menu   Home Answers Math Games Free Resources Contact Me  

Unlocking Fractions for the Confused and Bewildered

I teach remedial math on the college level, and I find that numerous students are left behind in the mathematical dust if only one strategy is used or introduced when learning fractions. Finding the lowest common denominator, changing denominators, not changing denominators, finding a reciprocal, and reducing to lowest terms are complex issues and often very difficult for many of my students. I classify my students as mathphobics whose mathematical anxiety is hard to hide. One of my classes entitled, Fractions, Decimals and Percents, is geared for these undergraduates who have never grasped fractions. This article encompasses how I use a different method to teach adding fractions so these students can be successful. Specifically, let's look at adding fractions using the Cross Over Method.

Below is a typical fraction addition problem.  After writing the problem on the board, rewrite it with the common denominator of 6.

1) Ask the students if they see any way to multiply and make a 3 using only the numbers in this problem.

2) Now ask if there is a way to multiply and make 2 using just the numbers in the problem.

3) Finally, ask them to find a way to multiply the numbers in the problem to make 6 the denominator.

4) Instruct the students to cross their arms. This is the cross of cross over and means we do this by cross multiplying in the problem.

5) Multiply the 3 and 1, then write the answer in the numerator.  *Note: Always start with the right denominator or subtraction will not work.

6) Next multiply the 2 and 1 and write the answer in the numerator. Don’t forget to write the + sign. *Note: One line is drawn under both numbers. This is to prevent the students from adding the denominators (a very common mistake).

7) Now have the students uncross their arms and point to the right using their right hand. This is the over part of cross over. It means to multiply the two denominators and write the product as the new denominator.

8) Add the numerators only to find the correct answer.

9) Reduce to lowest terms when necessary.

Fractions Resource
It is important that students know the divisibility rules for 2, 3, 5, 6, 9 and 10. In this way, they can readily reduce any problem. In addition, it is extremely important that the students physically do the motions while they learn. This not only targets the kinesthetic learner but also gives the students something physical that makes the process easier to remember. The pictures or illustrations for each technique also benefit the visual/spatial learner. Of course, the auditory student listens and learns as you teach each method. 

I have found these unconventional techniques are very effective for most of my students.  If you find this strategy something you might want to use in your classroom, a resource on how to add, subtract, multiply, and divide fractions is available by clicking on your right.

A Go Figure Debut for a Canadian Who is New


Today we move north, way north to British Columbia to meet a Teachers Pay Teachers seller. Sandra has been teaching for 22 years in the very urban and ESL environment of East Vancouver. She spent ten years in Kindergarten and the rest in first and second grades. For one of those years, she taught kindergarten in New Zealand which is a long ways from Canada!

Like many of us, her teaching style evolved over the years. She strongly believes in demonstrating and preserving respect for all of her students while having classroom structure and firm boundaries. She feels that children work best in an environment where they do hands-on activities in addition to being able to walk around and talk while learning. She recognizes that children learn to read when they read every day, and this is particularly true for struggling readers.

She has three university degrees…a B.A. in English Language (the history and development of the English tongue, not the literature developed from it), a B. Ed and a Masters of Education. What is even more impressive is that she has ten years of classical piano training from the Royal Conservatory of Toronto. This is why she describes herself as a classroom teacher who loves to teach music.

In her former life as a single, carefree woman, she traveled while having lots of adventures. Now she is a full-time teacher with two small children (oldest in kindergarten). Besides creating outstanding products for Teachers Pay Teachers, she loves paper crafting and scrap-booking as well as a playing and watching ice hockey. (Did she say playing?)

Falling Leaves
Thanksgiving Unit
Sandra currently has 54 products in her store that comprise various grade levels and subjects. Since it is October, her Falling Leaves (K-2) is a perfect resource, and it’s free. There are four mini books in this download that can be used for different levels of reading in a K/1 class. The books focus on interpreting the text, copying, signs of fall, drawing and coloring as well as using fine motor skills.

Sandra also has a 35 page Thanksgiving unit that includes two big books, a shape book, a pattern book, and a finger play poem with language and art activities. This unit is language based, and includes lessons on reading, writing, singing, finger plays and art.

I trust you will take a few minutes to visit her store and see the many first class resources she is offering.  You might also enjoy her blog which is called Sandra's Savvy Teaching Tips.  While you are there, why not become her newest follower?

Learning Geometry Using Number Tiles

My college students will soon start the unit on plane geometry.  I love teaching geometry because it is so visual, but there are others who despise it because of the numerous new words to learn.  In fact, our plane geometry unit alone contains over 50 terms that must be learned as well as understood.

I have found that with my students, mathematical language is either a dead language (It should be buried and never resurrected!), a foreign language (It sounds like a different language from a far away country.), a nonsense language (It makes no sense to me - ever!) or a familiar, useful language. Many times, they are unduly frustrated because mathematical language has never been formally taught or applied to real life.  For example, many primary teachers will have their children sit on the circle when in fact, the children are sitting on the circumference of the circle.  What a wonderful, concrete way to introduce children to the concept of circumference!  Yet, this teaching moment is often missed, and circumference doesn't surface again until it is time to teach the chapter on circles.

Plane Geometry + Number Tiles
Because I believe it is important to find different ways to introduce and practice math vocabulary, I created a new resource for Teachers Pay Teachers entitled: Geometric Math-A-Magical Puzzles.  It is a 48 page handout of puzzles that are solved like magic squares. Number tiles are positioned so that the total of the tiles on each line of the geometric shape add up to be the same sum. Most of the geometric puzzles have more than one answer; so, students are challenged to find a variety of solutions.

Before each set of activities, the geometry vocabulary used for that group of activities is listed. Most definitions include diagrams and/or illustrations. In this way, the students can learn and understand new math words without difficulty or cumbersome words. These activities vary in levels of difficulty. Because the pages are not arranged in any particular order, the students are free to skip around in the book. All of these activities are especially suitable for the visual and/or kinesthetic learner.

A ten page free mini download of this item is available if you want to try it with your students. Check it out!