Place Value

One important element of understanding number sense is to understand place value.  Here is a variety of place value mats that I use in my classroom.  Like many of my other materials, I like to place these mats in clear sheet protectors.  This helps the mats to hold up, it allows them to be easily stored in a binder, and students can write on them like dry erase boards.  I use the Two Digit Place Value Mat with my K-2 students.  This mat can be used in several ways.  You could cut the sheets in half so that each student has a half sheet for working with one two-digit number at a time, or you could leave the sheet intact so that each student has two sets of boxes for comparing one number to another.  You could ask students to write one digit in each box with a dry erase marker, or they could place counters in the boxes to represent numbers, or they could place base ten blocks in the boxes.  If comparing numbers, I ask them to star or circle the larger number.  Other examples include asking a student to write a number that has four tens and eight ones, to tell you how many tens or ones are in the number 36, or you could show or tell them a number and ask them to write the number that comes before or after it.  If you are using base ten blocks, you may also want to try the Base Ten Place Value Mat.  This three-digit place value mat includes pictures of the base ten blocks above each column.  With these mats, you can ask students to "build" a specific number such as 368.  You could also ask them to build a number that has 2 hundreds (or flats), 3 tens (or rods), and 7 ones (or units).  You could also designate one of those place values, allow them to select the numbers they will place in the other two places, and ask them to read their final number to you.  This mat can be used to talk about trading ten units for a rod or ten rods for a flat.  After using the physical manipulatives, I also have them use dry erase markers to draw squares to represent hundreds, lines to represent tens, and dots to represent ones.  I use the Large and Small Number Place Value Mats with my 3-5 students.  The large numbers side is used for numbers that go as high as one million.  The small numbers mat is used for decimal places to the hundredth.  One way I use these mats is for comparing numbers.  I ask students to write two numbers that use the same digits but have some of the digits rearranged in the second number.  Then I ask them to determine which number is larger by comparing the numbers in each column.  Sometimes, I write a number on the mat and ask students to read it properly.  Sometimes, I say a number and ask them to write it without seeing it first.  I use numbers that contain zeros, such as 1,209,045 to see if they will know where to place the zeros when they hear the number orally.  We discuss the fact that we say the words "million" and "thousand" when we come to the commas.  In working with decimals on the other side, I often find that a student will think a number like 0.09 is larger than a number like 0.1.  I find this mat especially useful for that lesson, and I make note of the fact that then names of the decimal place values are counter-intuitive because the tenth is the larger number and the thousandth is the smaller.  I often ask them, "If you had to share a pizza with ten people or 100 people, which would you rather do?"  I also use these mats for rounding activities.  I ask them to write one number on the top row.  I name a place value to round to, and they write that rounded number on the bottom row.  I may then ask them to round that same number to a different place value.  One turn and talk activity that you can try is having each student create their own top number and trade mats.  They then have to round someone else's mat, and you can have them check each other's work.