Basic Addition & Subtraction

A solid understanding of number sense can make or break your child’s success in mathematics!

Anyone can be strong in math.  It’s all a matter of understanding the basics of how our number system works.  The very cool thing is that our number system follows a definite pattern.  Once kids learn the pattern, they can begin to play with the patterns.  This actually makes math fun.

Let’s take a look at a typical mistake.  When adding or subtracting simple problems like 12 – 8, children often count on their fingers rather than understanding the pattern within our base ten number system.

I have seen students in 6^th, 7^th, and even 8^th grade who still struggle with basic number sense.  This is not because they are not smart.  It is not because they can’t do math – anyone can.  It is because the math was not presented in a manner that made sense to them.

I have found that using manipulatives really helps children understand mathematics.  What are manipulatives?  They are math tools that teachers use to give a concreate understanding of mathematics.  Mathematics tends to be extremely abstract.  It is difficult to see or feel how the math works.  That is unless you use manipulatives, or you have your children draw a mathematical model of what is happening.  I have my students do these two strategies every day.  It helps give them a concrete understanding of the math.

Let’s go back in time for a moment.  When I was in school I was taught to memorize facts, algorithms, and theorems.  I was never shown why a particular fact, algorithm, or theorem worked.  As a matter of fact, when learning to multiply and divide fractions, I was perplexed.  I wondered why multiplying a fraction made it smaller and dividing a fraction made it bigger.  At the time, it made no sense.  I remember asking my teacher, but he could not explain the reasoning of it to me.  He simply told me to memorize the algorithm, “Multiply the Reciprocal”.

I’m getting ahead of myself.  Let’s pull back to addition and subtraction.

How do you instill an understanding of adding & subtracting numbers?

Use Manipulatives!  You can use square cubes like I do in the video below.

Follow the pattern that I demonstrated in the video.  If you don’t have cubes, you could use anything: Macaroni Noodles, M&M’s, or Starbursts.  Here is the pattern:

1. Put 3-cubes in your palm.
2. Ask your child to count the blocks. They can pick them up to count them if they like.
3. Put all the blocks back into your palm and hide them behind your back.
4. Take one block away. Hold it in your other palm and keep it behind your back.
5. Hold the palm out with the two blocks, and ask how many blocks are behind your back.
6. Your child should say 1.
7. Now, hold both palms out. You can show them the family of facts:

• 1 + 2 = 3
• 2 + 1 = 3
• 3 – 1 = 2
• 3 – 2 = 1

Repeat this pattern with only three cubes until your child is correct every time.  First hold 1 cube behind your back.  Then hold 2 cubes behind your back.  I realize that three cubes may seem too easy, and your child may be ready to move to four cubes quite quickly.  However, I have found that by starting small and moving slowly children gain self-confidence and establish a solid understanding more quickly.

Move Up to 4-Cubes

1. Put 4-cubes in your palm.
2. Ask your child to count the cubes. They can pick them up to count them if they like.
3. Put all the cubes back into your palm and hide them behind your back.
4. Take one, two, or three cubes away. Hold them in your other palm and keep them behind your back.
5. Hold the palm out with the remaining cubes, and ask how many cubes are behind your back.
6. Your child should say the correct answer.
7. Now, hold both palms out. Let’s say for instance that you held 3-cubes behind your back.  The family of facts would be:

• 1 + 3 = 4
• 3 + 1 = 4
• 4 – 1 = 3
• 4 – 3 = 1

As you can see, by doing this activity, children are learning both addition and subtraction at the same time.  Work your way up through 5-cubes, 6-cubes, 7-cubes, all the way up to 15 cubes.  Move through the cubes slowly, making sure that your child fully understands the family of facts for each group of cubes.  By the time you get to 15-cubes your child will have a strong sense of how our base ten number system works.  They will be one-step closer to being successful in mathematics.

One more thing –

I developed my educational fantasy game, TeachersDungeon, with the intension of helping children reach their academic potential.  The game self-adjusts to each players level of academic ability.  If you would like to see how my game might help your child, click on the photo below.

Are you interested in a particular concept, like multiplication, sentence structure, adding fractions, or anything else?  Please let me know.  I would love to give a feature review on that concept in a future post.

Novels by McCoy –

I have written a number of books that are available on Amazon.  I have nonfiction books on mathematics that link to video tutorials and are designed to help children gain a deeper understanding of the math.  Here is a link to the first book in my series on fractions.  I have also written a chapter book and a young adult novel.  You can have a free preview by clicking on the links below.

MY ADVENTURES WITH CHICKENSPIKE – This is a chapter book that is perfect for children in 3rd and 4th grades.  My Adventures with ChickenSpike is a Children’s Fantasy Book.  The main character is a young boy who is being bullied.  He travels to a distant planet and finds his inner strength.  By the time he returns home not only is he no longer a victim, he is a hero!

RED – This is a young adult novel that is especially designed for children in 5th and 6th grades.  Red is an action packed adventure with two main characters and a number of supporting characters that add humor and drama to this novel.  Bruno Vic and Evelyn Rose attend Sir Francis Drake Middle School.  Bruno is big, street-wise, and tough, but he also has high morals and undying loyalty to his friends.  Evelyn Rose was born rich, but an unfortunate turn of events has landed her in the heart of the Tenderloin District of San Francisco.  Bruno, Evelyn, and their friends are desperate to steer clear of the gangs, so the turn to a mysterious man that the gangs seem to fear.  His name is Red.

Until next time, have a great day –

Brian McCoy