## What does multi-unit place value mean?

Many of the processes needed in addition, subtraction, multiplication and division require students to see the tens in numbers such as thirty-four. Understanding 34 as three tens and four, or 340 as 34 tens, is essential in using the multi-unit place value structure of numbers in carrying out the four operations. More than knowing the positional value name of any digit in a number (e.g. the “3” in 340 is in the “hundreds” position), multi-unit place value relies on flexibility in exchanging unit values, which supports mathematical power in calculating.

Research carried out by Sharon Ross (1989) helped to clarify the difference between *positional* *place value* knowledge and *multi-unit* place value. In her research, she conducted interviews with students from second through fifth grade. These interviews included a number of tasks designed to evaluate the student’s understanding of the base-ten numeral system. In one task, the student was given a bag of 25 sticks that were not grouped. The student was asked to determine the number of sticks. Once the quantity was established in writing, the digits 2 and 5 were circled individually and the child was asked, ‘Does this part of your twenty-five have anything to do with how many sticks you have?’. Less than half of the participants were successful. One-fifth of the participants thought there was no connection at all. Just over another fifth of the students “invented numerical meanings, such as that the 5 meant ‘half of ten’ . . . or that the 2 meant ‘count by twos.’” (p. 48).