Using Checkbooks as a Teaching Tool

Bank account balance problems can be a part of everyone’s life and it used to be a problem for me in my early twenties, just getting started with a young daughter to raise.  

We start to teach students this concept typically in the fourth or fifth grade because that is when the basic math concepts are developed, however the students will not have the opportunity to legally have a checkbook until they are sixteen and they must share the account with a parent or guardian.

An understanding the the basics of the associative property, additive inverse property and additive identity property is necessary to balance a checkbooks. and bank accounts. We are constantly adding money, the withdrawing, perhaps using a check card to return something and a credit is added to our accounts.

Having a checking account is a necessity for most people in this fast pace world and can be a bigger issue today than in years past with a high percentage of young students having check cards and not paying attention to their balance. The speed at which the money comes out of our accounts is far greater than 20 years ago.

In Practice

A prime example of this particular problem could be a single mother with a young child, just getting out on her own. She can deposit $200.00 in her checking account and then spend $90.00 for daycare and $75.00 on gas. She deposits another $75.00 and spends $95.00 on diapers and groceries. She goes to the local restaurant to meet with friends and pays her dinner tab of $35.00 with a check card assuming she has the funds to do so. This actually puts her in the red -$20.00. 

The above example is very easy for people to do if they do not use their check register properly, using the basic math they learn in elementary school.   This video shows how a teacher uses a pretend business to help students understand deposits and withdrawals, and the use of a checkbook.

Free printable checkbooks are available online and can be used in the classroom to carryout exciting activities.

Brainpop offers a game to help understand the associative property. This website offers a free trial, but continued use requires a subscription.

Proper Fractions

Proper fractions, like ¼, ½, ¾ are used frequently in everyday life. Improper fractions such as 9/8, 11/4 are also used, but less frequently by the average person like myself. Today I am narrowing my discussion down to proper fractions.

Every day life Examples

As found in Mathematics: For Elementary School Teachers by O’Daffer et al, a cartoon from the paper provides a good example of how children need to understand fractions. The cartoon shows siblings, a little boy and a little girl, who receive sandwiches for lunch. The girl has her sandwich cut in 1/2 and the boy’s is cut in ¼’s. The girl does not understand why she only gets 2 sandwiches and her little brother gets 4.

A real world example used at the work place is a construction worker, such as a house framer. The framer would use proper fractions with his tape measure with every cut of a board he may use to finish building his project.

An example of how a parent may use proper fractions at home could be when the parent divides up chores at home for her children: there are 6 six jobs to be completed by three of her children. Each child receives 2 chores, splitting the work load into 1/3 per child.

Learning Tools

This video provides some examples with the use of visuals to help generate a deeper understanding of proper fractions and would be useful to show children in your elementary math class:

Since fractions play such a role in our lives, it is important that young children understand them and are able to use them. Dr Mike's Math Games for Kids offers a great idea for a game that can be used to help children understand fractions while having fun.

Prime Numbers vs Composite Numbers

What is the difference between a prime number and a composite number? First, let us define them both. A prime number is any number greater than 1 that is only divisible by itself and the number 1.

Examples of prime numbers: 2, 3, 5, 7, 11, 13, 19…

A composite number is any number greater than 1 that is divisible by at least three numbers, including 1 and itself.

Examples of composite numbers: 4, 6, 8, 9... These are valid examples because the number 4 can be divided by 1, 2, and 4:

4÷1 = 4

4÷2 = 2

4÷4 = 1

Notice both prime numbers and composite numbers include numbers greater than 1. The number one is neither prime nor composite.

Watch this educational video that helps us better understand the difference between prime and composite numbers.

For a fun way to practice your knowledge of prime and composite numbers, try the Fruit Shoot Game.

Mental Computation vs Estimating

We use mental computation all the time in our every day lives without even realizing it. For example, if you are at the store shopping on a limited budget, you want to keep track of your spending to ensure you don't go over a certain dollar limit. In your mind, you would add up the dollar amounts of everything you put in your cart. Mental computation is the process used to find an exact answer to a problem using no tools other than your mind. Therefore we must put aside the pen and paper or the calculator and draw upon our amazing minds to help us arrive at the answer.

I have loosely used the terms mental computation and estimating interchangeabley. This is incorrect because they are two distinct processes.  Estimating is getting “close” to the right answer, whereas mental compuation will get you to the exact answer. There is a time and place for both, but understanding these difference are very important.

To illustrate the difference between mental compuation and estimating, follow my thought process as I personally had the revaltion that there is a difference between the two process. I visited a webpage Valuing Mental Computation Online . This website asked a simple question: how many 45 cent stamps can you buy with ten dollars. In my typical thought process, I mentally rounded the stamps to 50 cents each, and then considered this to be two stamps per dollar. If I have ten dollars, then I can buy 20 stamps. This is where I left my answer, and thus, where I realized I had a lazy throught process. I failed to consider the balance of 5 cents per stamp and how many that would equate to, which is an additional two stamps. I clicked on the link for the answer, and much to my surprise, I was not right in my 20 stamp guess. See the image below for how the mental computation may be correctly executed:

Constructive Learning

Constructive learning is a way to “use the tools you have” to gain new set of tools. More specifically, the concept of constructive learning helps us use the knowledge we already have and apply it in a matter that allows us to learn something new. Educators use this tactic in the classroom with great success. The video on constructivist math correcting showed how students worked together to correct their own math assignments. The neat thing about the exercise in this video is the students were able to learn from each other. This is a great way for students to learn because often times they can relate to each other more easily than a student/teacher relationship. The students are basically closes in knowledge and life experiences (especially comparing an elementary student to the teacher) so they can draw upon their life experiences to explain things in a way that makes more sense to them. Take a look at this video:

Now think about this skills learned in this exercise. It wasn’t simply learning how to solve the math problems. The students learned other valuable skills such as how to respectfully work together and how to communicate effectively with one another. Additionally, for those who had the right answer, and then had to explain it to his or her peers, they were able to use this method to reinforce their learning experience in a memorable way.

Constructivist lessons do not only need to come from the direction of peers alone. Mr. McCloud uses constructivist math lessons in his seventh grade math classroom to find the surface area of a cylinder. Watch the video of his exercise. Notice how the students work together to solves the problem. They also use real objects- a can – to help them relate the problem to something they have seen before. Review this lesson at the link below by watching the video.

Discovering Surface Area of a Cylinder

Now, let’s go beyond the classroom and think about the lessons created at home that could be considered constructivist math. We may not realize it but the common card games we play, such as cribbage or rummy requires basic math skills for addition and subtraction. Playing these games with children requires them to use their math skills in a practical application. The same could be said of dice games, such as the game 10,000.  If a parent wants to be really proactive, they could go out on the web and find games online that require students to use their math skills to “win” or earn points in a game. The website Learning Games for Kids is an example of online resources that combine learning and fun to enhance student enagement. Check it out: Learning Games for Kids.

Working with Base Numbers

Who would have thought Mathematics for Elementary School Teachers would be so different that what I learned in elementary school 35 years ago. I guess this is a sign of the times and the increased level of importance that math plays in our lives. I invite you on this journey with me by following my blog throughout this semester.

Blog Week ONE: Base numbers... what are they and why do they matter?

You may never have given it much thought, but we operate on a decimal system referred to as base-10 system. We use a numbering scheme of  0, 1, 2, 3, 4, 5, 6, 7, 8, 9. No matter what you do with these numbers, you will always end up with some configuration of them. For example:

1+ 9 = 10

10 is not beyond the base-10 system simply because it runs from 0-9. Rather, we look at is "rolling over" and starting at the beginning 0 and add a one in the tenths place. This cycle continuously repeats itself. This idea has been adopted from Ryan Somma, a software developer who shared his knowledge with the world through his website. Refer to think link below to reach his website:

Why a Base-10 System


A couple interesting facts of a base-10 system:
Consider the metric ruler. A ruler deals only in centimeters and millimeters. A millimeter is 1/10th of a centimeter. This format is used universally.

We have 10 fingers... one for each base!

Learning the base-10 system can sometimes be tricking. I have posted links to two videos I found useful in understanding the concept. Refer to the two videos below: