Place value is the term we use to talk about how numbers, when arranged in different places, show different amounts. If we write the number 372, we know there are 3 hundreds, 7 tens, and 2 ones; it does not mean 3+7+2, which is what it may look like to a young first grader.
Imagine how difficult this is to learn. You know that this number is 3, but now you are being told that when it is a little farther over here it’s 30, and way over there it is 300! It is a tremendously tricky concept, and needs quite a bit of practice and exposure before children begin to feel comfortable with it. They will need skills in counting to 100, and they need to know their basic addition facts and subtraction facts and be able to skip count before they should begin working directly with place value.
Kids know that the number is 3, but now they are being told that when you put the number here it’s 30, and when you move it over there it’s 300!
That counting can be organized in groups. When learning to count, numbers seem to proceed along one long line, with no real relationship to each other. Practice in grouping numbers and skip counting will prepare children for the concepts of number groupings in place value.
How to count many objects by organizing them into tens and ones and regrouping these when necessary.
That the same written number can have different amounts (7, 70, 700) depending on where it sits within a number.
That pennies, dimes, and dollars are organized this way.
How to use counters to show regrouping of addition and subtraction problems up to 100.
In the beginning of first grade, children will strengthen their skills in counting to 100, addition facts and subtraction facts, and skip counting.
Around the middle of first grade, they will learn to separate numbers and objects into tens and ones.
Near the end of first grade, children will begin using regrouping when adding and subtracting 2-digit numbers (“borrowing” to subtract, and “carrying” to add).
In second grade, children will work with regrouping and place value concepts for 3-digit numbers.
Place value is one of those concepts that you have to know well before you move on to other things. (There seem to be a lot of such concepts in first grade.) Children who do not have a secure understanding of place value will have a terrible time with adding or subtracting larger numbers, regrouping, estimating, and later skills of multiplication and division. They will have a hard time getting a practical sense of how much a number refers to, and may have poor number sense skills. They may reverse numbers when reading or writing, such as writing 68 instead of 86, because the order of the numbers means very little to them. Later on, this skill will be essential to understanding money (the difference between $55 and $505, for example) and numbers in general.
Place value takes years to master, and there are many things that will likely prove difficult for first graders at one time or another, such as:
When grouping objects by 10s, kids forget to stop at 10 and keep going. Once they realize it, they have to stop and start over again.
Not knowing when to count by 1s, and when to count by 10s. When kids are finding out “how many tens” there are before writing a number, they are expected to count by 1s. (“One, two, three tens.”) When they are counting up the whole number at the end, they are expected to count by tens first, then add on the ones (“Ten, twenty, thirty, thirty-one, thirty-two.”)
Feeling that the larger numeral is a bigger quantity no matter where it is located. In the number 27, they think the 7 is bigger than the 2 (20).
Understanding that there are tens and ones, but getting confused about which one goes where.
Just finding the whole concept downright confusing.
Take baby steps. Spend lots of time on tens and ones to start with. Have kids count a jar of pennies by making stacks of 10, then show what the tens and ones look like written down. Point out the tens and ones place in the numbers you see every day. Then, when kids seem to be getting the hang of tens and counting by tens, you can introduce the hundreds place.
This is a brand new concept, and new concepts take time. Kids will need lots of time manipulating objects like place value manipulatives and regrouping them in order to understand place value in written numbers. Give kids opportunities for making numbers, adding, and subtracting with objects.
NOTE: Some children may not be developmentally ready to jump right into regrouping with tens. Here is a video by a teacher who makes a strong case for starting out by teaching a “Base 2” and a “Base 3” system first, to help kids really visualize the concept, before moving on to base 10. Take a look:
After kids have had lots of practice making numbers that visually look like what they represent, introduce the idea that the value of a number can change even though it still looks the same; where you put it the number changes how much it is worth.
Finally, show kids how to write numbers as you say them, and do regrouping with written addition and subtraction problems. Bear in mind that, even at this last level, first graders will still need a great deal of hands-on practice with place value manipulatives to give the written numbers meaning.
So take it nice and slow, and give kids lots of practice with place value activities. When they start to get the hang of these, take kids to the next level with place value games to cement their understanding of those tricky skills.
Some kids will grasp these concepts more quickly than others. If a couple of kids seem to be doing fine with 2-digit numbers, go ahead and challenge them with 3-digit numbers. They can do all the same activities that the rest of the class is doing, only with the challenge of working with hundreds, or even thousands, instead of just tens.
