Archive for the ‘Tips for Teaching the Times Tables’ Category

Tricks to the Multiplication Tables

Tuesday, April 20th, 2010

You may have learned the Trick to the 9′s on your fingers when you were a child.   For example for 2 x 9, hold out both hands in front of you and bend the ring finger of your left hand.  This bent finger represents 2.  Look at the remaining fingers and you’ll see 1 for the finger to the left of the bent joint and 8  for the eight fingers remaining for 18.  For 3 times 9, you’ll bend the middle finger on your left hand and have 2 fingers on the left and 7 remaining for 27.  It’s easy and fun!

Another way of learning table 9 is to number 9 to 0 in a column and 0 to 9 to the left of the column.  You’ll end up with: 09, 18, 27, 36, 45, 54, 63, 72, 81 and 90.  Now how easy is that!

This “trick” is really a fun easy pattern.  So the trick in this case is a mnemonic device to help us remember.  Sometimes these mnemonic devices have fun rhymes such as “Thirty days has September . . .”

In my workbook, Teach Your Child the Multiplication Tables, Fast, Fun & Easy, I present easy number patterns for all the tables.  Patterns like the Trick of the 9′s aid memory.  Special needs children such as those with dyslexia, autism of ADD/HD benefit from patterns.  All children do.  Patterns provide structure. 

Our brains are wired to find patterns.  If someone were to tell you their phone number was 214-314-4114, you might not even have to write it down.  Why?  You’d recognize the pattern.  Our brain instinctively sorts and organizes.  So why not have your child use this brain function when learning the times tables?  Rote memorization is tedious and boring.  My son hated rote memorization!  So I developed an innovative way of teaching him. 

If all children could be engaged by numbers in the third grade, really fascinated by math, we’d have students who love math.  Students who love math are more likely to have positive self-esteem.  They are more likely to do well in other disciplines and succeed in school.  Wouldn’t that be something!

“Who’s Afraid of the Seven Times Table?” Ian Stewart Asks

Monday, March 29th, 2010
Dr. Ian Stewart

Dr. Ian Stewart



I happened to come across an interesting article on,  the London Times’ website.   What caught my attention was the title:  “Who’s Afraid of the Seven Times Table?”  by Dr. Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick

When I developed my method for my son, we found table 7 the most difficult.  Why?  First of all, 7 in an odd number.   Even numbers are easy.  Table 10 has a super easy pattern and then tables 2, 4, 6 and 8 all end in some combination of 2-4-6-8-0!  How easy is that?  Now for the tables for odd numbers 1, 3, 5, 7 and 9.   Table 1 is a cinch, as is table 5 with its super easy pattern (don’t you love the rhyme?) and how about the pattern for 9?  Could any table be more fun?  Number 0-9 in the left column and 9 to 0 on the right.  See, you just completed table 9!   All multiples of 9 add up to 9.  Go ahead and try it:  18 (1  +9), 27 (2 + 9) and so on! 

I knew if the 9′s had a fun pattern, so would the 3′s because 9 is a multiple of 3 and math is always logical.  So my son and I sat down and guess what?  When you add up the multiples of 3, you get a 3-6-9 pattern.  Go ahead and try it:  12 (1+2), 15 (1+5), 18 (1+8).  So now only table 7 was left for us to ponder.  What I discovered is the last number decreases by 3.  So its pattern is the opposite of table 3 which increases by 3.

In Teach Your Child the Multiplication Tables, I present the tables in order of difficulty.  First, come tables 1 & 10, then tables 2 and 8 because of their similar patterns and then tables 4 and 6.  Now come odd numbers in this order: 5, 9, 3 and 7.   After publishing my book, it was gratifying to discover that mathematicians opined that table 7 was indeed the hardest to master.

In his article, Dr. Stewart states there are better ways of teaching the times tables than rote memorization.  That, in fact,  “times tables need not be boring at all.”  He goes on to say, “There are lots of hidden patterns in the numbers, lots of easy short cuts, lots of interesting fact with which to have fun.”  That’s what I found too.

Dr. Stewart describes the pattern for tables 10, 5, 9 and 7.  The last number of the 7′s, he explains, decreases by 3 .  He explains how you can figure out the 7′x on your mobile phone keypad.  You can do this because of how the numbers are configured on the keypad.   The column on the left is : 1, 4 and 7. Start with the 7 in the bottom row and work upward.  7 x 1 = 7.  Move up the keypad to 4 and 7 x 2 =14.  Move up to 1 for the third operation and 7 x 3= 21.   Patterns are fun!

Our mind is designed to search for patterns.  Patterns please us. Babies react more favorable to symmetical faces.  Symmetry is a pleasing pattern.

Patterns are easy to remember because we learn one rule and apply it to the whole.  If I told you my phone number was (214) 314-4114, you instantly would recognize a pattern and might not need to write the number down. So why not learn easy patterns for each of the tables?

My son loved disvereing patterns.  There’s excitement in discovery. I published Teach Your Child the Multiplication Tables to help other families.   If all third graders thought “math is cool,” we’d have fewer school dropouts.  I won’t begin to ennumerate here the social consequences of children in the U.S. and elsewhere not knowing their times tables.  What I will do is urge parents to teach their children their times tables.   This skill is too important to be left to schools alone.  You can do it.  Better yet, you must do it.

INTERVIEW with Home Education Magazine

Friday, January 22nd, 2010

Home Education Magazine

Home Education Magazine

Shortly after the publication of my workbook, Mary Nix of Home Education Magazine interviewed me.  In the interview, I comment on how I came to write my workbook.  I also discuss the benefits of my method for special needs children.



Guide to Resource News      October 2006

Recently, Eugenia Francis, author of “Teach Your Child the Multiplication Tables, Fast, Fun & Easy with Dazzling Patterns, Grids and Tricks!”, wrote to Home Education Magazine to tell us about her book and the methods she uses in it.

I learned from her website:

“Eugenia Francis has spent 15 years developing creative teaching materials. She has taught both high school and university students (University of California at Irvine) and mentored other teachers. Faced with the challenge of teaching her son the multiplication tables, she developed her own innovative method, discovering patterns and tricks to the multiplication tables.”

I began by asking Eugenia to tell us more about how she came upon her method of teaching the multiplication tables.

Eugenia:  When my son Scott was in the third grade, I was teaching at UC Irvine.  My challenge there was to teach literary analysis and writing to freshman students, many of whom had poor writing and analytical skills.  At home, my challenge was to get Scott through the third grade.

One afternoon, Scott came home with page after page of multiplication drills.  He was overwhelmed!  I knew there had to be a better way. So I drew a 100 square grid for tables 1 – 10 and asked him to fill in the tables he knew. Scott quickly filled in tables 1, 2, 5 & 10.  I saw that these were the tables with a nice, easy pattern.   But what of the other tables?  I remembered a trick for table 9.  I had Scott fill in the right side of the column 9 to 0 and to the left of these 0 to 9.  “There you know the 9′s!” I said.  Scott was amazed by this trick.  The 9’s, he decided, were super easy! 

With one simple “trick” or pattern, Scott had mastered the 9′s.  Why not find patterns for the rest of the tables?  Patterns are fun, fast and easy!  Patterns enhance recall.

As Scott filled in the grid, we noticed that multiples of ODD numbers had a hopscotch ODD-EVEN pattern.  On the grid which has 100 multiples, only 25 were ODD.  Why was that?

Scott and I soon discovered that an ODD number multiplied by an ODD number produces an ODD multiple.   

         The Secret Code for ODDS was: ODD x ODD = ODD.

Whereas when an EVEN number multiplied ANY number the multiple was EVEN!


The Secret Code gave Scott a new-found confidence in math!  With new tables, he could PREDICT whether the answer would be ODD or EVEN.  The tables for EVEN numbers we found were remarkably easy to learn.  Why?  The multiples of tables 2, 4, 6 and 8 end in some combination of  2, 4, 6, 8 & 0.  Soon the fridge was papered with patterns and tricks.  Discovery made learning fun!

As a seven year old, Scott was developing analytical skills.  He was finding patterns.  He was making connections.  He was seeing the big picture.  Most of all he was intrigued by the times tables.  Learning these became a game to him.

Mary:  You mention that your workbook teaches a child to discern patterns among odd and even numbers and discover the secret codes of multiplication.  Can you share a bit about how that is done?

In designing the workbook, I followed the sequence that I used with Scott.  The workbook starts with patterns for EVEN numbers.  Once these are mastered, the ODD numbers are introduced along with the Secret Code for ODD and EVEN numbers.

At 165 pages, my workbook has a variety of exercises.  First, I explain the concept of multiplication and show that 2 x 3 is the same as 3 x 2.  I explain how multiplication is a fast form of addition.  There are grids and patterns and often tricks for every table, exercises on number sequencing, games, interpreting graphs, exercises on the ODD/EVEN rule, fill-in-the-blank multiplication problems, squaring numbers, word problems of increasing difficulty as well as division and two-digit multiplication.  Each page has artwork.  The original artwork we found was extremely important.  The artwork is in shades of gray rather than color.  However, I found that this worked well as children can color in the circus animals as they learn the tables. 

The key to my method is patterns.  Why not divide the tables among ODD and EVEN since each has DISTINCT PATTERNS rather than learning them the standard way — 1 through 10?  Two months ago, I sent a copy of my workbook to Laura Bush.  Her office forwarded it to the U.S. Secretary of Education.  Their response to my workbook:

“The recognition of patterns is a creative way to have students develop understanding for the concept of multiplication.  Pattern analysis should be part of the elementary study in mathematics as it is also viewed as foundational skills for algebraic reasoning.”

Algebraic reasoning  . . .   wow!  Why not develop these skills at an early age?  Why not teach analytical skills to young children?  Analysis needs to start in the early grades.

Mary:  You also mention that the book may be helpful to a child with special needs.  Can you explain why?

Eugenia:  Soon after publication, a teacher emailed me saying the workbook would immensely benefit children with special needs.  A mom of a dyslexic child reported that her son took to my book “like a duck to water.”  A parent of an autistic child wanted a copy. I needed to learn more.  In Sandra Rief’s How to Reach and Teach Children with ADD/ADHD, I learned the following: 

Patterns provide structure.  Children with ADD/ADHD need structure. These children have a difficulty memorizing the times tables.  The visual-spatial method of patterns and grids works better.  Patterns also help dyslexic children as they strictly order number sequence.  Special needs children can better visualize and recall where a number is placed if they see a pattern.  My son too was a visual/spatial learner.

Special needs children (this is true of ALL children) respond best to methods that are interesting, innovative and motivating.  I believe my method based on distinct patterns for ODD and EVEN numbers is that.  I wanted to motivate children through an encouraging tone. The “you-can-do-it” approach. My workbook was designed for collaboration between parent and child.  I came up with the circus motif to engage young children.  The artwork and the story had to be appealing, interesting and relevant.  There had to be visual cues that make solving word problems so much easier.  I had to have a variety of strategies that engaged a child’s attention.  I had to appeal to a child’s affective senses – his feelings, his emotions.  Can you imagine my workbook without the story or artwork?

I was pleased to learn that a spatial learner is often “art smart.”  Had I known this, I would not have been surprised that special needs children love the art exercises in my workbook  – the “Can you copy Rudy on the grid?” pages.  I use the grid for fun as well as instruction.  If you look closely, you will see that all grids have “watermark” figures in them that a child can trace.  Why not reinforce the relationship between art and math?

Also important are the differences between children who are left-hemisphere dominant and those who are right-hemisphere dominant.   Whereas the left-hemisphere dominant child learns from parts to the whole, the right dominant prefers the big picture, seeing patterns and making connections.  The right side is the creative and emotional side of the brain.  Special needs children are often right-brain dominant.  That is why I believe my method works so well with them.  My method presents left-brained learning through both left and right-brained strategies.  Both sides of the brain are needed for learning.

Mary:  Can you share a couple of tips that will help a child learn their multiplication tables?

Eugenia:  I endorse hands-on techniques of teaching math.  Make a double batch of your favorite brownies and have your child do the measuring.  Take an egg carton and trim it to 10.  Ask your child to divide 12 beans or beads equally into 4 egg cups.  Then ask: “How many go in each?  That’s right, 3 x 4 is 12!”   Division reinforces multiplication.  It is the inverse of multiplication. 

Mary:   The website states your book is designed for a child who is in 2nd or 3rd grade, but many homeschoolers do not go by a system of grade levels.  Would this method be helpful to anyone learning their multiplication tables or would an older child find it designed for a younger child?

Eugenia:  On the first edition, I had “Grades 2 – 3” on the cover of the workbook.  However, I deleted this as grade level is arbitrary.   One child might be ready for the workbook at a much younger age.  Another might be a bit older.  The illustrations in the workbook were designed to appeal to a young child.  I am considering a second version for an older child.  One high school math teacher told me that 30% of her Algebra 1 students did not know their times tables!  I imagine homeschool moms aren’t shocked but I was!   I need to consider the older child with special needs.  I also want children in other countries to benefit as well. I have been reaching out to homeschool communities overseas.   My workbook will be available in Spanish in December.  It is currently listed on Amazon in Canada, the United Kingdom, France and Japan.  I want to reach children there as well.

My goal is to reduce the time it takes to learn the times tables, eliminate frustration and develop analytical skills.

Mary: Do you have any other tips you would like to share for children once they have learned their multiplication tables?

Once children have mastered the times tables through patterns and the Secret Code for ODD and EVEN numbers, they are ready for complex word problems such as those found in the last pages of my workbook.  You’ll notice I simplified these by giving visual cues such as tickets to the circus or the circus menu and then I broke the problem into parts.    Have children quickly sketch their own visual cues and then break the problem into parts.  This is an effective learning strategy.  Also teach them to decipher math word problems:  “How many in total?”  is very different from “How many were left?”  Have your child be fluent in the language of math.  I am not a math teacher nor have I taught elementary school.  My forte is literature.  I urge parents to integrate literature and math.  Sandra Reif (page 297) lists stories for children that integrate math concepts. Math should be fun.  It should engage your child’s imagination.

I hope that my workbook instills in your child a love of numbers and confidence in math.

Mary: Eugenia, thank you so much for taking the time to share your method and book with our readers.  If our readers would like to learn more, they can visit:


Multiplication Tips for ADD/ADHD Students from Green Chimneys School

Tuesday, June 30th, 2009

Last week, I posted on HARO asking parents, teachers and students to submit tips on teaching Times Tables to students with ADD/ADHD.  Many thanks to teacher, Louise Loya-Mayne from the Green Chimneys School for the following tips:

We draw circles, group marbles [counting one by one] in each circle. 5 circles with 2 marbles in them = 10.

“Nines” – use your fingers [7x9 you count on your fingers to 7,that 7th finger goes down as a space, then count  the fingers to the left and right 6 and 3 = 63.]

Dice, playing cards, and Dominoes, are good to use, once they have been practicing for  a while.

Blow up beach ball or cube with number facts on them, for practice. Make a tossing game out of them. I’ve also use bean bag games, with numbers on the circles.

An egg carton or Mancala board game, you can use marbles (or anything small), and count them out into the sections [2 groups of 3 marbles=6]

Dot math with white boards and markers, draw  dots … … … three groups of three dots = 9. [on nice days, you can use side walk chalk].

I find the more ‘flexible grouping, and moving the students, helps with ADD/HD, such as having the students write on the overhead projector, then break into groups for games (with the dice and cards), then go outside and use the sidewalk chalk, etc.

On Fridays, we have a Math Carnival, where you set up different stations around the room, with manipulatives, and the students have fun going around to each one, practicing facts, problem solving, etc

Deborah Bernstein, the Director of Marketing and Communications at Green Chimeneys submitted the following:  Teachers at Green Chimneys School, a year-round 853 special education school in Brewster, NY, know how to help children learn!  They’ve implemented a number of successful techniques to teach children.  Dawn Looby, one of our teachers, has found a number of successful methods to teach the multiplication tables, as she explains below:   

I use flash cards a lot because it allows the student to work with a peer and move their hands. Another great technique is to play Multiplication catch. The students stand in a circle. The teacher will call out a multiplication problem and pass the ball to a student. The student must state the answer, call a new multiplication problem and pass the ball to another student. If the student drops the ball, they are out of the game. If a student cannot think of the answer they may get help from a peer. I also like to use math baseball at  

Founded in 1947, Green Chimneys operates a special education school, residential treatment center for children, farm and wildlife rehabilitation center and a variety of other programs that help restore possibilities and create futures for children with emotional, behavioral, social and learning challenges (including ADHD and Asperger’s Syndrome).  You can find more information on Green Chimneys at Deborah M. Bernstein, Director of Marketing and Communications,Green Chimneys, 400 Doansburg Rd. – Box 719, Brewster, NY  10509-0719