value of digits change

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The class is silent. Nothing is heard except for the teacher’s voice droning on like a scene from Charlie Brown. “The value of digits change as they move up or down in a number. A digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.”

Students are doodling in their notebooks, twirling their hair, and ordering the newest game off of Amazon Prime.

The lesson continues with a few examples drawn on the board, and then the dreaded, “Take out your math books and practice how digits change in a number.”

The students dutifully pull out their books, but moans fill the air. The page rustle and the chatter of numerous children fill the calls room as the get ready to answer the 20 questions on the page. Yes, they are doing the work. Yes, they may even be getting their answers right. The big question is, do they understand the concept?

Some children who are gifted with a mathematical brain will instantly see the connection. The majority of students will be able to answer the questions, but not have a clue why or even what they are doing. Our little ones that struggle may not even be able to do the problem without some hands on instruction.

Not What We Want!

I don’t want my students to lack an understanding of any math concept.  I definitely don’t want my precious students that I spend numerous hours a week with to walk from my classroom being able to do problems, but not knowing the why. If you are taking the time to read this, you don’t want that either.


At the moment I’m teaching the cutest Kindergarten student (yes, I’m a little bias),but the majority of my teaching career has been spent in upper elementary. As upper grade teachers we often get into the mindset that maniputives and place value are for those early years, but they are just as important in 3-5 as they were in k-2.

Much of fourth and fifth grade is spent with fractions and decimals, so it imperative that our students are seeing how the place value they learned in 2nd grade corresponds with decimals.

One way is to teach what happens when a number is moved one place to the left or to the right, and to know that a 5 in the one’s place is very different from the 5 in the 10’s place.

So what happens when a digit in the one’s place is moved one place to the right? You guessed it, it is multiplied by 10.

What happens when you move a digit one place to the left? Yep, you have divided by 10!


How to Teach This

So how do you teach this? Get out those base ten blocks and play with them. Get out grid paper and have the children color and cut to help them understand what is happening.

  1. If you are using grids, grab some scissors  and coloring pencils.
  2. Start off with any number like three tenths, and have the students color in that number.
  3. Next ask them to draw 10 circles in their notebook and divide the three tenths up equally into the circles.
  4. At the point comes one of the hardest things for me to do. Step away, and see what they can do on their own. If a student is totally stuck you can ask how many cubes are in each row. This may give them an idea, but if they continue to be totally at a lost suggest they cut out every cube and place one in each circle.


Now ask them what number is represented in each circle. In a perfect word you should get the answer three hundredths. The value of the digit three changed as it moved to the hundredths place.


Now instead of telling your students that a digit is 1/10 of what it represents in the place to its left, you have showed them and allowed them to explore it.

You can do same teaching the opposite way, and this way is even easier.

  1.  Start by having each child color in five hundredths, and explain that they will be multiplying five hundredths by 10.
  2. Since your students are multiplying by 10 have them draw 10 circles and place five hundredths in each circle.
  3. Finally, your students figure out how many cubes they now have in all.


Have fun showing your children how the value of digits change instead of reminding them of a scene from Charlie Brown.

You’ve Got This

Still a little unsure how to teach this? Check out this  video from Learn Zillion is a great example of using manipulitves to understand the value of a digit changing as it moves up or down in a number. You can also check out these other two posts that can add to your students learning.

decimal relationshipsmaze of zero game board

Or download this interactive notebook FREEBIE to give your students one example of what happens when you move one digit to the right, and one digit to the left!!!

    Get all my resources for multiplying by 10 and .10 HERE

digits change

Click HERE to get your freebie.


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