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).