Category Archives: math

Summer Education Goal: Master Multiplication Facts

For the past month I have been tutoring Marine recruits who are struggling with the math portion of the ASVAB test, which is required to join the military.  It is really sad to see people over eighteen years of age still struggling with basic math concepts.  It has inspired me to have my younger students become proficient with their basic facts so that they can spend more time learning the larger math concepts.

So why learn math facts?

  1. Automaticity allows you to see the numbers in your head, leading to less mental energy used.
  2. It allows you to manipulate numbers more easily.
  3. Decreases the probability of making errors in calculations.

There are many wonderful websites that make this process fun for children.  One that I’ve been using is math magician.  You pick the type of operation that you want to focus on and then refine the parameters that you will use.  For example, I have several students who will be entering 4th grade and I want to make sure that they have their multiplication/division facts mastered.  I will either pick a number that they have not mastered or one hundred mixed facts.  The site provides a timer based on the test that is being taken.  If they complete it in the allotted time, they receive a certificate with the percent that they correctly answered.  The students really enjoy it.

Here are some websites that I have found to be useful:

Make a goal of so many minutes a day to work on facts, such as 20 minutes.  This short amount of time invested will make all the difference in long term math skills.


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Filed under addition, division, education, math, multiplication, number sense, subtraction

Teacher’s Websites are a Treasure of Resources

Teacher’s websites are a great source of information to assist your child academically.  Most teachers have websites that inform you about what is going on in the classroom, the weekly schedule for specials, assignments that are due, etc.  Often you can find spelling lists for the week or even the year.  This is great for when your child says that they left their homework at school or that they can’t remember when something is due.
What do you do if your child’s teacher doesn’t have a website or it isn’t up to date?  Check for another teacher in your child’s school that is at the same grade level.  Teachers often, though not always,  work together so the students are reading the same stories or working on the same math lessons.  If I am working with a student and I’m not finding information on the teacher’s website, I look at a different school within the district, find the grade level and see if they have resources that will help me.
If your child’s teacher has a tab for links on it, make sure to take the time to visit it.  Many textbooks now have links that allow you to go in the book and review lessons.  The link will have any passwords that you need.  If not, ask your child or your child’s teacher.  There are also educational game links that will help to reinforce concepts in a fun way.  
Thanks to the time that teachers have taken to find and list resources for you, there is no need to reinvent the wheel.  Take advantage of these free resources to enrich your child’s education.

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Filed under addition, comprehension, education, elementary reading, math, reading, school, teacher communication, tutoring

Colored Candy to Advance Number Sense

In my last post, I discussed the importance of number sense, which is the ability to use and understand the meaning of numbers.  In this post I will talk about a fun activity that your child will enjoy as they learn the properties of numbers.

The manipulative that we will use is any small bag of colored candies that you can pick up at the checkout counter such as M & M’s™,  Skittles™, jelly beans, etc.  If you buy more than 2 ounces, split the candy up into a sandwich bag with a total of about 50.


Have your child separate the candies by color.  On a piece of paper, have them write the total number of each color.  Then you can ask questions comparing the colors such as:  

  1. Which color has the most?
  2. Which color has the least?
  3. How many red candies do you have?
You can then ask greater than, less than or equal to questions such as:
  1. Are there more than, less than or the same number of blue and green candy?
Change up this question to compare the different colors.
Using colored candies is also a great way to learn about fractions.   Have your child count the total number of candies and explain that this is the whole or total number of candies.  You can also introduce the mathematical term of denominator, depending on the age.  Then have your child separate the candies by color.  Just as before, you ask how many red there are.  This time, though, explain that this a part of the whole.  Again, you can give the mathematical name of numerator if it is age appropriate.
How many total candies do you have?
I have 50 candies.
How many candies are red?
14 candies.
So 14 of the 50 candies are red.  I could write it 14/50 .  This tells me that of the total number of candies, 14 are red.    Lets do this with the rest of the candies.
After all the candies have been divided into fractional groups, you can then do comparisons as described in the first part.
Have fun!

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Filed under math, number sense, tutoring, Uncategorized

The Importance of Number Sense

What is number sense?  “Number sense is the ability to use and understand numbers” ( In the article by Russell Gersten and David J. Chard, “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities” , (2001) the authors compare number sense to phonemic awareness.  In order to understand how to read, a child needs to understand how sounds work together to make words.  In math, students have to understand the attributes of numbers in order to become proficient problem solvers.

Here are some of the characteristics of number sense:

Fluidity-It is important for students to learn that numbers are flexible.  10 can be broken up to 8+2 or 14-4.   This concept is used in Singapore Math to demonstrate how numbers can be broken apart in order to solve more complicated problems.

Meaning-Just as words have meaning so do numbers.  Students, especially during early elementary school, need to be able to express numeric meaning through representation.  This can be shown through manipulatives (dried beans, cubes, candy, etc.).  The student should be able to show the meaning of 10 by counting out 10 cubes or drawing 10 circles.

Mental Math-Students who develop fluidity in math can begin to picture and manipulate numbers in their head.  By conserving energy on math facts, the brain is able to spend more time on problem solving.

Strategies-The beauty of math is there is more than one way to solve a problem.  As a student becomes more proficient in understanding the properties of numbers, they can spend more time on figuring ways to solve a problem.  For example, a multiplication problem can be represented with pictures, through repeated addition, broken down into a smaller multiplication problem and added together, using a known to find an unknown, etc.  What is important is for the student to see that math is pliable and there is not just one way to find an answer.

Recognizing Patterns-Math patterns occur everywhere in nature, such as the pattern on the outside of a pineapple or the nautilus shell.  Finding patterns in math  increases a students ability to solve problems more quickly and accurately.  One example of a pattern in multiplication is the products of 9.  The digits in the product, when added together, equal 9.  For instance, 9×9=81.  8+1=9.

Recognizing Errors-A person with good number sense is able to recognize errors in problems.  They understand that if the answer for a subtraction problem is greater than the number they started with then there is something wrong.  The student is able to understand that 8 is greater than 6.

These skills can be incorporated in everyday activities.  Whether it is cooking, shopping or playing a game, these concepts can be part of an informal home program that will make math learning fun.  In my next post, I will go into some specific ideas that you can use.

If you would like to read the article cited in this blog, this link will take you there:

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The Joy of 9

When asked what my favorite number is, the answer is easy.  It’s the fabulous  number 9.  No matter whether you are adding, subtracting, multiplying or dividing, there are tricks that make finding the answer easy.  Math is all about patterns.  Once you see the pattern and understand it, problem solving becomes easy.


Let’s start with addition.  First, we know that 1+9=10.  Know this information is the first step to understanding how easy finding the sum of 9 and any number.  Let’s take the example of 9+3.

First, I take the 1 from the 3 and I add it to 9, which gives me 10.  This leaves me with 2.  2+10=12    Notice that the sum of the number 12 in the answer is equal to 3 (1+2) Here’s another example:

17     1+9=10, 7+10=17; 1+7=8


Subtraction has a similar shortcut to addition.  Let’s take a look at the problem 16-9.  Once again we look at what we know, 9+1= 10.  The difference between 16 and 10 is 6.  I still have to add the 1 that I added to 9 to the 6.  Therefore, 16-9=7.  Notice that when I take the number 16 and add the two digits (1+6), I get 7, which is also the answer to the problem.  Here’s another example:

– 9

Notice, that the digits in 14, when added together equal 5.  This works when I subtract 9 from any number.  Here’s another example.

– 9
15     2+4=6 and 1+5=6


Just like addition and subtraction, multiplication has some neat tricks.  Let’s look for the pattern by lining the facts up vertically.

1×9=  9










There are a couple of patterns that we can observe with the facts lined up in this manner.  First, we notice that the digits in the tens column progress from 0-9 and the digits in the ones column progress from 9-0.  Secondly, the sum of the digits of each product is equal to nine.  This is a pretty neat trick and a great way to remember the facts.

Another way to find the products of 9 is by using your hands.  Place your hands palms down on the table.  Count from the pinky on the left hand the number that you are multiplying 9 by.  When you get to the number, fold that finger under.  The fingers that are up on the left of the folded finger are the number of tens and the fingers remaining up to the right of the folded finger are the number of ones in the answer.  So if I’m multiplying 3×9, I’ll fold the middle finger on my left hand.  This leaves two fingers to the left of the middle finger up.  This tells me that I have two tens or twenty.  I have 7 fingers to the right of the middle finger or seven ones.  20+7=27, the product of 3×9.


Let’s look at a division problem:  .  I can determine whether the dividend (7425) can be divided evenly by 9 by finding the sum of the digits in the dividend.  If the sum is a multiple of 9, the quotient will have no remainder.  Since 7+4+2+5=18, I know that the quotient will have no remainder.

No matter what operation I do with nines, there is an easy pattern that I can follow to determine the answer.

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Filed under addition, division, education, math, multiplication, number sense, subtraction, tutoring