# Decimal Thinking!

### Decimal Place Value Challenges

Today was our first day back to school, and I had a decision to make.  We wrapped up our decimal unit before break, and I wasn’t super pleased with the results of our summative assessment.  I was pretty disappointed—all the formatives had looked pretty good, I had done lots of small group and one on one work, and I really felt like the students were really understanding some key things…that decimals help us show numbers between whole numbers, that decimals and fractions both are ways to show these numbers, and then the basics—the numbers in front of the decimal point are “wholes”, the digit after the decimal point is how many “tenths”, and so on.  We used base 10 blocks.  We used money.  I was feeling pretty good about things.  After looking back at the assessment, I decided we simply weren’t quite ready to wrap up this unit…especially when you look at what the Common Core requires for depth of math understanding!

### Decimal Lessons That Matter

So…I spent some time trying to come up with some “hands on” ways to try to help the students review these ideas—focusing on sequencing decimals because that seemed to be tricky for quite a few of them.  NOTE:  Sequencing decimals is a much more complex task than simply using “<” and “>” signs…it requires students to have a grasp of “benchmark” decimals such as 0. 5 and 1.0 so that they can “sense” where decimals would go on a number line.
Today I set up three rotations in my class—one to do some computation practice (to wake those vacation brains up!), one with our inclusion teacher, and one with me.  I just wanted to share these ideas with you because we had some GREAT discourse about numbers!  I wrote up 3 decimal activities over break and today we did the first two…Here they are!

First, one of our “stations” involved putting some decimal “cards” in sequence.  Students were each given a stack of 3-5 cards and were asked to put them in order from smallest to largest.  The teacher guided them through a review of some of the place value concepts, built some of the numbers with base 10 blocks to review what they “look like”, and then the group worked to sequence the entire set of 35 decimal numbers!  They had great discussions about why certain numbers went in different places and practiced using math language along the way.  There was one “trick” in the set—two numbers that were written differently but represented the same amount (0.1 and 0.10) which was a great review for the kids!
The other station was VERY telling!  I created some “benchmark cards” which said “Close to 0”, “Close to ½” and so on.  Students then worked to place all the decimal cards I had made in columns to match.  We had very heated discussions about HOW they determined which category the decimals belonged in! This let us review our decimal place value (tenths are larger, hundredths are smaller), review the idea of number lines and what the halfway point of two numbers is, the “halfway of the halfway” point and so on!  We linked this activity to money as well…how much is ½ of a dollar?  What is halfway between 2 and 3 dollars?  I asked students to justify their ideas to me—to PROVE why they placed the decimals where they did which led to discussions about adding and subtracting (0.81 is 0.31 away from 0.5 but only 0.19 away from 1.0) and was a great review!
So…you can easily replicate these activities on your own, but I do them have all ready to go if you want 3 quick and easy activities without the prep work!  All the materials needed for these 2 activities plus one more (using <, >, and =) are ready to print out if you want to save time.  I also made quick “exit slips” (quizzes) to use to see how your students can do on their own!   Hope you got some ideas for reviewing decimal concepts or to incorporate into your lessons this year!
I also love to use number lines to work on decimal place value.  Here is the collection that I use to help my students think, talk, and write about decimals.