Understanding Place Value

A solid understanding of place value will, among other things, allow your children to progress with addition and subtraction and with multiplication and division operations. Working with and handling base ten blocks (ask at school for recommendations) will provide a good foundation for this understanding.

2-Digit Numbers - Tens and Ones

To make larger numbers we use a number system that has place values. The number 64 has 4 in the ones place and 6 in the tens place.

64 with tens and ones shown

Explore different numbers with your children. Discuss who many tens and how many ones (units) there are in each number. You can use a hundred chart and, for example, note that in the shaded column below, all the numbers have 4 ones and, that in the shaded row, all the numbers have 6 tens.

0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99

If your child needs more help with place value then consider buying linking cubes or something similar to help model numbers.

Here are some more numbers shown with digits and with blocks.

37 showing ones and tens
47 shown in tens and ones
23 shown with tens and ones
70 shown with tens and ones

Showing numbers on a number line helps develop an understanding of place value. It will help your children appreciate where numbers are positioned relative to other numbers. You will find lots of number lines here.

Use these two place value charts to help your child practice with place values.

Hint: Uncheck the "Show Numbers" box to print charts onto which you can write any number you like.

Try this worksheet to practice with place value.

3-Digit Numbers - Hundreds, Tens, and Ones

We'll use this block showing 100 place value block to represent one hundred as shown in the numbers below.

247 using number blocks
the number 422 in blocks
571

Watch where the 0 goes

Look at the numbers 206 and 260 below. It is very important to use 0 when there are no ones or tens or hundreds. The place where the 0 goes makes a big difference.

Illustration showing difference between 206 and 260

Discuss with your children the important role zero plays in our place value system. For example, with the number 206, the zero acts as a place holder; it shows the position of the tens’ place and makes it clear where the hundreds position is. Similarly, with the numbers 500 and 5000, emphasize that the zeros show the position of the 5. Avoid stating that the numbers ending in 00 are hundreds or ending in 000 are thousands. Instead discuss how the 5 is in the hundreds or thousands place. This a subtle point but helps develop a full understanding of place value.

You don't need to include the zeros at the left of the number.

58 illustrated as 0 hundreds, 5 tens, and 8 ones

We think 0 hundreds, 5 tens, and 8 ones.
We write 58.
We say fifty-eight.

Try these two charts to help your child practice with place values with numbers to 999.

  • Place Value Chart #3 - Highlight the hundreds, tens, and ones blocks to match the number shown on the right-hand side.
  • Place Value Chart #4 - Write the value of the hundreds, tens and the ones to make the number shown on the right.

Hint: Uncheck the "Show Numbers" box to print charts onto which you can write any number you like.

Try this worksheet to practice with place value.

4-Digit Numbers: Thousands, Hundreds, Tens, & Ones

We can use this one thousand block place value block to represent one thousand.

2,143 shown as 2 thousands, 1 hundred, 4 tens, and 3 ones
4,276 shown as 4 thousands, 2 hundreds, 7 tens, and 6 ones

This place value chart showing thousands can be used to help your child practice with place values for numbers up to 9,999. Uncheck the "Show Numbers" box to give blank charts that can be marked up with any combination of number.

Try this place value worksheet to practice working with numbers up to 9,999.

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