5 Growth Mindset Books Every Math Teacher Should Read

Are you ready to help your kids think about and learn math with a growth mindset?

By teaching your students to embrace mistakes as learning opportunities, persevere through challenging problems, and focus on growth over final results, you are empowering them to excel inside and outside of the classroom.

Achieving a growth mindset requires a purposeful and well-planned strategy to ensure that your students consistently hear the right messages, receive meaningful feedback, and engage in learning opportunities that help develop this new way of thinking. 

Fortunately, there are plenty of resources to help you create a classroom environment that supports learning with a growth mindset. Whether you teach elementary, middle, or high school math students, the following books will give you all the tools you need to start changing students' attitudes and mindsets for learning and making math more open and exciting for every child.

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1.) Mindset: The New Psychology of Success

By Carol Dweck 

Summary: After decades of research, world-renowned Stanford University psychologist Carol S. Dweck, Ph.D., discovered a simple but groundbreaking idea: the power of mindset. In this brilliant book, she shows how success in school, work, sports, the arts, and almost every area of human endeavor can be dramatically influenced by how we think about our talents and abilities. People with a fixed mindset—those who believe that abilities are fixed—are less likely to flourish than those with a growth mindset—those who believe that abilities can be developed. Mindset reveals how great parents, teachers, managers, and athletes can put this idea to use to foster outstanding accomplishment.

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2.) Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching

By Jo Boaler

Summary: Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

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3.) The Growth Mindset Coach: A Teacher's Month-by-Month Handbook for Empowering Students to Achieve

By Annie Brock

Summary: The Growth Mindset Coach is a complete and easy-to-follow guide for inspiring every student with the power of a growth mindset Created by teachers for teachers, this is the ultimate guide for unleashing students’ potential through creative lessons, empowering messages and innovative teaching. The Growth Mindset Coach provides all you need to foster a growth mindset classroom, including a month-by-month program, research-based activities, hands-on lesson plans, real-life educator stories, constructive feedback, and sample parent letters.
 

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Looking for fun ways to get your kids WRITING about math?

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4.) Mind for Mathematics, A: Meaningful Teaching and Learning in Elementary Classrooms—useful classroom tactics and examples for K–6 math

By Nanci N. Smith

Summary: What does it take to be a good mathematics teacher who actively engages students and addresses learning differences? Gain a mental picture of an effective mathematics learning environment and why it must be founded on growth mindset principles. This easy-to-read text breaks down the complex components of mathematics teaching and divides them into practical strategies. Combining mathematics research, useful tactics, and examples from K–6 classrooms, the book includes reflection questions, action tasks, and activities to inspire and engage mathematical minds.

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5.) 101 Growth Mindset Quotes for Kids

By Anthony Persico

Summary: Nurturing a growth mindset with your kids starts with sharing the right messages every day. This PDF eBook shares 101 growth mindset quote graphics that will give your kids a daily reminder that mistakes are the stepping stones along the path to success, with motivational quotes by individuals including Albert Einstein, Michael Jordan, J.K. Rowling, Ellen DeGeneres, Barack Obama, Thomas Edison, Taylor Swift, Kid President, and many more! Each quote is displayed on a full-page graphic that is meant to be printed and/or displayed in your classroom--they are perfect for sparking open discussions and for Growth Mindset bulletin boards. You can learn more by clicking here.

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Have more growth mindset book suggestions for your fellow math teachers? Join the conversation and share yours in the comments section below.

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By Anthony Persico

How to Find the Surface Area of a Cube

How to Find the Surface Area of a Cube in 3 Easy Steps

Learning how to find the surface area of a cube and how to apply the surface area of a cube formula is a critical and important math/geometry skill that every student should master. Fortunately, calculating the area of a cube is a pretty straightforward task as long as you are able to follow three simple steps for finding the surface area of any cube that are demonstrated in this lesson.

Are you ready to get started?

The following free How to Find the Surface Area of a Cube lesson guide is a step-by-step tutorial that will teach you how to use a simple method for calculating the surface area of a cube using the surface area of a cube formula to solve homework problems, test questions, and more.

This guide also includes a completely free surface area of a cube calculator that can be used to make fast calculations and find the surface area of a cube almost immediately (and while we do not recommend relying on a calculator to solve surface area problems, having access to a calculator can be a very helpful tool when it comes to checking your work—but more on that later!)

Now we are ready to learn how to find the surface area (sometimes referred to as SA) of a cube and we will start with a quick recap of some very important vocabulary and definitions.

In math, what is a cube?

Definition: A cube is a box-shaped three-dimensional figure that has six equal and identical square faces.

The most important word in this definition is equal. A cube is unique in that all of its faces are squares with side lengths, also known as edges, that have the same length (unlike rectangular prisms).

Also make a note that the terms cube and rectangular cube both mean the exact same thing (some questions will refer to a cube as a rectangular cube).

What is the surface area of a cube? What is the SA of a cube?

Definition: The surface area of a cube refers to the total area of all of the faces on the outside of the figure.

The key word in this definition is outside since surface area refers to how many square units it would take to cover the outside of the figure

Surface area is always expressed in square units.

Surface Area of a Cube Formula

Before we get to the practice problems, you need to understand how to use the surface area of a cube formula, which states that the SA of a cube is equal to six times the side length, s, raised to the second power (also known as squared).

If you know the length of one of the edge lengths (or sides), you can simply input the value into the formula and solve to find the surface area.

 Again, remember that SA is measured in square units and that your answers should always include units.

Formula Reference:

Now that you know the surface area of a cube formula, you can use the following 3-step method to solve the practice problems below:

Step 1: Identify the value of s, the edge length of the cube

Step 2: Substitute that value for s into the surface area of a cube formula

Step 3: Solve and express your answer in square units

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Example #1: Find the Surface Area of the Cube

Find the surface area of a cube with a side length of 4 cm.

To solve this problem, we will use the previously mentioned 3-step process:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube has a side length of 4 cm, so S=4

Step 2: Substitute that value for s into the surface area of a cube formula

Next, substitute 4 for s in the SA of a cube formula as follows

SA = 6(s^2) ➝ SA= 6(4^2) ➝ SA = 6(16) ➝ SA = 96

Step 3: Solve and express your answer in square units

Finally, you can conclude that SA equals 96, therefore…

Final Answer: The surface area of the cube is 96 square centimeters.

Remember that surface area is always expressed in square units (square centimeters in this example).

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Example #2: Find the SA of the Cube

Find the SA of a cube-shaped box with a height of 9 inches.

In this example, the figure in question is a cube-shaped box or just a cube, so you will be using the process as Example #1 to find the surface area:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube-shaped box has a side length of 9 inches, so S=9

Step 2: Substitute that value for s into the SA of a cube formula

Next, substitute 9 for s in the SA of a cube formula as follows

SA = 6(s^2) ➝ SA= 6(9^2) ➝ SA = 6(81) ➝ SA = 486

Step 3: Solve and express your answer in square units

Finally, you can conclude that SA equals 486, therefore…

Final Answer: The SA of the cube is 486 square inches

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How to Find the Surface Area of a Cube Video

Are you looking for more help with finding the volume and surface area of cubes? Check out our free step-by-step video lesson below:

Surface Area of a Cube Calculator

If you want to use a surface area of a cube calculator to help you when solving SA problems, we recommend Google’s free Surface Area of a Cube Calculator, which allows you to input the edge length (which they refer to as a instead of s) and find the SA with just one click.

Keep in mind that relying on a calculator is never a substitute for learning how to solve problems on your own. However, there are occasions when such a tool can come in handy, like when you want to check your final answers.

(Note: Google’s calculator uses the letter a, not s, to represent the value of the edge length.)

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What About the VOLUME of a Cube?

Now that you’ve learned how to find the surface area of a cube, you’re ready to move on to learning how to use a different formula to find the volume of a cube.

You can use the link below to access our free guide to finding the surface area of a cube.

Click here to access a free Volume of a Cube step-by-step guide.

Conclusion: How to Find the Surface Area of a Cube

You can find the SA of any cube with edge length S by following this easy 3-step process:

Step 1: Identify the value of s, the edge length of the cube

Step 2: Substitute that value for s into the surface area of a cube formula

Step 3: Solve and express your answer in square units

Keep Learning:

How to Find the Volume of a Cube

How to Find the Volume of a Cube in 3 Easy Steps

Understanding how to find the volume of a cube and how to use the volume of a cube formula is an important and useful mathematics and, more commonly geometry, skill that is relatively simple and easy to do as long as you can follow the 3 easy steps that will be outlined in this lesson.

 This free How to Find the Volume of a Cube step-by-step guide will teach you an easy method for finding the volume of a cube using the volume of a cube formula. By learning this skill, you will be able to solve any problems that call on you to find the volume of a cube (or a rectangular cube) involving any type of units.

This lesson also shares a free volume of a cube calculator that you can use to quickly input values and find the volume of a cube with just one click.

But before you learn the 3 steps for finding the volume of a cube, we will do a quick review of key vocabulary and definitions related to this topic.

What is a cube in math?

Definition: A cube is a box-shaped three-dimensional figure that has six equal and identical square faces.

The key word in this definition is equal. Unlike a rectangular prism, all of the faces of a cube are squares whose side lengths, also known as edges, have the same length.

Note that there is no difference between the term cube and rectangular cube. They both mean the same thing!

What is the volume of a cube?

Definition: The volume of a cube refers to the number of unit cubes it would take to completely fill the inside of the figure.

The key word in the definition is inside, since volume refers to how much space is inside of the figure.

Volume is always expressed in cubic units.

Volume of a Cube Formula

Before we work through a few practice problems, you need to be familiar with cube volume formula, which states that the volume of a cube is equal to the value of the side lengths, s, raised to the third power (also known as cubed).

 So, if you know the length of one of the sides (also known as edges), all that you have to do raise that value to the third power to find the volume.

 Again, remember that volume is measured in cubic units and that your final answer should always include the units.

Formula Reference:

Now that you are familiar with the formula for finding the volume of a cube, you can use the following 3-step method to solve the practice problems below:

Step 1: Identify the value of s, the edge length of the cube

Step 2: Substitute that value for s into the volume of a cube formula

Step 3: Solve and express your answer in cubic units

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Example #1: Find the Volume of the Cube

Find the volume of a cube with a side length of 4 cm.

To solve this problem, we will use the previously mentioned 3-step process:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube has a side length of 4 cm, so S=4

Step 2: Substitute that value for s into the volume of a cube formula

Next, substitute 4 for s in the volume of a cube formula as follows

V = s^3 ➝ V = 4^3 ➝ V = 4x4x4 ➝ V = 64

Step 3: Solve and express your answer in cubic units

Finally, you can conclude that 4^ 3, or 4x4x4, equals 64, therefore…

Final Answer: The volume of the cube is 64 cubic centimeters.

Remember that volume is always expressed in cubic units (cubic centimeters in this example).

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Example #2: Find the Volume of the Cube

Find the volume of a cube-shaped box with a height of 9 inches.

In this example, we are dealing with a cube-shaped box, which is still just a cube, so we can use the same three steps as Example #1 to find the volume:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube-shaped box has a side length of 9 inches, so S=9

Step 2: Substitute that value for s into the volume of a cube formula

Next, substitute 9 for s in the volume of a cube formula as follows

V = s^3 ➝ V = 9^3 ➝ V = 9x9x9 ➝ V = 729

Step 3: Solve and express your answer in cubic units

Finally, you can conclude that 9^ 3, or 9x9x9, equals 729, therefore…

Final Answer: The volume of the cube is 729 cubic inches

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How to Find the Volume of a Cube

Are you looking for more help with finding the volume and surface area of cubes? Check out our free step-by-step video lesson below:

Volume of a Cube Calculator

Are you looking for a free volume of a cube calculator to quickly solve problems? While we recommend learning how to solve problems without relying on a calculator, there are times when this tool can be very useful (like when you need to check your answers for accuracy).

There are many cube volume calculator options available online, but we recommend Google’s free calculator, which you can access by Googling “volume of a cube calculator” or by clicking this link.

Note that Google used the letter a instead of the letter s.

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What About the Surface Area of a Cube?

Now that you know how to use a formula to find the volume of a cube, you are ready to learn how to use a different formula to find the surface area of a cube.

Whenever you are ready, use the link below to access our free guide to finding the surface area of a cube.

Click here to access a free Surface Area of a Cube step-by-step guide.

Conclusion: How to Find the Volume of a Cube

You can find the volume of any cube with edge length S by following this easy 3-step process:

Step 1: Identify the value of s, the edge length of the cube

Step 2: Substitute that value for s into the volume of a cube formula

Step 3: Solve and express your answer in cubic units

Keep Learning:

Using Cheez Its to Teach Kids Area and Perimeter

Are you looking for a fun and engaging activity to help your kids explore and understand the properties of area and perimeter?

In my recent VLOG, I share how you can use Cheez It crackers as a hands-on tool for exploring area and perimeter. The activity includes a free worksheet and includes ideas for higher-level applications.

This lesson can be applied at the elementary and middle school levels.

Download the free lesson worksheet: CLICK HERE 

Have any thoughts on this lesson idea? Share your thoughts and suggestions in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

How to Find Mean, Mean, Mode and Range: Your Complete Guide

Central Tendency: Mean, Median, Mode, and Range

Welcome to this complete step-by-step guide to central tendency and how to find the mean, median, and mode of a data set.

This post will share key information, formulas, and vocabulary so that you can use math to determine the mean, median, mode, and range of any data set and understand what these values represent.

After working through two examples, you will also have access to a free mean, median, and mode pdf practice worksheet that includes an answer key.

Key Questions

Now let’s go ahead and begin this lesson by raising two key questions:

 For a given set of data…

• What does the mean, median, mode, and range represent?

• How can you find the mean, median, mode, and range of a data set?

What is Central Tendency?

Mean, median, and mode are measures of central tendency and are three different ways of expressing averages of a set of data.

 The key term here is average. In math, central tendency is a number or value that can be used to describe a central position, or average value, within a data set.

 Furthermore, the range of a set of data is the difference between the highest and lowest values.

With this key math vocabulary in mind, let’s take a look at two examples

Example 01: Find the Mean, Median Mode, and Range

 Find the mean, median, mode and range of the data set: 1, 6, 7, 4, 6, 8, 3

*Before you find the mean, median, mode, and range of a data set, be sure to rewrite the list of values in either ascending (least to greatest) or descending (greatest to least) form.

For today’s examples, we will be rearranging the original data set into ascending form where the values are placed in order from least to greatest as follows:

Now that we have rearranged the values of the data set in ascending order, we are ready to find values of central tendency.

Step 01: Find the Mean

 How to Find the Mean of a Data Set

 The mean is the numerical average of a data set.

 To determine the mean of the data set, divide the total sum by the total amount of numbers.

 In this example, to find the total sum, add all seven values in the data set together as follows:

 1 + 3 + 4 + 6 + 6 + 7 + 8 = 35

 The total sum is 35.

 Next, divide the total sum by the total amount of numbers in the data set (which, in this example is 7).

 35/7 =5  >>> The mean is 5 goals per game.

Mean Formula

For future reference, here is a handy formula that you can always use to find the mean of a data set. To determine the mean, simply divide the total sum of all of the values in the data set by the total number of values as follows:

Step 02: Find the Median

The median is the middle number or value of a data set.

To determine the median of numbers in the data set, simply find the middle value.

In this example, notice that there is an odd number of values in the data set (7 total). To find the median of numbers, start crossing the “bookend values” on each side of the data set as you make your way towards the middle until only one value remains as follows…

Clearly, the middle value is 6, so you can conclude that the median of the data set is equal to 6.

*Note that when there is an even number of values in the data set, using this strategy to find the median will require one extra step (we will go more in depth in example 2).

Median Calculator

Looking for a quick way to central tendency values? This median calculator (which is really a mean, median, mode calculator from Calculator Soup) is an excellent tool for quickly finding these values. However, this website should only be used a tool for checking your work and not a substitute for understanding how to actually find the mean, median, mode, and range of a data set.

Step 03: Find the Mode

 The mode of a data set is the most common number. It is possible to have more than one mode, or no mode at all.

 If you’re looking for a simple answer to how to find the mode of a data set, then you’re in the right place. To find the mode, simply look for the value that occurs the most often (i.e. the value that repeats more than any other value).

In this example, notice that the only value that repeats is 6…

Therefore, you can conclude that the mode for this data set is 6.

How to find the mode of a data set…

Just like in example 01, you can find the mode of a data set by determining which value is the most common. You can find this value by looking for numbers that repeat.

And remember that it is possible to have more than one mode or no mode at all!

Step 04: Find the Range

The range is the difference between the highest and lowest values in the data set (the largest number minus the smallest number).

 To calculate range math, simply determine the largest and smallest values and then find the difference by subtracting (rearranging the numbers in ascending order at the very start of this example males calculating the range very easy).

In this example, the largest number in the data set is 8 and the smallest number in the data set is 1.

To find the range, simply perform 8 – 1 = 7

Therefore, the range is 7 goals.

Quick Summary:

 And now we have found all values of central tendency for this example. Here is a quick summary of what you just did!

 Keep in mind that the process for determining mean, median, mode, and range of any data set is pretty much always the same. So, now let’s try a second example that involves a larger data set!

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Example 02: Find the Mean, Median Mode, and Range

Find the mean, median, mode and range of the data set: 15, 9, 16, 9, 20, 14, 10, 9, 10, 9

Again, just like in Example 01, start by rearranging the numbers in the data set so that they are in ascending order from left to right…

*Note that the values in the data set have not changed. All that you did was rewrite them in order from least to greatest, which will make finding the mean, median, mode, and range much easier for you (with or without a calculator).

Now you are ready to find the mean, median, mode, and range of this data set.

Step 01: Determine the Mean

To find the mean of the data set, remember to apply the mean formula, where you find the total sum of all of the numbers and divide it by the total number of values in the data set.

In this case…

9 + 9 + 9 + 10 + 10 + 14 +15 + 16 + 19 + 20 = 131 (the total sum)

and there are 10 total numbers.

131/10 =13.1  >>> The mean is 13.1 hours studying

*Note that it will often be the case that the mean value is decimal.

Step 02: Find the Median

Remember that the median represents the middle value of a data set.

To determine the median of numbers in the data set, you perform the same process of crossing out the “bookend values” on the left and right of the data set until you reach the middle. Unlike the last example where the data set had an odd number of values, this data set has an even number of values (ten in total), which means that there will one be extra step involved to find the median.

After crossing out the outside values and working your way to the middle, you will notice that, because the data set has an even number of values, there are two values in the middle (in this case, 10 and 14).

So, which value is the median?

In cases like this, the median is the average of the two values. To find the average, simply add the two values together and divide the sum by two as follows:

10+ 14 = 24 >>> 24/2 =12

The median of the data set is 12 hours.

Step 03: Find the Mode

Remember that the mode of any data set is the most common number and that the key to finding the mode is to look for repeat values.

Notice that this data set has two values that occur more than once: 9 and 10. In this case, 9 shows up three times and 10 shows up twice. Since 9 shows up more often than 10, you can conclude that 9 is the most common number in the data set and that the mode is 9.

Step 04: Find the Range Math

The last remaining measure of central tendency that you must find is the range, which is the difference between the largest number and the smallest number.

To calculate range for this example, look at the data set and identify the largest value (20) and the smallest value (9) and then find the difference as follows

20 -9 = 11 >>> The range of the data set is 11.

Example 02 Conclusion

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You can click the link below to watch the animated video that accompanies this lesson.

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Have thoughts? Share your thoughts in the comments section below!

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By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.