# Place Value – How Important Is It Really?

By Esther White

#### Place Value - How Important is it Really?

Place Value is the most important concept when teaching maths to any student. It is the foundation of every maths concept from preschool to algebra level maths and is essential for a complete mathematical understanding. Students can not progress if they haven't mastered Place Value as a basic concept first.

However, Place Value is often a tricky subject to teach and students continuously struggle with understanding the value of a number based on it's place. How does an "8" in the units house mean only 8 "ones" or "units", whereas the same number 8 in the tens house means eighty?

Why do students find such a simple concept so hard to understand? Why do parents and teachers alike struggle to teach such a key component of maths? The concept of Place Value is often even more frustrating for students with dyslexia and learning differences, and if they can't understand it, they are often left without any support.

#### What is Place Value?

Place Value is the position of a number that tells what value it is assigned, and is vital in our communication of maths as a universal language. However, when students attempt to learn this key maths concept with only a basic, abstract understanding of numbers, they continuously struggle and often end up giving up on maths.

Let me explain what Place Value is in an easy way. Place Value is as simple as the knowing that "every value has a place". The place tells us “what kind”, the value tells us “how many" of that kind is being shown.

For example, in the number 285, the digit 8 indicates there are eight (how many) tens (what kind).

This simple understanding is used from small numbers to hundreds of thousands. The same principle applies, no matter how big the number is.

#### Why is Place Value important?

Despite its simple definition, Place Value can be a challenging concept for a young child or student to grasp. Regardless of whether dad is in the kitchen, the living room, or the garage, he is still dad, but if the digit 3 is in different locations (tens or hundreds place, for example), it means something different.

From the first level in the Math-U-See curriculum, Place Value is introduced using the famous"Decimal Street". Each of the "houses" on Decimal Street represents a separate place value. This concept of Place Value is reiterated in the following levels, and when taught using the hands-on manipulatives, it becomes a strong foundation for your child's entire maths education.

This is what Place Value looks like when you build it with the blocks:

See how you can see that there are five units in the "units house," eight tens in the "tens house" and two hundreds in the "hundreds house"?

Therefore, the number shown above using the manpulatives is 285.

“Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum. It is the beginning and end of everything to do with mathematics.”

Place Value is important because it provides the foundation for regrouping, multiple-digit multiplication, and more in the decimal system, as well as a starting point for the understanding of other base systems. Place value allows your 12-year-old son to understand the difference between the \$50 he received for his birthday and the \$500 price tag on the iPad he’s saving for. Place value allows the student learning scientific notation to understand why 54,800,000 can be represented as 5.48 X 10.

According to Sherman, Richardson, and Yard, “Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum.”

Almost all mathematical concepts build on the understanding of Place Value. It's definitely worth your time to get it right!

#### Why do students find Place Value hard?

This is a question that regularly finds parents and teachers frustrated, overwhelmed and ready to give up. How do you teach students proper place value when you have been through all the correct maths curriculum the way it was laid out, and still they don't know how to add tens and hundreds correctly?

I'll tell you a story:

A little girl sits puzzling over the problem on the page. She’s only in grade two, but the stress of high performance expectations is already in place. Here’s the problem she needs to solve:
500 – 78
The little girl remembers that she needs to cross out the five and make it a four. She also knows that one of the zeros becomes a nine and the other one becomes a ten, but she just can’t remember which is which, and it’s so frustrating! Finally, she has an idea. She tries different values and adds 78 to each of them until she comes up with:
422 + 78 = 500
She writes 422 as the answer and receives that coveted gold star on her paper. No one knows that she doesn’t understand how to complete this type of subtraction with regrouping (or “borrowing,” as it was called in her day).

Throughout primary and high schools across Australia, I have seen the same issue happening time and time again. The little girl did exactly what most students continue to do well after the Place Value lesson has been taught to them.

So what is the issue? It isn’t a faulty memory or that the concept is particularly difficult.
It's what happens when a student is taught only an algorithm and a formula for maths and is not given any conceptual understanding of the role of place value.

#### How do you teach Place Value?

The way you teach Place Value to your student is crucial to their ongoing understanding. Research has shown a correlation between using manipulative representations of numbers (as opposed to one-to-one representations e.g numbers drawn on paper) is huge in the understanding of place value. In other words, representing the number 24 with two 10 blocks and four units rather than writing down "24" or showing 24 units (without showing that the tens and hundreds are distinctly different from the units) correlates with a better understanding of place value. The Math-U-See presentation of place value using Decimal Street and our color-coded pieces for units, tens, and hundreds supports this research-based hands-on and multisensory representation.

Additionally, studies have shown that the way numbers are verbalised by English-language speakers may negatively influence the way students think about and represent numbers in comparison to Asian-language speakers. Here's a short article about the importance of using correct languaging in maths that provides some alternate number naming strategies to help bridge this gap and promote better understanding of base ten.

You can watch this short video on how to teach Place Value and how you can help your students gain a better understanding of this foundational concept.

Studies have also strongly proven that Place Value understanding has a positive correlation with overall mathematics achievement. For the grade 2 student described above, place value would have helped her understand that when she crossed out the 5 in 500, she was really decomposing 1 hundred into 10 tens, of which 1 needed to go to the ones or units place to allow her to subtract, leaving 9 to go to the tens place. There would have been no need to memorise (and forget) an algorithm!

If your student can use the hands-on manipulatives to see, touch and feel where the each number goes, they will successfully learning Place Value. By engaging a multi-sensory awareness and experience of numbers in their proper place, students will gain a strong understanding of this basic maths concept and a knowledge of maths they can retain (and use) for life.

If you were wondering if your student can really understand place value, you can check their understanding of place value (and other maths topics from basic addition to algebra) by using our free Online Placement Tests.

These diagnostic tests are easy to use and the results are automatically calculated to show where you student is at, and what you can do to help them.

You can take the Online Placement Test here:

If you have any questions about your student's results, or what you can use to strengthen their overall According to Sherman, Richardson, and Yard, “Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum.”maths understanding, you can contact us directly here.

Good luck teaching maths!

Warmly,

Esther White

References

1. Kouba, V. L., Brown, C. A., Carpenter, T. P., Lindquist, M. M., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Number, operations, and word problems. Arithmetic Teacher, 35(8), 14-19.

2. Miura, I. T., & Okamoto, Y. (1989). Comparisons of U.S. and Japanese first graders’ cognitive representation of number and understanding of place value. Journal of Educational Psychology,81(1), 109-114.

3. Miura, I. T., Okamoto, Y., Kim, C. C., Steere, M., & Fayol, M. (1993). Cross-national comparisons: France, Japan, Korea, Sweden, and the United States. Journal of Educational Psychology,85(1), 24-30.

4. Sherman, H. J., Richardson, L. I., & Yard, G. J. (2014). The impact of place value on mathematics. Retrieived January 13, 2017, from http://www.education.com/reference/article/impact-place-value-mathematics/.

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