Today I am joining some great math teacher bloggers to bring you a new series of blog hops: Fly on the Math Teacher's Wall. These blog posts will be all about SQUASHING teacher, student and parent misconceptions. They will give you a look inside math teachers classrooms and help you find new ideas and understandings across the grade levels. Today we are talking about place value.
Today I want to talk about decimals. I feel like teachers have gotten pretty good at using manipulatives with young students first learning about place value. However, I think there is a huge misconception that older kids learning decimals don't need as much hands on practice with models to develop their understanding. I would like to SQUASH that misconception and share with you 6 different models for learning decimals. Moving between these models will give your students the hands on experience they need while helping them to see how decimals are used in the world around us.
Base 10 Blocks
This is by far the most popular way for teachers to introduce decimals. I use these myself when working on decimals with kids. In fourth grade, when I first introduce decimals, I make a big production of using the document camera to "zoom in" on one of the units. I tell kids I am getting really really close. While doing this the camera goes out of focus a big and I trade the unit (1) for the mat (100). I tell them that when you get really close to the unit, you can see it is really broken into 100 pieces. Of course they know right away that I traded pieces because it is usually very obvious. However, this is where we reestablish that the mat which in the past has been worth 100 is now worth just one. This means the strip which was formerly 10 is now worth a tenth and so on. It takes kids a few tries to adjust to this way of thinking but they eventually do. If you are looking to extend this or don't have a class set of base 10 blocks handy, I would recommend checking out this applet on the National Library of Virtual Manipulatives. (You need Java for it to run)
This is often the most useful connection for students between decimals and real life. By the time kids learn about decimals, they have often had some real life experiences with money and have a much better understanding of decimals when they are in a money context or written to the thousandths place. If you ask a fourth grader who is just starting out with decimals if 1.8 or 1.09 is larger, they may or may not be able to answer it correctly. If you ask them which is more money $1.80 or $1.09 they will probably think that is an easy question. Connecting tenths and hundredths to dimes and pennies is one of the best ways to build on students prior understanding and help them construct new knowledge. I like to make the connection between money and base 10 blocks explicit with these money value pieces from the Math Learning Center.
An model that is often overlooked in math classes for teaching decimals and other kinds of numbers is number lines. I find teachers are spending more time modeling number lines in the lower grades now but it is still often something that is missing from decimal units. Number lines are a great way to help kids think about ordering and comparing numbers. They also make a great conversation starter to talk with kids about the density of numbers. Asking questions such as "how many numbers are between 1.2 and 1.3" get at the idea that the numbers are infinite. A meter stick is perfect for this kind of activity because it is already split into hundredths. You can read more about how I use meter sticks for decimal number lines here.
100 Bead String
I use 100 bead strings for a huge variety of activities around counting, place value, decimals and percents. They are easy to make and cost under $1 each so I make sure I always have plenty on hand. They make a great number line because like the meter stick they are already broken into hundredths. They also switch color every ten beads so the tenths are also easy to see. There are no numbers written on the model to start with so it is a little bit different than the meter stick. Read more about how I use the 100 bead string for decimals here.
Decimal Arrow Cards
I love arrow cards for teaching place value and find them to be a vital tool to use in K-3 to work on numbers up to 10,000. If kids are already familiar with arrow cards from younger grades, these are a super easy way to extend their understanding to the right of the decimal point. If your kids haven't used them in previous grades it will only take you part of a class period to get them familiar with them on the whole number side and you will be ready to use them with decimals in no time. You can grab a free set of printable arrow cards here and the decimal version is available here. To read more about how I use arrow cards with kids, check out this post!
Digit BlocksI first heard of Digi Blocks last fall and was very intrigued by the implications for place value. I received a small collection of them from a colleague and have used them a great deal with intervention kids. I recently watched a colleague at another school use decimal digi blocks and was super impressed with how well the kids understood place value. They are one of the more expensive manipulatives but have actual pieces for tenths and hundredths. You can read more about my first impression of digi blocks or head over to their website to learn more.
Head over to Beyond Traditional Math to see what she has to say about teaching place value!