“Numerical Fluency” vs. Memorizing “Number Facts”

By Mathnasium | July 30, 2018

We want to introduce the importance of “numerical fluency” and learning basic “number facts.”

Picture this scenario. A teacher asks a classroom, “If you spend 70 cents, 80 cents, and 90 cents, how much did you spend altogether?”

The teacher is thinking:

“7 + 8 + 9 = 24.  With a zero at the end, the answer would be 240 cents.”

However, our “finger counting” students, which is sadly too many of them, are thinking:

Proportional Thinking (Number Sense Series, Part 3)

By Mathnasium | May 14, 2018

“If the world was the size of a basketball, my house would be as big as a flea’s flea!”

This is an example of how a seven year old once expressed proportional thinking to Mathnasium’s Co-Founder and Chief Education Officer, Larry Martinek. Of course, this seven year old didn’t know he was expressing proportional thinking at the time, he just knew it was fun to think about familiar objects changing size in relation to other familiar objects!

“Wholes and Parts” (Number Sense Series, Part 2)

By Mathnasium | March 13, 2018

Number Sense is the ability to appreciate the size and scale of numbers in the context of the question at hand. Three elements establish Number Sense: Counting, Wholes and Parts, and Proportional Thinking. We already introduced Counting in Part 1 of our Number Sense Series. Today, we will focus on Wholes and Parts.

The two aspects of the concept of Wholes and Parts form the backdrop for many mathematical concepts: fractions and complements.

Getting Past Counting on Fingers and Toes

By Mathnasium | January 17, 2017

When very young children first learn how to count, they use their fingers as manipulatives (physical objects used to teach math concepts).

However, many kids continue to rely on their fingers as their primary computation tools once they move on to mastering addition and subtraction. It is at this juncture that finger counting becomes problematic. While this computation method can be effective to an extent when working with small numbers, it ultimately stifles a child’s mathematical development by keeping them in the limiting headspace of one-by-one counting.

As such, finger counters soon find that this technique quickly becomes cumbersome, inefficient—and more often than not, inaccurate—once they start working with bigger numbers.

It is far more effective in the long term to encourage students to develop numerical fluency. What is numerical fluency? It’s a student’s ability to recall basic number facts mentally and effortlessly by way of developing frameworks for learning. For instance, a fundamental cornerstone of numerical fluency is learning to see and work with numbers in groups mentally rather than one by one.

Let’s look at some examples of numerical fluency in action!

9 + 7

A one-by-one counter attempts to solve this by figuring out “9 + 1 + 1 + 1 + 1 + 1 + 1 + 1.” By contrast, a student who has developed numerical fluency (and therefore, a broader understanding of the relationships between numbers and how numbers work) solves this problem mentally by working with a friendlier number, in this case, 10:

9 + 1 = 10

10 + 6 = 16

(As one-by-one counters develop numerical fluency, they’ll discover very quickly that the number 10 is their friend!)

Let’s try 7 + 8!

Instead of thinking, “7 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1,” a numerically fluent child sees that 8 is one more than 7 and can default to the strategy of doubling 7 and adding 1:

7 + 7 = 14

14 + 1 = 15

Let’s do one more!

13 – 9

In this situation, our friend, the number 10, comes in handy once again! How far apart are 13 and 9? Well, 9 is 1 away from 10, and 13 is 3 away from 10. Add the differences together and you get the answer, 4. This is far more efficient than thinking, “13 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1”!

When children transition to techniques beyond using their fingers for computation, their confidence with counting and numbers in general will grow exponentially, and their ability to handle larger numbers effortlessly will follow. As time progresses and they bid farewell to basic addition and subtraction practice, numerically fluent students will find it easier to tackle more complex operations like multiplication and division. While building numerical fluency won’t happen overnight (it requires steady, consistent practice working with these frameworks over time), students will continuously reap the benefits of becoming stronger, more nimble problem solvers and mathematical thinkers … long after they close the books on elementary math!

Achieving numerical fluency is a critical step on the path toward developing solid number sense—an intuitive, logical understanding of how numbers work. Mathnasium offers personalized programs designed to help students of all ages develop numerical fluency. Contact your neighborhood math experts to learn more!

Great Gifts for Math Lovers, Teachers, and Smart Folk of All Ages

By Mathnasium | December 8, 2016

We all have that one person in our lives who’s impossible to buy for. What do you get for the person who has everything? Stress no more! Whether you’re looking for holidays, birthdays, Mother’s Day, Father’s Day, Teacher Appreciation, or just because, these fun and clever gifts will thrill the recipient, and give them a sophisticated way to express their inner nerd. 

Exercises to Improve Beginner Math Skills: Counting and Grouping

By Mathnasium | April 26, 2016

Many times, when students of all ages come to Mathnasium in need of math help, their math troubles can be traced back to a lack of number sense—an intuitive grasp of how numbers work! What’s the first step to gaining number sense? Well, the most basic skills in mathematics involve counting and grouping (seeing numbers in groups). When mathing with your kids, try the exercises outlined below. While they may seem easy at first glance, these exercises are anything but child’s play. They’re appropriate for any person of any age who needs help gaining fluency in basic math skills. The trick is to do these exercises mentally—with little to no writing. However, using pictures as visual aids and real-world objects (counters, coins, blocks, raisins, etc.) as manipulatives can make math come alive!


To develop counting skills, help your child learn to count from any number, to any number, by any number!

  • Count by 1s, starting at 0 (0, 1, 2, 3, … 250…)

… then starting at any number (28, 29, 30…)

  • Count by 2s, starting at 0 (0, 2, 4, 6, 8… 24…)

… then starting at 1 (1, 3, 5… 25)

… then starting at any number (23, 25, 27… 49 …)

  • Count by 10s, starting at 0 (0, 10, 20 … 500 …)

… then starting at 5 (5, 15, 25 … 205 …)

… then starting at any number (37, 47, 57, 67 … 347 …)

  • Count by 1/2s , starting at 0 (0, ½, 1, 1 ½, … 5 …)

… then by 1/4s, starting at 0 (0, ¼, 2/4 or ½, ¾, 4/4 or 1, 1 ¼ …)

… then by 3/4s, starting at 0 (0, ¾, 1 ½, 2 ¼, 3 …)

  • Count by 15s, starting at 0 (0, 15, 30 … 120 …)
  • Count by 3s, 4s, 6s, 7s, 8s, 9s, 11s, 12s, 20s, 25s, 50s, 75s, 100s, and 150s, starting at 0.

Can you see how this type of counting practice will, in time, result in strong addition skills and the painless mastery of times tables?


To help your child strengthen number sense, expand their thinking processes and help them see numbers in groups! Ask questions like:

  • “7 and how much more make 10?” “70 and how much more make 100?” “700 and how much more make 1,000?”
  • “10 and how much more make 15?” “10 and how much more make 18?” “10 and how much more make 25?”
  • “17 and how much more make 20?” “87 and how much more make 100?” “667 and how much more make 1,000?”
  • “How far is it from 6 to 10?” “How far is it from 89 to 100?” “How far is it from 678 to 1,000?”
  • “How many 10s are there in 70? …100? …200? …340? … 500? … 1,000? … 10,000? … 1,000,000 … a quadrillion (15 zeroes!)?”
  • “How many 4-person teams can you make out of 12 kids? … 20 kids? … 50 kids? … 100 kids?”
  • “How much is 5, four times? … ten times? … a hundred times? … a thousand times?”

Notice how these questions focus on the number 10, multiples of 10, and powers of 10. Also, these questions are a great way to introduce multiplication and division concepts before your child encounters them in school!

Which techniques do you use when you math with your child at home?

Parents, Do You “Math” With Your Child?

By Mathnasium | February 5, 2015

Most parents are eager to help their children do well in school, but they’re not giving them the tools necessary for success in their math classes. Parents play a huge role in instilling the number sense their children require to be successful. 

When I go out to schools and talk with parents, I ask them, “How many of you read with your kids?”

I usually get a room full of raised hands and proud faces.

Then I ask them, “How many of you math with your kids?”

While many parents have never heard math used as a verb before, they instantly understand my meaning, and I see those  proud faces turn sheepish.

There is a classic, widely read book on phonics recommended by the US Department of Education called “Why Johnny Can’t Read: And What You Can Do About It.”

The teaching techniques that form the backbone of The Mathnasium Method™  are essentially “Why Johnny Can’t Math: And What You Can Do About It.”

I’d like to introduce you to a verb I use often, and one I hope will become part of your daily life.

Math /mæθ/

Verb (intransitive): math, mathed, mathing

: to practice mathematics

: to work on developing number sense

: to use math skills in every day life

Examples: “Please turn the TV off, I’m mathing and I need to concentrate.” 

“Let’s math together after school today.”

“I mathed with Mom after dinner last night, and I was prepared for my geometry pop quiz this morning.”

Parents understand the necessity of reading with their child and make an effort to do so often, but when it comes to mathing with their child, they are often at a loss, particularly when their student moves beyond primary school curriculum. Many parents simply haven’t been taught how to help their children build the skills they need to be successful in math.

Mathing is as fundamental to a child’s cognitive development as reading, and it can be fun. After all, children don’t innately hate math, they hate being confused, frustrated, and embarrassed by math. Math with your child often to work through confusion and boost their confidence. Once they understand math and possess number sense and numerical fluency, curiosity and passion will follow naturally.

I’ve created some simple Dos and Don’ts to follow as you work with your child to stay on track in their math studies.


1) Do “math” with your children just as you read with them.

2) Do make sure your children get their math homework done in a timely fashion.

3) Do meet with your child’s math teacher from time to time so that you know what is going on beyond the report card (your child’s attitude, whether there is a need for extra help or enrichment, etc). Work with your child’s teacher to set REALISTIC GOALS for the current school year and for the future.


1) Don’t let your negative experiences in the math classroom influence your child’s education.

2) Don’t let your child use a calculator until the child has developed genuine number sense.

3) Don’t let your child be put in a math class that the child is not ready for – that is, a class where the child does not have the prerequisite knowledge necessary for success.

Following these Dos and Don’ts will not solve everything, as students need to continuously nurture their math skills and number sense with practice.

Here are some additional in-depth tips for mathing with your K-5 child.

Tips for parents to help you do math with your child and improve their Number Sense.

Check out these further in-depth tips for students grades 6 and up to ensure they have acquired the number sense necessary to be successful in their classes.

Tips for parents to help you do math with your child and improve their Number Sense.

These booklets provide a starting point for your family mathing sessions at home. I’ll endeavor to provide more guidance on mathing with your student here on the Number Sense blog.

If you ever find yourself on the receiving end of the question, “Do you math with your child?” I hope your answer will be an emphatic and proud, “Yes!”