Determining Place Value

NOTE: to teach place values, a learner MUST KNOW how to count, recognize and know printed numbers. It’s also important that the learner know how to count by groups of “tens” to 100 or more. If the learner does not know how to do this, please stop and go HERE.

Helping learners understand place values is an important step in learning math. Whenever a number is present, place values are present. For example, the whole number 7654321 has seven different values in seven different places or positions in the number.

… 7654321, there is a 1 (value) in the ones (1) place.
… 7654321 a 2 (value) in the tens (10) place.
… 7654321 a 3 (value) in the hundreds (100) place.
… 7654321 a 4 (value) in the thousands (1000) place.
… 7654321 a 5 (value) in the ten thousand (10,000) place.
… 7654321 a 6 (value) in the hundred thousand (100,000) place.
7654321 has a 7 (value) in the million (1,000,000) place.

In the area below, use the information from above to write the place of each underlined number.

Example: In the number 345 there are 4 tens

In the number 6781234 there are _________ .
In the number 728 there are __________ .
In the number 47218 there are _____________.
In the number 156 there are ____________.
In the number 2125072 there are ___________.

One of the first objectives is to help the learner understand that we “GROUP” numbers to help us count. The first “GROUP” to know is the “ONES.” Write the numbers 1 – 9 on a piece of paper and explain that there is only one digit in the numbers 1 – 9.

Then, write the numbers 10-20 on a piece of paper and show that each of these has two digits. Explain that the reason it has two is because the number of digits has to do with the size or amount of the number. Further explain that the more digits a number has the bigger it is. Now use the following exercise to further demonstrate place value.

Try this, on a piece of paper, write the word “Tens” and to the right of it write the word “Ones.” Next, place a line down the paper separating the the words “Tens” and “Ones.” Now, write out the numbers 0-12 in columns, making sure that the numbers 0-9 are written to the right of the line and the numbers 10, 11, and 12 are written with the 1 to the left of the line and the 0, 1 and 2 are written to the right of the line something like this:

Hundreds Tens Ones

Next, show each of the numbers using objects (manipulatives) such as pennies. Make sure that for the numbers 1-9 that pennies are stacked into the “Ones” column. I think it’s best to place the coins to the right of their respective numbers. This helps demonstrate that each WRITTEN number actually represents an amount of “things,” in this case pennies.

When you get to the number 10, place ten pennies onto a stack making sure you place them under the “Tens” column, preferably to the left of the numbers written on the paper. Then, remove all the pennies from within the “Ones” column.

Now, for the number 11, add one penny to the “Ones” column on the right side of the line and keep the stack of ten pennies in the left column. Point out to the learner that WE do this because it helps us keep track of things we have counted.

Try to summarize the operations at this point. Make it clear that coins in the right column represent “Ones” but that when you get to the number 10, you have to put something worth 10 into the left column.

At this point, complete writing the rest of the numbers to 20. Make sure that you continue writing “1s” in the left column and the numbers 1-9 in the right column. As you write the numbers, place pennies into columns till you reach 19.

When you reach the number 20, place two stacks of ten pennies each into the “Tens” (left) column and remove all the pennies from the “Ones” (right) column.

Explain that the righthand column shows that there are now “zero” numbers in the “Ones” group and two groups of coins in the “Tens” (left) column. Now say that there are two groups of 10 in the “tens” column so this means there are 20 pennies.

Now group pennies into three sets of 10. Explain that 3 groups of 10 is 30, etc…keep going to 100 (if the learner’s attention span is not waning).

At 100, it’s time to introduce a new column called “Hundreds.” Now place 100 pennies in the “Hundreds” column and remove all the pennies from the “Tens” and “Ones” columns. It’s important, too, to write the number 100 with the 1 in the “Hundreds” column and the 0s in the “Tens” and “Ones columns.

****During this activity, try placing pennies in the columns and ask what number they represent. For example, place a stack of 10 pennies in the left column and 5 pennies in the right column and ask, what number is this? When the learner answers correctly go on trying numbers of greater value. If the learner fails to grasp that a stack of 10 pennies in the left column and 5 pennies in the right column is 15 then, go back and reteach the activity. Try explaining it differently or maybe wait and try it at another time.

NOTE: This activity works well in teaching money, too.