Face Value or Place Value?

Throughout my teaching career, I’ve found that an understanding of place value is often at the root of a student’s struggle with math. Some researchers say we introduce place value too soon, others say we don’t do it soon enough. The Common Core Math Standards tell us to begin place value instruction as early as Kindergarten with increasingly sophisticated instruction through throughout the elementary grades.

A major understanding to grasping place value has to do with understanding the difference between face value and place value of a digit. Try this with your primary students:
 1. Show a child “16” on a piece of paper. Ask what does the “1” means?
 2. Ask what does the “6” mean?
 3. Put out a cup of counters and ask her to show you 16 counters.
 4. Ask her to show you with the counters what the “1” means?
 5. Ask her to show you with the counters what the “6” means.

Here’s an example of the responses I often hear from primary children, even ones who consistently give correct answers to #1 and #2
 1. Show a child “16” on a piece of paper. Ask what does the “1” mean?
               Child responds  “10” 
 2. Ask what does the “6” mean?
               Child responds, “6 ones”
 3. Put out a cup of counters and ask her to show you 16 counters.
 4. With the counter show me what the “1” means?
                She points to one counter.
 5. Show me with the counters what the “6” means.
                Counts out six counters.

So what’s the teacher to do?

First don’t assume that a child who can verbally identify the place value of numbers understands the structure of our base-ten number system.  Students need to understand the role of 10s and learn to see 10 objects both as one group (the 1 in the tens place) and as 10 individual objects.

Teachers can support a child’s conceptual learning by providing many opportunities to count quantities of objects by grouping them into 10s and ones, and recording the number.  Teachers can help their students see the pattern that exists when they record how many there are—that the digit on the left represents the number of groups of ten and the other digit represents how many left over. The recording is very important; it connects the conceptual level with symbolic representations. This will help a child differentiate face value and place value.

Neal Manegold

Producer, DreamBox Learning | MBA, Technology Management | NBCT, Middle Childhood