Do your students understand place value? From 1st grade to 5th grade, place value is such an important concept. Place value is the backbone of so many other skills. Let’s take a look at some manipulatives and activities that can help our students develop a deeper understanding.
Quick Check for Primary
I find it only takes one question to deduce whether a student has a basic grasp of place value.
For my primary students, I have them take out a white board and ask them to write the answer to this question.
If you have 6 tens and 12 ones, what number do you have?
Many students will draw tens and ones place and write the numbers in each. If they do this, I’ll ask, what number is that. Some will confidently announce, “Six hundred and twelve.” For those kids, I know we need to start with manipulatives and lots of practice not saying ‘and’. (Mathematically, and means something when they get to decimals and its best to break the habit early.)
Others will look confused and say, “Um… um…” The um kiddos are actually a little further along. They know 612 isn’t right but they don’t know what is. They have probably been told they need to only put one number in each place but don’t have any strategies other than a place value chart.
Then there are the kids who know the answer is 72. Be careful. They clearly know more than the others, but I follow up with those kids and ask, “If you have 3 thousand and 4 ones, what number do you have?” Some of the ones that relied on addition, get lost when it comes to the zeros.
Quick Check for Upper Grades
For my upper grade students, I might have them do it on paper. Some are so self conscious, they’ll look around for answers if they aren’t sure.
Write the number 638 in three forms. (or 638.03 if they are in fifth grade)
Some students will write it in standard, expanded, and word forms. Some will draw pictures. Some will ask over and over, “What do you mean?” It is a great way to get a quick check about where they are starting from.
Place Value Manipulatives
Flats, Rods, and Units / Place Value Blocks
Place Value Blocks are a useful manipulative. Recently, my math program has even moved to place value flats, but they work the same.
I have to pause and gripe. Why do some math programs insist on calling these by names other than hundreds, tens and ones? My school has more than 70% ELLs and we need to be using math vocabulary as much as possible. I heard an argument once that in 5th grade they are used for decimals and get different names. But, honestly, if my 5th graders can go from seeing a flat as 100 to seeing a flat as a whole, they can go from saying Hundreds to saying Wholes. Thank you for indulging my rant. 🙂
I love Digi-Blocks. No, they aren’t paying me to say that. I use them all the time. The kids love them. For many years, it was their favorite rainy day recess toy. One of my sixth graders last year saw them on the shelf and freaked out. “OMG! You still have those! I loved those in second grade. Can we use them?” I smiled at the joy and said, “I tell you what. If you can think of a way Digi-Blocks can help us learn to write an argumentative paragraph today, sure.”
The great thing about Digi-Blocks is that they are mistake proof. If you put 9 ones into a ten container, it won’t close. If you are working on regrouping, there is no “trading ten ones for one ten”. Ten ones becomes one ten. If you are borrowing, no trading involved, just open it up.
Ten ones fit in one ten. Ten tens fit in one hundred. Ten hundreds fit in one thousand. Then it goes on the shelf. I can tell kids that till I’m blue in the face but the depth of understand comes when they see it happen in real life. I see them as the nesting dolls of math.
When our students started making rekenreks of 20 beads in their homeroom classes. I thought, let’s make one with 100. It is a great manipulative for making two digit numbers. It can also be used for addition, subtraction, and multiplication.
I made them with a group of kids last year with beads, pipe cleaners, and pizza boxes.
Eventually, I ordered one on Amazon that stands up so they could see what I was doing easily.
Dollar Bills (and Coins)
Kids love play money. (They love it enough I even had some 6th graders steal some of my hundreds. Yes, you are sooo cool now that you have fake hundreds. Sigh.)
Since the kids loved playing with the money so much, there energy level gets pretty high. To help keep them focused, I created some spinners and worksheets to go with our money games. If you already own my Strike It Rich Place Value Games, be sure to download it again. I just added a new Standard, Expanded, and Word Form page.
When I work with 5th graders that struggle with decimals, even talking about dimes and pennies helps decimal place value connect to real life for them.
Place Value Manipulative Activities
I like to mix up the manipulatives we use. It keeps the games and activities we play feeling fresh. Now that we have some tools, what are some activities we can use?
Open Number Line
My new favorite activity for place value is using manipulatives to create open number lines to represent two digit numbers. First, I tape a long piece of paper to the desks to be the number line. Then, I write numbers I want them to create on sticky notes.
I have the kids place the sticky notes where they think they’ll go first. Then, they they use their manipulatives to measure and decide exactly where the sticky note belongs.
The biggest challenge for them is learning not to leave empty space between the pieces. I’m a big believer in repetition with a slight change. So, we usually do this activity with a different manipulative the next day.
Afterwards, we turn this concrete understanding into writing numbers on the number line.
I made this Open Number Line Work Mat which I use with a variety of grades. You can find this for FREE here.
I start with a my Open Number Line: Hop to a Target Number PowerPoint. The kids play Beat the Clock by trying to hop to a number on their number line before the frog does. First, they start by learning to write zero on the left side.
Then, they make hops of tens, fives, and ones to get to a number.
When we make the ten hops, I prompt them to remember how they put out their tens pieces on their number lines.
I love when they start to notice that there is more than one way to hop to a number.
I love to have students build the numbers. Sometimes we use place value mats, but to keep it fun, sometimes I have them build something with their number. This developed over years when some kids built numbers much quicker than others. Allowing them to turn their tens and ones into a structure kept them focused while other kids were counting.
Calling an activity a game is a quick way to make something fun.
For this game, each partner chooses two number cards. They each build their number and then compare with symbols on a white board. The process of comparing numbers with manipulatives helps students realize the relationship between numbers as seen through the lens of place value.
Sometimes we’ll do those activities with dice instead of cards.
Once students have a firm grasp from representing numbers with concrete manipulatives, it is time to learn to represent numbers in multiple ways. Of course, students won’t always have access to manipulatives, but they can draw pictures of what they would have built.
Writing Explanation Sentences
Beginning to be able to articulate what is happening is key to deeper understanding.
Standard, Word, and Expanded Form
Students who have been building expanded form models, quickly grasp the connection between the standard number and the version with the plus sign.
I have a few PowerPoints that I use for introducing Standard, Word, and Expanded Forms. One is for numbers within 1,000. Another is for numbers to a million. There is also one for numbers with decimals. Students learn the vocabulary and practice writing numbers in the different forms.
As they begin to internalize it, we use those forms while comparing.
I mentioned many of the resources I’ve used in my classroom. You can find them all here in my Place Value Category.