Fly on a Math Teachers Wall: Place Value

Welcome to the Fly on the Math Teacher’s Wall Blog hop.  Today 15 talented math educators are hopping along to discuss place value.  Place Value is such an important topic but many of our students have a difficult time applying many of the principles.

Today my focus will be on utilizing place value charts when comparing numbers.  Let’s start with a definition of place value.

Mastery of place value leads to greater understanding with the following topics:  decimals, rounding, addition, subtraction, order and comparing numbers.

As many of us know, comparing numbers is a difficult concept for our students. I know this will be a controversial statement but, “the sole focus when comparing numbers should not be on the alligator eating the larger number strategy.” You maybe asking why? Comparing numbers is about our students truly understanding why one number is larger than the other through exploration and examination of each number place.

• 1 ten (the smallest 2 digit number) is greater than any amount of ones represented by a one-digit number; thus we compare 2 digit numbers by looking at the tens place first.

• 1 hundred (the smallest 3 digit number) is greater than any amount of tens and ones represented by a two-digit number; thus we compare 3 digit numbers by looking at the hundreds place first.

• 1 thousand (the smallest 4 digit number) is greater than any amount of hundreds, tens and ones represented by a three-digit number; thus we compare 4 digit numbers by looking at the thousands place first.

To support this concept, I typically use place value charts.

Below you will find an example in which a student uses place value charts to compare numbers in the  primary grades.

Notice how the student used base ten blocks within the place value chart.  Using the base ten blocks within the chart helped build the understanding that 32 is larger than 23 because 3 tens is larger than 2 tens.  If you do not have base ten blocks, connecting cubes are also another good tool.  It is critical that students provide an explanation that supports their findings.

Two important questions that guide this work are:

• How are _____   and _____ alike?  Prove it by showing me.

• How are _____   and _____ different? Prove it by showing me.  

Check out a page from my Comparing 2 Digit Numbers product.  It is very much aligned to the same process of using models within a place value chart to compare numbers.

I have been talking a lot about comparing numbers for primary grades, I am sure that the upper grades teachers are wondering, “How does this help me?”  Check out the comparing numbers problem below.  

If you have not used place value charts in this way before, I encourage you to try them out!

I hope you enjoyed this post.  Be sure to hop along to the next post by the incredibly talented Evil Math Wizard.  It is sure to be wicked!!!

P.S. Several of the math bloggers have joined Tsu (pronounced Sue).  It is a new social network that is similar to Facebook.  Sign up here to see my page.