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.

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.

Anita says

I really want to turn my math class into a place of fun and joy. A lot of our fifth grade students are having difficulty with place value. I like your ideas but what do you have to help with decimals?

angie clark says

I really enjoyed reading your blog post and I think this activity with comparing the numbers is great. This gives the students an opportunity to compare the likes and the differences.

Sarah M says

Really enjoyed reading your post! Thanks so much for sharing your "Comparing 2 Numbers" sheet. We do a lot of exploration with tools and comparing numbers to determine the greater or lesser of two. I really like the set-up of your sheet. Your upper grade comparison chart is great, too!

Smiles,

Sarah

TheElementary MathManiac says

I like how your sample question for primary grades is phrased as a do you agree question. I find that kids like answering questions like this and can be very motivated to prove someone wrong.

Tara

The Math Maniac

Brandi Wayment says

Great post as always, Greg! I love the comparison charts, I will be giving those a try.

Jameson Michelle says

I was just going to say that I really like the comparison that you set up! Nice Job! I will be using this with my 6ers but with decimals. Thanks for the awesome post.

Cheers,

Jameson

The Math Spot says

I really love the layout of your comparison chart for the upper grade levels. I have my students compare on a place value chart, however, the extra step of comparing in expanded form makes the connection between digit, place value and value in a place value so clear! I will definitely be adding this chart to my teaching repertoire! The Math Spot