How to Help My Child with Math at Home

How to Help My Child with Math at Home: 7 Tips

How to help my child with math at home. (Image: Mashup Math via Getty)

Many parents want to understand how important mathematics is for their child’s future and they genuinely want to excel in the subject.

But many parents also struggled with mathematics when they were students, and they don’t feel confident in supporting their child’s math learning outside of the classroom.

In fact, studies show that parents with math anxiety can actually undermine their children’s math achievement by spreading their negative attitudes towards the subject to their kids.

When parents push too hard, their child can feel overwhelmed and stressed. When parents are too hands-off, then their child may not value the importance of mathematics at all.

As a result, far too many students learn to view math as a chore instead of an invaluable life skill.

If you are a parent wondering how to help my child with math at home, then the following tips will help you to support your child’s math learning and prevent you from passing on any negative attitudes or math anxiety.

The following collection of tips will not require you to spend hours relearning tricky elementary math topics like the order of operations or simplifying fractions. Instead, the focus will be on developing a positive attitude for learning mathematics combined with a reliable support system to ensure that your child continues to pursue math education beyond the point where many give up.

How to Help My Child with Math at Home

Tip #1: Keep Your Cool

How to help your child with math at home: There is a growing body of research suggesting that playing games can support the development of mathematical thinking skills. (Image: Mashup Math MJ)

The idea that only certain people are capable of learning math is a harmful misconception.

The idea of being a math person has caused an extreme amount of damage to student attitudes and has given many of them an excuse to quit learning mathematics prematurely.

This idea, however, is simply untrue. Just like it is completely reasonable to expect every student to become skilled in reading and writing, we can expect every student to be able to think and solve problems mathematically.

While you may have fallen victim to out-of-touch teaching practices that failed to meet your needs as student and, as a result, have adopted this belief that you are simply not a math person, it does not mean that your child has to suffer the same fate.

A recent study showed that sharing negative feelings with our children can severely increase anxiety and degrade their attitude towards learning math. Education has been continuously evolving over the past few decades and no longer resembles the environment that many parents were exposed to.

Modern students think about and learn mathematics in very different ways. Parents do their children a disservice when they impart their negative experiences about math education onto them.

If you want to help your child with math at home, then you need to leave your past negative experience with mathematics behind and approach the situation with an open mind.

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Tip #2: Understand the Purpose

How to Help My Child with Math at Home: Help them understand why math is important. (Image: Mashup Math MJ)

Just because you do not remember the ins-and-outs of fractions or even algebra does not mean that you cannot support your child with math at home.

It is, however, necessary that you reinforce why learning math is useful and advantageous. When you say things like “you are never going to use this in life,” your children respond by devaluing the skills they are learning.

While your child will likely never have to simplify a square root in the real world, he or she will have to solve complex problems. To be successful in life, students must develop into creative problem solvers who can think critically and mathematically.

If you want to help your children with math at home, then you need to help them to understand why they are learning it in the first place.

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Tip #3: Hire a Tutor

Studies show that children who meet regularly with a tutor have reduced math anxiety. (Image: Mashup Math MJ)

Wondering how to help your child with math at home? Hiring a tutor is a good place to start.

This tip for supporting your child’s math education may seem obvious, but many parents do not fully appreciate the impact that a one-on-one tutor can have.

NPR recently reported on a study that focused on the effect of one-to-one tutoring relationships on student anxiety and math test scores. The conclusion of the study was that students who had regular meetings with an individual tutor had significantly lower levels of academic anxiety than students who did not. Students with a one-to-one tutoring relationship were also better able to get through areas of difficulty without becoming discouraged.

That’s why individualized online learning formats, such as one-on-one math classes, are gaining popularity among parents looking for flexible and effective ways to support their children’s progress in math.

Hiring a private math tutor for your child can have huge benefits, but it can also be cost- and time-prohibitive for many, which is why the next tip offers an effective and more accessible alternative.

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Tip #4: Build a Relationship with Your Child’s Teacher

How to Help My Child with Math at Home: Stay in touch with your child’s teacher by phone or email on a bi-weekly basis. (Image: Mashup Math MJ)

One thing that every parent can do to support their math education at home is to establish consistent and positive communication with their child's teacher.

Why? Because staying in tune with what your child is learning and being aware of how he or she is responding to classroom instruction will help you to understand where and when support is needed.

Most teachers have regularly scheduled before or after-school hours (which is essential free private tutoring) for your child to gain extra help and small-group or even one-on-one instruction.

Additionally, teachers tend to give more attention to students whose parents are more involved.

This extra attention is not a matter of treating students unfairly, but when a teacher regularly communicates with one of her student’s parents, then, as a result, she starts to spend more time thinking about ways to better meet that student's individual needs.

Parents should be aware that teachers have limited time and refrain from bombarding them with phone calls and emails. A weekly or bi-weekly phone or email conversation is perfectly sufficient, in most cases, for establishing regular and meaningful communication. 

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Tip #5: Use Online Resources

How to help your child with math at home: Virtual Math Manipulatives (or digital hands-on activities) are a great resource for exploring difficult math concepts in a visual way at home. (Image Source: Mashup Math MJ)

Many parents do not take advantage of so many helpful free online math resources made specifically for children.

One math resources—ranging from practice worksheets to virtual hands-on activities to animated video lessons—give children opportunities to explore and learn difficult math procedures and concepts and procedures at home.

Here are a few links to free online math resources that you can start using with your child at home today:

• Free Virtual Math Manipulatives Library

• Free Animated Math Video Library for Grades K-8

• Free Math Puzzles and Worksheets (with Answer Keys)

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Tip #6: Gamify

How to Help My Child with Math at Home: Utilize hands-on activities—like building fraction kits out of construction paper—as opportunities to explore and learn math at home. (Image: Mashup Math ST)

There’s to practicing, exploring, and earning mathematics than completing worksheets.

There are tons of benefits to working on hands-on activities that are fun, engaging, and powerful opportunities for your child to explore challenging math concepts and build meaningful conceptual understanding of topics like fractions, probability, and geometry.

While even activities like Sudoku puzzles or building structures using Legos can help your child to develop problem solving, creative thinking, and spatial awareness, there are even further benefits to hands-on activities specifically designed to help your child to develop math skills through play.

Here are a few links to fun hands-on math activities that you can start using with your child at home today:

• Building a Fraction Kit at Home

• Exploring Area and Perimeter Using Cheez-Its

• Starburst Probability Activity

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Tip #7: Become a Student Again

Your child can deeper her understanding of math concepts by teaching them to you at home. (Image: Mashup Math MJ)

 One of the best ways to better understand something is to teach it to someone else—and mathematics is no exception. This idea is often used to support the use of peer tutoring, where teachers group struggling students with higher performing classmates.

When you have to teach something to someone else, then you have to stop and think about the best way to express your understanding, which ultimately strengthens your grasp of the material.

As a parent, take advantage of these benefits by allowing your child to teach you what they have learned in school. Work through practice problems together and ask thoughtful questions. In this role reversal, your child will be the teacher and you the student.

You may just be pleasantly surprised by how much of a difference such a simple practice can make on your child’s academic development. 

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How to Factor a Trinomial in 3 Easy Steps

How to Factor a Trinomial in 3 Easy Steps

 Learning how to factor a trinomial is an extremely important and useful algebra skill, but factoring trinomials can also be very tricky.

This free How to Factor a Trinomial step-by-step guide will teach you how to factor a trinomial when a=1 and when a does not equal one (more on what a refers to later) using a simple three-step process.

Before you learn how to factor a trinomial, let’s do a quick review of some very important vocabulary and definitions related to trinomials.

Trinomial Definition

A trinomial is a polynomial that has three terms. The first time is an x^2 term, the second term is an x term, and the third term is a constant (just a number).

Furthermore, when discussing trinomials, you will see references to vales for a, b, and c., where:

a = the x^2 term coefficient

b = the x term coefficient

c= the constant value

For example:

For this trinomial: a=1, b=5, and c=6.

Note that, when a=1, the coefficient will not be written in front of the x^2 term.

Factoring Trinomials: a = 1

For the first few examples, let’s learn how to factor a trinomial when a, the leading coefficient is 1.

How to Factor a Trinomial Example #1

For the first example, let’s factor the trinomial: x^2 + 6x + 8

Again, note that a=1 in this example.

Now let’s factor the trinomial:

Step 1: Identify the values for b and c.

In this example, b=6 and c=8.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

This step can take a little bit of trial-and-error.

For instance, you could pick 5 and 1 because 5+1=6. But 5 x 1 does not equal 8, so these numbers would not work.

However, if you chose 4 and 2, you could easily confirm that:

4 + 2 =6 (the value of b); and

4 x 2 = 8 (the value of c)

Step 3: Use the numbers you picked to write out the factors and check

For this example, the factors would be (x+2) and (x+4)

Final Answer: (x+4)(x+2)

You can check your answer by multiplying the two factors (binomials) together to see if the result is the original trinomial as follows:

Notice that 2x and 4x are like terms that can be combined.

Multiplying the factors results in the original trinomial.

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How to Factor a Trinomial Example #2

Let’s get more practice factoring trinomials when a is 1.

Factor: x^2 + 9x + 20

Step 1: Identify the values for b and c.

In this example, b=9 and c=20.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Finding the right numbers won’t always be as easy as it was in example 1.

To make factoring trinomials easier, write down all of the factors of c that you can think of.

In this case, c=20, so:

20 x 1 = 20

10 x 2 = 20

5 x 4 = 20

Remember that the two numbers have to multiply to c AND add to b.

The only factors of 20 that meet both of these requirements are 4 and 5.

Step 3: Use the numbers you picked to write out the factors and check

The last step is to write out the factors: (x+5)(x+4)

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How to Factor a Trinomial Example #3

Factor: x^2 - 5x -24

Notice that this example includes subtraction signs, but the process of factoring is still the same.

Step 1: Identify the values for b and c.

In this example, b= -5 and c= -24.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Again, you have to find two values to ADD to -5 and MULTIPLY to -24.

This step can get tricky when you’re dealing with negative numbers. Remember that a negative times a negative is positive, so only one of the values can be negative if the product has to be -24.

After writing out all of the possible factors, you can conclude that:

-8 x 3 = -24

and

-8 + 3 = -5

Step 3: Use the numbers you picked to write out the factors and check

The last step is to write out the factors: (x-8)(x+3)

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How to Factor a Trinomial when A does not equal 1

How can you factor a trinomial when the leading coefficient does not equal one? This free video tutorial will show you how:

How to Factor a Trinomial Using the Completing the Square Formula

Finally, there is an alternate method to factoring a trinomial that is called completing the square. This method applies to factoring quadratic equations (when a trinomial equals a value, namely zero).

You can learn more about factoring using the completing the square formula by checking our free step-by-step guide.

This Complete Guide to the Completing the Square includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free worksheet and answer key.

Click here to access a free Completing the Square step-by-step guide.

Conclusion: How to Factor a Trinomial

You can factor a trinomial of the form ax^2 + bx + c, when a=1, by using the following 3-step method:

Step 1: Identify the values for b and c.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Step 3: Use the numbers you picked to write out the factors and check

Please review the above examples, watch our video on how to factor a trinomial when the leading coefficient, a, is not 1, and check out our free guide to factoring by completing the square.

Keep Learning:

10 Best Math Movies for All Ages

The 10 Best Math Movies for All Ages

What are the absolute best movies with math as a major theme?

The 10 Best Math Movies for All Ages (Image: Mashup Math MJ)

Are you looking for a list of the best math movies ever made? The following list celebrates math in the movies by highlighting a collection of the best math movies, all of which are appropriate for children and adults alike. In fact, all of the movies on the list are rated PG-13, PG, or G, making them all school appropriate.

(Jump right to the list of the 10 Best Movies About Math)

Seeing math in the movies is more than just entertainment. Mathematics and its applications shown on the big screen can inspire students to consider pursuing careers in STEM, appreciate mathematical concepts and how they apply to real life, and understand how mathematics can be used to solve problems in a variety of circumstances.

The following list of school-appropriate math movies can be enjoyed by adults and children alike. If you are a teacher looking for movies with math a main theme to show in your classroom, there are options on this list suitable for students in elementary school, middle school, and high school, as the parental guidance recommendations range from G to PG to PG-13.

via GIPHY

So, whether you want to give your kids a break from testing, supplement your instruction, or share some well-earned Friday fun time, showing movies about math in class can be an educational and enjoyable experience. 

While it can be challenging to find movies that are directly related to mathematics, there are plenty of creative ways to appropriately show full movies and/or movie clips in your classroom. If you are struggling to find a math movie that is right for your kids, check out the following list, get the popcorn ready, and enjoy!

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*Disclaimer: You should always get permission from your administration and use discretion before showing any movie or movie scene to your students.

*Copyright Disclaimer: All film poster images beloware scaled-down, low-resolution images used for the sole purpose of providing critical commentary on the film in question or of the film poster itself.

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1.) Queen of Katwe (PG)

IMDb Synopsis: A Ugandan girl sees her world rapidly change after being introduced to the game of chess.

Why? This relatively unknown Disney movie about 10-year-old Phiona and her incredible rise to become a chess master might be my favorite of any of the math movies for kids on this list. If you are looking to open up the possibilities of mathematics to a diverse group of students, Queen of Katwe is an excellent option.

Math Movies for Kids: Queen of Katwe is one of the best PG-rated movies with math as a main theme. (Image: Fair Use)

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2.) Stand and Deliver (PG)

IMDb Synopsis: Jaime Escalante is a mathematics teacher in a school in a Hispanic neighborhood. Convinced that his students have potential, he adopts unconventional teaching methods to help gang members and no-hopers pass the rigorous Advanced Placement exam in calculus.

Why? Stand and Deliver is an incredibly inspiring true story that is a must-see for teachers and students alike. If you are looking to motivate students of any background and inspire them to reconsider their personal limits and potential for growth and achievement, then showing Stand and Deliver is a no brainer.

Stand and Deliver may be the greatest movie about a math teacher ever made! (Image Source: Fair Use)

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 3.) A Beautiful Mind (PG-13)

IMDb Synopsis: After John Nash, a brilliant but asocial mathematician, accepts secret work in cryptography, his life takes a turn for the nightmarish.

Why? A Beautiful Mind is more than just an interesting tale about a paranoid mathematician, it shares several examples of how beautiful mathematics truly is and how it applies to our everyday world.

Famous Math Movies: A Beautiful Mind (Image: Fair Use)

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4.) Flatland (G)

IMDb Synopsis: Based on Edwin Abott's classic novella "Flatland", this is an animated film about geometric characters living in a two-dimensional world. When a young girl named "Hex" decides to "think outside the box" (in a world where such thought is forbidden), her life becomes in danger and it is up to her grandfather to save her life.

Why? This short animated film released in 2007 teaches math concepts through an interesting story driven by fun characters (one of which is voiced by Martin Sheen) living in a two-dimensional world and mathematically inspired world. You can access the movie at flatlandthemovie.com.

Math Movies for Kids: Flatland (Image Source: Fair Use)

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Released in 2015, The Man Who Knew Infinity is one of the best math movies for middle school students and older. (Image: Fair Use)

5.) The Man Who Knew Infinity (PG-13)

IMDb Synopsis: The story of the life and academic career of the pioneer Indian mathematician, Srinivasa Ramanujan, and his friendship with his mentor, Professor G.H. Hardy.

Why? The Man Who Knew Infinity is simply a fantastic story about the rise of a famous mathematician and a beautiful mentorship that allowed him to overcome great odds to change the field of mathematics forever. While the movie is not very well known, it is a must-see for any math enthusiast.

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Moneyball is another excellent addition to our collection of movies with math a central theme. (Image: Fair Use)

6.) Moneyball (PG-13)

IMDb Synopsis: Oakland A's general manager Billy Beane's successful attempt to assemble a baseball team on a lean budget by employing computer-generated analysis to acquire new players.

Why? You won't find a movie that demonstrates the tremendous role that mathematics plays in professional sports better than Moneyball. Showing the full movie will give your kids a better idea of how mathematics applies to the real world as well as possible career paths, such as becoming a Major League Baseball scout, that require a deep understanding of applied mathematics.

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Math in the Movies: Is The Martian the best STEM movie ever? (Image: Fair Use)

7.) The Martian (PG-13)

IMDb Synopsis: An astronaut becomes stranded on Mars after his team assume him dead, and must rely on his ingenuity to find a way to signal to Earth that he is alive.

Why? The Martian is probably the best STEM movie ever. There are countless scenes where Matt Damon has to use mathematics and mathematical reasoning to overcome challenges and advance his quest for survival. If you are looking to show your kids that math can take you places, then The Martian is your best choice!

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When in doubt, one of the best math movies to show is Hidden Figures. (Image: Fair Use)

8.) Hidden Figures (PG)

IMDb Synopsis: The story of a team of female African American mathematicians who served a vital role in NASA during the early years of the U.S. space program.

Why? Hidden Figures is an incredible and inspiring movie that demonstrates the power of mathematics and the fact that the subject is open to individuals of all genders and backgrounds.

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9.) The Imitation Game (PG-13)

IMDb Synopsis: During World War II, the English mathematical genius Alan Turing tries to crack the German Enigma code with help from fellow mathematicians while attempting to come to terms with his troubled private life.

Why? The Imitation Game is a compelling movie because it tells the story of Alan Turing, a brilliant mathematician who, during World War II, made significant contributions to the field of mathematics and cryptography. The film highlights Turing's ability to use mathematical thinking and problem-solving skills to crack the German “Enigma” code and help the allied powers win WW2. The movie also presents complex mathematical concepts in an accessible way, making it an effective teaching tool for students of all levels.

Math in the Movies: The Imitation Game highlights how mathematics influenced the outcome of WW2. (Image: Fair Use)

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Math Movies for Middle School Students: Donald in Mathmagic Land (Image: Fair Use)

10.) Donald in Mathmagic Land 

IMDb Synopsis: Donald Duck goes on an adventure in which it is explained how mathematics can be useful in real life. Through this journey it is shown how numbers are more than graphs and charts, they are geometry, music, and magical living things.

Why? Did you really think that this 1959 classic would not be on this list? This timeless gem was made to show kids that mathematics is more than just a set of procedures and rules. Despite its age and short duration (it's only 27 minutes long), it still stands up and is a beloved by students and teachers alike. And did I mention that you can watch the full movie for free on YouTube? 

Did I miss your favorite math movie or TV show? Share your suggestions in the comments section below. Subscribe to our mailing list here to get more free daily resources, lessons, and tips in your inbox every week.

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Free 4th Grade Math Puzzles (Printable)

Free Printable 4th Grade Math Puzzles

Whether it’s the start of a new school year, the everlasting stretch between October and April, or the final weeks leading up to summer break, keeping your 4th grade students engaged and interested in practicing and learning math every day is no easy task.

While there a ton of free resources, worksheets, puzzles, and activities for 4th graders available online, they are not all created equally—and, probably, the last thing that you need right now are more repetitive black-and-white practice worksheets.

Fortunately, if you are looking to mix things up and share some math activities that your 4th grade students will actually enjoy working on, then you’re in the right place. This post shares ten 4th Grade Math Puzzles that come in the form of printable pdf worksheets that include complete answer keys and are 100% free.

All of the free math puzzles for 4th grade students are samples from the worksheet libraries available on our membership website. Don’t worry, you do not have to be a member to download or print all ten of the free 4th grade math puzzle pdf worksheets.

Our puzzle worksheets can also be shared on online learning platforms like Google Classroom.

Each puzzle includes a brief description, suggestions for use, and links to learn more in case you are interested in accessing more information about puzzle activities including Two Truths and One Lie, Which One Doesn’t Belong?, our Order of Operations Puzzles, and more!

Additionally, all of our puzzles are designed with research-backed strategies that are proven effective for boosting student engagement and improving student performance. For more information, you can learn more about Stanford Education Professor Jo Boaler and her support of using visual math puzzles and activities to improve engagement and student performance.

Each of the following 4th Grade Math Puzzles includes a preview image along with a link to download.

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10 Free Printable 4th Grade Math Puzzles

4th Grade Math Puzzle #1

▶ Order of Operations

(This puzzle is a sample from the 4th Grade Order of Operations puzzle library available on our membership site)

Puzzle Objective: Use your math skills to find the value of each symbol and the ? in the puzzle.

Download: ⤓ Click here to download your pdf worksheet

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4th Grade Math Puzzle #2

▶ Multiplication Table

(This puzzle is a sample from the 4th Grade Multiplication Tables puzzle library available on our membership site)

Puzzle Objective: Use your multiplication skills to find the value of each symbol in the times table.

Download: ⤓ Click here to download your pdf worksheet

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Free Printable Color Multiplication Table Practice Chart for Students

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4th Grade Math Puzzle #3

▶ Area Model

(This puzzle is a sample from the 4th Grade Area Models puzzle library available on our membership site)

Puzzle Objective: Find the value of each symbol in the area model so that the entire box represents the given value.

Download: ⤓ Click here to download your pdf worksheet

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How to Teach Students to Multiply Using Area Models

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4th Grade Math Puzzle #4

▶ Logic Puzzles

(This puzzle is a sample from the 4th Grade Logic puzzle library available on our membership site)

Puzzle Objective: Observe the scales below and use your math skills to find the weight of each object, then answer the follow-up question.

Download: ⤓ Click here to download your pdf worksheet

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Gain access to ALL of our 4th grade activity libraries with a membership plan. Start a free 7-day trial today

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Puzzle Preview

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Join our mailing list to get free K-8 math activities, puzzles, and worksheets in your inbox every week (plus two free pdf math workbooks!)

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4th Grade Math Puzzle #5

▶ Two Truths and One Lie!

(This puzzle is a sample from the 4th Grade Two Truths and One Lie! puzzle library available on our membership site)

Puzzle Objective: Use math skills and the given information to determine which of the three statements is a lie! Explain how you made your decision.

Download: ⤓ Click here to download your pdf worksheet

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Idea: How to Engage Your Students at the Start of Any Lesson with Two Truths and One Lie!

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4th Grade Math Puzzle #6

▶ Which One Doesn’t Belong?

(This puzzle is a sample from the 4th Grade Two Which One Doesn't Belong? puzzle library available on our membership site)

Puzzle Objective: Carefully observe each of the four graphics and decide which one does not belong with others. Explain your answer in writing.

Download: ⤓ Click here to download your pdf worksheet

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Why You Should Be Using "Which One Doesn't Belong?" to Ignite Student Thinking in Math

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4th Grade Math Puzzle #7

▶ Think-Notice-Wonder

(This puzzle is a sample from the 4th Grade Think-Notice-Wonder Writing Prompts puzzle library available on our membership site)

Puzzle Objective: Observe the graphic below and, in writing, complete the following: I think…, I notice…, I wonder…

Download: ⤓ Click here to download your pdf worksheet

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Are You Using This Genius Strategy for Math Writing?

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4th Grade Math Puzzle #8

▶ Riddles and Brain Teasers

(This puzzle is a sample from the 4th Grade Riddles and Brain Teasers puzzle library available on our membership site)

Puzzle Objective: Figure out the relationship/pattern between the numbers to determine the value of the ?

Download: ⤓ Click here to download your pdf worksheet

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10 Super Fun Math Riddles for Kids! (with Answers)

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4th Grade Math Puzzle #9

▶ Riddles and Brain Teasers

(This puzzle is a sample from the 4th Grade Riddles and Brain Teasers puzzle library available on our membership site)

Puzzle Objective: Figure out the relationship/pattern between the numbers to determine the value of the missing numbers

Download: ⤓ Click here to download your pdf worksheet

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Can your students solve the famous handshake math riddle?

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4th Grade Math Puzzle #10

▶ Geometry Puzzles

(This puzzle is a sample from the 4th Grade Geometry Puzzles puzzle library available on our membership site)

Puzzle Objective: This one is trickier than you may think! Figure out how many total rectangles are in the diagram.

Download: ⤓ Click here to download your pdf worksheet

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Why is a Square also a Rectangle? Video Explanation for Students

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Wait!

Do you want on-demand access to hundreds of 4th grade math activities, worksheets, and puzzles like the ones shared in this post?

Why are more and more math teachers using Mashup Math resources every school year? Because our activities are super engaging and loved by students—and having access to all of our resources in one convenient place will take your lessons to the next level and cut your planning time in half!
Plus, all plans include a risk-free 14-day trial so that you can make sure that our resources will be useful to you and your students. Note that you while you do have to enter your payment information to create an account, as long as you cancel during the trial period, you will not be charged.

Click here to sign-up for your free 14-day trial and find out why so many teachers rely on Mashup Math!

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Calculating Percent Change in 3 Easy Steps

Calculating Percent Change in 3 Easy Steps

Learning how to calculate percent change is an immensely handy and essential mathematical skill that has various applications inside of your classroom and in the real world as well.

(Looking for a Percent Change Calculator to make a super fast calculation: Click here to access our free Percent Change Calculator)

The ability to calculate, comprehend, and analyze percentages does not only come in handy on class assignments, assessments, quizzes, exams, the SAT, etc., but also in practical matters associated with every day life and several careers as well. In fact, percentages is one of the most useful math skills outside of the classroom, so understanding them is should not be discounted or overlooked.

While it is common for students to think that calculating percent change can be a confusing and demanding task with many steps, the reality is that correctly solving any percent change problem is actually extremely simple and painless.

Are you ready to learn how to easily solve any percent change problem? This post shares a free Calculating Percent Change step-by-step lesson guide that will painlessly teach you how to calculate percent change using an uncomplicated three-step process. If you can learn how to follow the three-step process demonstrated in this guide, you will gain the ability to swiftly and flawlessly solve any math problems or exercises that require you to find percent change.

Now that we are just about ready to learn the three-step process for calculating percent change, lets quickly review a handful of essential vocabulary words, concepts, and definitions related to percentages and percent change.

Looking to learn how to calculate percent increase or percent decrease? Use the links below to download our free step-by-step guides:

• How to calculate the percent increase between two numbers

• How to calculate the percent decrease between two numbers

Percent Definition

In terms of numeracy and mathematics, the word percent relates to parts per one hundred and the numerical symbol used to express percentages is %.

A simple example of a percent would be the value 60%. In this case, 60% represents 60 per 100.

Take a look at the diagram below. You should notice that the green shaded region makes up 60% of the whole.

Another way to express percent is to say that it is defined as a ratio of a value out of one hundred.

For another simple example, consider 30%. In this case, 30% is defined as 30 out of every 100. When viewing percentages as ratios of values out of one hundred, you can conclude that if 30% of 500 total people ride the train to work, then 150 total people ride the train—since 30 out of every 100 means that for every group of 100, we have to consider 30 people. So, 30 x 5 = 150 and 30% of 500 is 150.

Absolute Value Definition

To correctly calculate percent change, you will have to use absolute values. So, let’s do a quick review before we move on.

In math, the absolute value of a real number x, denoted using the vertical brackets |x|, is the positive (or non-negative) value of x.

The key thing to understand is that absolute values are always positive.

For example, the absolute value of 25 is equal to positive 25 AND the absolute value of -25 is equal to positive 25.

• |25| = 25

• |-25| = 25

This fact also applies to expressions inside of absolute value bars, for example:

• | 5 - 7 | = | -2 | = 2

• | 88 - 10 | = | 78 | = 78

• | 0 - 33 | = | -33 | = 33

Again, notice how the result is always positive.

Percent Change Definition

Now you are ready to consider the question: what is percent change?

In math, the percent change between two values—a starting value and a final value—is simply the difference between those two values expressed as a percentage.

Note that percent change can also be referred to in terms of percent increase or percent decrease. These terms are more specific than percent change.

• Percent Increase means that the final value is larger than the starting value. Final Value > Starting Value

• Percent Decrease means that the final value is smaller than the starting value. Final Value < Starting Value

Note that percent change will be expressed as a number with a percentage (%) symbol attached to it.

As for identifying the starting value and the final value, simply look for the first value that is given and the second value that is given (percent change problems will always involve two values).

For example, if Chris drove 120 miles in September and 150 miles in October, and you wanted to calculate the percent change in miles driven between the two months, you would start by identifying that the starting value is 120 and the final value is 150.

Simple enough? If not, please review the previous section again as being able to correctly identify the starting value and the final value is critical for finding the solution to percent change math problems.

Calculating Percent Change

Are you ready to learn how to calculate percent change by apply our easy three-step process?

For our first example, we will continue with the scenario involving Chris and his monthly driving mileage totals.

Calculating Percent Change Example #1

In our first example, we will calculate the percent change for the following situation:

Chris drove 120 miles in September and 150 miles in October. What is the percent change in miles driven between the two months?

Remember that you already figured out that the starting value is 120 and the final value is 150.

Now, you are ready to apply the three-step process to calculating percent change. Here is a preview of how it will work:

Step 1: Find the absolute value of the difference.

To perform step one, simply take the absolute value of the difference of the starting value and the final value.

• | Starting Value - Final Value | = ?

In this example:

• | 120 - 150 | = | -30 | = 30

Again, since absolute value is involved, the end result of step 1 will always be a positive number.

Step 2: Divide the difference by the starting value.

The second step is to take your result from step 1 (30 in this example) and divide it by the starting value (120 in this example) as follows:

• 30/120 = 0.25

For the second step, you will always express your result as decimal (never as a fraction). Otherwise, you will not be able to perform the third and final step.

Step 3: Multiply by 100

The last step is easy and straightforward: take your decimal result from step 2 and multiply it by 100, then express your final result using a % symbol as follows:

• 0.25 x 100 = 25.0%

Final Answer: 25% Change (or 25% Increase)

Note that this final answer can also be considered a percent increase since the final value was larger than the starting value (the number of miles driven increased over time).

That’s all there is to it! Applying the three-step process allows you to conclude that there was a 25% change in miles driven between September and October.

Now, let's take a look at another calculating percent change example problem where you will gain more practice applying the three-step process.

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Looking for a free Percent Change Calculator?

If you need a faster way to calculate the percent change between two numbers, check out our free Percent Change Calculator tool, which lets you input the starting and final values to get an instant answer!

▶ Click here to access our free Percent Change Calculator for students

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Calculating Percent Increase Example #2

Last semester, Ariana spent a total of 107 hours studying for exams. This semester, she spent a total of 86 hours studying for exams. What was the percent change in the total number of hours she spent studying between last semester and this semester?

Let’s start by identifying the starting value and the final value:

• Starting Value: 107

• Final Value: 86

Step 1: Find the absolute value of the difference.

Just like Example #1, start by finding the absolute value of the difference of the starting value and the final value.

• | 107 - 86 | = | 21 | = 21

Step 2: Divide the difference by the starting value.

The next step is to take your result from step 1 (21 in this example) and divide it by the starting value (107 in this example) as follows:

• 21/107 = 0.1962616822… ≈ 0.196

Remember to express your result as decimal!

Step 3: Multiply by 100

Finally, take your decimal result from step 2 and multiply it by 100, then express your final result using a % symbol as follows:

• 0.196 x 100 = 19.6%

Final Answer: 19.6% Change (or 19.6% Decrease)

Note that this final answer can also be considered a percent decrease since the final value was smaller than the starting value (the number of hours spent studying decreased over time).

All done! You have concluded that there was a 19.6% change in the total hours Ariana spent studying between last semester and this semester.

Now, let’s gain some more experience using the three-step process for calculating percent change by working through one final example.

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Calculating Percent Decrease Example #3

In 2023, 395 students attended the Loha High School Dance. In 2024, 861 students attended the Loha High School Dance. What was the percent change in the number of students who attended the Loha High School Dance between 2023 and 2024?

We will start example #3 the same as the previous two examples, by identifying the starting value and the final value:

• Starting Value: 395

• Final Value: 861

 Just like the last two examples, you can solve this problem by following the three-step process:

Step 1: Find the absolute value of the difference.

Start by finding the absolute value of the difference of the starting value and the final value.

• | 395 - 861 | = | -466 | = 466

Step 2: Divide the difference by the starting value.

The next step is to take your result from step 1 (466 in this example) and divide it by the starting value (395 in this example) as follows:

• 466/395 = 1.179746835… ≈ 1.18

Step 3: Multiply by 100

Finally, take your decimal result from step 2 and multiply it by 100, then express your final result using a % symbol as follows:

• 1.18 x 100 = 118.0%

Final Answer: 118% Change (or 118% Increase)

Note that this final answer can also be considered a percent increase since the final value was larger than the starting value (the number students in attendance increased over time).

Also note that it is totally fine to have an end result that is greater than 100%. In this case, a 118% increase means that the number of students in attendance more than doubled!

After working through three percent change examples, you should be feeling more confident in your ability to solve percent change problems using the three-step process. However, I highly recommend working through the examples again to further solidify your understanding so that you are successful on problems.

Conclusion: Calculating Percent Change

You can calculate percent change using a given starting value and final value by applying the following 3-step process:

Step 1: Find the absolute value of the difference between the starting value and the final value.

Step 2: Divide the result from Step 1 by the starting value and always express the result in decimal form.

Step 3: Multiply the result from Step 2 by 100 and express your final answer as a percentage (%).

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What about Calculating Percent Increase and Percent Decrease?

Learn how to calculate a percent increase or a percent decrease between two numbers using our free step-by-step guides. Click the links below to get started.

⇥ Calculating Percent Increase in 3 Easy Steps

⇥ Calculating Percent Decrease in 3 Easy Steps

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Don’t forget about our Free Percent Change Calculator

Click here to get started using our free Percent Change Calculator

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