The Best Place Value Chart Ever: Your Free Printable Place Value Accordion

A place value chart is an essential math resource in any elementary school teacher’s toolkit. Place value underpins the foundations of many math standards, and having a simple way to help learners grasp these concepts is invaluable.

However, finding a place value chart to use and reuse can be difficult.

Not any more!

Our printable place value chart is simple, easy-to-use and easy-to-recreate. It’s a brilliant math resource to have in your back pocket ready for the start of the year!

What is place value?

Place value refers to the value of a digit in relation to its position in the number, for example, ones, tens, hundreds etc.

For example, the place value of 3 in 236 is 3 tens, or 30.

What is a place value chart?

A place value chart is a simple pictorial guide to support students’ understanding of the place value of a digit in a whole number or decimal number. It is a helpful tool to build a conceptual understanding of the number system.

The size and complexity of the place value chart will vary as a child progresses from kindergarten to 5th grade and the place value of the digits for each grade.

In kindergarten, your place value chart probably has nothing more than the tens place and the ones place on it, looking like this

Then by the time students reach 5th grade, their place value chart will not only go up to the millions place on the left-hand side but include decimals to the thousandths place on the right-hand side.

How to use a place value chart

Place value charts help students with:

• Finding the value of any given digit in a number
• Rounding numbers
• Quickly and accurately help learners find the result of multiplying and dividing a given number by 10, 100 and even 1000 or more

When multiplying or dividing numbers, students must move numbers left and right on the place value chart through different place values, depending on the value the number is multiplied or divided by. 

For example, to divide a three-digit number by 10, students must move all three digits one column to the right. Multiplying by 100 would mean moving the digits two columns to the left.

As place value charts can represent decimal numbers as well as whole numbers, children can visualize what dividing or multiplying decimals does to the value of each digit.

Why use a place value chart?

The beauty of math manipulatives like place value charts is that they can be used in math lessons from kindergarten through 5th grade and beyond if needed.

In lower elementary (1st and 2nd grade), you may only make use of tens and hundreds. But place value charts can be easily modified to cover the thousands place, ten thousands, hundred thousands and beyond for upper elementary math.

You can create a decimals place value chart that focuses on the ones place and below or one that looks at place value for negative numbers.

Once the basics of using a place value chart have been established in class, they can be used to aid learning of all manner of place value-related topics; they are a good way to help students get to grips with ordering numbers, for example. 

Of course, they can also be used in conjunction with other place value math worksheets and math manipulatives, such as place value mats and place value arrow cards 

Put an end to place value misconceptions

You’ll likely hear time and again in discussions about the place value system is this:

“To multiply a number by 10 you just need to add a 0 to the end of a number.”

Sound familiar? It is of course a complete myth! Whether it’s a previous teacher or a parent who’s taught this, it’s tricky to move students on from believing this. Because it does sometimes work. If you multiply 29 x 10 adding a zero gives you the right answer of 290. 

But, this concept is wrong and causes major problems with students’ understanding of place value with decimal places. For example, 2.9 multiplied by 10 is not 2.90!

When teaching place value to 4th grade students for the first time or correcting this misconception ahead of teaching multiplication/division by 10, you’ll need a simple, tried and tested way to explain it so it sticks and your students don’t make the same mistake again.

While base ten blocks and other math resources can be useful for understanding place value for different numbers in isolation or for addition and subtraction, more complex operations need something else.  

The best place value chart

As a teacher, you already know how important the place value chart is in your teaching but did you know there was a way to supercharge its effectiveness?

All it takes is some colored cards, pens, and scissors. Within ten minutes you can have a foolproof tool for showing how to move numbers to the left or right when teaching place value. It’s so simple you can even get your students to make it with you!

How to make your place value accordion

What you will need:

• 2 A4 sheets of colored card stock (preferably two different colors)
• Scissors 
• Felt tip pen 
• Pencil 
• Ruler

Instructions:

How to use your place value chart or place value accordion

Once you’ve made your place value accordion, simply ask students to make a number. In the example below we have made 369.

Multiply by 10 using your place value chart

Then ask them to multiply by ten, moving the numbers one column each to the left. They will also need to add a zero as the placeholder in the ones column. Not for nothing did my class always call it Zero the Hero!

Divide by 10 using your place value chart

If you want to divide 369 by 10 then you simply move the numbers one column each to the right as seen in the picture below.

Students are quick to pick up the idea and process of physically moving the digits, following place value charts. This embeds the concept correctly, helping them to move on to large numbers and more complex concepts.

On a place value chart (as shown below), not only is it clear that this is the answer, but children can further see that 9 is now the tenths place. Dividing by 10 once again would move the 9 into the hundredths place and the 6 into the tenths place etc.

You can also move on to multiplying by 100, moving two columns left and needing two zeros, and so on.

Place value chart activity ideas

My students have always loved this place value accordion resource and we would play games with them.

Acitivity 1: What number am I?

I would call out clues for a number and my students would add the right digits into the columns to show the answer. 

Example:

• I am a three-digit number.
• My tens digit is 6 less than my ones digit and 1 less than my hundreds digit.
• If you multiply me by 7, the estimated product is 1,400.
• What number am I?

For trickier numbers, I might ask them to work in pairs or groups. 

Activity 2: Writing numbers

• Ask each child to make a number (you may want to specify for example a 3-digit or 2-digit number or a number with 1 decimal place) in their accordion.
• Students show their number to a partner and together, they try adding/ subtracting one number from the other.

This will help to reinforce place value in addition and subtraction. 

I hope you find this place value chart useful. This free resource has not only worked brilliantly for me during the many years of my own teaching career but it was passed down to me by my own teacher (now retired). So thank you very much Mr Bell – we all owe you one!

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The content in this article was originally written by EdTech consultant Jodie Lopez and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza