Hundreds, Tens, and Ones

The big idea

The position of a digit tells what size units it counts. In 347, the 3 counts hundreds, the 4 counts tens, and the 7 counts ones. The same total can be regrouped: one hundred is equal to ten tens, and one ten is equal to ten ones.

Regrouping changes the description of the number, not the number itself.

Worked example

The number 326 is 3 hundreds, 2 tens, and 6 ones. If one hundred is traded for ten tens, the same number becomes 2 hundreds, 12 tens, and 6 ones.

Both descriptions have the same value: 300 + 20 + 6 = 200 + 120 + 6 = 326.

How children may show it

Children may use base-ten blocks, quick drawings of squares, sticks, and dots, a place-value table, expanded form, or equations. A strong representation shows both the unit name and the number of those units.

Common mix-up

A child may read 306 as 36 or treat the zero as unimportant. The zero is a placeholder showing that there are no tens. Another error is changing 3 hundreds to 3 tens during a trade. Ask how many of the smaller unit equal one larger unit.

Try it together

Choose a three-digit number and write it in a hundreds-tens-ones table. Make one legal trade and describe the number again. Try to find three different decompositions. Check each one by converting every group back to its value and adding the parts.