menu   Home Answers Math Games Free Resources Contact Me  

You're Teaching Fractions All Wrong! Don't Flip!

My college students in remedial math just finished the chapter on fractions. Talk about mathphobia. Dividing fractions was the most confusing for them because it requires finding the reciprocal of the second fraction, changing the division sign to a multiplication sign, and then multiplying the numerator times the numerator and the denominator times the denominator.

Let me introduce a new method entitled "Just Cross".

First and foremost, you must understand what division is. The statement 8 ÷ 4 means 8 divided into 4 equal sets, OR how many fours are in eight, OR how many times can we subtract 4 from 8? (Yes, division is repeated subtraction.)

Let me explain this using a hands-on visual. Let’s assume the fraction problem is:
The question being asked is, “How many ¼’s are in ½?” 
First, fold a piece of paper in half. The figure on the left represents ½. Next, fold the same sheet of paper in half again to make fourths as seen in the illustration on the right. When you unfold the paper, you will notice a total of four sections. So answering the original question: “How many ¼’s are in ½”, you can see that the half sheet of paper contains two parts; therefore:
Using the same example, to work the problem, the fraction 1/4 would have to be flipped to 4/1 nd then 1/2 would have to multiplied by 4/1 to get the correct answer of 2. That is why the division of fractions requires that the second fraction be inverted and the division sign be changed to a multiplication sign.

Let’s use the same fraction problem, but let’s utilize a different method entitled Just Cross. 
  • Cross your arms as a hands-on way of remembering the process.
  • Now multiply the denominator of 4 by 1 the denominator of 2 by1 as seen below. (We do nothing with the denominators.) Notice we always start on the right side and then we go to the left side. If it is done the opposite way, the answer will be incorrect. The answer of our first "cross" is the numerator (4 x 1); the answer to our second "cross" (2x1) is the denominator.
  • Now simply divide 4 by 2 to get the answer of 2.
No flipping; no reciprocal, no changing the division sign to a multiplication sign. Just Cross and divide. Amazingly, it works every time. 

Although fractions are something every student should learn, often times numerous students are left behind in the mathematical dust when a math textbook is followed page by page. I have a resource that features different ways to teach fractions using hands-on strategies similar to the one above. The unconventional techniques described in this math resource will always work.  Just go to Unlocking Fractions for the Confused and Bewildered.

A 2022 Go Figure Debut for a Reading Specialist Teacher Who is New!

Gini was a teacher for 31 years, 29 as a reading specialist. She has also taught ALL grades, K-12, in many formats - large class, small group, co-teaching, push-in, pull-out. You name it; she did it. She has always tried to meet her students where they are, learn about them individually, and group them accordingly for maximum progress. Retired now, she is still tutoring struggling readers, although she has been doing it only virtually since the pandemic started. Amazingly, remote learning has been going very well.

Surprise! Her favorite pastime is, reading. She loves non-fiction, mostly biographies, history, poetry, and educational research. Nerd that she is, Gini still looks for new and effective teaching ideas. Once in a while, she even reads a fiction book if it comes highly recommended.

Gini is also an avid gardener (So am I!). You can see photos of her Pittsburgh garden on Pinterest @ Loving Her Garden. On the left is just one of the many beautiful photos.

Believe it or not, Gini has no grass in her yard. She claims she was well ahead of climate change concerns when she developed it almost 40 years ago. She rarely has to water her garden, but oh, the weeds! She used to do all of the weeding and pruning herself until about 10 years ago when she started needing joint replacements. She now has a total of five (two knees, two hips, one shoulder). One more, and she will be totally bionic.

She is also an avid golfer. She used to play golf with her husband for 40 years about 3-4 times a week, mostly after school and in the summer. They often played moonlit golf as they usually were the last ones on the course. All that practice helped her win eight Women’s Championships and eight Husband and Wife Championships, though not in the same years. Her hubby still plays golf and often shoots his age or under, but she rarely plays anymore.

Gini joined TPT (Teachers Pay Teachers) in the first or second year of its development. (Me, too! We're oldies but goodies!) Currently, she has 122 resources in her store called Reading Spotlight with 20 of them being free. She joined because she wanted to share her best resources for effective and enjoyable practice for beginning and struggling readers. Having been an English teacher, her store also contains many fun grammar practice activities.

Her first free item ever posted on TPT was Johnny Appleseed: A Tall Tale Grammar Story, and it is still a popular download.  It is a Tall Tale Grammar story to practice grammar and spelling skills with intermediate and middle school students. The tale focuses on the most common errors in homophones, subject (verb agreement, apostrophe, capitalization, punctuation, irregular verbs and irregular plurals).

Gini's featured paid resource is a bundle entitled Learn To Read Bingo: Vowels.  Effective, enjoyable, and easy-to-use, this bargain bundle is a terrific way to practice the basic fundamentals of decoding. It is so-o-o much better than passing out another boring phonics worksheet.

The latest brain research indicates that humans remember in patterns. These games reinforce the most common short and long vowel phonograms in English. This word family approach improves reading, writing, and spelling, and the games are especially effective with students who do not hear phonics sounds well.

Gini developed many more Bingos and Word Searches for word analysis practice because she found that many struggling readers simply had gaps in their skills due to a lack of mastery for various reasons. She discovered all that many of them needed was extra practice in that skill.

Having taught several thousand struggling readers to read is the most rewarding experience of her life. Gini thanks all of them for their trust in her. Continuing to help them makes her feel useful and makes her happy every day.

Gini has other places where you can view her resources, read her blog posts or just get teaching ideas and strategies.


Again, I am featuring a TPT seller who is also a member of The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC) of which Gini and I are members. TBOTEMC is made up of teachers who work together to take their Teachers Pay Teachers stores to the next level. We use the power of cross-promotion to collaborate with our Pinterest, Facebook, and Teacher Talk blog marketing teams. For more information on how you can join this group, go to The Best of Teacher Entrepreneurs Marketing Cooperative

Using Two-Sided Colored Beans to Add and Subtract Positive and Negative Numbers

When it comes to adding and subtracting positive and negative numbers, many students have great difficulty. In reality, it is a very confusing and abstract idea; so, it is important to give the students a concrete visual to assist them in seeing the solution. This idea is based on the Conceptual Development Model which is important to use when introducing new math concepts. (See the August 14, 2019 post for more details about this learning model.) As a result, when teaching the concept of adding and subtracting positive and negative numbers, what would fall into each category?

When using the two-sided colored beans, the concrete stage of the Model would be where two-sided colored beans are used as an actual manipulative that can be moved around or manipulated by the students. There are a few rules to remember when using the beans.
  1. The RED beans represent negative numbers.
  2. The WHITE beans represent positive numbers. 
  3. One RED bean can eliminate one WHITE bean, and one WHITE bean can cancel out one RED bean. 
  4. All problems must be rewritten so that there is only one sign (+ or -) in front of each number.
Sample Problem

1) The student is given the problem - 5 + 2.

2) Since -5 is negative, the student gets out five red beans, and then two white beans because the 2 is positive.

3) Since some of the beans are red and two are white, the student must match one red bean with one white bean. (I tell my students that this is barbaric because the red beans eat the white beans. They love it!)

4) Because three red beans have no partner (they're left over) the answer to – 5 + 2 = - 3. (See example above.)

After mastering the concrete stage of the Conceptual Development Model, the students would move on to the pictorial stage. Sketching a picture of the beans would be considered pictorial. Have students draw circles to represent the beans, leaving the circles that denote positive numbers white and coloring the circles that represent negative numbers red.

As an example, let’s do the problem 3 - +5. First, rewrite the problem as 3 - 5. Now draw three white beans. Draw five more beans and color them red to represent -5. Match one white bean to one red bean. Two red beans are left over; therefore, the answer to 3 - +5 is -2.

3 - +5 = 3 – 5 = -2 

When students understand the pictorial stage, then abstract problems such as the ones in textbooks can be presented. (Notice, the textbook is the last place we go for an introduction.) I have found that most of my remedial college students move straight from the concrete stage (beans) to the abstract stage without any problem. Many put away the beans after two or three lessons. What works best for your students as they master this algebraic concept is something you will have to determine.

If you would like a resource that gradually goes through these lessons, you can purchase it on Teachers Pay Teachers. It introduces the algebraic concept of adding and subtracting positive and negative numbers and contains several integrated hands-on activities. They include short math lessons with step-by-step instructions on how to use the beans, visual aids and illustrations, four separate and different practice student worksheets with complete answers in addition to detailed explanations for the instructor.

You are invited to the Inlinkz link party!

Click here to enter

Be-Leaf Me! Fall is Great! Using Leaves in Science Investigations

When my husband's Aunt Sue moved to Florida, she would send home some strange requests.  One year, she wanted us to send her a box of fall leaves.  Since Florida lacks deciduous trees, her students were unaware of the gorgeous colors produced by the trees up north.  The only problem with her request was that the leaves we sent would be dry and crumbling by the time she received them. What to do?

I solved the problem by ironing the leaves between two sheets of wax paper.  It was something I had learned in elementary school many, many years ago (back when the earth was cooling).  My granddaughters still collect leaves so we can do the activity together.  Here is how you do it.
  1. Find different sizes and colors of leaves.
  2. Tear off two sheets of waxed paper - about the same size.
  3. Set the iron on "dry".  No water or steam here!
  4. The heat level of the iron should be medium.
  5. Place leaves on one piece of the waxed paper.
  6. Lay the other piece on top.
  7. Iron away!
On the right, you will see what ours looked like when we were finished.

Only $5.25
You can also use this activity to identify leaves.  According to my husband who knows trees, leaves and birds from his college studies, we "waxed" a maple leaf, sweet gum leaf, elm leaf, cottonwood leaf (the state tree of Kansas), and two he doesn't recognize because they are some kind of ornamentals. So my suggestion is to get out there and start gathering leaves because your students, children and grandchildren will love me!

Do you want your students to have fun with leaves? Check out  a six lesson science performance demonstration for the primary grades which utilizes leaves. This inquiry guides the primary student through the scientific method of 1) exploration time, 2) writing a good investigative question, 3) making a prediction, 4) designing a plan, 5) gathering the data, and 6) writing a conclusion based on the data. A preview of the investigation is available. Just click on the title. After all you might have an unbe-leaf-able time!

Sock It Away! What To Do With Those Annoying Cell Phones in the Classroom

Most of us can't live without our cell phones.  Unfortunately, neither can our students.  I teach on the college level, and my syllabus states that all cell phones are to be put on "silent", "vibrate", or turned off when class is in session.  Sounds good, doesn't it?  Yet, one of the most common sounds in today's classrooms is the ringing of a cell phone, often accompanied by some ridiculous tune or sound effect that broadcasts to everyone a call is coming in.  It’s like “technological terror" has entered the classroom uninvited.  Inevitably, this happens during an important part of a lesson or discussion, just when a significant point is being made, and suddenly that "teachable moment" is gone forever.

What are teachers to do?  Some instructors stare at the offender while others try to use humor to diffuse the tension. Some collect the phone, returning it to the student later.  A few have gone so far as to ask the student to leave class.

In my opinion the use of cell phones during class time is rude and a serious interruption to the learning environment. What is worse is the use of the cell phone as a cheating device.  The college where I teach has seen students take a picture of the test to send to their friends, use the Internet on the phone to look up answers, or have answers on the phone just-in-case.  At our college, this is cause for immediate expulsion without a second chance.  To avoid this problem, I used to have my students turn their cell phones off and place them in a specific spot in the classroom before the test was passed out.  Unfortunately, the students’ major concern during the test was that someone would walk off with their phone.  Not exactly what I had planned!

It's a CUTE sock and
perfect for a cell phone!
A couple of years ago, a few of us in our department tried something new.  Each of us has purchased those long, brightly colored socks that seem to be the current fashion statement.  (I purchased mine at the Dollar Tree for $1.00 a pair.)  Before the test, each student had to turn off their cell phone, place it in the sock, tie the sock into a knot and place the sock in front of them. This way, the student still had control over their cell phone and could concentrate on doing well on the test, and I did not have to constantly monitor for cheating.

At the end of the semester, we compared notes.  Overall, we found that the students LOVED this idea.  Many said their students were laughing and comparing their stylish sock with their neighbor's.  I was surprised that a few of the students even wanted to take their sock home with the matching one – of course.  So here is a possible side benefit....maybe socking that cell phone away caused my students to TOE the line and study!


Need more ideas for helping with those annoying classroom irritations? Here is  resource that offers a number of practical and realistic ideas about classroom management and how to eliminate those day-after-day aggravating and annoying student problems that keep resurfacing in your classroom. It is perfect for novice teachers, beginning teachers or for student teachers. It is also a good review for those who have been teaching for a number of years.