Questions? Call 215.842.0400

One on One Tutor Blog

The purpose of our blog page is to provide resources, ideas, and suggestions to assist parents in guiding their children as we believe parent involvement is the single most important part of a child's success in school and in life.

6th Grader on a 10th Grade Math Level: The Importance Of Mastering Basic Skills

Thaddeus Falana M.ed - Thursday, June 23, 2011

Two days ago, I had the pleasure of administering an achievement test to a 6th grader who has been enrolled at One On One Tutoring Service since she was in the 3rd grade.  For privacy reasons, we will call the student Susan.  When Susan came to One On One Tutoring in the summer of 2008, she was in the 3rd grade and functioning on a 2nd grade math level.  We recommended that she complete 40 hours of instruction in which we targeted her learning gaps by using systematic, direct instruction in a one-to-one setting.  By the end of the summer, she was on a 3rd grade instructional level in mathematics.  Her mother enrolled her at One On One Tutoring Service every summer after that.  This summer, after grading her assessment in order for her to begin instruction, I was pleased to see her functioning on a 10th grade level even though she is currently in the 6th grade and going into the 7th.  It was evident by her test results that math no longer was a problem area for her.  The question is, how was she able to make such a remarkable leap in just three short summers?  Well, in order to answer the question, we must first understand the landscape of education today. 

When I was in school in the 80's and 90's, teachers made sure we mastered the basics in mathematics computation.  When I refer to "the basics" I mean addition, subtraction, multiplication and division.  I knew all of my multiplication facts in the 2nd grade.  I knew how to divide with one and two digit divisors in the 3rd grade and was able to understand and compute with fractions by the 6th grade.  By the time we moved into higher level mathematics, I was able to understand new material taught to me because I had already built a solid foundation.  I did not have to be retaught how to multiply, divide or work with fractions as is necessary to work with higher level math skills.  I was able to keep up with classroom instruction because the building blocks were already in place.

Fast forward to my adulthood as an educator.  I have worked with countless number of students in mathematics who are in junior high or high school trying to learn higher level math but are unable to because they never mastered basic skills.  Today, students in elementary school are allowed to use calculators.  No longer are students required to master basic computation skills before moving on to higher level math skills.  Studies show that there has been a steady decline in student gains in regards to computation skills since the 1980's.  Although many reasons contribute to this, it is important to understand the neccessity of mastering these basic skills early on in a student's elementary years.  Fact is, students who have not mastered basic whole number computation by the end of the 4th grade are more likely to struggle in mathematics. 

When Susan came to One On One Tutoring Service in the summer of 2008, I made sure that her learning path focused on building a solid foundation in her basic skills.  Although today's curriculum covers a broad range of math skills, we only focused on addition, subtraction, multiplication and division.  The same applied the following summer until she demonstrated mastery.  We then moved on to fractions, which she worked on until she demonstrated mastery, as she advanced in grade level.  By building a solid base, she was able to understand and apply newly taught math concepts in school without much frustration. 

According to (Loveless, 2003) and I agree wholeheartedly, basic skills are important because:

1.) Basic skills serve equity.  The black-white achievement gap expanded in every computation skill area in the 1990's as a result of a lack of focus on teaching basic skills.  When basic skills are not taught, the least privilaged in our society, those who cannot afford tutors, computer programs or academic summer camps, suffer.

2.) Basic skills are necessary to advance in math.  Basic skills are a floor, not a ceiling.  Students must learn arithmetic so that they can move on to more demanding mathematics.

3.) Basic skills predict adult earnings. Skills and knowledge students learn in school is correlated with success later in life.

In conclusion, it is imperative that parents understand the importance of a solid foundation not only in mathematics but in reading as well.  Unfortunately, the demand of today's curriculum does not allow adequate time for teachers to ensure that all students master their basic skills in mathematics.  Parents must realize that school is not the one and only solution to a child's education and that there are outside sources such as One On One Tutoring Service that will work diligently to make sure that their children are fully prepared to succeed in school.

How To Teach Multiplication Facts

Thaddeus Falana M.ed - Tuesday, June 07, 2011

How to teach multiplication facts

By: Thaddeus Falana, M.Ed

 

Many elementary and middle school students struggle with math because of their inability to recall multiplication facts.  It is imperative that students learn the multiplication tables as it is used in division, fractions and other higher level math skills.  If you are a parent and are looking to assist your child with his/her multiplication facts, here are a few steps to help you along the way:

 

Step 1

 

2

3

4

5

10

11

2 x 1

3 x 1

4 x 1

5 x 1

10 x 1

11 x 1

2 x 2

3 x 2

4 x 2

5 x 2

10 x 2

11 x 2

2 x 3

3 x 3

4 x 3

5 x 3

10 x 3

11 x 3

2 x 4

3 x 4

 

5 x 4

10 x 4

11 x 4

2 x 5

3 x 5

 

5 x 5

10 x 5

11 x 5

2 x 6

3 x 6

 

5 x 6

10 x 6

11 x 6

2 x 7

3 x 7

 

5 x 7

10 x 7

11 x 7

2 x 8

3 x 8

 

5 x 8

10 x 8

11 x 8

2 x 9

3 x 9

 

5 x 9

10 x 9

11 x 9

2 x 10

3 x 10

4 x 10

5 x 10

10 x 10

 

2 x 11

3 x 11

4 x 11

5 x 11

10 x 11

 

 

  • The 2’s table is fairly easy as one would need to learn how to count by 2’s. 
  • The 3’s are similar as well. Teach your child how to count by 3’s. 
  • Once your child knows how to count by 2’s and 3’s, drill him/her daily just on those facts.  Your child will learn how to quickly count by 2’s and 3’s until it is memorized.
  • Next, turn your attention to bottom half of the 2’s and 3’s.  Let your child know that any number multiplied by 10 is that number plus a zero.  i.e. 2 x 10 = 20, 3 x 10 = 30, 4 x 10 = 40, 10 x 10 = 100 etc.  In addition, any number up to 9 that is multiplied by 11 is that number written twice. i.e. 2 x 11 = 22, 3 x 11= 33, 4 x 11= 44, 9 x 11 = 99 etc.
  • Drill your child with flash cards everyday until facts are memorized.
  • Next, address the 4 times table.  Your child will already know 4 x1 through 4 x 4 because he/has already memorized the inverse of these facts.  i.e. 4 x1 = 1 x 4, 4 x 2 = 2 x 4, 4 x 3 = 3 x 4.  Your child will also have already master 4 x 10 as well as 4 x 11.
  • Again, drill your child with flash cards everyday until facts are memorized.
  • Move on to the 5 times table.  This step is easy as your child will need to learn how to count by 5’s.  The same technique used for the 2’s and 3’s will be used for the 5’s.
  • Again, drill your child with flash cards everyday until facts are memorized
  • The 10’s are also pretty simple as the rule states that any number multiplied by 10 is that number plus a zero.
  • The 11’s also follow a similar rule as any number up to 9 that is multiplied by 11 is that number written twice. i.e. 9 x 11 = 99, 8 x 11 = 88, 7 x 11 = 77 etc.
  • Again, drill your child with flash cards everyday until facts are memorized

 

Step 2

6

7

8

6 x 1

7 x 1

8 x 1

6 x 2

7 x 2

8 x 2

6 x 3

7 x 3

8 x 3

 

  • You will not have to spend much time on the above facts.  Your child will already have a good understanding as he/she should have already memorized through drilling, their inverses.  i.e. 6 x 1= 1 x 6, 6 x 2 = 2 x 6, 7 x 2 = 2 x 7, 8 x 3 = 3 x 8.
  • Again, drill your child with flash cards everyday until facts are memorized

 

Step 3

 

4

7

8

11

12

4 x 7

7 x 4

8 x 4

11 x 11

12 x 11

4 x 8

7 x 6

8 x 7

11 x 12

12 x 12

 

7 x 8

8 x 8

 

 

  • The above facts are the most challenging and will require rote memorization.  Drill using flashcards to help your child memorize the above.
  • Again, drill your child with flash cards everyday until facts are memorized

 

Step 4

6

7

8

6 x 5

7 x 5

8 x 5

 

  • The above follows the inverse rule of multiplication.  If your child has already memorized his/her 5’s table then the inverse of 6 x 5 = 5 x 6.  The same goes for 7 x 5 and 8 x 5.

 

Step 5

6 x 6

6 x 4

6 x 8

 

  • Above are math facts that rhyme. i.e. 6 x 6 = 36, 6 x 4 = 24, 6 x 8 = 48.
  • Again, drill your child with flash cards everyday until facts are memorized

 

Step 6

9 x 1

9 x 2

9 x 3

9 x 4

9 x 5

9 x 6

9 x 7

9 x 8

9 x 9

9 x 10

 

Use the following trick to teach the 9 times table:

  • Hold your hands in front of you with your fingers spread out
  • For 9 x 3 bend your third finger down. (9 x 4 would be the fourth finger etc.)
  • You have 2 fingers in front of the bent finger and 7 after the bent finger.
  • Therefore the answer must be 27.
  • This technique works for the 9 times tables up to 10.

 

Step 7

12 x 1

12 x 2

12 x 3

12 x 4

12 x 5

12 x 6

12 x 7

12 x 8

12 x 9

12 x 10

 

  • Your child should know all of his/her 11 times table by now.  If you know your 11’s, then any number up to 10 that is multiplied by 12 should be easy to figure out.  For example, if asked 12 x 9, then you should know that 12 x 9 = 9 x 12.  If 9 x 11 is 99, and we add 9 to 99, we should have our answer.  12 x 9 =  99 + 9 =  108.
  • Any number multiplied by 12 should be treated as such.  If you know the answer of that number multiplied by 11 then you should be able to add the factor to the product and get your answer.  i.e. What is 8 x 12?  Well, 8 x 11 = 88, therefore, 88 + 8 = 96, thus 8 x 12 = 96.

 

Again, drill your child with flash cards everyday until facts are memorized

 

It is recommended that parents purchase workbooks that offer ample worksheets for your child to use for practice.  Visit: www-one-on-onetutor.com and visit the bookstore which offers a wide array of student workbook.


iconiconicon