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.

But Wait…  What if your child has a test coming up and they do not know how to add or subtract yet?

Conquer Three-Digit Addition with This Powerful Strategy!

Are your kids feeling frustrated with three-digit addition? Does the thought of adding large numbers leave your child overwhelmed and defeated? Don’t worry—I’ve got a special strategy designed to help your child build confidence, master their math facts, and add numbers like a pro!

The Challenge of Learning Math Facts

Many children struggle with basic math facts, and this makes adding large numbers feel nearly impossible. Without a solid foundation in addition and subtraction, math can quickly become a source of frustration. When kids experience repeated failure, they often develop math anxiety, which leads to a loss of confidence in their abilities.

But don’t lose hope! I’ve developed a super-secret strategy that’s proven to help kids who struggle with their math facts. Whether you’re a parent helping with homework or a teacher seeking new methods for your classroom, this strategy can make a world of difference.

The Magic Strategy for Three-Digit Addition

So, what’s the big secret? It’s all about breaking the problem into smaller, manageable steps and using visual strategies to simplify the process.

Here’s how it works:

1. Start with the Ones Place: Begin by adding the digits in the ones place. If the sum is greater than nine, carry the extra value to the tens place.
2. Move to the Tens Place: Add the digits in the tens column, plus any value you carried from the ones column. Again, if the total is greater than nine, carry that extra value to the hundreds column.
3. Finish with the Hundreds Place: Add the digits in the hundreds place, including any value carried from the tens column. Write down your final answer, and celebrate your victory!

By breaking the process into smaller steps, your child can focus on one part of the equation at a time—boosting their confidence and improving accuracy.

Real-World Case Study: From Frustrated to Fantastic!

Let me tell you about Daniel, one of my students who once struggled terribly with math. Daniel often froze when faced with three-digit addition problems. No matter how hard he tried, he kept making mistakes and felt like he would never understand math.

We introduced this step-by-step strategy in our tutoring sessions. Daniel started by practicing just the ones column. He used number blocks to visualize the concept, which helped him stay calm and focused. Slowly but surely, he gained confidence. Within weeks, he was adding three-digit numbers without hesitation. His math scores improved dramatically, and more importantly, he believed in himself again.

Daniel’s story is proof that with the right strategy, any child can unlock their math potential!

Why This Strategy Works

This strategy combines two powerful learning techniques: chunking and visual aids. Chunking breaks math problems into smaller steps, making them less intimidating. Visual aids, such as number blocks or drawings, help children see the logic behind the math.

This method is especially helpful for children who haven’t mastered their math facts yet. By teaching them to focus on one section at a time, they gain the skills they need to succeed.

Tips for Parents and Teachers

Here are some extra tips to help you reinforce this strategy at home or in the classroom:

✅ Use Color-Coding: Highlight the ones, tens, and hundreds columns with different colors to help kids stay organized.

✅ Practice with Real-Life Scenarios: Ask your child to add grocery prices, calculate change, or count total points in board games.

✅ Celebrate Progress: Focus on effort rather than perfection. Every small improvement is a step toward mastery!

Take Learning to the Next Level with TeachersDungeon

If your child is ready to take their math skills to the next level, check out my educational game, TeachersDungeon! This interactive learning platform offers a full series of math books, including strategies for adding, subtracting, multiplying, and dividing. Each math book comes with step-by-step video tutorials designed to provide immediate help when your child needs it most.

TeachersDungeon combines adventure, challenges, and personalized learning to keep kids motivated while reinforcing essential math skills. Plus, every membership includes access to my entire collection of math books—ensuring your child has all the tools they need to succeed.

Ready to Watch Your Child Shine?

Don’t let math frustration hold your child back. Empower their learning with proven strategies that make adding and subtracting numbers easier than ever. Visit TeachersDungeon.com today to explore our interactive learning platform and watch your child’s math skills soar!

Let’s turn confusion into confidence and frustration into success. Click the link above and join the math adventure today!