How to Build a Solid Mathematics Foundation

There is one vital concept all math students must know in order to be successful. Does your student have it mastered?

Maybe your student struggles with multi-digit addition or multiplication. Maybe it’s division that’s got them hung up. Or perhaps, it’s subtraction with (gasp!) regrouping. In all likelihood all of these struggles can be boiled down to one issue:

Place value.

Want to ensure you set your kids up for success in math? There is one thing that's a key building block to a solid math foundation. Click to read more and get tons of ideas and resrouces to support this conceptual understanding in your students.

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This is a guest post from Danielle at Blessedly Busy.

Place value is the foundation for our number system. All operations (multiplication, addition, etc…) build on top of it.

We don’t want our math house to have a weak foundation and risk it coming down on us when we get to a tricky math concept. We want a firm foundation. So what does a solid foundation look like?

What Students Need to Know:

Place value is understanding how much a digit is worth. The value changes depending on its position in a number.

For the number 983, the 9 really means 900. In 91, the 9 means 90.

Our system is really efficient, but it can be confusing for students first learning.

There are also concepts that support an understanding of place value.

I looked at all of the Common Core Standards for grades K-5th. There are 5 big concepts students learn that support place value: Counting, reading and writing numbers, comparing numbers, understanding multiples of 10 and rounding.

Here is a brief list to give you an idea what a firm foundation looks like:

  • Count by 1’s, 2’s, 5’s, 10’s, and 100’s up to 1000.
  • Read and write numbers as: a numeral, written word and expanded form (it’s also useful to use base ten blocks)
  • Compare numbers using <,> or =
  • Understand that our system is a base 10 system. To move place values, multiply or divide by 10.
  • Round to the nearest 10 or 100

Why Place Value Matters–The Tale of a Struggling Math Student

Charles is in 5th grade. Next year, he will be in middle school. He’s very excited about moving on to middle school next year, but there’s a problem.

He hates math!

He is terrible at it (so he believes). It started around 2nd grade, double digit addition. He dutifully wrote his numbers vertically and added down the columns. 23 + 34 is 57. Easy. He didn’t know why he had to line them up the way he did, but it worked so he didn’t worry about it.

Then he gets to the problem 55+36. His answer 811. Why is this wrong? He did what he always did, add down the columns.

Next comes subtraction. 55-36=21. Apparently you are supposed to borrow. What’s borrowing? The teacher explains it again, for what feels like the 50th time. He can solve the problem, most of the time. Again, he is just following steps, he doesn’t know why they work.

Now he is being introduced to multiplication. At first it’s easy. Memorizing things has always been easy for Charles. And now, we are into double digit multiplication. After many explanations and many failed attempts he finally has all of the steps memorized. He is starting to think that math is not really his thing and maybe he is stupid at math or maybe just stupid.

And now, the nail on the coffin, division. Multi-digit division. There’s no way! He gives up.

Hope For the Struggling Math Student

Charles’ story is sad. The saddest part is that all of his struggles could have been avoided if he understood place value and was able to use that knowledge to solve problems.

If your student is struggling in operations (addition, subtraction, etc…) I encourage you to start over and make sure their foundation is firm. Even if they are in 5th grade.

You can also find lessons that show students how to solve problems using place value. Like this post on multi-digit multiplication, for example.

For more ideas on how to teach place value visit: 100 Activities, Games, and Lessons to Teach Place Value to the Elementary Student.

More FREE Place Value Resources:

Danielle is a homeschooling mamma of 5.  She is committed to making life with young children easier and sharing her passion for math.  If you would like to learn more about teaching math to multiple age groups visit Blessedly Busy or follow her on:  Facebook, Instagram, Pinterest  or Twitter.


  1. Struggling in math is very frustrating since it is used in everyday life. I speak from experience when I say that I disliked math all through my elementary and high school life and to this day I still struggle when I am having to help my daughter with her math homework. Thank you for explaining the importance of place value and having that strong foundation.

  2. I have always struggled with math concepts and throughout my elementary, middle, and high school years, I have felt hopeless on the subject. I really want to be able to help those who feel the same and really appreciate the resources you have provided to help me do so! Thank you!

    1. You’re so welcome Katie! I hope you find lots of helpful articles and resources. Let me know anytime if you other questions or concerns!

  3. This blog has help me connect my past experiences to my present experiences as a student teacher.

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