Teaching place value in 1st grade can be tricky. It feels so abstract and confusing to kids. How can one number (2) mean a different number (200)? Sometimes our instruction inadvertently adds to the confusion. Read about some mistakes teachers make when teaching place value and how to avoid those mistakes.
I was recently teaching place value in 1st grade. The task: Identify the value of the underlined digit. The number 26 was on the board. We’d been working on this for 4-5 days by this time.
Audrey had a confused look on her face. I checked in with her privately and asked “Does that 2 mean 2 or 20?” She hesitated, then whispered “2? No 20?” She was clearly confused – and I clearly had to step up my instruction!
If you have taught place value to 1st grade students, I’m sure you’ve been in this situation, too. It can feel frustrating when you have taught the concept and practiced it repeatedly and kids still don’t understand. Sometimes when that happens, the confusion lies farther back in the learning process – with some underlying confusion. Here are some things I consider when I have students who are confused by place value.
What is place value?
In math, each digit in a number has a value – it is represents a given amount. For instance, if we talk about 482 leaves, the 4 doesn’t actually mean 4 leaves; it represents 400 leaves. We know this because of where it is located in the number. The digit 4 is the 3rd digit from the right, putting it in the hundreds place. That means its value is that digit X100.
Place value is the amount that the digit represents. Understanding place value is critical for working with larger numbers in our numeric system.
Why is place value important?
Teaching place value in 1st grade is important because it is the foundation for larger (and smaller) numbers. First, it helps us compare numbers. You use your understanding of place value to know that 824,502 is more than 84,502. And first graders need to start understanding place value as they work with larger numbers.
Additionally, place value allows us to add, subtract, multiple and divide numbers that are more than 10. It is the foundation of numerous math concepts.
Understanding that one digit can actually represent a much larger number (or a fraction of a number, once we add decimals) is a very abstract concept. However, it’s a critical concept for making sense of adding and subtracting numbers in the hundreds and thousands.
Because it is so abstract, it is important to make sure students develop a solid understanding of place value. Students who don’t understand place value are likely to mindlessly apply addition or subtraction strategies and not recognize that their answer doesn’t make sense.
For instance, a child who is confused about place value might add 824 + 68 and get 8812 (not realizing that the 12 from 8+4 needs to be broken into 10 and 2, so the 10 can join 2 and 6 in the “tens” grouping.)
How do students develop place value skills?
Before students develop place value skills, they need to develop strong skills in basic number sense and subitizing. These skills can include things like:
- counting forward and backward
- skip counting (by 10s, 5s, and 2s)
- counting from a given number, such as counting up from 7
- automatically recognizing quantities in sets of items (such as the dots on dice)
- comparing and sequencing numbers
- recognizing various ways to compose the same number (such as 4+2, 5+1, 0+6)
- being flexible about ways to solve a math problem mentally (for instance, seeing 14+15 as 10+10+4+5 OR 15+15-1)
This solid foundation in the number system will support students as they develop place value skills. Place value will make more sense when students understand numbers and can work with them flexibly. (For ways to strengthen subitizing skills, check out this blog post.)
In order to understand place value, students need to work with larger numbers in concrete ways. This means we can’t simply teach place value by expecting students to memorize a place value chart and apply various algorithms to solve math problems. They need time to link these abstract ideas to concrete representations of numbers.
Because it is so abstract, there are a few common mistakes teachers make when teaching place value. Fixing these mistakes can really strengthen your students’ overall math performance. Here are some tips and tricks for teaching place value in 1st grade.
What are the most common mistakes when teaching place value?
- Focusing on the abstract
- Moving too fast
- Discouraging flexibility
- Ignoring expanded form
- Over-relying on expanded form
How should you teach place value in 1st grade?
Here are some tips and tricks for avoiding these mistakes when you are teaching place value to beginners.
Make it Concrete
We can demonstrate and talk all we want, but kids need to experience place value in order to understand it. Longs and cubes are great, at the right time. But first students need to understand exactly how a cube (one unit) becomes a long (ten unit.)
To do this, students need to practice counting ten items and trading them for one item that contains ten in a group. This can happen with ten frames, plastic straws bundled together, ten snap cubes traded for a stack of ten… Be creative, but give kids lots of opportunities to see how ten (ones) can actually equal one (ten). Just reading that helps you see how confusing and attract this can be!
Master Teen Numbers before Moving to Bigger Numbers
What does it really mean to “know” the teen numbers? It’s easy to look at students who can count to 20 and name the teen numbers (out of sequence) and feel that they know all there is to know about teen numbers. In reality, teen numbers serve as the foundation of the base ten system, and are the perfect introduction to place value.
Once students can name teen numbers, help them to see the teens as a group of ten and some ones. To help students do this, give them lots of opportunities to count groups that have 10-20 items. Let them count the items one by one. Then show them how to group ten of the items and count the group of ten plus the remaining items.
You can do this with blank ten frames. (First, be sure your children are familiar with ten frames and how they work.) Give children a set of pennies or counters to count. After counting, have them fill each box in the ten frame with a penny. They can set the additional pennies to the side of the ten frame. Next, help them to count the completed ten frame as 10, then count up from ten with the remaining pennies. So, for the picture below, students would count 10, 11, 12, 13, 14, 15, 16.
After counting the set, help students to see that 16 can be broken up into a set of ten plus six more. (This will make more sense if students are familiar with complements of ten, or flexible ways to make ten or any given number.) Repeat this with lots of different teen numbers. Some students will need to experience this activity repeatedly to truly understand it.
Focus on Bundling and Exchanging – Being Flexible
It’s easy to have students spend lots of time counting tens and ones. This is great for helping them understand the value of a number.
But, in order to help students understand regrouping (borrowing in subtraction and carrying in addition), you need to have students practice creating bundles and exchanging larger groups.
For instance, you might have students start out with 3 tens and 13 ones. Help them to see how they can exchange ten of the ones to create a new ten. This will set the foundation for regrouping when adding.
On the flip side, have students start with 5 tens and 3 ones. Challenge them to exchange one of the tens for ones to see show the number a different way. Practicing this will help them better understand borrowing when subtracting large numbers.
One way to practice this flexibility is to state a number and encourage students to show it two ways, using the tens and ones blocks. One way would include the standard representation; the second way would include more than ten ones.
If you want to turn this type of activity into a game, I have a popular Base Ten War game in my store that has students compare numbers using tens and ones that need to be exchanged. You can check it out here.
Give Expanded Form its Due – and no more
We all remember learning how to write big numbers as super long math equations that represent place value: 54,826 = 50,000 + 4,000 + 800 + 20 + 6. Breaking numbers down like this is an important way to demonstrate an understanding of place value. It’s critical to realize that the number 5 actually represents 50,000, not just 5.
But it’s easy for this to become a rote activity for students. They learn how to jump through the hoops of the problems without truly understanding it.
As you introduce expanded form, pull those base ten blocks back out. Have students represent the number with base ten blocks, then write it in expanded form. (This will only work for numbers into the thousands, because base ten blocks for the 10,000s would be too cumbersome. But that’s fine. You really just want kids to understand how the concrete version with the blocks is linked to the abstract expanded form.)
Once kids seem to understand expanded form, move it. The huge equations are clearly not the most efficient way for kids to work with numbers. Of course you’ll need to revisit it from time to time to help students remember what “expanded form” means. It probably makes sense to practice it a few times as you move into even bigger numbers. Just don’t belabor it; expanded form is time-consuming. So use it just as long as you need to, but no more.
Looking for more tips on solidifying place value skills? The Two Boys and a Dad blog shares some great ideas here.
Fix those mistakes
As you are teaching place value in 1st grader, remember these important tips:
- Master teen numbers first
- Focus on bundling and exchanging
- Make it concrete
- Encourage flexibility
- Give expanded form the appropriate weight
By making small changes to your instruction, you will help your students become amazing mathematicians. Their strong place skills will help them mentally solve math problems with ease.
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