fractions, and measurements.
• Word problems for 3rd graders require more advanced comprehension skills.
• Place Value: Understanding place value helps us read and write numbers correctly and compare their values.
• Look for opportunities for your child to practice their math at home–worksheets, math games , or a math practice app will help strengthen new mathematical knowledge. While consistency is key, math practice for 3rd graders should be engaging and fun.

Table of contents

• Subtraction
• Multiplication
• Measurement
• Multi-step word problems

Answer sheet

In addition to reviewing and strengthening the skills learned in previous years, 3rd graders learn multiplication and division, explore fractions, calculate measurements, and more. Also, word problems for 3rd graders are often multi-step, requiring students to understand what operations to perform and how to perform them correctly. 

This list of 3rd grade math problems is intended to reinforce concepts students have already been taught. The list is divided into sections: addition, subtraction, multiplication, division, fractions, measurement, and multi-step problems. These sections allow students to specifically focus their practice, but feel free to skip around and choose the 3rd grade math practice problems that best suit your child’s needs. 

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Select a year group

• Kindergarten

Measurement and data

Sample questions, 35 third grade math problems, section 1: addition.

At the school carnival, Hattie won 25 tickets at ring toss and 40 tickets at balloon darts. How many tickets did she win altogether?

There are 15 baby chicks at the barn. 12 more chicks are born. How many baby chicks are at the barn now?

How can you represent the number line with an equation?

Using the number line, solve 7+ _ = 22

Amir practices basketball three days a week. On Tuesday, he practices basketball for 60 minutes. On Wednesday, he practices for 37 minutes. On Thursday, he practices for 15 minutes. Which expression shows how to find the total number of minutes Amir practiced? Circle the correct answer

Section 2: Subtraction

Using the number line, solve 17-6=

There are 224 Lions fans and 212 Tigers fans at the football game. How many more Lions fans than Tigers fans are at the game?

An animal shelter has 27 kittens available for adoption. On Friday, 8 kittens are adopted. How many kittens are left at the shelter?

Gemma has 130 beads for bracelets. She gives 75 beads to Piper and 6 beads to Claire. Which expression shows how to find the total number of beads Gemma has left? Circle the correct answer.

Using the number line, solve 30- _ = 14

Section 3: Multiplication

Using the picture below, write a multiplication equation to find the number of shapes

Francis and Jane are playing a card game. Francis has 7 cards. Jane has 3 times as many cards as Francis. How many cards does Jane have?

Using the number line to show hops, complete the multiplication sentence

Solve the equation

Mariela has 8 pages of math homework. There are 4 problems on each page. How many total problems does Mariela have for math homework?

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Section 4: Division

Connor has 80 crayons that he will put into crayon boxes. Each crayon box can hold 8 crayons. How many crayon boxes does he need?

Using the number line to show hops, complete the division sentence

Natalie divided 12 marbles into equal groups of 3. Draw a representation to show equal grouping.

Craig’s mom brought 12 cookies to the soccer game. She shared them equally among Craig and 3 teammates. Which expression will solve the problem correctly? Circle the answer.

Section 5: Fractions

Using the number line, work out what A, B and C represent.

Plot ¼ on this number line:

A cheese pizza has 8 slices. Marco ate 2 of the slices. His dad at the rest.  What fraction of the pizza did Marco eat? What fraction of the pizza did his dad eat?

There are 15 flowers in a garden. 10 flowers are yellow and the rest are red. What is the fraction of red flowers in the garden?

Using the number line, find the value of K and L. Which is bigger?

Section 6: Measurement

A school bus is 12 feet long and a car is 4 feet shorter than the bus. How long is the car?

John is 64 inches tall, Mabel is 59 inches tall, and Phoebe is 57 inches tall. How much taller is John than Phoebe?

Use the ruler provided to measure to the nearest ¼ inch:

Find the area of the square below

Find the perimeter of the rectangle below

Section 7: Multi-step word problems

Sarah has two $10 bills. Her sister has one $5 bill. They combine their money to buy a game that costs $22 dollars. How much change will they receive?

Dad baked 36 cookies for the bake sale. Jonas baked 24 cookies for the bake sale. His brother ate 5 cookies before the bake sale started. How many cookies do they have left to sell?

The school bus seats 75 students in all. On Friday, the school bus was full. At the first stop, 7 students got off. At the second stop, 15 students got off. How many children were left on the bus?

George has 25 water balloons. He wants to divide the water balloons equally between himself and 2 friends. How many water balloons will each get? Will there be any water balloons left over?

On Monday, 5 inches of snow fell. On Tuesday, 3 inches of snow fell. On Wednesday, 7 inches of snow fell. The school will have a snow day if it snows 21 inches or more. How many more inches would it have to snow for the school to have a snow day?

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Addition answers

25+40= 65. Hattie won 65 tickets

15+12= 27. 27 baby chicks are at the barn

7+ 15= 22. This should be represented by 15 “hops” on the number line

Subtraction answers

17-6=11. This should be represented by 11 “hops” on the number line

224-212= 12. There are 12 more Lions fans than Tiger fans

27-8= 19. There are 19 kittens left at the shelter.

Multiplication answers

2×3=6; 3×2=6

7×3=21. Jane has 21 cards.

8×4= 32

Division answers

40÷8= 5. It will take Max 5 days to pay Bennett.

Drawing should show 3 groups of 4 marbles each.

Fractions answers

The ¼ should be plotted on the point between 0 and ½

Marco ate 2/8 (or ¼) of the pizza. His dad ate 6/8 (or ¾) of the pizza

5/15 (or ⅓)

K= ⅜, L= 6/8 (or ¾). L is larger.

Measurement answers

12-4=8. The car is 8 feet long.

64-57=7. John is 7 inches taller than Phoebe

8×8=64. The area is 64 yd2

8+8+2+2=20 cm

Multi-step word answer answers

$10+$10= $20. 

$20+$5=$25.

$25-$22= $3

 Sarah and her sister will receive $3 in change

They have 55 cookies left to sell

53 students are left on the bus

George and his friends each get 6 water balloons, with one left over.

• 5 in+ 3 in+ 7 in= 15 in

21 in- 15 in= 6 in

It must snow 6 more inches to get a snow day. 

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

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Division Worksheets Grade 3 Solving Division Problems

Welcome to our Division Worksheets Grade 3 page.

Here you will find a wide range of free 3rd Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

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Division Worksheets Grade 3

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 3rd grade to the end.

The first two sheets involve drawing out different amounts in groups and solving simple problems which do not require any reasoning skills.

Sheets 3 to 5 involve understanding and working out division word problems that require a little more reasoning and thinking about.

Sheets 6 and 7 are the most complicated and involve division problems with remainders. In order to solve the word problem, the remainder needs to be rounded up or down, depending on the context.

Division Worksheets Grade 3 - Worksheets

Simple division worksheets problems.

• Division Problems Sheet 3.1
• PDF version
• Division Problems Sheet 3.2

Medium Level Division Word Problems

• Division Problems Sheet 3.3
• Division Problems Sheet 3.4
• Division Problems Sheet 3.5

Harder Division Problems (interpreting remainders)

• Division Problems Sheet 3.6
• Division Problems Sheet 3.7

Looking for some harder Division worksheets

Our 4th grade division worksheets are similar to those on this page but at a more challenging level.

The links below will take you to our division worksheets for 4th grade.

These sheets involve solving a range of division problems.

• Division Worksheets Grade 4 Word Problems
• Divding by Multiples of 10 and 100 Worksheets
• 4th Grade Long Division Worksheets

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Division Worksheets

• Divide a 2 digit number by a single digit;
• Use remainders when dividing;
• Calculate division facts related to multiplication facts.
• Division Facts to 10x10 Worksheets
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More 3rd Grade Math Word Problems

Here are a range of problems solving sheets for 3rd graders. Most of the sheets contain 'real-life' problems which involve real data.

Using the sheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• develop their knowledge of fractions;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

All the 3rd grade sheets in this section support Elementary math benchmarks.

These sheets involve solving one or two more challenging longer problems.

• 3rd Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• Math Word Problems for kids 3rd Grade
• 3rd Grade Addition and Subtraction Word Problems (3- and 4-digits)

These sheets involve solving a range of multiplciation problems.

• Multiplication Word Problem Worksheets 3rd Grade
• Third Grade Math Games

Here you will find a range of free printable Third Grade Math games. All children like to play Math games, and you will find a good range of 3rd Grade Math Games here for your child to play and enjoy.

The following games involve different Third Grade Math activities which you and your child can enjoy together.

All the free Third Grade Math sheets in this section are informed by the Elementary Math Benchmarks for Third Grade.

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Rate Problems with Fractions

Grade 7 math worksheets.

Rate problems typically involve quantities changing over time or in relation to each other. When fractions are involved, it often means that the rates of change or comparison are not whole numbers.

Here’s a general approach to solving rate problems with fractions:

1. Identify the Rates : Determine what quantities are changing and at what rates. These rates might be given in fractions, percentages, or other forms.

2. Set Up Equations : Use the given information to set up equations that represent the relationship between the quantities and their rates. This might involve using proportions or ratios.

3. Solve for the Unknowns : Solve the equations to find the unknown quantities. This often requires basic algebraic manipulation, such as cross-multiplication or finding common denominators.

4. Check Your Solution : Once you have found the solution, check to ensure it makes sense in the context of the problem. Verify that the rates and quantities align with the given information.

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Rate Problems with Fractions - Grade 7 Math Worksheet PDF

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Steps to Follow to Solve Rate Problems with Fractions: 

To solve unit rate problems with fractions, you typically follow these steps:

• Understand the Problem: Read the problem carefully to understand what is being compared and what units are involved. Identify the quantities and units mentioned in the problem.
• Identify the Numerator and Denominator: Determine which quantity is the numerator (the top part) and which is the denominator (the bottom part) of the fraction in the unit rate.
• Set Up the Ratio: Create a ratio with the numerator representing the quantity of interest and the denominator representing the corresponding unit. Make sure the units in the ratio match.
• Simplify Fractions: Simplify any fractions in the ratio by finding their greatest common factor and dividing both the numerator and denominator by it if possible.
• Calculate the Unit Rate: Divide the numerator by the denominator to find the unit rate.
• Interpret the Result: Make sure you understand what the unit rate represents in the context of the problem.

Solved Example: Water Flow Rate: A water tank fills up in 5/6 hours when water flows at a rate of 4/5 gallons per hour. What is the unit rate of water flow in gallons per hour?

• Identify the Numerator and Denominator: The numerator is 4/5 gallons of water, and the denominator is 5/6 hours.
• Set Up the Ratio: Let x be the unit rate of water flow in gallons per hour. The ratio is (4/5) / (5/6).
• Simplify Fractions: The fractions (4/5) and (5/6) are already simplified.
• Calculate the Unit Rate: Divide (4/5) by (5/6): (4/5) / (5/6) = (4/5) * (6/5) = 24/25.
• Interpret the Result: The unit rate of water flow is 24/25 gallons per hour

Solved Example : Fuel Efficiency: A car travels 2/3 of a mile on 1/4 gallon of gasoline. What is the unit rate of fuel efficiency in miles per gallon?

• Identify the Numerator and Denominator: The numerator is 2/3 mile, and the denominator is 1/4 gallon.
• Set Up the Ratio: Let x be the unit rate of fuel efficiency in miles per gallon. The ratio is (2/3) / (1/4).
• Simplify Fractions: The fractions (2/3) and (1/4) are already simplified.
• Calculate the Unit Rate: Divide (2/3) by (1/4): (2/3) / (1/4) = (2/3) * (4/1) = 8/3.
• Interpret the Result: The unit rate of fuel efficiency is 8/3 miles per gallon.

These examples illustrate how to solve unit rate problems involving fractions by setting up the ratio, simplifying fractions if necessary, and calculating the unit rate.

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Practice Questions

Q1. Sarah can paint 3/4 of a wall in 2 hours. What is her painting rate per hour in square feet?

Q 2. A car can travel 7/8 of a mile on 1/4 gallon of gasoline. What is the car’s mileage rate in miles per gallon (mpg)?

Q3. Sam bakes cookies and can make 2/3 of a batch in 30 minutes. What is his baking rate per minute in batches?

Q4. Anna is baking cookies, and the recipe calls for 3/4 cup of sugar for every 2 dozen cookies. What is the unit rate of sugar required for one dozen cookies in cups?

Solution 1: Sarah’s painting rate per hour is 3/8 of a wall in square feet. This means she can paint 3/8 of a wall in one hour.

Solution 2 : The car’s mileage rate is 7/2 miles per gallon (mpg), which is equivalent to 3.5 mpg. So, the car’s mileage rate is 3.5 miles per gallon.

Solution 3 : Sam’s baking rate per minute is 1/45 of a batch. It means he can bake 1/45 of a batch in one minute.

So, the unit rate is 1/45 of a batch per minute.

Solution 4: Anna needs 3/8 cup of sugar for one dozen cookies. So, the unit rate is 3/8 cup of sugar per dozen cookies.

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What is a rate problem involving fractions?

A rate problem with fractions is a mathematical question that relates two quantities, such as distance and time, where one or both of the quantities are expressed as fractions or involve fractional parts.

How do I calculate the rate when dealing with fractions?

To calculate the rate, you can use the formula: Rate = Quantity / Time. If either the quantity or time involves fractions, make sure to perform the necessary operations to simplify and work with the fractions.

What are some common examples of rate problems with fractions?

Common examples include calculating the speed of a car in miles per hour (mph) when the distance is given in fractions of a mile or calculating the time it takes for a job to be completed when fractional parts of the job are done in each hour.

How do I convert mixed numbers to fractions when solving rate problems?

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. For example, 2 1/4 becomes (2 * 4) + 1 = 9/4.

What if the rate problem involves adding or subtracting fractions?

When adding or subtracting fractions in a rate problem, make sure the fractions have the same denominator. If not, find a common denominator, perform the operation, and simplify the result.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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Unit 4: Intro to division

About this unit.

Now that you know all about multiplication, it's time to divide and conquer! In this unit, you'll learn the basics of division and how it's connected to everything you've already learned about multiplication.

Division intro

• Division as equal groups (Opens a modal)
• Visualizing division with arrays (Opens a modal)
• Division with groups of objects Get 5 of 7 questions to level up!
• Division with arrays Get 5 of 7 questions to level up!
• Divide with visuals Get 5 of 7 questions to level up!

Division in contexts

• Division in context (Opens a modal)
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Relating multiplication and division

• Relating division to multiplication (Opens a modal)
• Multiplication word problem: parking lot (Opens a modal)
• Division word problem: school building (Opens a modal)
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• Relate multiplication and division equations Get 5 of 7 questions to level up!
• Fact families Get 5 of 7 questions to level up!
• Relate division to multiplication word problems Get 3 of 4 questions to level up!

Divide by 1, 2, or 4

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• Divide by 1 Get 8 of 11 questions to level up!
• Divide by 2 Get 7 of 10 questions to level up!
• Divide by 4 Get 7 of 10 questions to level up!

Divide by 5 or 10

• Divide by 5 Get 7 of 10 questions to level up!
• Divide by 10 Get 7 of 10 questions to level up!

Divide by 3 or 6

• Divide by 3 Get 7 of 10 questions to level up!
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Divide by 7, 8, or 9

• Divide by 7 Get 7 of 10 questions to level up!
• Divide by 8 Get 7 of 10 questions to level up!
• Divide by 9 Get 7 of 10 questions to level up!

1-digit division

• Intro to division: FAQ (Opens a modal)
• Basic division Get 5 of 7 questions to level up!

What is the 3-body problem, and is it really unsolvable?

The three-body problem is a physics conundrum that has boggled scientists since Isaac Newton's day. But what is it, why is it so hard to solve and is the sci-fi series of the same name really possible?

A rocket launch. Our nearest stellar neighbor. A Netflix show. All of these things have something in common: They must contend with the "three-body problem." But exactly what is this thorny physics conundrum?

The three-body problem describes a system containing three bodies that exert gravitational forces on one another. While it may sound simple, it's a notoriously tricky problem and "the first real worry of Newton," Billy Quarles , a planetary dynamicist at Valdosta State University in Georgia, told Live Science.

In a system of only two bodies, like a planet and a star, calculating how they'll move around each other is fairly straightforward: Most of the time, those two objects will orbit roughly in a circle around their center of mass, and they'll come back to where they started each time. But add a third body, like another star, and things get a lot more complicated. The third body attracts the two orbiting each other, pulling them out of their predictable paths .

The motion of the three bodies depends on their starting state — their positions, velocities and masses. If even one of those variables changes, the resulting motion could be completely different. 

"I think of it as if you're walking on a mountain ridge," Shane Ross , an applied mathematician at Virginia Tech, told Live Science. "With one small change, you could either fall to the right or you could fall to the left. Those are two very close initial positions, and they could lead to very different states."  

There aren't enough constraints on the motions of the bodies to solve the three-body problem with equations, Ross said. 

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But some solutions to the three-body problem have been found. For example, if the starting conditions are just right, three bodies of equal mass could chase one another in a figure-eight pattern. Such tidy solutions are the exception, however, when it comes to real systems in space.

Certain conditions can make the three-body problem easier to parse. Consider Tatooine , Luke Skywalker's fictional home world from "Star Wars" — a single planet orbiting two suns. Those two stars and the planet make up a three-body system. But if the planet is far enough away and orbiting both stars together, it's possible to simplify the problem. 

"When it's the Tatooine case, as long as you're far enough away from the central binary, then you think of this object as just being a really fat star," Quarles said. The planet doesn't exert much force on the stars because it's so much less massive, so the system becomes similar to the more easily solvable two-body problem. So far, scientists have found more than a dozen Tatooine-like exoplanets , Quarles told Live Science.

But often, the orbits of the three bodies never truly stabilize, and the three-body problem gets "solved" with a bang. The gravitational forces could cause two of the three bodies to collide, or they could fling one of the bodies out of the system forever — a possible source of "rogue planets" that don't orbit any star , Quarles said. In fact, three-body chaos may be so common in space that scientists estimate there may be 20 times as many rogue planets as there are stars in our galaxy.

When all else fails, scientists can use computers to approximate the motions of bodies in an individual three-body system. That makes it possible to predict the motion of a rocket launched into orbit around Earth, or to predict the fate of a planet in a system with multiple stars.

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With all this tumult, you might wonder if anything could survive on a planet like the one featured in Netflix's "3 Body Problem," which — spoiler alert — is trapped in a chaotic orbit around three stars in the Alpha Centauri system , our solar system 's nearest neighbor. 

"I don't think in that type of situation, that's a stable environment for life to evolve," Ross said. That's one aspect of the show that remains firmly in the realm of science fiction.

Skyler Ware is a freelance science journalist covering chemistry, biology, paleontology and Earth science. She was a 2023 AAAS Mass Media Science and Engineering Fellow at Science News. Her work has also appeared in Science News Explores, ZME Science and Chembites, among others. Skyler has a Ph.D. in chemistry from Caltech.

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